Vadose Zone Hydrology: Cutting Across Disciplines

As an illustration, consider the case when
which is the exact solution for a flux of jr/3, per unit length of the line source and for the diffusivity given by

At the wall, r} = r2 = ^/(L2 + y2') and #(x = L, y) = &L is given by

Figure 4.6 shows &L for y = 0 as a function of time, taking L = 1. Comparison with numerical results shows the remarkable accuracy for the simple analytical result. Up to now, we have treated the wetting front as smooth. If any perturbations occurred at the front, they are dampened by the sorptivity forces. In the next two sections, water moves in preferential flow paths downward due to the predominance of gravity force.

116

VADOSE ZONE HYDROLOGY

Figure 4.6 Numerical simulation (dashed line) and prediction from equation (4.54) (solid line) of water content at the position on the wall closest to the source.

Fingered Flow in Homogeneous Sandy Soils Interest in subsurface transport mechanisms responsible for unusual behavior has increased with increasing concern over groundwater contamination by pesticides and nonaqueous liquids. One particular mechanism that is attracting attention is fingered flow due to instability of the wetting front. Chuokc et al. (1959) tried to extend the Hele-Shaw cell result of Saffman and Taylor (1958) by introducing the curve-fitting parameter of the "effective surface tension." More fundamentally, Parlange and Hill (1976) looked at the balance between capillary and gravity forces in a diffuse wetting front as it penetrates into a coarse sand. The resulting description of fingering predicted the finger width and this was later improved by Baker and Hillel (1990), who discussed the effect of the water entry pressure. Glass et al. (1991) extended the theory to threedimensional fingers, while Selker et al. (1992) analyzed the water distribution within a finger, and Liu et al. (1995) showed the importance of hysteresis in the formation of fingers. Tn its simplest form, the width, da, of the most unstable finger for an air-water system is given as (Parlange and Hill, 1976)

where subscript "a" represents the displaced phase (air) and F refers to properties at the wettest point in the finger, namely the tip. Baker and Hillel (1990) pointed out that for a fully developed finger, "F" should refer to the water entry value. However, drier conditions can be observed (figure 4.7) as a result of hysteresis (Liu et al., 1994, 1995). In equation (4.56), two-dimensional fingers are considered. In three dimensions, the same expression holds for the diameter of the finger, but with n simply replaced by 4.8 (Glass et al., 1991). Behind the wetting tip, the water content decreases, so that as a finger passes by a tensiometer the pressure increases rapidly following the passage of the tip when the tip reaches it. and then pressure decreases slowly as the tip progresses further on. The following equation was developed by Selker et al. (1992):

SOIL PROPERTIES AND WATER MOVEMENT

11 7

Figure 4.7 Fingers moving from a dry sand into the same sand at field capacity. The widening reflects the different wetting curves.

where z is the distance measured upward from the finger tip and v is the constant finger velocity. As z -> oo, the pressure stabilizes so that v(9/K)x. = 1. In practice, the pressure may stabilize at a higher value if the lingered flow ceases to exist. This progression is presented in figure 4.8. Many new and interesting fingering phenomena arise when the fluids are oil/ water, rather than air/water. In particular, if the oil phase is free to move, then

Figure 4.8 Lowering of pressure with time at two tensiometer locations in the chamber as a finger passes through. At the upper position, the pressure levels off early (500 s) reflecting the change from finger to dimensional flow. At the lower position, the leveling off reflects the finger reaching the bottom of the chamber at 600 s and the eventual capillary rise reaching equilibrium around 900 s.

11 8

VADOSE ZONE HYDROLOGY

the diameter, d0, of a finger in oil can be compared to the air value da in equation (4.56), with

where a is the surface tension of water with oil, or air, and p is the density of the respective phases. The contact angles r\ have also to be taken into account. For instance, oil may interfere with water contact by leaving a smear on the grain, such that surfactants, by altering r), may have a significant influence. Normally, we find that d0/da > 1 because [cr0/aa]/[l — p0/pw] > 1. This was about 2 to 3 in the experiment shown in figure 4.9, where it was assumed that r\a = r\0. If oil does not move freely but moves opposite and in response to the mobile water, then the width of fingers increases with depth. It goes from d0 given in equation (4.58) to a value that is eventually [1 + Mo/^wl larger where the // values are the viscosities. Figure 4.9 shows the beginning of finger widening due to this effect. Preferential Flow in Structured Clay Soils In previous sections, water movement into only homogeneous soils has been discussed. We saw that in coarse, or water-repellent soils, preferential fingered flow can take place due to an instability in the wetting front. Other soils, such as those which have more fines or organic matter, have a soil matrix with cracks, wormholes, and other biopores through which preferential flow can occur. This would apply especially to the no-till fields and permanent grasslands in a semihumid climate. Preferential flow in such cases can occur after saturation at the surface or within the profile above a slowly permeable layer. Although the causes are quite different for fingering, there are many similarities in the flow behavior. In both cases, gravity is the dominant force in moving the finger-like-shaped wetting profile downward into soil with sideways movement restricted because sorptivity is small. It is obvious that solutions of Richards' equation are not valid for structured soil with macropores. Compare, for example, a wetting front in a structured soil in which the infiltrating water was traced with FD&C blue #1 dye with that which Richards' equation for a homogeneous soil would predict (figure 4.10). Although preferential flow involves usually a small portion of the infiltrating water (Steenhuis et al., 1990), it can be extremely important for movement of solutes that are toxic. Recharge principally depends on the water balance at the surface while early arrival of solutes mainly depends on its path. These solutes bypassing the soil matrix may not have the time to degrade or adsorb to the soil. In order to describe preferential flow phenomena in structured soils, we need to capture the different velocities that occur in the larger pores and soil matrix. By assuming that gravity is the main driving force, the soil can be considered to have near-constant hydraulic gradient, namely unity for a vertical flow. Dividing the soil up into different flow paths allows a rather simple closed-form solution to be found for the moisture content in the soil with depth. Although the various flow paths are distributed throughout the soil, they can be thought of as being grouped together and connected to each other. Such groups then are called pore groups. The total

SOIL PROPERTIES AND WATER MOVEMENT

11 9

Figure 4.9 Water fingering in an oil-saturated sand, showing the widening of the finger as the displaced oil has to travel larger distances.

amount of moisure, 9(z, ?), is the sum of all individual moisture contents for each pore group 9p (Steenhuis et al., 1990; Stagnitti et al., 1994, 1995). Therefore,

where 9p is the individual moisture content for the pih pore group, and TV is the total number of pore groups. The maximum amount of moisture that each pore group can hold or transmit is

where Mp are the various moisture contents that represent upper and lower limiting values for the pih group. These are functions of the size of the pores in each group, OP < &Mp.

120

VADOSE ZONE HYDROLOGY

Figure 4.10 Preferential flow paths as indicated by a blue dye applied at the surface. Downward movement up to 3 m depth occurred in less than 10 min.

The group's moisture content, Op, depends on the flux reaching that group, qp, and the effects of evaporation, and the loss or gain of moisture from interactions and exchanges with other groups. Therefore, from continuity, the transport equation may be written as

where Ap(x, f) is a source/sink term that represents the effects of evaporation and exchange with other groups, t is time, and z is the depth—with z = 0 being the soil surface. From consideration of Darcy's law for each pore group by assuming an overall hydraulic gradient equal to £ (/3 < 1), which also for a shallow soil over a hardpan could be the angle of the hillslope, we can require equation (4.61) as

where vp is the average velocity in the pih pore group. Steenhuis et al. (1988) found

The solution of equation (4.62) obtained by the method of characteristics is then given by

SOIL PROPERTIES AND WATER MOVEMENT

1 21

where the moisture content in each pore group, ^(ZQ.O) is a given function of the depth when t — 0. Equation (4.65) can only be integrated easily if Ap is a simple function or just some constant. This last case is when there is no exchange of water between the pore groups. Similar expressions can be written for z < fivt, which is controlled by the boundary condition at z = 0, rather than the initial condition as in equation (4.65). For more complex situations, with realistic water exchange between pore groups, a numerical solution of equation (4.65) can be obtained by taking a fixed time step A?. Equation (4.64) shows that over time step A;, the moisture in class p will travel a distance Azp resulting in a solution at times I for the pth pore group:

where Ip is the integral of Ap from (t — At) to (. The numerical solution is simplified by choosing the ratio of the velocities [equation (4.63)] in two successive pore groups that are integer multiples. This is accomplished by introducing an appropriate piecewise linear conductivity function (figure 4.11). In the "Darcy flow region," it consists of a number of lines tangent to the conductivity function, with the slope of each consecutive tangent line always an integer multiple of the preceding line [equation (4.63)]; here, for instance, twice. The procedure to find the limiting moisture contents of the pore groups from the unsaturated soil conductivity curve is given in Steenhuis and Parlange (1988). How the model works—and how it differs from models based on the Richards' equation— can be demonstrated with an example of steady-state saturated flow through a vertical column. The limiting moisture contents for each category of pores is shown schematically in figure 4.12. The moisture contents of the intersections of the conductivity function's linear pieces are illustrated in figure 4.11. For example, the limiting moisture contents for pores in the category, labeled p = 1, are 0.10 and 0.20 cm3/cm3. Employing equation (4.63), we find that the velocity of flow for pores in categories p = Q,p = \,p = 2, and p = 3 are 0, 1, 2, and 4 cm/h, respectively.

Figure 4.11 Conductivity function for pores of varying moisture content as used in the preferential flow model.

122

VADOSE ZONE HYDROLOGY

Figure 4.12 Velocity of water penetration as a function of moisture content. Pore groups correspond to linear pieces in figure 4.11. The preferential-flow model (left) shows that flow is faster through pores with greater moisture content. After 2 h, water in category p = 3 pores has penetrated 8 cm below the surface; in contrast, convective-dispersive averaging (right) predicts penetration to only 3.5 cm.

Then, by using equation (4.66), we find, for example, that after 2 h, the water in the pores of category/; = 0 has not moved at all. The water in category/; — 3 pores has moved, by contrast, 8 cm. This is very different to a convective-dispersive analysis based on the average flow path, which would place the average depth of penetration at a uniform 3.5 cm, albeit with some minor dispersion around this depth. The importance of modeling solute movement on the type of model used can also be shown by a series of experiments performed by Anderson and Bouma (1977a, 1977b) using undisturbed and well-structured soil cores. A 300-ppm chloride solution was applied at a rate of 1 cm/day as either a sudden pulse or at a steady-state rate. The resulting breakthrough curves were different, with the pulse application resulting in a faster response than the steady-state rate (figure 4.13a, b). We used the preferential-flow model to simulate this phenomenon, assuming that there was some exchange of the solutes between the flow paths. Additional details are given in either Steenhuis et al. (1990) or Stagnitti et al. (1994, 1995). The two simulations shown in figure 4.13 make different assumptions about the velocities in the pore groups. For simulation 1, the velocities in the nine pore groups increased by a factor of 2 from one group to the next larger pore group. In simulation 2, the only difference was that the velocity in the largest pore group was four times greater than in simulation 1. Figure 4.13 shows that the simulation model is capable of matching the breakthrough curve without changing any of the model parameters, except the input rate of chloride solution. In contrast, Anderson and Bouma (1977a, 1977b) tried to fit dispersion coefficients to the breakthrough curves by using the convectivedispersive equation. They found that the coefficients were highly dependent on the flow regime, indicating that the use of the convective-dispersive equation was not appropriate. The different behavior of this preferential flow model and the Richards' equation can seem surprising because both models are based on Darcy's law and the continuity equation. But, Richards' equation is in some sense just a special case of the preferential-flow model. By choosing a function for "A" in equation (4.62) that

SOIL PROPERTIES AND WATER MOVEMENT

123

Figure 4.1 3 Simulated and observed breakthrough curves. The lines represent the simulations and each symbol set represents a column, (a) Pulse application of 1 cm/day; (b) continuous application of 1 cm/day.

assigns all moisture to the pore group with the smallest pore that is not filled up, a solution with a sharp wetting front can indeed be obtained with the preferential-flow model. However, the solution cannot be the same at early times because the preferential-flow model assumes a unit gradient. It cannot, therefore, represent the initial square root of time behavior. However, it is able to simulate the early arrival of invading water to the groundwater and the arrival of "passenger" chemicals with the first rainstorm after application.

Water Movement—Large Scale In this review, which is based on the analysis of just a few problems, we have tried to present our current understanding of water transport processes in soils. However, there is still the need to connect our knowledge of local-scale processes to that of the modeling of watersheds. This connection is often tenuous or even trans-scientific, so empirical large-scale models are sometimes used in practice. However, as more processes are studied and become understood, such as preferential-flow paths, these large-scale models should become more realistic and physically based. For instance, in humid, well-vegetated areeas with shallow soils, such as in the northeastern United States, many no-till fields and permanent grasslands have a soil

1 24

VADOSE ZONE HYDROLOGY

matrix with macropores and cracks (Parlange et al., 1989). On these soils, infiltration capacities are almost always higher than most rainfall events and runoff is generated from areas that have little pore space left to store the water that infiltrates and so become saturated during the storm. These saturated areas can be found in areas that are initially wet, and where either the hardpan or water table is close to the surface. This is known as "variable area hydrology" (Hewlett and Hibbert, 1967; Dunne and Black, 1970a, 1970b). This is quite different from the Hortonian approach where the whole watershed is contributing at the time the rainfall intensity exceeds the infiltration capacity. Particulate and adsorbed pollutants arc transported in surface runoff receiving waters. Increasing the infiltration capacity of the soil would result in less soil erosion and smaller nutrient loadings. In the variable area model, runoff comes from a few saturated areas, such that pollutants come only from the saturated areas. The remainder of the watershed that is not saturated does not contribute pollutants via the surface route but only via the subsurface route. In principle, one would like to subdivide the watershed into smaller and smaller areas until, eventually, areas with more or less uniform properties can be defined and detailed transport equations considered. Several tools are available for this purpose. For instance, GIS (Geographic Information Systems) leads to subdivisions based on spatial variability of slopes, soil depths, and types of vegetation. Using the information obtained from GIS, it is possible to obtain a rough estimate of the watershed response to a storm by using a simple mass balance approach, and by delineating the areas that contribute to runoff (Beven and Kirkby, 1979). At this level of large-scale mass balance, difficult problems like the soil-atmosphere interaction can be greatly simplified. For instance, it might be sufficient to estimate the actual evaporation and available moisture as linearly related to the water content between permanent wilting point and field capacity. At, or below, wilting point the actual evaporation can be taken as zero, and above field capacity it can be set equal to the potential evaporation (Thornthwaite and Mather, 1955; Steenhuis and van der Molen, 1986). A crude approach is the SCS curve number method, originally proposed by Mockus "on grounds that it produces rainfall-runoff curves of a type found on natural watersheds" (quoted by Rallison, 1980). This is often used in practice, instead of the more physical mass balance models, and yet it can be surprisingly accurate in predicting the areas contributing to runoff. We can show that the fraction, Af, of the watershed that contributes to runoff can be expressed as (Steenhuis et al., 1995)

where Pe is the effective rainfall and S is the maximum depth of water storage in the watershed. Surprisingly, for large-scale phenomena on shallow soils in humid areas, equation (4.67) shows that the total runoff for each storm is independent of the precipitation intensity. This is in accordance with the interpretation of Mockus, as expressed in a letter to Orrin Ferris in 1964 (quoted by Rallison, 1980), that "In practice, rainfall intensity can be neglected."

SOIL PROPERTIES AND WATER MOVEMENT

1 25

Conclusions In this chapter, we have mainly discussed the physical processes of water movement within, and over, the soil at the local scale that influence water movement at the watershed scale. Since 1856, when Darcy first found an empirical relationship between hydraulic head and flux, we have come a long way in describing the local-scale processes mathematically. When the parameters needed for our mathematical models are known, we can predict the water flow very accurately, especially at the local scale. In order to predict water movement at the watershed scale in addition, we need to have accurate information about the topography, soil types, and subsoil structure. Our ability to measure these parameters at the watershed scale so as to describe surface phenomena has improved tremendously, but measurement of subsoil characteristics has not kept up with our mathematical ability to describe the processes. Therefore, because of the lack of accurate subsoil data, the approaches to predict water movement for a watershed have remained largely empirical. In a certain sense, our ability to predict watershed-scale phenomena is at the level of local-scale phenomena 150 years ago. Hydrologists can look forward to another 150 years of reasearch!

References

Anderson, J.L. and J. Bouma, 1997a, Water movement through pedal soils: I. Saturated flow, Soil Sci. Am. Proc., 37, 408-413. Anderson, J.L. and J. Bouma, 1997b, Water movement through pedal soils: II. Unsaturated flow, Soil Sci. Am. Proc., 37, 419-423. Arya, L.M. and J.F. Paris, 1981, A physioempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data, Soil Sci. Soc. Am. J., 45, 1023-1030. Baker, R.S. and D. Hillel, 1990, Laboratory tests of a theory of fingering during infiltration into layered soils, Soil Sci. Soc. Am. J., 54, 20-30. Barry, D.A. and J.-Y. Parlange, 1994, Comment on 'Estimating the sorptivity for a wide range of diffusivity dependence on water content,' Transp. Porous Media, 14, 89-92. Barry, D.A., J.-Y. Parlange, R. Haverkamp, and J. Touma, 1992, Comment on 'Solution of a nonlinear absorption model of mixed saturated unsaturated flow,' Water Resour. Res., 28, 1737-1738. Barry, D.A., J.-Y. Parlange, and R. Haverkamp, 1994, Falling-head ponded infiltration with evaporation—comment, /. HydroL, 162, 211-213. Barry, D.A., J.-Y. Parlange, R. Haverkamp, and P.J. Ross, 1995, Infiltration under ponded conditions: 4. An explicit predictive infiltration formula, Soil Sci., 160, 8-17. Barry, D.A., J.-Y. Parlange, and R. Haverkamp, 1996, Comment on 'Variable-head ponded infiltration under constant or variable rainfall' by J.R. Philip, Water Resour. Res., 32, 1467-1469. Bautista, E. and W.W. Wallender, 1993, Identification of furrow intake parameters from advance times and rates, /. Irrig Drain., ASCE, 119, 295-311. Beven, K.J. and M.J. Kirkby, 1979, A physically based, variable contribution area model of basin hydrology, HydroL Sci. Bull., 24, 43-69. Broadbridge, P., 1990, Solution of a nonlinear absorption model of mixed saturatedunsaturated flow. Water Resour. Res., 26, 2435-2444.

126

VADOSE ZONE HYDROLOGY

Brooks, R.H. and A.T. Corey, 1964, Hydraulic properties of porous media, Hydrol. Papers #3. Colorado State University, Fort Collins, CO. Bruce, R.R. and A. Klute, 1956, The measurement of soil-water diffusivity, Soil Sci. Soc. Am. Proc., 20, 458^62. Brutsaert, W., 1967, Some methods of calculating unsaturated permeability. Trans. ASAE 10:400 404. Childs, B.C. and N. Collis-George, 1950, The permeability of porous materials. Proc. R. Soc. London, Ser. a, 201, 392-405. Chuoke, R.L., P. van Meurs, and C. van der Poel, 1959, The instability of slow immiscible, viscous liquid-liquid displacements in porous media. Trans. Am. Inst. Min. Eng., 216, T.P. 8073. Clapp, R.B. and G.M. Hornberger, 1978, Empirical equations for some soil hydraulic properties, Water Resour. Res., 14, 601-604. Clothier, B.E. and I. White, 1981, Measurement of sorptivity and soil water diffusivity in the field. Soil Sci. Soc. Am. J., 45, 241-245. Connell, L.D., R. Haverkamp, C. Cote, and P.J. Ross, 1998, An inverse methodology for the determination of soil physical properties from positive head infiltration: I. Theory. Water Resour. Res. (submitted). Culligan, P.J., D.A. Barry, J.-Y. Parlange, T.S. Steenhuis, and R. Haverkamp, 1998, Infiltration with controlled air escape: determining soil hydraulic properties from air pressure measurements, Water Resour. Res. (submitted). Dunne, T. and R.D. Black, 1970a, An experimental investigation of runoff production in permeable soils. Water Resour. Res., 6, 478-490. Dunne, T. and R.D. Black, 1970b, Partial area contributions to storm runoff in a small New England watershed. Water Resour. Res., 6, 1296-1311. Elrick, D.E. and J.J. Robin, 1981, Estimating the sorptivity of soils. Soil Sci., 132, 127 133. Fuenles, C., R. Haverkamp, and J.-Y. Parlange, 1992, Parameter constraints on closed-form soil water relationships, /. Hydrol., 134, 117-142. Fuentes, C., M. Vauclin, J.-Y. Parlange, and R. Haverkamp, 1996, A note on the soil-water conductivity of a fractal soil. Transp. Porous Media, lit, 31-36. Gardner, W.R., 1958, Some steady state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci., 85, 228232. Glass, R.J., J.-Y. Parlange, and T.S. Steenhuis, 1991, Immiscible displacement in porous media: stability analysis of three-dimensional axisymmetric disturbances with applications to gravity driven wetting front instability. Water Resour. Res., 27, 1947-1956. Green, W.A. and G.A. Ampt, 1911, Studies in soil physics: 1. Flow of air and water through soils. J. Agric. Sci., 4, 1-24. Gupta, S.C. and W.E. Larson, 1979, Estimating soil water retention characteristics from particle-size distribution, organic matter percent and bulk density. Water Resour. Res., 15, 1633-1635. Haverkamp, R. and J.-Y. Parlange, 1986, Predicting the water-retention curve from particle-size distribution: 1. Sandy soils without organic matter. So/7 Sci., 142, 325-339. Haverkamp, R., J.-Y. Parlange, J.L. Starr, G. Schmitz, and C. Fuentes, 1990, Infiltration under ponded conditions: 3. A predictive equation, Soil Sci., 149, 292-300. Haverkamp, R., P.J. Ross, K.R.J. Smettem, and J.-Y. Parlange, 1994, Three-dimensional analysis of infiltration from the disk infiltrometer. 2. Physically based infiltration equation. Water Resour. Res., 30, 2931 2935. Heaslet, M.A. and A. Alksne, 1961, Diffusion from a fixed surface with a concentration-dependent coefficient, J. Soc. Ind. Appl. Math., 9, 584-596.

SOIL PROPERTIES AND WATER MOVEMENT

127

Hewlett, J.D. and A.R. Hibbert, 1967, Factors affecting the response of small watersheds to precipitation in a humid area. Proceedings of the International Symposium on Forest Hydrology, W.E. Sopper and H.W. Lull (Eds.). Pergamon Press, Oxford, UK. pp.' 275-290. Hillcl, D. and R.S. Baker, 1988, A descriptive theory of fingering during infiltration into layered soils, Soil Sci., 146, 51-56. Hogarth, W., J. Hopmans, J.-Y. Parlange, and R. Haverkamp, 1988, Application of a simple soil-water hysteresis model, /. Hydro!., 98, 21-29. Katopodes, N.D. and T. Strelkoff, 1977, Hydrodynamics of border irrigation. Complete model, /. Irrig. Drain., ASCE, 103, 309-324. Katopodes, N.D., J.-H. Tang, and A.J. Clemmcns, 1990, Estimation of surface irrigation parameters, /. Irrig. Drain., ASCE, 116, 676-695. Kostiakov, A.N., 1932, On the dynamics of the coefficient of water percolation in soils and on the necessity of studying it from a dynamic point of view for purposes of amelioration, Trans. Com. Int. Soil Sci., 6th Moscow, Part A, 17-21. Liu, Y., T.S. Stccnhuis, and J.-Y. Parlange, 1994, Formation and persistence of fingered flow fields in coarse grained soils under different moisture contents, J. Hydrol, 159, 187-195. Liu, Y., J.-Y. Parlange, and T.S. Steenhuis, 1995, A soil water hysteresis model for fingered flow data. Water Resour. Res., 31(9), 2263-2266. Millington, R.J. and J.P. Quirk, 1961, Permeability of porous solids. Trans. Faraday Soc., 57, 1200-1206. Pachepski, Y.A., R.A. Shcherbakov, and L.P. Korsunskaya, 1995, Scaling of soil water retention using a fractal model, Soil Sci., 159, 99-104. Parlange, J.-Y., 1972, Theory of water movement in soils: 8. One-dimensional infiltration with constant flux at the surface, Soil Sci., 114, \-4. Parlange, J.-Y., 1973, Note on the infiltration advance front from border irrigation. Water Resour. Res., 9, 1075-1078. Parlange, J.-Y., 1975a, Theory of water movement in soils: 11. Conclusion and discussion of some recent developments, Soil Sci., 119, 158-161. Parlange, J.-Y., 1975b, On solving the flow equation in unsaturated soils by optimization: horizontal infiltration, Soil Sci. Soc. Am. Proc., 39, 415^-18. Parlange, J.-Y., 1976, Capillary hysteresis and the relationship between drying and wetting curves, Water Resour. Res., 12, 224-228. Parlange, J.-Y., 1980, Water transport in soils, Anna. Rev. Fluid Mech., 12, 77-102. Parlange, J.-Y. and D.E. Hill, 1976, Theoretical analysis of wetting front instability in soils. Soil Sci., 122, 236-239. Parlange, J.-Y., I.G. Lisle, and R.D. Braddock. 1982, The three parameter infiltration equation, Soil Sci., 133, 337-341. Parlange, J.-Y., R.D. Haverkamp, and J. Touma, 1985, Infiltration under ponded conditions. Part 1. Optimal analytical solution and comparison with experimental observations, Soil Sci., 139, 305-311. Parlange, J.-Y., D.A. Barry, M.B. Parlange, and R. Haverkamp, 1992b, Note on the sorptivity for mixed saturated unsaturated flow. Water Resour. Res., 28, 25292531. Parlange, J.-Y., D.A. Barry, M.B. Parlange, D.A. Lockington, and R. Haverkamp, 1994, Sorptivity calculation for arbitrary diffusivity, Transp. Porous Media, 15, 197-208. Parlange, J.-Y., W.L. Hogarth, C. Fuentes, J. Sprintall, R. Haverkamp, D. Elrick, M.B. Parlange, R.D. Braddock, and D.A. Lockington, 1995a, Superposition principle for short-term solutions of Richards's equation: application to the interaction of wetting fronts with an impervious surface, Transp. Porous Media, 17, 239-247.

128

VADOSE ZONE HYDROLOGY

Parlange, J.-Y., W.L. Hogarth, C. Fuentes, J. Sprintall, R. Haverkamp, D. Elrick, M.B. Parlange, R.D. Braddock, and D.A. Lockington, 1995b, Interaction of wetting fronts with an impervious surface—longer time behaviour, Tramp. Porous Media, 17, 249-256. Parlange, M.B., T.S. Steenhuis, D.J. Timlin, F. Stagnitti, and R.B. Bryant, 1989, Subsurface flow above a fragipan horizon, Soil Sci.. 148(2), 77-86. Parlange, M.B., S.N. Prasad, J.-Y. Parlange, and M.J.M. Romkcns, 1992a, Extension of the Heaslet-Alksne technique to arbitrary soil water diffusivities, Water Resour. Res., 28, 2793-2797. Perrier, E.. C. Mullon, M. Rieu, and G. deMarsily, 1995, Computer construction of fractal soil structures: simulation of their hydraulic and shrinkage properties, Water Resour. Res., 31, 2927-2943. Philip, J.R. and D.A. Farrell, 1964, General solution of the infiltration-advance problem in irrigation hydraulics, J. Geophys. Rex., 69, 621-631. Poulovassilis, A., 1962, Hysteresis of pore water. An application of the concept of independent domain. Soil Sci., 93, 405^12. Purcell, W.R., 1949, Capillary pressures—their measurement using mercury and the calculation of permeability therefrom. Petr. Trans. Am. Inst. Min. Metal Eng., 186, 39^18. Rallison, R.E., 1980, Origin and evolution of the SCS runoff equation. Symposium on Watershed Management. ASCE, New York, NY. pp. 204-215. Rawls, W.J. and D.L. Brakensick, 1982, Estimating soil water retention from soil properties. ,/. Irrig. Drain., ASCE, 108(IR2), 166-171. Reichardt, K., D.R. Nielsen, and J.W. Biggar, 1972, Scaling of horizontal infiltration into homogeneous soils, Soil Sci. Soc. Am. Proc., 36, 241-245. Rieu, M. and G. Sposito, 1991, Fractal fragmentation, soil porosity, and soil water properties: I. Theory, Soil Sci. Soc. Am. J., 55, 1231-1238. Rijtema, P.E., 1965, An analysis of actual evapotranspiration. Report 659, Centre for Agricultral Publications and Documents. Wageningen, The Netherlands. Rose, C.W., W.R. Stern, and J.E. Drummond, 1965, Determination of hydraulic conductivity as a function of depth and water for soil in situ. Austr. J. Soil Res., 3, 1-9. Ross, P.J., J.-Y. Parlange, and R. Haverkamp, 1995, Two-dimensional interaction of a wetting front with an impervious layer: analytical and numerical solutions, Transp. Porous Media, 20, 251-263. Saffman, P.G. and G.I. Taylor, 1958, The penetration of a fluid into a porous medium of Hele-Shaw cell containing a more viscous liquid, Proc. R. Soc. London, A245, 312-329. Schmitz. G. and G.J. Seus, 1990, Mathematical zero-inertia modelling of surface irrigation: advance in borders, /. Irrig. Drain., ASCE, 116, 603-615. Selker, J., J.-Y. Parlange, and T.S. Steenhuis, 1992, Fingered flow in two dimensions. 2. Predicting finger moisture profile, Water Resour. Res., 28, 2523-2528. Smettem, K.R.J., J.-Y. Parlange, P.J. Ross, and R. Haverkamp, 1994, Three-dimensional analysis of infiltration from the disc infiltrometer. 1. A capillary-based theory. Water Resour. Res., 30, 2925-2929. Smettem, K.R.J., P.J. Ross, R. Haverkamp, and J.-Y. Parlange, 1995, Three-dimensional analysis of infiltration from the disc infiltrometer. 3. Parameter estimation using a double disc tension infiltrometer, Water Resour. Res., 31, 2491-2495. Stagnitti, F., J.-Y. Parlange, T.S. Steenhuis, B. Nijssen, and D. Lockington, 1994, Modelling the migration of water soluble contaminants through preferred paths in the soil. Groundwater Quality Management, K. Kovar and J. Soveri (Eds.). IAHS Publication No. 220. pp. 367-379. Stagnitti, F., J.-Y. Parlange, T.S. Steenhuis, J. Boll, B. Pivetz, and D.A. Barry, 1995, Transport of moisture and solutes in the unsaturated zone by preferential

SOIL PROPERTIES AND WATER MOVEMENT

129

flow. Environmental Hydrologv, V.P. Singh (Ed.). Kluwer Academic Publishers, Norwell, MA. pp. 193-224. Steenhuis, T.S. and W.H. van der Molen. 1986, The Thornthwaite-Mather procedure as a simple engineering method to predict recharge, J. Hydro!., 84, 221-229. Steenhuis, T.S. and J.-Y. Parlange, 1988, Simulating preferential flow of water and solutes on hillslopes. Validation of Flow and Transport Models for the Unsaturated Zone, P.J. Wicrenga and D. Bachelet (Eds.). New Mexico State University, pp. 381-391. Steenhuis, T.S., J.-Y. Parlange, M.B. Parlange, and F. Stagnitti, 1988, A simple model for flow on hillslopes, Agric. Water Mgmt., 14, 153-168. Steenhuis, T.S., J.-Y. Parlange, and M.S. Andreini, 1990, A numerical model for preferential solute movement in structured soils. Geoderma, 46, 193-208. Steenhuis, T.S., M. Winchell, J. Rossing, J.A. Zollweg, and M.F. Walter, 1995, SCS curve number equation revisited for variable-source runoff areas. /. Irrig. Drain., ASCE, 121, 234-238. Talsma, T., 1969, In situ measurement of sorptivity, Aust. J. Soil Res.. 7, 269-276. Talsma, T. and J.-Y. Parlange, 1972, One-dimensional vertical infiltration. Aust. J. Soil Res., 10, 143-150. Thornthwaite, C.W. and J.R. Mather, 1955, The water balance. Publ. Climatoi, 8(1). Tyler, S.W. and S.W. Wheatcraft, 1990, Fractal process in soil water retention. Water Resour. Res., 26, 1047-1054. van Genuchtcn, M.Th., 1980, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898. Wooding, R.A., 1968, Steady infiltration from a shallow circular pond, Water Resour. Res., 4, 1259-1273.

5

Nonideal Transport of Reactive Solutes in Porous Media Cutting Across History and Disciplines

MARK L. BRUSSEAU

The potential for human activities to adversely affect the environment has become of increasing concern during the past three decades. As a result, the transport and fate of contaminants in subsurface systems has become one of the major research areas in the environmental/hydrological/earth sciences. An understanding of how contaminants move in the subsurface is required to address problems of characterizing and remediating soil and groundwater contaminated by chemicals associated with industrial and commercial operations, waste-disposal facilities, and agricultural production. Furthermore, such knowledge is needed for accurate risk assessments; for example, to evaluate the probability that contaminants associated with a chemical spill will reach an aquifer. Just as importantly, knowledge of contaminant transport and fate is necessary to design "pollution-prevention" strategies. A tremendous amount of research on the transport of solutes in porous media has been generated by several disciplines, including analytical chemistry (chromatography), chemical engineering, civil/environmental engineering, geology, hydrology, petroleum engineering, and soil science. This research includes the results of theoretical studies designed to pose and evaluate hypotheses, the results of experiments designed to test hypotheses and investigate processes, and the development and application of mathematical models useful for integrating theoretical and experimental results and for evaluating complex systems. While much of the previous research has focused on transport of nonreactive solutes, it is the transport of "reactive" solutes that is currently receiving increased attention. Reactive solutes are those subject to phase-transfer processes (e.g., sorption, precipitation/dissolution) and transformation reactions (e.g., biodegradalion).

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

1 31

Of special interest in the field of contaminant transport is so-called nonideal transport. In the most general sense, nonideal transport can be described as transport behavior that deviates from the behavior that is predicted using a given set of assumptions. A homogeneous porous medium and linear, instantaneous phase transfers and transformation reactions are the most basic set of assumptions for ideal solute transport in porous media. As discussed in a recent review, transport of reactive contaminants is often nonideal (Brusseau, 1994). The potential causes of nonideal transport include rate-limited and nonlinear mass transfer and transformation reactions, as well as spatial (and temporal) variability of material properties. The purpose of this chapter is to review briefly nonideal contaminant transport in porous media. I will begin with a review of basic concepts related to contaminant transport, followed by a review of conceptual and mathematical approaches used to represent nonideality factors in mathematical models. In the spirit of the conference at which this material is being presented, I will attempt to review pertinent research contributed by non-earth-science disciplines. Portions of this paper are adapted from recent reviews of reactive contaminant transport (Brusseau, 1994, 1998).

Characterizing Solute Transport in Porous Media Four processes that control the movement of contaminants in porous media are advection, dispersion, interphase mass transfer, and transformation reactions. Advection, also referred to as convection, is the transport of dissolved matter (solute) by the movement of a fluid responding to a gradient of fluid potential. Dispersion represents spreading of solute about a mean position, such as the center of mass. Phase transfers, such as sorption liquid-liquid partitioning, and volatilization, involve the transfer of matter in response to gradients of chemical potential. Transformation reactions include any process by which the physicochemical nature of a contaminant is altered. Examples include biotransformation, radioactive decay, and hydrolysis. The initial paradigm for transport of contaminants In porous media was based on assumptions that the porous medium was homogeneous and that interphase mass transfers and transformation reactions were linear and instantaneous. For discussion purposes, transport that follows this paradigm is considered to be ideal. The onedimensional form of the equation that governs transport of dissolved solutes, following the assumptions associated with ideal transport, is

where x is a spatial coordinate, / is time, C is the concentration of contaminant in the fluid (e.g., water), v is the average linear velocity of the fluid in the pores of the medium, D is the dispersion coefficient, /u, is a first-order reaction coefficient, and R is the retardation factor, defined as

1 32

VADOSE ZONE HYDROLOGY

where p is the bulk density of the porous medium, 6 is the fractional volumetric fluid content (equal to porosity when pores are completely saturated with the fluid), and Kd is a coefficient representing distribution of the contaminant between the solid and liquid phases (e.g., sorption). The dispersion coefficient is usually defined as

where a is the dispersivity, DQ is fluid-phase diffusion coefficient, and T is a factor accounting for the tortuosity of the porous medium. The first and second terms on the right-hand side of equation (5.3) represent the contribution of mechanical mixing and axial or molecular diffusion, respectively, to total dispersion. Equation (5.1), known as the advection-dispersion equation, is, in one form or another, the most widely used equation for describing the transport of dissolved matter in porous media. It is used in chemical engineering, petroleum engineering, and chromatography, in addition to the earth sciences. The term on the left-hand side of equation (5.1) represents the change in contaminant mass that occurs at a specified location in response to transport and fate processes. The retardation factor represents the influence of phase transfer (sorption) on transport. The first term on the right-hand side represents advectivc transport, while the second term represents dispersive transport. The third term represents a loss of contaminant from the solution due to reaction. Despite the widespread use of equation (5.1), it is well known that the subsurface is heterogeneous and that many phase transfers and transformation reactions are not linear or instantaneous. Thus, contaminant transport usually deviates from that which is expected based on the original paradigm, especially at the field scale. Such transport can be considered as nonideal. Most of the work reported to date for nonideal transport has involved analyses of the second temporal moment (i.e., spreading or dispersion of a breakthrough curve) and the first and second spatial moments (i.e., retardation and spreading of a plume). Under "ideal" conditions (e.g., homogeneous porous medium, instantaneous mass transfer), solute transport will be characterized by constant values of the retardation factor (K) and a minimal degree of spreading. The existence of nonideal transport could, therefore, be defined by the observation of increased dispersion compared with the laboratory (second spatial or temporal moment) and time-dependent /^-values (first spatial moment). These phenomena will be the focus of the present discussion.

Selected Factors Responsible for Nonideal Transport Nonlinear Sorption Most solute transport models, especially for field-scale applications, include the assumption that the distribution of solute between liquid and solid phases can be described as a linear process. Such a condition would be reflected, for example, in linear sorption isotherms. Numerous laboratory experiments have shown that sorp-

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

1 33

tion is often linear for low-polarity organic compounds. However, this assumption should be evaluated for each case because nonlinear isotherms have been reported, especially when measured over a wide range of concentrations (e.g., Ball and Roberts, 1991; Weber et al., 1992; Allen-King et al., 1996). Nonlinear isotherms arc the norm rather than the exception for many polar organic, as well as for inorganic, chemicals (e.g., Brusseau and Rao, 1989; Weber and Miller, 1989). It is important to note that the nature of the isotherm is influenced by properties of the sorbent and the solution, in addition to those of the solute. Several equations exist for describing sorption isotherms (for reviews, sec Travis and Etnier, 1981: Kinniburgh, 1986). It is well known that nonlinear sorption can cause asymmetrical breakthrough curves and concentration-dependent retardation factors. In chromatography, for example, the impact of nonlinear sorption on spatial and temporal distributions of solute has received attention for a long time (cf., Tiselius, 1940; Martin and Synge, 1941). Early investigations of the effect of nonlinear sorption on solute transport in soil were reported by Rao and Davidson (1979) and van Genuchten and Cleary (1979). The influence of nonlinear sorption on contaminant transport has recently received increased attention in the earth sciences (e.g., Burgisser et al., 1993: Tompson, 1993; Bosnia et al., 1994; Cvetkovic and Dagan, 1994; Rabideau and Miller, 1994; Brusseau, 1995; Spurlock et al., 1995; Streck et al., 1995; Srivastava and Brusseau, 1996). Rate-Limited Sorption/Desorption Most field-scale solute transport models include the so-called local equilibrium assumption, which specifies that interactions between the solute and the sorbent are so rapid in comparison with hydrodynamic residence time that the interactions can be considered instantaneous. Based on laboratory experiments, it has long been known that sorption/dcsorption of many organic compounds by porous media can be significantly rate-limited. Numerous experimental and theoretical studies have shown that rate-limited sorption/desorption can cause nonidcal transport. This was discussed as early as 1920 by Bohart and Adams, who were investigating the transport of gases through carbon filters. The impact of rate-limited sorption/desorplion on transport in soil was discussed as early as 1957 by Upchurch and Pierce. This nonideality can take the form of asymmetrical breakthrough curves that exhibit early breakthrough and tailing, as well as decelerating plumes (temporally increasing ,R-values). An example of the effect of rate-limited sorption/desorption on transport is presented in figure 5.1, which shows breakthrough curves for transport of several solutes through a sandy soil. Note that the breakthrough curves for the nonreactive tracers [tritiated water (3H2O) and pcntafluorobenzoate] arc sharp and symmetrical, signifying ideal behavior. In contrast, the breakthrough curve for the sorbing organic solute (naphthalene) is asymmetrical. This suggests that the nonideality factor involves the sorption process. A phenomenon that, in many cases, is related to rate-limited sorption/desorplion is "contaminant aging." Recent research has shown that contaminants that have been in contact with porous media for long times are much more resistant to

1 34

VADOSE ZONE HYDROLOGY

Figure 5.1 Influence of rate-limited sorption on transport through a sandy soil. (Adapted from Brusseau et al., 1991.)

desorption, extraction, and degradation. For example, contaminated soil samples taken from field sites exhibit solid-to-aqueous distribution ratios that are much larger than those measured or estimated based on spiking the porous media with the same contaminant (e.g., adding contaminant to uncontaminated sample) (Steinberg et al., 1987; Pignatello et al., 1990; Smith et al., 1990; Scribner et al. 1992). In addition, the magnitude of the desorption rate coefficients determined for previously contaminated media collected from the field have been shown to be much smaller than the values obtained for spiked samples (Steinberg et al., 1987; Connaughton et al., 1993). These field-based observations are supported by laboratory experiments wherein measured values of desorption rate coefficients have been observed to decrease with increasing time of contact prior to desorption (Karickhoff, 1980; McCall and Agin, 1985; Coates and Elzerman, 1986; Brusseau et al., 1991). The causes of the phenomena associated with contaminant aging are under investigation, and may involve diffusive flux into domains from which release is greatly constrained, as well as binding of the contaminant to components of the soil.

Spatially Variable Sorption Due to the heterogeneity of subsurface systems, it is logical to expect sorption to be spatially variable. Several field-scale investigations have shown that this is indeed the case (Pickcns et al., 1981; Williams et al., 1985; Elabd et al., 1986; Mackay et al., 1986; Rao et al., 1986; Wood et al., 1987; Bunzl and Schimmack, 1988; Robin et al., 1991). Depending on the form of the spatial variability, nonuniform sorption

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

1 35

may cause nonidcal transport. Consider, for example, a porous medium that comprises several layers, each with a different sorption coefficient, but all with the same hydraulic conductivity. Solute is injected simultaneously into all layers. As transport proceeds, the solute fronts in each of the layers will move at different rates because of the variations in retardation. This differential-front advancement will lead to the observation of increased dispersion at a depth-integrated sampling point down-gradient of the injection point. In real situations, spatial variations in both hydraulic conductivity and sorption would be expected. The possible existence, and nature, of correlations between the two properties would be important for such cases. The impact of spatially variable sorption on transport has begun to receive increased attention. Smith and Schwartz (1981), with a series of model simulations, evaluated the influence of spatially variable cation exchange capacity (i.e., variable retardation) on solute transport. They assumed that sorption was negatively correlated with hydraulic conductivity. Dispersion was observed to increase as the variability in retardation increased. However, they concluded that this effect would be of secondary importance in comparison with the effect of spatially variable hydraulic conductivity. Spatially variable sorption was proposed as one cause of the enhanced dispersion exhibited by lithium, in comparison with bromide, in a recent naturalgradient experiment performed at Cape Cod, MA. In a theoretical analysis of the effect of coupled physical and chemical heterogeneity, Garabedian et al., (1988) observed enhanced dispersion compared with the uniform sorption case when a negative correlation between sorption and hydraulic conductivity was assumed. Similar results, based on theoretical and modeling exercises, have been reported by several other researchers (Bahr, 1986; Valocchi, 1989; Cvetkovic and Shapiro, 1990; Andricevic and Foufoula-Georgiou, 1991; Kabala and Sposito, 1991; Bosnia et al., 1993). There have been few experimental investigations of the impact of spatially variable sorption on solute transport. One such study was reported by Brusseau and Zachara (1993), who investigated the transport of Co2 + in a column packed with layers of two media of differing hydraulic conductivities and sorption capacities. The sorption capacities of the two media differed by about a factor of 3. The asymmetrical breakthrough curve obtained for transport of a nonreactive tracer through the column demonstrated the effect of the physical heterogeneity on transport. The breakthrough curve obtained for transport of Co 2+ was shifted to the left of a simulated curve obtained for ideal conditions (homogeneous, instantaneous sorption) and exhibited tailing (see figure 5.2). The comparison reveals that transport of Co 2+ through the heterogeneous porous medium was significantly nonideal. The optimized curve obtained for the simulation that included hydraulic-conductivity variability, sorption-capacity variability, rate-limited mass transfer between the two layers, and rate-limited sorption/desorption matched the experimental data quite well. In contrast, the curve for the simulation that included all factors except spatially variable sorption did not match the data well. Hence, the influence of sorption variability had to be considered to accurately simulate the transport of Co2 + .

1 36

VADOSE ZONE HYDROLOGY

Figure 5.2 Influence of soil heterogeneity, rate-limited sorption, and rate-limited mass transfer on transport of a reactive solute. (Adapted from Brusseau and Zachara, 1993.)

Structured/Locally Heterogeneous Porous Media Nonideal transport, often referred to as physical nonequilibrium, can result from a structured or heterogeneous flow domain at the macroscopic scale (centimeter to decimeter range). The existence of regions of smaller hydraulic conductivity within the flow domain creates a spatially variable velocity field, with minimal flow and advection occurring through the small-conductivity domains. Due to the small advective flux, these domains may act as sink/source components, with rate-limited diffusional mass transfer between the advective and nonadvective domains that causes dispersion of the solute front. These sink/source regions can take various forms, including the internal porosity of aggregates, dead-end pores, the bulk matrix of fractured media, and the small hydraulic conductivity microlayers or laminae typically found in aquifers of sedimentary origin. The possibility that structured or locally heterogeneous porous media may influence flow and transport has long been recognized. For example, the influence of "macropores" on water flow in soil was discussed more than 100 years ago by Schumacher (in 1864) and Lawes et al. (in 1882) as referenced by Beven and Germann (1982). The impact of "dead-end pores" and intraparticle porosity on flow and transport was quantified in the early 1950s by chemical engineers (cf., Kasten et al., 1952; Rosen, 1952; Danckwerts, 1953).

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

1 37

During the last few decades, the effect of aggregated or macroporous media on solute transport has been well documented (see Brusseau and Rao, 1990 for a recent review). Miscible displacement studies performed with well-characterized aggregated or macroporous media packed in columns clearly demonstrate that these structures cause asymmetrical and tailed breakthrough curves and enhanced dispersion (cf., Biggar and Nielsen. 1962; van Genuchlen and Wierenga, 1977; Calvet et al., 1978; Rao et al.. 1980; Nkedi-Kizza et al., 1983). Experiments performed with undisturbed cores or lysimeters demonstrate that naturally occurring structures can cause nonidel solute transport (cf, McMahon and Thomas, 1974; Richter and Jury, 1986; Scyfricd and Rao, 1987). It has also been shown that nonideal behavior can occur during transport of solutes through fractured media (cf., Grisak et al., 1980; Bibby, 1981; Neretnieks, 1983). Research has demonstrated that locally heterogeneous porous media (e.g., microstratified laminae of different hydraulic conductivities, ranging from several millimeters to centimeters in thickness) can also cause nonideal transport. Several laboratory-scale miscible displacement experiments have been performed to investigate the effect of locally heterogeneous or microstratified media on solute transport (Skibitzkc and Robinson, 1963; Sudicky et al., 1985; Cala and Greenkorn, 1986; Refsgaarrd, 1986; Silliman and Simpson, 1987; Herr et al., 1989; Haselow and Greenkorn, 1991; Brusseau and Zachara, 1993). The results of these experiments show that the presence of local heterogeneities can cause enhanced dispersion, early breakthrough, and extensive tailing. The influence of local-scale heterogeneities on field-scale transport has been illustrated in recent research (Killey and Moltyaner, 1988; Poulsen and Kueper, 1992; Jensen et al., 1993). Spatially Variable Hydraulic Conductivity The influence of large-scale (e.g., field-scale) spatially variable hydraulic conductivity fields on water flow and contaminant transport in porous media has been a major research topic for many years. The impact of hydraulic conductivity variability on transport is often discussed in terms of the "scale effect," wherein apparent dispersivity values measured for field-scale transport are usually much larger than those measured for transport in packed columns (cf, Fried, 1975; Anderson, 1979; and references cited therein). A clear description of how spatially variable hydraulic conductivities could cause enhanced solute dispersion (compared with that measured in the laboratory) was given in the early 1960s (cf., Theis, 1963; Warren and Skiba, 1964). Since then, a tremendous amount of research has demonstrated that the additional dispersion, often called macro- or full-aquifer dispersion, observed for field-scale transport of nonreactive solute is primarily a result of hydraulic conductivity variability (cf., Schwartz, 1977; Gelhar et al., 1979; Molz et al., 1983). The general effect of macrodispersion is similar to the nonideal transport associated with structured porous media discussed above. Furthermore, both arc caused by the same phenomenon: spatially variable velocity (advection) fields. However, they differ by scale. For example, the two can be operationally differentiated by the relative spatial resolution of the sampling device employed to monitor solute concentrations. The increased dispersion (compared with laboratory-measured

1 38

VADOSE ZONE HYDROLOGY

values) measured by vertically averaged sampling in heterogeneous systems (i.e., a monitoring that is well screened over a substantial portion of an aquifer) is considered to be macrodispersion. Conversely, the increased dispersion observed at the scale of a single, discrete zone within a porous medium, and which can be measured in laboratory columns of undisturbed material, is considered to be the result of local heterogeneities (structured media). The use of discrete, multilevel sampling devices or complementary laboratory experiments is necessary to separate the effects of the two phenomena. The two factors also differ in the manner in which they are usually represented in mathematical models. The influence of structured media on solute transport is most often simulated with a dual porosity approach, wherein advective/dispersivc flux is assumed to occur in only a fraction of the porous medium, and solute interaction with the nonadvective fraction is described with mass transfer or diffusion equations. Such models have been applied to solute transport in aggregated and macroporous soils, fractured media, and media that contain hydraulic conductivity laminae and microlayers. Conversely, field-scale heterogeneity (hydraulic conductivity variability) is respresented usually by either the stratified (layer) or stochastic approach. Dual porosity models have been applied to field-scale problems, but they are confined to operation in a calibration mode only. The use of stochastic approaches to represent heterogeneities associated with millimeter- or centimeter-scale structures would generally be problematic. It is probable that multiple scales of heterogeneity exist in most systems. In such cases, differentiation between the scales pertinent to the investigation would depend on the focus of the investigation and the scale of the measurement devices. Flow and transport in porous media with multiple scales of heterogeneity (e.g., hierarchical porous media) has recently become the subject of research in the earth sciences (cf., Cushman, 1990).

Transport of Reactive Contaminants at the Field Scale Transport in the Vadose Zone Many field experiments have been performed to investigate various aspects of solute transport from the surface through the vadose zone. Much of this research has focused on agricultural-related problems. A recurring observation associated with many of these field experiments has been transport of solute to depths greater than those expected based on ideal transport theory. Jury (1985) provided an earlier summary of several of these field experiments, and a comprehensive compilation of field experiments that involve pesticide transport has recently been published by Flury (1996). Hence, there is no need to repeat such a review. An early detailed field study of pesticide transport in the vadose zone was reported by Rao et al. (1974), who investigated the transport of picloram in a highly structured soil under ponded conditions. Transport of a significant fraction of pesticide mass was observed to depths approximately three times greater than those

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

1 39

expected based on ideal water flow and instantaneous sorption. This "preferential flow" of organic compounds has since been observed in several other well-controlled field studies (cf., Bowman and Rice, 1986; Jury et al., 1986; Ghodrati and Jury, 1992). Relatively few experiments have been performed in such a manner that allows detailed analysis of the factors causing nonideal transport. Thus, the factors responsible for the observed nonideal transport, and their relative importance, have not been fully elucidated. Transport in Groundwater Systems A multitude of field-scale experiments have been performed with nonreactive tracers to investigate solute transport in groundwater systems (for a recent review, see Gclhar et al., 1992). Conversely, relatively few controlled field experiments have been conducted to evaluate the transport of reactive solutes under natural or forced gradients. These experiments were recently reviewed by Brusseau (1994), who concluded that some form of nonideal transport appeared to be present for all experiments. Some of the first controlled field studies of the transport of reactive solutes in aquifers were associated with efforts to investigate the feasibility of underground disposal of radioactive wastes. For example, several tracer experiments were performed in the late 1950s to investigate the transport of 3H2O, chloride, strontium, and cesium in a confined aquifer located at the University of California's Richmond field station (Ewing, 1959; Kaufman, 1960; Inouc and Kaufman, 1963). Personnel from the U.S. Department of Agriculture and the U.S. Environmental Protection Agency (R. S. Kerr Laboratory) were involved in one of the first attempts to evaluate the field-scale transport of sorbing organic solutes in an aquifer. In two separate experiments, solutions containing DDT (Scalf ct al., 1969) and three herbicides (picloram, atrazine, and trifluralin) (Schneider et al., 1977) were first injected into, and then extracted from, a portion of the Ogallala aquifer. Several experiments were conducted at a field site at Palo Alto Baylands, CA to evaluate the behavior of inorganic and organic solutes during groundwater recharge (Roberts et al., 1978, 1980. 1982). Probably the two most well-known sites where field experiments for reactive solutes have been conducted are the Borden site in Ontario and the Cape Cod site in Massachusetts. Some of the numerous experiments that have been conducted by a number of investigators at the Cape Cod and Borden sites have been reviewed by Garabedian and LeBlanc (1991) and Cherry et al. (1996), respectively.

Analysis and Mathematical Modeling of Nonideal Transport To provide a historical background to the subject of nonideal solute transport, tables 5.1, 5.2, and 5.3 present a synopsis of research efforts associated with various factors and processes. Attempts were made to identify the early investigations for each aspect. However, there is no guarantee that the earliest works have been identified

Table 5.1 Analyses of Nonideal Solute Transport: Earth Science Reference

Topic

Gardner and Brooks (1957) Upchurch and Pierce (1957) Biggar and Nielsen (1962) Hamaker et al. (1966) Elrick et al. (1966) Kay and Elrick (1967) Green et al. (1968) Oddson et al. (1970) Tanji (1970) Passioura (1971) Davidson and McDougal (1973)

Present version of "two-region" model for transport Discuss relation between velocity and impact of RLS on transport Discuss impact of PNE on solute transport Attribute nonideal transport of reactive solutes to impact of RLS Attribute nonideal transport of reactive solutes to impact of PNE Attribute nonideal transport of reactive solutes to impact of PNE + RLS Attribute nonideal transport of reactive solutes to impact of PNE + NLS Present transport equation with "one-site" RLS Use chromatographic theory for solute transport with holdback and NLS (Langmuir) Present lumped version of "two-region" model for transport Attribute nonideal transport of reactive solutes to combination of factors Test performance of transport model with "one-site" RLS Test performance of transport model with "one-site" RLS Present transport equation with "two-region" representation (with diffusion interaction) Present "two-region" concept (no interaction) Present transport equation with "two-region" representation and first-order MT Present transport equation with "two-site" representation of RLS Present transport equation with "two-site" representation of RLS Present transport equation with "two-site" representation of RLS Analysis of impact of NLS on transport Present nonreactive transport equation with intraparticle diffusion based on Pick's law Present "two-region" mass transfer approach with flow in both regions Present transport equation with NLS (Freundlich) + "one-site" RLS Present reactive transport equation with intraparticle diffusion based on Pick's law Present transport equation with NLS (Langmuir) + "two-site" RLS Present transport equation with FMT + IPD + NLS (Freundlich) Present "three-region" approach for transport (rapid, slow, and no flow) (with first-order MT) Present "three-site" aproach for representing RLS in transport, also included NLS (Freundlich)

Hornsby and Davidson (1973) Skopp and Warrick (1974) van Genuchten et al. (1974) van Genuchten and Wierenga (1976) Leistra and Dekkers (1976) Selim et al. (1976) Cameron and Klute (1977) Rao and Davidson (1979) Rao et al. (1980) Skopp et al. (1981) Murali and Aylmore (1981) Nkedi-Kizza et al. (1982) Fluhler and Jury (1983) Crittenden et al. (1986) Morisawa et al. (1986) Boesten et al. (1989)

FMT, film mass transfer; IPD, intraparticle diffusion; MT, mass transfer; NLS, nonlinear sorption; PNE, physical nonequilibrium; RLS, rate-limited sorption.

Table 5.2 Multifactor Analyses of Nonideal Transport of Reactive Solutes in Heterogeneous Porous Media Reference Smith and Schwartz (1981) Jury (1983) Bahr(1986) van der Zee and van Riemsdijk (1987) Garabedian el al. (1988) Valocchi (1988) Brusseau (1989) Brusseau et al. (1989) Dagan (1989)

Valocchi (1989) Cvetkovic and Shapiro (1990) Andricevic and Foufoula-Georgiou (1991) Brusseau (1991) Destouni and Cvetkovic (1991) Kabala and Sposito (1991) Brusseau (1992) Schafer and Kinzelbach (1992) Selroos and Cvetkovic (1992) Bosnia ct al. (1993) Brusseau and Zachara (1993) Dagan and Cvetkovic (1993) Tompson (1993) Quinodoz and Valocchi (1993) Bosnia ct al. (1994) Burret al. (1994) Cvetkovic and Dagan (1994) Rabidcau and Miller (1994) Srivastava and Brusseau (1994) Bellin and Rinaldo (1995) Selroos (1995) Srivastava and Brusseau (1996)

Factors"

Form h SM2 SM2 MF/BTC SM2 SM2 SMO-2 SM2 MF/BTC SMI,2 SMO -2 MF/BTC SM2 MF/BTC MF/BTC SMI,2 MF/BTC MF/BTC MF/BTC SM2 MF/BTC SMO-3 MF/BTC t SMI-3 SMI,2 SM1.2 SM.1,2 SMI,2 MF/BTC MF/BTC SMI,2 MF/'BTC SM1-3 + MF/BTC

After Srivastava and Brusseau (1996). "A/f, spatially variable hydraulic conductivity; AK,,. spatially variable sorption; RLS, rate-limited sorption; MT smaller scale heterogeneity and associated mass transfer; NLS, nonlinear sorption. b Focus of analysis; MF/BTC, mass flux (e.g.. breakthrough curves); SMn. spatial moments, where n is moment number. '•Simulations were presented for either rate-limited sorption or mass transfer (not both simultaneously). ""Spatially variable sorption (with spatially variable conductivity and linear, instantaneous sorption) considered separately.

Table 5.3 Analyses of Nonideai Solute Transport: Non-Earth Science Reference

Topic

Botiart and Adams (1920) Wicke( 1939) Weyde and Wicke (1940) Wilson (1940)

Discuss impact of RLS on transport Present transport equation with D + IMT + linear, instantaneous sorption Present transport equation with NLS Discuss relation between velocity and impact of RLS Discuss relation between velocity and impact of diffusion Present "retardation factor" equation Present "retardation factor" equation Discuss impact of NLS on solute pulse shape Compare A'-values obtained from column and batch measurements Compare A-values obtained from column and batch measurements Discuss impact of NLS on shape, spreading, and velocity of pulse Present transport equation with mass transfer term Fit model to data to obtain coefficient values Discuss impact of IPD on tailing of BTC Present differential form of transport equation with retardation factor term Use of Freundlich and Langmuir isotherms for transport Present transport equation with "one-site" RLS Present transport equation with FMT + linear, instantaneous sorption Discuss impacts of IPD and FMT Comopare A'- and A'-values obtained from column and batch measurements Use of "breakthrough curve" term Present first-order linear driving force equation for approximating IPD Present equation with IPD + NLS Discuss interaction between rate-limited and nonlinear sorption impacts on transport Present transport equation with RLS + NLS Present transport equation with FMT + IPD + "one-site" RLS Discuss similarity between kinetic sorption reactions and diffusive mass transfer Present transport equation with D — "one-site" RLS Discuss impact of "dead water" on BTC Present transport equation with D — IPD — linear, instantaneous sorption Introduction of "two-site" representation for RLS in transport Discuss "N-sites" representation for RLS Present transport equation with FMT + IPD + NLS Present transport equation with D + FMT + NLS Present "two-region" model for transport Add D to Deans (1963) model Present transport equation with D + FMT + IPD + "one-site" RLS Use of "N-sites" representation of RLS in transport

Tiselius (1940) Tiselius (1941) Claesson (1941) Martin and Synge (1941) Beaton and Furnas (1941) DeVault (1943) Weiss (1943) Thomas (1944) Boyd et al. (1947)

Glueckauf and Coates (1947) Thomas (1948) Smith and Amundson (1951) Hiester and Vermeulen (1952) Lapidus and Amundson (1952) Danckwerts (1953) Deisler and Wilhelm (1953) Giddings and Eyring (1955) Tien andThodos (1959) Funk and Houghton (1960) Deans (1963) Coats and Smith (1964) Kucera (1965) Villermaux (1974)

BTC, breakthrough curve; D, longitudinal diffusion/dispersion; FMT, film mass transfer; IMT, intraparticle mass transfer; IPD, intraparticle diffusion; NLS, nonlinear sorption; PNE, physical nonequilibrium; RLS, rate-limited sorption.

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

143

for all cases. No attempt has been made to provide an exhaustive list of every application or analysis that involves each aspect. The focus of table 5.1 is research that involves mass transfer and sorption during transport. Thus, research related primarily to flow, including multiregion, capillary bundle/stream tube, and transfer function models, are not included. In addition, the coupling of transformation reactions and transport is not included. This latter topic was the focus of a recent review by Brusseau et al. (1992). The last citations in table 5.1 are 1989 references. This does not indicate that research on this topic ended in 1989. Rather, the more recent research is listed in table 5.2, which will be discussed in greater detail below. Inspection of table 5.3 reveals that a great number of advancements made in fields such as chromatography, chemical engineering, and petroleum engineeering are applicable to earth scientists interested in solute transport in porous media. For example, the impacts of mass transfer, rate-limited sorption, and nonlinear sorption on solute transport, as well as models for describing these impacts, were examined in the 1940s and 1950s in chromalography and chemical engineering. We in the earth sciences field should make full use of this extensive literature. Not only might it prevent "the wheel from being reinvented," but also we might actually learn something! There is no doubt that research associated with chromatography, chemical engineering, and petroleum engineering is a valuable resource. However, it is important to recognize that the systems employed in these fields are different from those of interest to earth scientists, and that one should not expect direct or wholesale transferability of concepts or models. For example, packed-bed reactors and chromatography columns are designed to provide as close to ideal flow and transport as possible. In addition, such systems usually have one major scale of heterogeneity, and that scale is generally smaller than the transport scale. Conversely, heterogeneity, possibly at multiple scales, is an overriding factor for solute transport in subsurface systems. For another example, reactive transport in reactors and chromatography columns usually involves well-known and controlled reactions. Conversely, we often do not know which processes are controlling transport of reactive solutes in subsurface systems. Research on transport of reactive contaminants in porous media is progressing on many fronts—too numerous to mention herein. However, one broad topic that is of particular interest is the study of "coupled-processes" transport. It is possible, even probable, that a number of physical, chemical, and biological factors and processes can influence contaminant transport, especially at the field scale. While continued research on individual processes is important, it is critical that the influence of multiple processes on transport be examined. The full range of behavior associated with coupled processes, including possible antagonistic and syncrgistic interactions, can be investigated only by direct analysis of coupled-processes systems. It is imperative, therefore, that we focus some of our laboratory- and field-scale research efforts on coupled processes. A major challenge is combining coupled processes with transport in heterogeneous systems. The development of mathematical models that incorporate coupled processes is integral to advancing the field. The application of models that account for only a

144

VADOSE ZONE HYDROLOGY

single source of nonideality to systems affected by more than one factor yields lumped parameters. Values of these lumped parameters can usually be obtained only by calibration, and will be valid only for the specific set of conditions for which they were obtained. In addition, these lumped parameters cannot supply process-discrete information and, thus, are useless for elucidating the relative contributions of various nonideality factors to total nonideality. Such information can only be obtained with the use of a model that accounts explicitly for the existence of multiple nonideality factors. To date, very few such models have been presented. Previous research that involves quantitative analyses of "multifactor" nonideal transport of reactive solutes in heterogeneous porous media are enumerated in table 5.2 (note that multifactor in this case means two or more factors). The influence of spatially variable hydraulic conductivity coupled with spatially variable sorption has received the most attention, followed by coupled hydraulic conductivity variability and rate-limited sorption. Until recently (e.g., Brusseau, 1991; Srivastava and Brusseau, 1996), at most three factors were considered simultaneously in the analyses of nonideal transport. It is expected that additional multifactor transport models will be developed in the coming years. Only a very few of the models listed in table 5.2 have been evaluated by using them to simulate measured field data. This step of "ground-truthing" a mathematical model has never been more critical or more difficult as we move to complex, multifactor models. Furthermore, the usual practice of fitting or calibrating a model to a set of measured data is becoming more and more uncertain as we develop models with more and more parameters. In such cases, the only truly valid way of evaluating a model's performance is to attempt to predict the measured data, with values for all parameters obtained independently. Successful predictions of field-scale nonideal transport of reactive solutes in heterogeneous porous media have been reported by Harmon et al. (1992) and Brusseau and colleagues (Brusseau, 1992; Brusseau and Srivastava, 1997). Harmon el al. (1992) attempted to predict breakthrough curves for trichloroethene. carbon tetrachloride, and vinyl chloride obtained from an experiment conducted in a shallow sandy aquifer in California. They successfully predicted the transport of the lower sorbing solutes using a one-dimensional model that was based on an assumption of a homogeneous aquifer and which accounted for ratelimited sorption. The homogeneous-based model was successful because the dispersion coefficient used in the simulations was obtained by fitting the breakthrough curve obtained for bromide, which incorporates approximately the influence of hydraulic conductivity variability on transport. However, they could not successfully predict the transport of the most sorptive solute, trichloroethene, which suggests that the model was inadequate for this case. The field-scale transport of several reactive solutes was successfully predicted by Brusseau (1992), who used a non-dimensional multifactor nonideality model to simulate breakthrough curves obtained from four field experiments. The model accounted for aquifer heterogeneity, mass transfer, and rate-limited sorption. More recently, Brusseau and Srivastava (1997) successfully predicted the plumescale transport of tetrachloroethene and carbon tetrachloride that was measured during the well-known Borden natural-gradient field experiment. Their two- and

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

145

three-dimensional model accounted for hydraulic conductivity variability, sorption variability, mass transfer, and nonlinear, rate-limited sorption. The importance of using predictions rather than calibrations for model evaluation, as well as for data analysis, is illustrated by the recent analysis of the wellknown Borden natural-gradient data mentioned above. In most previous analyses of these data, it has been concluded that the deceleration of the organic-solute plumes was caused by a rate-limited mass transfer mechanism. These conclusions were based on fitting mathematical models to the measured data. However, based on the use of independent predictions, Brusseau and Srivastava (1997) concluded that rate-limited mass transfer processes had relatively small influence on the transport of the organic solutes. This result clearly shows the danger of attempting to elucidate causative factors based on the fitting of mathematical models to measured data. This danger is compounded when the a priori selection of the specific transport factors to be included in the mathematical model is done without detailed consideration of the target system and, thus, excludes important factors. The development of coupled-processes models for field-scale problems leads to models with large numbers of parameters. This appears to be anathema to some investigators, who question how values will be obtained for all of the parameters, and whether the simulations will mean anything with such a large number of variables. There is merit to these concerns, especially if the model is used in a calibration mode. If, however, muitifactor transport models are used in the predictive mode, the uncertainty associated with a large number of parameters is greatly reduced. To accurately describe and understand contaminant transport, a model containing a larger number of independently measured parameters is preferable to a model containing fewer calibrated parameters. Thus, the fact that a model contains a number of parameters should not of itself cause concern. Rather, it is the manner in which the model is used that is of concern. It is recognized that application of the predictive approach may not be feasible in many cases due to a lack of information. However, if such an approach is taken when possible, sufficient information may be accumulated to allow simpler models to be used more successfully.

Conclusions The transport of contaminants in subsurface systems has been the focus of a tremendous research effort. The results of this work have greatly increased our understanding of the fate of contaminants in the subsurface environment. It is clear that a large number of physical, chemical, and biological factors and processes can influence contaminant transport. It is also clear that in some, and perhaps many, cases, contaminant transport is controlled by only a few major factors. Which factors are controlling will depend on properties of the system of interest. Given the probability that contaminant transport at the field scale is influenced by multiple factors, the need for continued research in the area of coupled processes in evident. While additional laboratory research and development and evaluation of muitifactor nonide-

146

VADOSE ZONE HYDROLOGY

ality models is important, of special importance is conducting additional controlled studies of reactive solute transport at the field scale.

Acknowledgment This research was supported in part by a grant from the National Institute of Environmental Health Sciences.

References

Allen-King, R.M., Groenevelt, H., Warren, C.J., and Mackay, D.M., 1996, Nonlinear chlorinated-solvent sorption in four aquitards, /. Contam. Hydro!., 22(3/ 4), 203-221. Anderson, M., 1979, Using models to simulate the movement of contaminants through groundwater flow systems, CRC Crit. Rev. Environ. Contr., 9(2), 97156. Andricevic, R. and Foufoula-Georgiou, E., 1991, Modeling kinetic non-equilibrium using the first two moments of the residence time distribution, Stochastic Hydro!. Hydraul., 5, 155-171. Bahr, J.M., 1986, Applicability of the local equilibrium assumption in mathematical models for groundwater transport of reacting solutes, Ph.D. Dissertation, Stanford University, Palo Alto, CA. Ball, W.P. and Roberts, P.V., 1991, Long-term sorption of halogenated organic chemicals by aquifer material. 1. Equilibrium, Environ. Sci. Technol., 25(7), 1223-1236. Beaton, R.H. and Furnas, C.C., 1941, Concentration of dilute solutions of electrolytes by base-exchange materials, Ind. Eng. Chem., 33(12), 1500-1513. Bellin, A. and Rinaldo, A., 1995, Analytical solutions for transport of linearly adsorbing solutes in heterogeneous formations. Water Resour. Res., 31(6), 1505-1511. Seven, K. and Germann, P.. 1982, Macropores and water flow in soils, Water Resour. Res., 18(5), 1311-1325. Bibby, R., 1981, Mass transport of solutes in dual-porosity media, Water Resour. Res., 17(4), 1075 1081. Biggar, J.W. and Nielsen, D.R., 1962, Miscible displacement: II. Behavior of tracers, Soil Sci. Soc. Am. Proc., 26. Boesten, .1., van der Pas, L., and Smelt, J.H., 1989. Field test of a mathematical model for non-equilibrium transport of pesticides in soil, Pestic. Sci., 25, 187203. Bohart, G.S. and Adams, E.Q., 1920, Some aspects of the behavior of charcoal with respect to chlorine, J. Am. Chem. Soc., 42, 523-544. Bosnia, W.J.P., Bellin, A., van der Zee, S., and Rinaldo, A., 1993, Linear equilibrium adsorbing transport in physically and chemically heterogeneous porous formations: 2. Numerical results. Water Resour. Res., 29(12), 4031-4043. Bosnia, W.J.P., van der Zee, S., Bellin, A., and Rinaldo, A., 1994, Instantaneous injection of a nonlinearly adsorbing solute in a heterogeneous aquifer, pp. 411417 in: Transport and Reactive Processes in Aquifers, Proceedings of the IAHRJ AIRH Symposium, Zurich, Switzerland, 11-15 April, 1994, T.H. Dracos and F. Staufer, eds., A. A. Balkema, Rotterdam. Bowman, R.S. and Rice, R.C., 1986, Accelerated herbicide leaching resulting from preferential flow phenomena and its implications for ground water contamina-

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

147

tion, pp. 413^425 in: Proceedings of the Conference on Southwestern Ground Water Issues, Phoenix, AZ, 20-22 October, National Water Well Association, Dublin, OH. Boyd, G.E., Myers, L.S., and Adamson, A.W., 1947, The exchange adsorption of ions from aqueous solutions by organic zeolites. II. Performance of deep adsorbent beds under non-equilibrium conditions, J. Am. Chem. Soc., 69, 2849-2859. Brusseau, M.L., 1989, Nonequilibrium sorption: investigation at microscopic to megascopic scales, Ph.D. Dissertation, University of Florida, Gainesville, FL. Brusseau, M.L., 1991, Application of a multi-process nonequilibrium-sorption model to solute transport in a stratified porous medium, Water Resour. Res., 27(4), 589-595. Brusseau, M.L., 1992, Transport of rate-limited sorbing solutes in heterogeneous porous media: application of a one-dimensional multi-factor nonideality model to field data, Water Resour. Res., 28(9), 2485-2497. Brusseau, M.L., 1994, Transport of reactive contaminants in heterogeneous porous media, Rev. Geophys., 32(3), 285-314. Brusseau, M.L., 1995, The effect of nonlinear sorption on transformation of contaminants during transport in porous media, J. Contam. Hydro!., 17(4), 277291. Brusseau, M.L., 1998, Nonideal transport of reactive solutes in heterogeneous porous media: 3. Model testing and data analysis using calibration versus prediction, /. Hydro!., 209, 147-165. Brusseau, M.L. and Rao, P.S.C., 1989, Sorption nonideality during organic contaminant transport in porous media, CRC Crit. Rev. Environ. Contr., 19(1), 3399. Brusseau, M.L. and Rao, P.S.C., 1990, Modeling solute transport in structured soils: a review, Geoderma, 46(1-3), 169-192. Brusseau, M.L. and Srivastava, R., 1997, Nonideal transport of reactive solutes in heterogeneous porous media: 2. Qualitative analysis of the Borden natural-gradient field experiment, /. Contam. Hydro!., 28(1-2), 115-155. Brusseau, M.L. and Zachara, J., 1993, Transport of Co 2+ in a physically and chemically heterogeneous porous medium, Environ. Sci. Techno!., 27(9), 1937-1939. Brusseau, M.L., Jessup, R.E., and Rao, P.S.C., 1989, Modeling the transport of solutes influenced by multi-process nonequilibrium, Water Resour. Res., 25(9), 1971 1988. Brusseau, M.L., Jessup, R.E., and Rao, P.S.C., 1991, Nonequilibrium sorption of organic chemicals: elucidation of rate-limiting processes, Environ. Sci. Techno!., 25(1), 134-142. Brusseau, M.L., Rao, P.S.C., and Bellin, C.A., 1992, Modeling coupled processes in porous media: sorption, transformation, and transport of organic solutes, pp. 147-184 in: Interacting Processes in Soil Science, Advances in Soil Science Series, J. Wagenet, P. Baveye, and B.A. Stewart, eds., Lewis Publishing, Ann Arbor, MI. Bunzl, K. and Schimmack, W., 1988, Distribution coefficients of radionuclides in the soil: analysis of the field variability, Radiochim. Acta, 44/45, 355-360. Burgisser, C.S., Cernik, M., Borkovec, M., and Sticher, H., 1993, Determination of nonlinear adsorption isotherms from column experiments: an alternative to batch studies, Environ. Sci. Techno!., 27(5), 943-948. Burr, D.T., Sudicky, E.A., and Naff, R.L., 1994, Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: mean displacement, plume spreading, and uncertainty, Water Resour. Res., 30(3), 791-815. Cala, M.A. and Greenkorn, R.A., 1986, Velocity effects on dispersion in porous media with a single heterogeneity, Water Resour. Res., 22(6), 919-926.

148

VADOSE ZONE HYDROLOGY

Calvet, R., Le Renard, J., Tournier, C., and Hubert, A., 1978, Hydrodynamic dispersion in columns of pumice particles, 29, 463-474. Cameron, D.R. and Klute, A., 1977, Convectivc-dispersive solute transport with a combined equilibrium and kinetic adsorption model, Water Resour. Res., 13, 183. Cherry, J.A., Barker, J.F., Feenstra, S., Gillham, R.W., Mackay, D.M., and Smyth, D.J.A., 1996. The Borden site for groundwater contamination experiments, pp. 101-127 in: Groundwater and Subsurface Remediation, H. Kobus, B. Barczewski, and H. Koschitzky, eds.. Springer-Verlag, Berlin. Claesson. S., 1941. Adsorption analysis of some triglycerides and fatty acids. Ark. Kemi Mineral. Geol, 15A(9), 1-9. Coates, J.T. and Elzerman, A.W., 1986, Dcsorption kinetics for selected PCB congeners from river sediments, /. Contam. Hydro!., 1, 191-201. Coats, K.H. and Smith, B.D., 1964. Dead-end pore volume and dispersion in porous media, J. Soc. Pet. Eng., 4, 73-81. Connaughton, D.F., Stedingcr, J.R., Lion, L.W., and Shuler, M.L., 1993, Description of time-varying dcsorption kinetics: release of naphthalene from contaminated soils. Environ. Sci. Techno!., 27(11), 2397-2403. Crittenden, J.C., Hut/ler, N.J., Geyer, D.G., Oravitz, J.L., and Friedman, G., 1986, Transport of organic compounds with saturated groundwater flow: model development and parameter sensitivity. Water Resour. Res., 22(3), 271-284. Cushman, J.H., 1990, Dynamics of Fluids in Hierarchical Porous Media, Academic Press, San Diego, CA. Cvetkovic, V.D. and Dagan, G., 1994, Effect of nonlinear sorption on contamination/remediation of heterogeneous aquifers, pp. 411-417 in: Transport and Reactive Processes in Aquifers, Proceedings of the 1AHR/AIRH Symposium, Zurich, Switzerland, 11-15 April, 1994, T.H. Dracos and F. Staufer, eds., A. A. Balkema, Rotterdam. Cvetkov, V.D. and Shapiro, A.M., 1990, Mass arrival of sorptive solute in heterogeneous porous media, Water Resour. Res., 26(9), 2057-2067. Dagan, G., 1989, Flow and Transport in Porous Formations, Springer-Verlag, Berlin. 1989. Dagan, G. and Cvetkovic, V., 1993, Spatial moments of a kinetically sorbing solute plume in a heterogeneous aquifer, Water Resour. Res., 29(12). 4053-4061. Danckwerts, P.V., 1953, Continuous flow systems, Chem. Eng. Sci., 2(1), 1-13. Davidson, J.M. and McDougal, J.R., 1973, Experimental and predicted movement of three herbicides in a water-saturated soil, /. Environ. Qua!., 2(4). 428-433. Deans, H.A., 1963, A mathematical model for dispersion in the direction of flow in porous media, Soc. Pet. Eng. J., March, 49-52. Deisler, P.F. and Wilhelm, R.H., 1953, Diffusion in beds of porous solids: measurement by frequency response techniques, Ind. Eng. Chem., 45(6), 1219-1227. Destouni, G. and Cvetkovic, V., 1991, Field scale mass arrival of sorptive solute into the groundwater, Water Resour. Res., 27(6), 1315-1325. DeVault, D., 1943, The theory of chromatography, .7. Am. Chem. Soc., 65, 532-540. Elabd, H., Jury, W.A., and Cliath, M.M., 1986, Spatial variability of pesticide adsorption parameters, Environ. Sci. TechnoL, 20(3), 256-260. Elrick, D.E., Erh, K.T., and Krupp, H.K., 1966, Application of miscible displacement techniques to soils, Water Resour. Res., 2(4), 717-727. Ewing, B.B., 1959, Field test of the movement of radioactive cations, /. Sanit. Eng. Div., Proc. Am. Soc. Civil Eng., 85(SA1), 39-59. Fluhler, H. and Jury, W., 1983, Estimating solute transport using nonlinear, rate dependent, two site adsorption models, Report No. 245, Swiss Federal Institute of Forestry Research. Flury, M., 1996, Experimental evidence of transport of pesticides through field soils: a review, /. Environ. Qual., 25(1), 25-^45.

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

149

Fried, J.J., 1975, Groundwater Pollution, Elsevier, New York, NY. Funk, J.E. and Houghton. G., 1960, A mathematical model for gas-liquid partition chromatography, Nature, 188(4748), 389-391. Garabcdian, S.P. and LeBlanc. D.R., 1991, Overview of research at the Cape Cod site, pp. 1-9, in: Water Resources Investigative Report 91-4034. U.S. Geological Survey, Washington, DC. Garabcdian. S.P., Gelhar, L.W., and Celia, M.A., 1988, Large-scale dispersive transport in aquifers: field experiments and reactive transport theory. Report No. 315, Department of Civil Engineering. Massachusetts Institute of Technology, Cambridge, MA. Gardner, W.R. and Brooks, R.H., 1957, A descriptive theory of leaching, Soil Sci., 83, 295-304. Gelhar, L.W., Gutjahr, A.L., and Naff, R.L., 1979, Stochastic analysis of macrodispersion in a stratified aquifer, Water Resour. Res., 15(6), 1387-1397. Gelhar, L.W., Welty, C., and Rehfeldt, K.R., 1992, A critical review of data on fieldscale dispersion in aquifers, Water Resour. Rex., 28(7), 1955-1974. Ghodrati, M. and Jury, W.A., 1992, A field study of the effects of soil structure and irrigation method on preferential flow of pesticides in unsaturated soil, /. Contam. Hydro/.., 11(1/2), 101-125. Giddings, J.C. and Eyring. H., 1955, A molecular dynamic theory of chromatography, /. Phys. Chem., 59, 416-421. Glueckauf, E. and Coates, J.I., !947, Theory of chromatography. IV. The influence of incomplete equilibrium on the front boundary of chromalograms and on the effectiveness of separation, /. Chem. Soc., 41, 1315-1318. Green, R.E., Yamane, V.K., and Obien, S.R., 1968, Transport of atrazine in a latosolic soil in relation to adsorption, degradation, and soil water variables, p. 195 in: International Congress of Soil Science Transactions, ISSS, Vol. 1. Grisak, G.E., Pickens, J.F., and Cherry, J.A., 1980, Solute transport through fractured media 2. Column study of fractured till. Water Resour. Res., 16(4), 731— 739. Hamaker, J.W., Goring, C.A.I., and Youngston. C.R., 1966, Sorption and leaching of 4-amino-3,5,6-trichloropicolinic acid in soils, in: Organic Pesticides in the Environment, Advances in Chemistry Series, American Chemical Society, Washington, DC. Harmon, T.C., Semprini, L., and Roberts, P.V., 1992, Simulating solute transport using laboratory-based sorption parameters, /. Environ. Eng., 118(5), 666-689. Haselow, J.S. and Greenkorn, R.A., 1991, An experimental investigation of the effect of idealized heterogeneity on the dispersion of miscible fluids, Water Resour. Res., 27(9), 2473 2482. Herr, M., Schafer, G., and Spitz, K., 1989, Experimental studies of mass transport in porous media with local heterogeneities, J. Contam. Hydro!., 4(2), 127-137. Hiester, N.K. and Vermeulen, T., 1952, Saturation performance of ion-exchange and adsorption columns, Chem. Eng. Prog., 48(10), 505-516. Hornsby, A.G. and Davidson, J.M., 1973, Solution and adsorbed fluometuron concentration distribution in a water-saturated soil: experimental and predicted evaluation, Soil Sci. Soc. Am. Proc., 37, 823-828. Inouc, Y. and Kaufman, W.J., 1963, Prediction of movement of radionuclides in solution through porous media, Health Phys., 9, 705-715. Jensen, K.H., Bitsch, K., and Bjerg, P.L., 1993, Large-scale dispersion experiments in a sandy aquifer in Denmark: observed tracer movements and numerical analyses, Water Resour. Res., 29(3), 673-696. Jury, W.A.. 1983. Chemical transport modeling: current approaches and unresolved problems, chap. 4 in: Chemical Mobility and Reactivity in Soil Systems, SSSA Special Publication No. 11, Soil Science Society of America, Madison, WI.

1 50

VADOSE ZONE HYDROLOGY

Jury, W.A., 1985, Spatial variability of soil physical parameters in solute migration: a critical literature review. Report EA-4228, Electric Power Research Institute, Palo Alto, CA. Jury, W.A., Elabd, H., and Resketo, M., 1986, Field study of napropamide movement through unsaturated soil, Water Resour. Res.. 22(5), 749-755. Kabala, Z.J. and Sposito, G., 1991, A stochastic model of reactive solute transport with time-varying velocity in a heterogeneous aquifer. Water Resour. Res., 27(3), 341-350. Karickhoff, S.W., 1980, Sorption kinetics of hydrophobic pollutants in natural sediments, in: Contaminants and Sediments, R.A. Baker, ed. Ann Arbor Science, Ann Arbor, MI. Kastcn, P.R.. Lapidus, L., and Amundson, N.R. 1952, Mathematics of adsorption beds. V. Effect of intraparticle diffusion in flow systems in fixed beds, /. Phys. Chem., 56, 683 688. Kaufman, W.J., 1960, The containment of radioactive wastes in deep geologic formations, pp. 535-546 in: Disposal of Radioactive Wastes, Vol. II, International Atomic Energy Agency, Vienna, Austria. Kay, B.D. and Elrick, D.E., 1967, Adsorption and movement of lindane in soils, Soil. Sci., 104, 314. Killey, R.W. and Moltyaner, G.L., 1988, Twin lake tracer tests: setting, methodology, and hydraulic conductivity distribution, Water Resour. Res., 24(10), 15851612. Kinniburgh, D.G., 1986, General purpose adsorption isotherms. Environ. Sci. Techno!., 20(9), 895-904. Kucera, E., 1965, Contribution to the theory of chromatography: linear non-equilibrium elution chromatography, /. Chromatogr., 19, 237-248. Lapidus, L. and Amundson, N.R., 1952, Mathematics of adsorption in beds VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns, J. Phys. Chem., 56, 984-988. Leistra, M. and Dckkcrs, W.A., 1976, Computed effects of adsorption kinetics on pesticide movement in soils, /. Soil Sci., 28, 340-350. Mackay, D.M., Ball, W.P., and Durant, M.G., 1986, Variability of aquifer sorption properties in a field experiment on groundwater transport of organic solutes: methods and preliminary results, J. Contam. Hydrol., 1(1/2), 119-132. Martin, A.J.P. and Synge, R.L.M., 1941, A new form of chromatogram employing two liquid phases, Biochem. J., 35, 1358-1368. McCall, P.J. and Agin, G.L., 1985, Desorption kinetics of picloram as affected by residence time in soil, Environ. Toxicol. Chem., 4. 37-45. McMahon, M.A. and Thomas. G.W., 1974, Chloride and tritiated water flow in disturbed and undisturbed soil cores, Soil Sci. Soc. Am. Proc., 38, 727-732. Molz, F.J., Guven, O., and Melville, J.G., 1983, An examination of scale-dependent dispersion coefficients, Groundwater, 21(6), 715—725. Morisawa, S., Horiuchi. M., Yamaoka, T., and Inoue, Y., 1986, Evaluation of solute transport in unsaturated soil column by multi-component flow model, Proc. Environ. Sanit. Eng. Res., 22, 9-17 (in Japanese). Murali, V. and Aylmore, L.A.G., 1981, A convectivc-dispcrsive-adsorptive flow model for solute transport in soils. I. Model description and some simulations, Aust. J. Soil Res., 19, 23-38. Neretnieks, I., 1983, A note on fracture flow dispersion mechanisms in the ground, Water Resour. Res., 19(2), 364-370. Nkedi-Kizza, P., Rao, P.S.C., Jessup, R.E., and Davidson, J.M., 1982, Ion exchange and diffusive mass transfer during miscible displacement through an aggregated oxisol, Soil Sci. Soc. Am. J., 46, 471.

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

1 51

Nkedi-Kizza, P., Biggar, J.W., van Genuchten, M.Th., Wierenga, P.J., Sclim, H.M., Davidson, J.M., and Nielsen, D.R., 1983, Modeling tritium and chloride transport through an aggregated Oxisol, Water Resour. Res.. 19(3), 691-700. Oddson, J.K., Letey, J., and Weeks, L.V., 1970, Predicted distribution of organic chemicals in solution and adsorbed as a function of position and time for various chemical and soil properties, Soil Sci. Soc. Am. Proc., 34, 412. Passioura, J.B., 1971, Hydrodynamic dispersion in aggregated media: theory, Soil Sci., 111,339. Pickens, J.F., Jackson,R.E., Inch, K.J., and Merritt, W.F., 1981, Measurements of distribution coefficients using a radial injection dual-tracer test, Water Resour. Rex., 17(3), 529-544. Pignatello, J.J., Frink, C.R., Marin, P.A., and Droste, E.X., 1990, Field-observed ethylene dibromide in an aquifer after two decades, J. Contam. Hydro!., 5,195-210. Poulscn, M.M. and Kueper, B.H., 1992, A field experiment to study the behavior of tctrachlorocthylcnc in unsaturatcd porous media. Environ. Sci. Techno/., 26(5), 889-895. Quinodoz, H.A.M. and Valocchi, A.J., 1993, Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic conductivity, Water Resour. Res., 29(9), 3227-3240. Rabideau, A.J. and Miller, C.T., 1994, Two-dimensional modeling of aquifer remediation influenced by sorption nonequilibrium and hydraulic conductivity heterogeneity, Water Resour. Res., 30(5), 1457-1470. Rao, P.S.C. and Davidson, J.M., 1979, Adsorption and movement of selected pesticides at high concentrations in soils, Water Res., 13, 375-342. Rao, P.S.C., Green, R.E., Balasubramanian, V.. and Kanehiro, Y., 1974, Field study of solute movement in a highly aggregated oxisol with intermittent flooding: II. Picloram, J. Environ. Qua!., 3(3), 197-202. Rao, P.S.C., Rolston, D.E., Jessup, R.E., and Davison, J.M., 1980, Solute transport in aggregated porous media: theoretical and experimental evaluation, Soil Sci. Soc. Am. J., 44, 1139-1146. Rao, P.S.C., Evardsson, K., Ou, L.T., Jessup, R.E., Nkedi-Kizza, P., and Hornsby, A.G., 1986, Spatial variability of pesticide sorption and degradation, pp. 100115 in: Evaluation of Pesticides in Ground Water, ACS Symposium Series 315. American Chemical Society, Washington, DC. Refsgaard, A., 1986, Laboratory experiments on solute transport in non-homogeneous porous media, Nordic Hydro!., 17, 305-314. Richter, G. and Jury, W.A., 1986, A microlysimeter field study of solute transport through a structured sandy loam soil. Soil Sci. Soc. Am. J., 50, 863-868. Roberts, P.V., McCarty, P.L., and Roman, W.M., 1978, Direct injection of reclaimed water into an aquifer, J. Environ. Eng., 104(EE5), 933-949. Roberts, P.V., McCarty, P.L., Reinhard, M., and Schreiner, J., 1980, Organic contaminant behavior during groundwater recharge. J. Water Pollut. Control Fed., 52(1), 161 171. Roberts, P.V., Schreiner, J., and Hopkins, G.D., 1982, Field study of organic water quality changes during groundwater recharge in the Palo Alto Baylands, Water Res., 16, 1025-1035. Robin, M.J.L., Sudicky, E.A., Gillham, R.W., and Kachanoski, R.G., 1991, Spatial variability of strontium distribution coefficients and their correlation with hydraulic conductivity in the Canadian forces base Borden aquifer, Water Resour. Res., 27(10), 2619-2632. Rosen, J.B., 1952, Kinetics of a fixed bed system for solid diffusion into spherical particles, J. Chem. Phys., 20, 387-394. Scalf, M.R., Dunlap, W.J., Mcmillion, L.G., and Keeley, J.W., 1969, Movement of DDT and nitrates during ground-water recharge, Water Resour. Res., 5(5), 1041-1052.

152

VADOSE ZONE HYDROLOGY

Schafer, W. and Kinzclbach, W., 1992, Stochastic modeling of in situ bioremediation in heterogeneous aquifers, ,/. Contam. Hydro!., 10(1), 47-73. Schneider, A.D., Wiese, A.F., and Jones, O.R., 1977, Movement of three herbicides in a fine sand aquifer, Agronomy J., 69, 432-436. Schwartz, F.W.. 1977, Macroscopic dispersion in porous media: controlling factors, Water Resour. Res., 13(4), 743-752. Scribner, S.L., Benzing, T.R., Sun, S., and Boyd, S.A., 1992, Desorption and bioavailability of aged simazine residues in soil from a continuous corn field, /. Environ. Qual.,2\, 1115-1121. Selim, H.M., Davidson, J.M., and Mansell, R.S., 1976, Evaluation of a two-site adsorption-desorption model for describing solute transport in soils, Proceedings of the Summer Computer Simulation Conference, National Science Foundation, Washington, DC. Selroos, J.. 1995, Temporal moments for nonergodic solute transport in heterogeneous aquifers, Water Resour. Res., 31(7), 1705-1712. Selroos, J. and Cvetkovic, V., 1992, Modeling solute advection coupled with sorption kinetics in heterogeneous formations, Water Resour. Res., 28(5), 1271-1278. Seyfricd, M.S. and Rao, P.S.C., 1987, Solute transport in undisturbed columns of an aggregated tropical soil: preferential flow effects, Soil Sci. Soc. Am. J., 51(6), 1434-1443. Silliman, S.E. and Simpson, E.S., 1987, Laboratory evidence of the scale effect in dispersion of solutes in porous media, Water Resour. Res.. 23(8), 1667-1673. Skibitzke, H.E. and Robinson, G.M., 1963, Dispersion in ground water flowing through heterogeneous material, U.S. Geological Survey Professional Paper 386-B, Washington, DC. Skopp, J. and Warrick, A.W., 1974, A two-phase model for the miscible displacement of reactive solutes in soils, Soil Sci. Soc. Am. Proc., 38(4), 545-550. Skopp, J., Gardner, W.R., and Tyler, E.J., 1981, Solute movement in structured soils: two-region model with small interaction, Soil Sci. Soc. Am. J., 45, 837841. Smith, J.A., Chiou, C.T., Kammer, J.A., and Kile, D.E., 1990, Effect of soil moisture on the sorption of trichloroethene vapor to vadosc-zone soil at Picatinny arsenal, New Jersey, Environ. Sci. Technol., 24, 676-682. Smith, L. and Schwartz, F.W., 1981, Mass transport 2. Analysis of uncertainty in prediction. Water Resour. Res., 17(2), 351-369. Smith, N.L. and Amundson, N.R., 1951, Intraparticle diffusion in catalytic heterogeneous systems, Ind. Eng. Chem., 43(9), 2156-2167. Spurlock, F.C., Huang, K., and van Genuchten, M.Th., 1995, Isotherm nonlinearity and nonequilibrium sorption effects on transport of fenuron and monuron in soil columns, Environ. Sci. Technol., 29(4), 1000-1007. Srivastava, R. and Brusseau, M.L., 1994, Effect of physical and chemical heterogeneities on aquifer remediation by pump and treat, pp. 262-265 in: Proceedings of the American Chemical Society National Meetings, Environmental Chemistry Division, San Diego, CA, 13-18 March 1994, Vol. 34(1), American Chemical Society, Washington, DC. Srivastava, R. and Brusseau, M.L., 1996, Nonideal transport of reactive solutes in heterogeneous porous media: 1. Numerical model development and moments analysis, /. Contain. Hydro!., 24(2), 117-143. Steinberg, S.M., Pignatello, J.J., and Sawhney, B.L., 1987, Persistence of 1,2-dibromoethane in soils: entrapment in intraparticlc micropores, Environ. Sci. Technol. ,21, 1201-1210. Streck, T., Poletika, N.N., Jury, W.A., and Farmer, W.J., 1995, Description of simazine transport with rate-limited, two-stage, linear and nonlinear sorption, Water Resour. Res., 31(4), 811-822.

NONIDEAL TRANSPORT OF REACTIVE SOLUTES IN POROUS MEDIA

153

Sudicky, E.A., Gillham, R.W., and Frind, E.O., 1985, Experimental investigation of solute transport in stratified porous media 1. The nonreactive case, Water Resour. Res., 21(7), 1035-1041. Tanji, K.K.. 1970, A computer analysis on the leaching of boron from stratified soil columns. Soil ScL, 110(1), 44-51. Theis, C.V., 1963. Hydrologic phenomena affecting the use of tracers in timing groundwater flow, pp. 193-207 in: Radioisotopes in Hydrology, International Atomic Energy Agency, Vienna. Thomas, H.C., 1944, Heterogeneous ion exchange in a flowing system, J. Am. Chem. Soc., 66, 1664-1666. Thomas, H.C., 1948, Chromatography: a problem in kinetics, Ann. N.Y. Acad. Sci., 49, 161-182. Tien, C. and Thodos, G., 1959, Ion exchange kinetics for systems of nonlinear equilibrium relationships, AIChE J., 5(3), 373 378. Tisclius, A., 1940, A new method for adsorption analysis of solutions. Ark. Kcmi Mineral. CeoL, 148(22), 1 5 . Tiselius, A., 1941, Adsorption analysis: experimental arrangement and some results with mixtures of glucose and lactose, Ark. Kemi Mineral. Geol., 14B(32), 1-8. Tompson, A.F.B., 1993, Numerical simulation of chemical migration in physically and chemically heterogeneous porous media, Water Resour. Res., 29(11), 37093726. Travis, C.C. and Etnier, E.L., 1981, A survey of sorption relationships for reactive solutes in soil, /. Environ. Qua!., 10(1), 8-17. Upchurch, R.P. and Pierce, W.C., 1957, The leaching of monuron from lakeland sand soil. Part I. The effect of amount, intensity, and frequency of simulated rainfall, Weeds. 6, 321-330. Valocchi, A.J., 1988, Theoretical analysis of deviations from local equilibrium during sorbing solute transport through idealized stratified aquifers, J. Contain. Hydrol., 2(3), 191-207. Valocchi, A.J., 1989, Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers, Water Resour. Res., 25(2), 273-279. van dcr Zee, S. and van Riemsdijk, W.H., 1987, Transport of reactive solute in spatially variable soil systems, Water Resour. Res., 23(11), 2059-2069. van Genuchen, M.Th. and Cleary, R.W., 1979, Movement of solutes in soil: computer-simulated and laboratory results, chap. 10 in: Soil Chemistry: B. Physicochemical Models, G.H. Bolt, ed., Elsevier, Amsterdam, van Genuchten, M.Th. and Wierenga, P.J., 1976, Mass transfer studies in sorbing porous media: analytical solutions, Soil Sci. Soc. Am. J.. 40(3), 473-479. van Genuchten, M.Th. and Wierenga, P.J., 1977, Mass transfer studies in sorbing porous media: experimental evaluation with tritium, Soil Sci. Soc. Am. ./., 41, 278-285. van Genuchten, M.Th., Davidson, J.M., and Wierenga, P.J., 1974, An evaluation of kinetic and equilibrium equations for the prediction of pesticide movement through porous media, Soil Sci. Soc. Am. Proc., 38, 29. Villermaux, J., 1974, Deformation of chromatographic peaks under the influence of mass transfer phenomena, J. Chromatogr. Sci., 12, 822-831. Warren, J.E. and Skiba. F.F., 1964, Macroscopic dispersion, Soc. Pet. Eng. J., 215230. Weber, J.B. and Miller, C.T., 1989, Organic chemical movement over and through soils, chap. 12 in: Reactions and Movement of Organic Chemicals in Soils, B.L. Sawhney and K. Brown, eds., Special Publication No. 22, Soil Science Society of America, Madison, Wl. Weber, W.J., McGinley, P.M., and Katz, L.E., 1992, A distributed reactivity model for sorption by soils and sediments. 1. Conceptual basis and equilibrium assessments, Environ. Sci. Teclmol., 26(10), 1955 1962.

154

VADOSE ZONE HYDROLOGY

Weiss, J., 1943, On the theory of chromatography, J. Chem. Sac., 297-301. Weyde, E. and Wicke, E., 1940, Die gestalt der sorptionsflachen bei der ad- und desorption unter verschiedenen bedingungen, Kolloid Z., 90(2), 156-168. Wicke, E., 1939, Empirische und theoretische untersuchungen der sorptionsgeschwindigkeit von gasen an porosen stoffen II., Kolloid Z., 86(3), 295-310. Williams, G.M., Alexander, L.S., Hitchman, S.P., Hooker, P.J., Noy, P.J., Ross, C.A.M., Stuart, A., and West, J.M., 1985, In situ radionuclide migration studies in a shallow sand aquifer, Report FLPU 85-7, British Geological Survey, Keyworth, UK. Wilson, J.N., 1940, A theory of chromatography, /. Am. Chem. Soc., 62, 1583-1591. Wood, L.S., Scott, H.D., Marx, D.B., and Lavy, T.L., 1987, Variability in sorption coefficients of metolachlor on a captina silt loam, /. Environ. Qua!., 16(3), 251256.

6

Recent Advances in Vadose Zone Flow and Transport Modeling

M. TH. VAN GENUCHTEN E. A. SUDICKY

The fate and transport of a variety of chemicals migrating from industrial and municipal waste disposal sites, or applied to agricultural lands, is increasingly becoming a concern. Once released into the subsurface, these chemicals arc subject to a large number of simultaneous physical, chemical, and biological processes, including sorption-desorption, volatilization, and degradation. Depending upon the type of organic chemical involved, transport may also be subject to multiphase flow that involves partitioning of the chemical between different fluid phases. Many models of varying degree of complexity and dimensionality have been developed during the past several decades to quantify the basic physicochemical processes affecting transport in the unsaturatcd zone. Models for variably saturated water flow, solute transport, aqueous chemistry, and cation exchange were initially developed mostly independently of each other, and only recently has there been a significant effort to couple the different processes involved. Also, most solute transport models in the past considered only one solute. For example, the processes of adsorption-desorption and cation exchange were often accounted for by using relatively simple linear or nonlinear Freundlich isotherms such that all reactions between the solid and liquid phases were forced to be lumped into a single distribution coefficient, and possibly a nonlinear exponent. Other processes such as precipitation-dissolution, biodegradation, volatilization, or radioactive decay were generally simulated by means of simple first- and/or zero-order rate processes. These simplifying approaches were needed to keep the mathematics relatively simple in view of the limitations of previously available computers. The problem of coupling models for water flow and solute transport with multicomponent chemical equilibrium and nonequilibrium models is now increasingly being addressed, facilitated by the introduction of

156

VADOSE ZONE HYDROLOGY

more powerful computers, development of more advanced numerical techniques, and improved understanding of the underlying transport processes. One major frustrating issue facing soil scientists and hydrologists in dealing with the unsaturatcd zone, both in terms of modeling and experimentation, is the overwhelming heterogeneity of the subsurface environment. Heterogeneity occurs at a hierarchy of spatial and time scales (Wheatcraft and Cushman, 1991), ranging from microscopic scales that involve time-dependent chemical sorption and precipitationdissolution reactions, to intermediate scales that involve the preferential movement of water and chemicals through macropores or fractures, and to much larger scales that involve the spatial variability of soils versus depth or across the landscape. Several lines of research are being followed to deal with the different types of soil heterogeneity. On the one hand, subsurface heterogeneity can be addressed in terms of process-based deterministic descriptions which attempt to consider the effects of heterogeneity at one or several scales (kinetic sorption, preferential flow, field-scale spatial variability). On the other hand, subsurface heterogeneity is often also addressed using stochastic approaches which incorporate certain assumptions about the transport process in the heterogeneous system (e.g., Jury and Roth, 1990; Dagan, 1993; Russo, 1993). Much can be learned from both approaches. In this chapter, we will focus on alternative conceptual approaches for deterministic modeling of solute transport in variably saturated media. Among the topics discussed are single-ion equilibrium and nonequilibrium transport, sorption, degradation, volatilization, and multicomponent transport. Transport in variably saturated structured systems is treated in somewhat more detail to illustrate the potential value of numerical models as useful tools for improving our understanding of the underlying transport processes at the field scale. We also briefly review recent developments in numerical techniques used for solving the governing flow and transport equations, including methods for solving large sparse matrices resulting from spatial and temporal numerical discretization.

Water Flow and Single-Species Solute Transport Governing Flow and Transport Equations Predictions of flow and transport in the vadose zone are traditionally based on the Richards equation that describes variably saturated water flow and the advectiondispersion equation that describes solute transport. For one-dimensional systems, these equations are given by

respectively, where 6 is the volumetric water content, h is the soil-water pressure head (negative for unsaturated conditions), I is time, z is distance from the soil surface

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

157

downward, K is the hydraulic conductivity as a function of h or 6, s is the solute concentration associated with the solid phase of the soil, c is the solute concentration of the liquid phase, p is the soil bulk density. D is the solute dispersion coefficient, S and 0 are sinks or sources for water and solutes, respectively, and q is the volumetric fluid flux density given by Darcy's law as

Similar equations may be formulated for multidimensional flow and transport. Assuming linear sorption such that the adsorbed concentration (s) is linearly related to the solution concentration (c) through a distribution coefficient, kD (i.e., .v = k[,c), equation (6.2) reduces to the simpler form

where R = 1 + pko/6 is the solute retardation factor. For conditions of steady-state water flow in homogeneous soils and in the absence of source or sink terms (S and 0), equation (6.4) further reduces to the standard advection-dispcrsion equation (ADE):

where v = q/6 is the average pore-water velocity. While models based on equations (6.1) and (6.2) have proved to be important tools in research and management, they are subject to a large number of simplifying assumptions and complications that compromise or limit their applicability (Nielsen el al, 1986). It may be instructive to list here some of these assumptions and complications. For example, the equations assume that (1) the air phase plays a relatively minor role during unsaturated flow, and hence that a single equation can be used to describe variably saturated flow; (2) Darcy's equation is valid at both very low and very high flow velocities (including those occurring in structured soils); (3) osmotic and electrochemical components of the soil water potential are negligible; (4) the fluid density is independent of the solute concentration; and (5) matrix and fluid compressibilities are relatively small. The equations are further complicated by (6) the hysteretic nature of especially the soil water-retention function, 9(K); (7) the extreme nonlinearity of the hydraulic conductivity function, K(h); (8) the lack of accurate and inexpensive methods for measuring the unsaturated hydraulic properties; (9) the extreme heterogeneity of the subsurface environment; and (10) inconsistencies between the scale at which the hydraulic and solute transport parameters in equations (6.1) and (6.2) are usually measured, and the scale at which the predictive models are being applied. In addition, equations (6.1) and (6.2) are formulated for isothermal soil conditions. In reality, most physical, chemical, and microbial processes in the subsurface are strongly influenced by soil temperature. This also applies to water flow itself, including the effects of temperature (Constantz, 1982; Hopmans and Dane, 1986) and the concentration and ionic composition of the soil liquid phase (Dane and Klule, 1977: Suarez and Simunek, 1996) on the unsaturated soil hydraulic

158

VADOSE ZONE HYDROLOGY

properties. Hence, a complete description of vadose zone transfer processes also requires consideration of heat flow and its nonlinear effects on most processes taking place in the soil-plant system. Root Water Uptake An important term in the variably saturated flow equation (6.1) is the source/sink term S used to account for water uptake by plant roots. Widely different approaches exist for simulating water uptake (Molz, 1981). Many of the early studies of root water uptake (e.g., Whisler et al., 1968; Bresler et al., 1982) used uptake functions of the general form

where hr is an effective root-water pressure head at the root surface and b\ is a depthdependent proportionality constant often referred to as the root effectiveness function. Equation (6.6) may be viewed as a finite difference approximation of Darcy's law across the soil-root interface. Anther class of models for root water uptake is given by (Feddes et al., 1978; Vanclooster et al., 1994)

where b2 is the potential root water uptake distribution function which integrates to unity over the soil root zone, u\ is a dimensionless water stress response function between 0 and 1, and Tp is the potential transpiration rate. The effects of soil salinity on water uptake may be accounted for by linearly adding the osmotic head, n, to the pressure head, h(z, t) in equations (6.6) or (6.7) (Bresler and Hoffman, 1986; Cardon and Letey, 1992a, 1992b), or by incorporating into equation (6.7) a separate salinity response function, a2(n), somewhat similar to ot{(h), to obtain (van Genuchten, 1987; Simunek ad Suarez, 1994)

Cardon and Letey (1992a, 1992b) showed that approaches based on equation (6.7) may be more appropriate than equation (6.6), particularly if suitably modified and used for saline conditions. Still, as pointed out by Nielsen et al. (1986), the above two classes of root water uptake models are essentially empirical by containing parameters that depend on specific crop, soil, and environmental conditions. Much research remains needed in the development of realistic process-based models of root growth and root water uptake as a function of various stresses (water, salinity, temperature, nutrients, and others) in the root zone, and to couple these descriptions with suitable crop growth models. Linear Equilibrium Solute Transport The term d(ps)/dt in equation (6.2) may be used to account for the effects of sorption or exchange on solute transport. Most often, a linear equilibrium isotherm, s = kDc, is used to describe solute interactions between the liquid and solid phases of the soil, leading to a constant retardation factor R in equation (6.4). The resulting advection-

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

159

dispersion equation given by equation (6.5) has been reasonably successful in describing solute transport data for relatively uniform laboratory or field soils. As an example, figure 6.1 shows solute breakthrough curves typical of the transport of an excluded anion, Cr, an essentially nonreactive solute (tritiated water, 3H2O), and an adsorbed tracer, Cr 6+ , through homogeneous soil columns. The first two tracers pertain to transport through 30-cm-long columns that contain disturbed Glendale clay loam (P. J. Wierenga, 1972, unpublished data; vanGenuchten and Cleary, 1979), while the Cr 6+ data are for transport through a 5-cm-long column of sand (P. J. Wierenga, 1972, unpublished data). The data in figure 6.1 are plotted versus number of pore volumes (T = vt/L) of tracer solution leached through the columns. Analysis of the breakthrough curves in terms of the ADE by using inverse procedures (van Genuchten, 1981) yielded ^-values of 0.681, 1.027. and 1.248, respectively, for the three tracers. Hence, Cl~ was strongly affected by anion exclusion (R < \\kD < 0) caused by the repulsion of chloride anions from negatively charged surfaces of clays and ionizable organic matter. Because water flow velocities are zero along pore walls, and maximum in the center of pores, anions such as Cl~ can travel much faster than water, especially in fine-textured soils. By comparison, 3H2O did travel with nearly the same velocity as water (R = 1.027), while Cr 6+ was about 25% slower (R = 1.248).

Nonlinear Adsorption The assumption of a linear isotherm can greatly simplify the mathematics of a transport problem; unfortunately, sorption and exchange reactions are generally nonlinear and often depend also on the presence of competing species in the soil solution. The solute retardation factor for nonlinear adsorption is then not constant anymore, as was the case for linear adsorption, but will change as a function of the slope ds/dc of the adsorption isotherm s(c) as follows:

Figure 6.1 Observed and calculated breakthrough curves for Cl~, 3 H2O, and Cr6 + .

160

VADOSE ZONE HYDROLOGY

A variety of models are available to describe nonlinear adsorption-desorption. Table 6.1 lists some of the most commonly used sorption isotherms that relate the adsorbed concentration, s, to the solution concentration, c. Although several of the equations in table 6.1 (e.g., the Langmuir and Freundlich equations) can be derived rigorously, such as for the adsorption of gases onto solids, the expression are generally used only in an empirical fashion. Of the equations listed in table 6.1, the most popular sorption models are the Langmuir, Freundlich, and Temkin equations. A general classification of adsorption as reflected by different features of the adsorption isotherm, such as the initial slope, the presence or absence of a plateau, or the presence of a maximum, was proposed by Giles ct al. (1960). They divided possible adsorption processes into four main classes: S, L (Langmuir), H (highaffinity), and C (constant partitioning) isotherms, and discussed mechanisms that explain the different types of isotherms. Increasing solution concentrations led to increasing or decreasing adsorption rates for the convex S and concave L isotherms, respectively (figure 6.2). An H isotherm is characterized by extremely high affinities

Table 6.1 Equilibrium Adsorption Equations (van Genuchten and Cleary, 1979; Barry, 1992) Equation

Model

Rcfcrence(s)

Linear

Freundlich

Lapidus and Amundson (1952); Lindstrom et al. (1967) Freundlich (1909)

Langmuir

Langmuir (1918)

Freundlich-Langmuir

Sips (1950)

Double Langmuir

Shapiro and Fried (1959)

Extended Freundlich

Sibbesen (1981)

Gunary

Gunary (1970)

Fitter-Sutton

Fitter and Sutton (1975)

Barry

Barry (1992)

Temkin

Bache and Williams (1971)

Modified Kielland

Lindstrom et al. (1971); van Genuchten et al. (1974) Lai and Jurinak (1971)

k}.k2,k],ki. Empirical constants; R, universal gas constant: T, absolute temperature; c,, maximum solute concentration; sr, maximum adsorbed concentration.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

161

Figure 6.2 Schematic of different, types of equilibrium sorption isotherms. (After Giles et al., 1960.)

of the exchanger for exchangeable ions, whereas a C isotherm reflects constant partitioning of the solute between the solution and adsorbed phases. We note that the shape of an isotherm can have significant impacts on the transport predictions. For example, S and L isotherms lead to unfavorable and favorable exchange situations, respectively, with the latter condition (e.g., for a Freundlich isotherm with &2 <S 1) producing sharp concentration fronts during transport in a soil profile. The effects of isotherm nonlinearity on solute front sharpening and front broadening have been discussed at length in the literature (e.g., Bolt, 1979; Schwcich and Sardin, 1981; van der Zee and van Riemsdijk, 1994).

Nonequilibrium Transport Application of the above equilibrium models to single-ion transport through repacked laboratory or relatively uniform field soils has been fairly successful. The equilibrium approach, however, has not worked well in several situations, most notably for many strongly adsorbed solutes, many organic chemicals, and when used for simulating transport in structured (aggregated) media. A number of chemical-kinetic and diffusion-controlled "physical" models have been proposed to describe noncquilibrium transport. Early models for nonequilibrium transport generally assumed relatively simple first-order type (one-site) kinetic rate equations. More refined noncquilibrium models introduced later invoked the assumptions of two-site or multisite sorption, and/or two-region (dual-porosity) transport that involves solute exchange between mobile and relatively immobile liquid regions. Models of this type generally resulted in better descriptions of observed laboratory and field transport data, mostly because of additional degrees of freedom in fitting observed concentration distributions. The different nonequilibrium approaches are briefly reviewed below.

One-Site Sorption Models The simplest nonequilibrium formulation arises when a first-order linear kinetic rate process is assumed. Ignoring any solute production or decay in the adsorbed phase, equation (6.2) is then augmented with the equation

1 62

VADOSE ZONE HYDROLOGY

where a is a first-order kinetic rate coefficient. Transport models using the above one-site kinetic sorption equation have generally resulted in only modest improvements in terms of their ability to match observed displacement data (e.g., Davidson and McDougal, 1973; van Genuchten et al., 1974). Success was usually limited only to experiments conducted at relatively low flow velocities; that is, for conditions where the equilibrium model already performed reasonably well. Moreover, one or both of the sorption parameters (kD and a), when adjusted to get better transport predictions, were often found to vary as a function of the pore-water velocity. Similar limitations hold for most or all of the other nonequilibrium rate expressions listed in table 6.2. Two-Site Chemical Nonequilibrium Transport The one-site first-order kinetic model may be expanded into a two-site sorption concept by assuming that sorption sites can be divided into two fractions (Selim et al., 1976): sorption on one fraction (type 1 sites) is assumed to be instantaneous while sorption on the remaining (type 2) sites is considered to be time-dependent. Assuming a linear sorption process, the complete two-site transport model is given by (van Genuchten and Wagenet, 1989)

where /j,/ and /A, are first-order decay constants for degradation in the liquid and sorbed phases, respectively, / is the fraction of exchange sites assumed to be at

Table 6.2 Nonequilibrium Adsorption Equations (van Genuchten and Clcary, 1979) Equation

Model

Reference(s)

Linear

Lapidus and Amundson (1952); Oddsonet al. (1970) Hornsby and Davidson (1973); van Genuchten et al. (1974) Hendricks (1972)

Freundlich

Langmuir

Frcundlich-Langmuir

Simunek and van Genuchten (1994) Fava and Eyring (1956) Lindstrom et al. (1971) Lccnhccr and Ahlrichs (1971); Enfield et al. (1976)

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 63

equilibrium, and the subscripts 1 and 2 refer to equilibrium (type 1) and kinetic (type 2) sorption sites, respectively. Note that if/ = 0, the two-site sorption model reduces to the one-site fully kinetic sorption model, i.e., only type 2 kinetic sites are present. On the other hand, if/ = 1, the two-site sorption model reduces to the equilibrium sorption model. The two-site sorption model has been quite successful in describing a large number of mostly laboratory-type miscible displacement experiments that involve a variety of organic and inorganic chemicals undergoing adsorption (Rao et al., 1979; Hoffman and Rolston, 1980; Parker and Jardine, 1986; Gonzalez and Ukrainczyk, 1999, among many others).

Two-Region Physical Nonequilibrium Transport The two-region physical noncquilibrium transport model assumes that the liquid phase can be partitioned into distinct mobile (flowing) and immobile (stagnant) liquid pore regions, and that solute exchange between the two liquid regions can be modeled as an apparent first-order exchange process. Using the same notation as before, the two-region transport model is given by (van Genuchten and Wagenet, 1989)

where the subscripts in and im refer to the mobile and immobile liquid regions, respectively, the subscripts / and s refer to the liquid and sorbed phases, respectively, / represents the fraction of sorption sites that equilibrates with the mobile liquid phase, and a is a first-order mass transfer coefficient that governs the rate of solute exchange between the mobile and immobile liquid regions. The two-region physical nonequilibrium model has been successfully applied to laboratory-scale transport experiments that involve a large number of tracers (tritiated water, chloride, different organic chemicals, heavy metals) as shown in studies by Gaudet et al. (1977) van Genuchten et al. (1977), and Gaber et al. (1995), among others. As an example, figure 6.3 shows breakthrough curves for the pesticide 2.4,5-T (2,4,5-trichlorophenoxyacetic acid) obtained from a 30-cm-long soil column that contained aggregated ( < 6 mm in diameter) Glendale clay loam (van Genuchten et al., 1987). Notice that the two-region model (TRM) provides an excellent description of the data, whereas the advection-dispersion equation (ADE) could not be made to fit the data. A close comparison of the two-site and two-region nonequilibrium models shows that both have the same mathematical structure. As shown previously by NkediKizza et al. (1984) and Toride et al. (1993), among others, the two models can be put into the same dimensionless form by using appropriately selected dimensionless parameters. Because the same dimensionless transport equations apply to conceptually different transport situations, it also follows that breakthrough curves such as

1 64

VADOSE ZONE HYDROLOGY

Figure 6.3 Observed and calculated effluent curves for 2,4,5-T movement through Glendale clay loam. The fitted curves were based on (a) the classical ADE and (b) two-region TRM transport models. (After van Genuchten et al., 1987.)

those shown in figure 6.3 generally contain insufficient information to differentiate between specific physical (mobile-immobile type) and chemical (kinetic type) processes that lead to nonequilibrium, unless nonadsorbing tracers are considered. Hence, independent parameter estimates are generally needed to effectively differentiate between presumed two-site and two-region nonequilibrium phenomena. On the other hand, the mathematical similarity of the two-site and two-region models also suggests that the two formulations may be used to macroscopically describe transport without having to delineate the exact physical and chemical processes at the microscopic level.

Vapor-Phase Transport and Volatilization Vapor-phase transport and volatilization from the soil surface are increasingly recognized as being important processes that affect the field behavior of many organic

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 65

chemicals, including pesticides, gasoline, and such industrial solvents as TCE and CC14 (Glotfelty and Schomburg, 1989; Mercer and Cohen, 1990; Yates et al., 1996). While many organic pollutants dissipate by means of chemical and microbiological degradation, volatilization may be equally important for volatile substances. A thorough understanding of vapor-phase transport is important for the proper design of in situ remediation techniques [such as air sparging and soil venting (DiGiulio, 1992)] for cleaning up hazardous waste sites contaminated with nonaqueous-phase liquids (NAPLs). The process of volatilization has gained additional interest recently because of concerns of the effects of a variety of gases, such as methyl bromide, on stratospheric ozone. Methyl bromide has been used for many decades as an effective soil fumigant for the control of nematodes, weeds, and fungi, but is now suspected to cause significant damage to the ozone layer (Gan et al., 1997). The volatility of a chemical is influenced by many factors, most important being the physicochemical properties of the chemical, soil texture and water content, and several environmental parameters, such as temperature and solar energy (Taylor and Spencer, 1990). Even though only a small fraction of a volatile chemical may exist in the gas phase, air-phase diffusion rates can be much larger than those in the liquid phase since gas-phase diffusion coefficients are about 104 times greater than those in the liquid phase. The solute tranport equation for volatile solutes may be written in the following general form (e.g., Wang et al., 1998):

where a is the volumetric air content, g is the solute concentration associated with the gas phase, DH. and Da are the solute dispersion coefficients in the liquid and gaseous phases, respectively, and , equation (6.13) reduces to the standard advcction-dispersion equation (6.5), where v — (
Degradation The source/sink term in equation (6.2) may be used to account for nutrient uptake and/or a variety of chemical and biological reactions and transformations insofar as these processes are not already included in the sorption/exchange term dpx/dl. Solute reactions and transformations can be highly dynamic and nonlinear in time and space, especially for nitrogen and pesticide products. For example, among the nitrogen transformation processes that may need to be considered are nitrification, deni-

166

VADOSE ZONE HYDROLOGY

trification, mineralization, and nitrogen uptake by plants (Stevenson, 1982). For microbially induced organic and inorganic transformations, the degradation process should also consider the growth and maintenance of soil microbes. Alexander and Scow (1989) gave a review of some of the equations used to represent the kinetics of biodegradation. These equations include zero-order, halforder, first-order, three-half-order, mixed-order, logistic, logarithmic, MichaelisMenton, and Monod type (with or without growth) expressions. Possible biological degradation equations arc listed in table 6.3. While most of these expressions have a theoretical basis, they are commonly used only in an empirical fashion by fitting the equations to observed data. Zero- and first-order kinetic equations remain the most popular models for describing the biodegradation of organic compounds, mostly because of the simplicity and ease in which these equations can be incorporated in solute transport models. Conditions for the application of zero- and first-order biodegradation equations are given by Alexander and Scow (1989). One special group of degradation reactions involves decay chains in which solutes are subject to sequential (or consecutive) decay reactions. Problems of solute transport that involves sequential first-order decay reactions frequently occur in soil and groundwater systems. Examples are the migration of various radionuclides (Rogers, 1978), the simultaneous movement of interacting nitrogen species (Cho, 1971), organic phosphate transport, and the transport of certain pesticides and their metabolites (Wagenet and Hutson, 1987; Simunek and van Gcnuchten, 1994; Simunck et al., 1998).

Multicomponent Solute Transport Except for the above decay chains, thus far we have considered the transport of only one chemical species, and hence assumed that the behavior of a solute is independent Table 6.3 Biological Degradation Equations Equation

Model First-order kinetics Zero-order kinetics Power rate kinetics Monod, Michaelis-Menten kinetics Monod with growth kinetics Haldane modification of Monod kinetics Logarithmic kinetics Logistic kinetics

/ f , , k2, Empirical constants; ju mas , maximum specific degradation; Ks, substrate concentration when the rate of decay is half the maximum rate; C0, initial substrate concentration; X0. amount of substrate required to produce the initial population; K / , inhibition constant that reflects the suppression of the growth rate by a toxic substrate rate.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

167

of other species present in the soil solution. In reality, the soil liquid phase always contains a mixture of many ions which mutually may interact, create complex species, precipitate, dissolve, and/or compete with each other for sorption sites on the solid phase. In this section, we give a very brief review of such more complex situations that involve multicomponent transport. More comprehensive reviews are given by Yeh and Tripathy (1989), Mangold and Tsang (1991), and Suarez and Simunek (1996). Attempts to model multicomponent transport initially focused primarily on the saturated zone, where changes in the fluid flux, temperature, and pH are relatively gradual and hence less important than in the unsaturated zone. Consequently, most multicomponent transport models assume one- or two-dimensional steady-state saturated water flow. Typical examples are given by Valocchi et al. (1981), Bryant et al. (1986), and Walter et al. (1994). Only recently have multicomponent transport models become more popular for application also to variably saturated flow problems (Liu and Narasimhan, 1989; Yeh and Tripathi, 1991; Simunek and Suarez, 1994). In a recent review, Yeh and Tripathi (1989) identified three different approaches for mathematically solving multicomponent transport problems: (1) a mixed differential and algebraic approach, (2) a direct substitution approach, and (3) a sequential iteration approach. In the first approach, the sets of differential and algebraic equations that describe the transport processes and chemical reactions, respectively, are treated simultaneously (Miller and Benson, 1983; Lichtner, 1985). In the second approach, the algebraic equations that represent the nonlinear chemical reactions are substituted directly into the differential mass balance transport equations (Rubin and James, 1973; Jennings et al., 1982). The third approach considers two coupled sets of linear partial differential and algebraic equations, which are solved sequentially and iteratively (Walsh ct al., 1984; Yeh and Tripathi, 1991; Simunek and Suarez, 1994; Walter et al., 1994). Based on a study of computer resource requirements, Yeh and Tripathi (1989) suggested that only the third method (sequential iteration) can be applied to realistic multidimensional problems. As an example, the partial differential equations that govern one-dimensional multicomponent advective-dispersive chemical transport during transient variably saturated flow may be written as (Simunek and Suarez, 1994)

where ck is the total dissolved concentration of aqueous component k (i.e., the sum of the component plus all complex species that contain component k), ck is the total sorbed concentration of the aqueous component k, ck is the total precipitated concentration of aqueous component k (i.e., the sum of all precipitated species that contain the component k), and Nc is the number of aqueous components. The second and third terms the left-hand side of equation (6.16) arc zero for components that do not undergo ion exchange or precipitation—dissolution reactions. The total concentration of a component fc, denned as the sum of the dissolved, sorbed, and mineral concentrations, is influenced only by transport processes which act on the solution concentration ck, but not by chemical reactions (Zysset et al., 1994). However, the

168

VADOSE ZONE HYDROLOGY

relative fraction of a component in each of the three phases (solution, sorbed, mineral) depends strongly on the specific chemical processes in the system. Therefore, equation (6.16) must be augmented with a set of equations that describe the different equilibrium or nonequilibrium chemical reactions, such as complexation, cation exchange, adsorption-
Transport in Structured Media Field soils generally exhibit a variety of structural features, such as interaggregate pores, earthworm or gopher holes, decayed root channels, or drying cracks in finetextured soils. Water and dissolved chemicals can move along preferred pathways in such structured media at rates much faster than what normally can be predicted with models based on the classical Richards and ADE equations. The resulting preferential-flow process has been shown to occur not only in aggregated field soils (Bcvcn and Germann, 1982) and unsaturated fractured rock (Wang, 1991), but also in seemingly homogeneous soils because of fingering or some other unstable flow process (Parlange and Hill, 1976; Hillel, 1993). An important implication of preferential flow is the accelerated movement of surface-applied fertilizers, pesticides, or other pollutants into and through the unsaturated zone. Deterministic descriptions of preferential flow in structured media are often based on dual-porosity, two-region, or bicontinuum models. Models of this type assume that the medium consists of two interacting pore regions, one associated with the macropore or fracture network, and one associated with the micropores inside soil aggregates or rock matrix blocks. Different formulations arise depending upon how water and solute movement in the micropore region are modeled, and how the micropore and macropore regions are coupled.

Geometry-Based Models A rigorous analysis of transport in structured soils can be made when the medium is assumed to contain geometrically well-defined cylindrical, rectangular, or other types of macropores or fractures. Models may be formulated by assuming that the chemical is transported by advection, and possibly by diffusion and dispersion, through the macropores, while diffusion-type equations are used to describe the transfer of solutes from the larger pores into the micropores of the soil matrix. As an example, the governing equations for transport through media that contain parallel rectangular voids (figure 6.4) are given by (e.g., van Genuchtcn and Dalton, 1986).

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

169

Figure 6.4 Schematic of rectangular porous matrix blocks of width la. The blocks, arranged as parallel slabs, are separated by a fracture pore system of width 2/7.

where the subscripts / and m refer to the interaggregate (fracture /) and intraaggregate (matrix m) pore regions, respectively, ca(z, x, /) is the local concentration in the aggregate, x is the horizontal coordinate, and Da is the effective soil or rock matrix diffusion coefficient. Equation (6.17) describes vertical advective dispersive transport through the fractures, while equation (6.18) accounts for linear diffusion in slab of width 2a in the horizontal (x) direction. Equation (6.19) represents the average concentration of the immobile soil matrix liquid phase. Equations (6.18) and (6.19) are coupled using the assumption of concentration continuity across the fracture matrix interface:

The water contents &/• and &„, in equation (6.17) are given in terms of the bulk soil volume; that is,

where viy is the volume of the fracture pore system relative to that of the total soil pore system. The total water content ((9) of the fracture-matrix system is given by the sum of !?/• and &,„. Similar models to thai above may be formulated for other aggregate or soil matrix geometries. Geometry-based transport models have been successfully applied to laboratory-scale experiments as well as to selected field studies that involve mostly saturated conditions. As an example, figure 6.5 shows calculated and observed Cl effluent curves from a 76-cm-long undisturbed column of fractured clayey till. The extremely skewed (nonsigmoidal) shape of the effluent curve is a direct result of water and dissolved chemical moving mostly through the fractures and bypassing the soil matrix, but with diffusion taking place between the fractures and the finetextured matrix. Sudicky et al. (1985) also demonstrated the skewing effect of matrix

1 70

VADOSE ZONE HYDROLOGY

Figure 6.5 Measured breakthrough curve for Cl transport through fractured clayey till (open circles; data from Grisak et al., 1980). The solid line was obtained with the exact solution (e.g., van Genuchten, 1985) of equations (6.17) through (6.20), using parameter values given by Grisak et al., 1980). The dashed line was obtained by ignoring dispersion in the inlet-aggregate region (Of = 0) and allowing the fracture spacing to go to infinity (a ->• oo).

diffusion on the shape of an effluent curve by means of two-dimensional, saturated sandbox studies in which a Cl tracer migrated through a thin sand layer sandwiched between the two silt layers. Several studies exist in which the above geometry-based approach has been extended to transient flow conditions. The approach assumes that the flow and transport equations of the macropore or fracture network of prescribed geometry can be solved simultaneously and in a fully coupled fashion with the corresponding equations for the porous matrix. Discrete-fracture numerical models of this type include those by Sudicky and McLaren (1992) for application to two-dimensional saturated flow and aqueous-phase transport problems, and those by Shikaze et al. (1994) for two-dimensional gas-phase flow and transport through a network of vadoze zone fractures embedded in a variably saturated porous matrix. The discrete-fracture flow and transport model of Sudicky and McLaren (1992) was recently extended by Therrien and Sudicky (1996) to three dimensions and variably saturated conditions by solving the Richards equation both along the network of interconnected fracture planes and in the adjoining porous matrix. They superimposed a network of two-dimensional finite elements that represent the interconnecting fractures onto the mesh of three-dimensional elements that represent the matrix. Their fully coupled approach assumes continuity in pressure head and concentration at the fracture-matrix interface, thus permitting a simultaneous solution of the Richards and transport equations for both the fracture network and the porous matrix without a need to explicitly calculate fluxes between the two regions. By solving the Richards equation also for the soil matrix region, the model of Therrien and Sudicky (1996) accounts for water flow into and through the matrix domain.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 71

While geometry-based models are conceptually attractive, they may be too complicated for routine applications since structured field soils usually contain a mixture of aggregates of various sizes and shapes. More important, the problem of macropore and fluid flow continuity is not easily addressed with geometry-based flow models. The issue of fluid flow continuity may be especially critical in the vadose zone because of possible preferential flow and channeling within the fracture domain itself during unsaturated conditions. Also, preferential flow paths may well change with the degree of saturation during unsaturated flow. Some of these processes are more easily considered by using first-order models as discussed below. Equivalent First-Order Exchange Models Rather than using geometry-based transport models, many of the preferential flow features can also be accounted for by using models that assume simple first-order exchange of solutes by diffusion between the macropore (mobile) and micropore (immobile) liquid regions. The governing equations then become identical to those used previously for physical nonequilibrium transport; that is, equations (6.13) and (6.14). Ignoring the degradation terms in equations (6.13) and (6.14) and assuming steady-state water flow, the dual-porosity model becomes

where cc, as before, is a first-order solute mass transfer coefficient that characterizes diffusional exchange of solutes between the mobile and immobile liquid phases. Notice that equation (6.22) is identical to equation (6.17) for the rectangular geometry-based model. The mass transfer coefficient is of the general form

where ft is a geometry-dependent shape factor and a is the characteristic length of the aggregate (e.g., the radius of a spherical or solid cylindrical aggregate, or half the width of a rectangular aggregate). Equation (6.24b) holds for a hollow cylindrical macropore for which £0 — h/a, where a now represents the radius of the macropore and b the outer radius of the cylindrical soil mantle that surrounds the macropore. The value of f) ranges from 3 for rectangular slabs to 15 for spherical aggregates (Bolt, 1979; van Genuchten and Dalton, 1986; Sudicky, 1990). Extension to Variably Saturated Flow Different types of models have been proposed to extend the above first-order dualporosity approach to variably saturated structured media (Wang, 1991; Zimmerman

1 72

VADOSE ZONE HYDROLOGY

et al., 1993). Here, we summarize the dual-porosity model developed by Gerkc and van Genuchlen (1993, 1996). This model assumes that the Richards equation for transient water flow and the advection-dispersion equation tor solute transport can be applied to each of the two pore systems. Similar to the first-order mobile-immobile approach, water and solute mass transfer between the two pore systems is described with first-order rate equations. The flow equations for the fracture (subscript/) and matrix (subscript m) pore systems are, respectively,

where F,,; describes the rate of exchange of water between the fracture and matrix regions:

in which a,,, is a first-order mass transfer coefficient for water:

where ft and a are the same as before, Ka is the hydraulic conductivity of the fracture-matrix interface, and yn, (= 0.4) is a dimensionless scaling factor. The solute transport equations for the fractures and matrix are given by, respectively,

where rs is the solute mass transfer term given by

in which a is the same as used in the first-order mobile-immobile model. The first term on the right-hand side of equation (6.31) specifies the diffusion contribution to Fj., while the second term gives the advective contribution. The above dual-porosity transport model reduces to the first-order model for conditions of steady-state flow in the fracture (macropore) region and no flow in the matrix pore system (qm = Fw = 0). The dual porosity model given by equations (6.25) through (6.31) contains two water-retention functions, one for the matrix and one for the fracture pore system, but three hydraulic conductivities functions: Kf(hf) for the fracture network, Km(hm) for the matrix, and Ka(h) for the fracture-matrix interface. The Kf(hf) function is determined by the structure of the fracture pore system; that is, the size, geometry, continuity, and wall roughness of the fractures, and possibly the presence of fracture fillings. Similarly. Km(hm) is determined by the hydraulic properties of single matrix

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 73

blocks, and the degree of hydraulic contact between adjoining matrix blocks during unsaturated flow. Finally, Ka(h) is the effective hydraulic conductivity function to be used in equation (6.28) for describing the exchange of water between the two pore systems. Several important features of preferential flow are illustrated here by using the above variably saturated dual-porosity model to calculate the infiltration of water at a constant rate of 50 cm/day into a 40-cm-dccp structured soil profile that has an initially uniform pressure head of —1000 cm. Water is allowed to infiltrate exclusively into the fracture pore system, thus assuming that the matrix pore system at the soil surface is sealed. The hydraulic properties of the fracture and matrix pore systems (figure 6.6) are indicative of relatively coarse- and fine-textured soils, respectively. The simulations assume a macroporosity of 5% (wf — 0.05), and rectangular aggregates (/? = 3) that have a width of 2 cm (a = 1 cm). The hydraulic parameters for Ka(H) were assumed to be the same as those for Km(hm), except for the saturated hydraulic conductivity, which was decreased by a factor of 100. Figure 6.7 shows simulated pressure head and water content distributions during infiltration. The results indicate a rapid increase in the pressure head of the fracture pore system, but a relatively slow response of the matrix (figure 6.7a). The resulting pressure head gradient between the two pore systems causes water to flow from the fracture into the matrix pore system (figure 6.7b), thus increasing the water content of the matrix (figure 6.7c). Significant pressure head differences between the two pore systems are still present when the infiltration front in the fracture system reaches the bottom of the soil profile after about 0.08 days (figure 6.7a). Notice that the water transfer rate. F,,., is highest close to the infiltration front, and gradually decreases toward the soil surface (figure 6.7b). The shapes of the FH.-curves reflect the combined effects on FH, of the pressure head difference between the two pore regions (which decreases in time) and the value of Ka (which increases in time) at any point behind the wetting front. Figure 6.8 shows the simulated concentration distributions. Results arc for the infiltration of solute-free water into a structured medium that has a relative initial concentration of 1. As expected, the solute concentration in the fracture pore system initially decreases rapidly as solute-free water infiltrates (figure 6.8a). Water with a relatively low concentration subsequently flows from the fracture into the matrix pore system. At the same time, however, solutes begin to diffuse back from the matrix into the fracture pore system because of the large concentration gradients that develop between the two pore systems (figure 6.8a). The net solute transfer rate, Fj. eventually becomes negative, indicating a net transfer from the matrix into the fracture pore system (figure 6.8b). The solute mass in the matrix pore system (9mcm) initially decreases only slightly (/ = 0.01 days in figure 6.8c), but starts to decrease more rapidly at later times (t > 0.04 days). The results in figure 6.8 illustrate the extremely transient and complicated nature of transport in a structured medium that involves vertical advective transport and dispersion, and horizontal mass transfer by advection and diffusion. Simulations such as those shown in figures 6.7 and 6.8 may be used to explain previously observed effects of several parameters on solute leaching during transient flow, including soil surface boundary condition (Bond and

Figure 6.6 (a) Water retention and (b) hydraulic conductivity functions of a dualporosity medium that involves (1) the fracture network, (2) the matrix pore system, (3) the composite medium, and (4) the conductivity of the fracture-matrix interface. (After Gcrkc and van Genuchten, 1993.)

Figure 6.7 Simulated distributions versus depth of (a) the pressure head, h, (b) the water transfer rate, F,,, and (c) the volumetric water content, #, for the matrix (dashed lines) and fracture (solid lines) pore systems at t = 0.01, 0.04, and 0.08 days. (After Gerke and van Genuchten, 1993.)

Figure 6.8 Simulated distributions versus depth of (a) the solute concentration, c, (b) the solute transfer rates, rs, and (c) the solute mass, &c, for the matrix (dashed lines) and fracture (solid lines) pore systems at / = 0.01, 0.04, and 0.08 days. (After Gerke and van Genuchten, 1993.)

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 77

Wierenga, 1990), water application rate (White et al, 1986; McLay et al., 1991), and initial condition (Kluitenberg and Horton, 1990). The potential value of process-based preferential flow simulations is further illustrated in figure 6.9, which shows the sensitivity of the infiltration process to changes in the hydraulic conductivity Ka of the fracture-matrix interface. Results obtained with a relatively large saturated conductivity, KSM, of 1 cm/day (equal to the matrix conductivity) closely approximate the limiting case of pressure head equilibrium (figure 6.9a) with little or no preferential flow. The moisture front in this case reached a depth of only 5 cm after 0.02 days. The water transfer rates (figure 6.9b) were so high that the two pore systems quickly approached equilibrium (Ksa = 1 cm/day). By comparison, for the smallest Ks a (0.001 cm/day), water percolated rapidly downward through the fracture pore system to a depth of 35 cm during the same time period (t = 0.02 days or 20 min). This last situation represents an extreme case of preferential flow with significant pressure head differences between the two pore systems (figure 6.9a). The results in figure 6.9 indicate that equilibrium between the fracture and matrix pore systems should be expected when the hydraulic conductivity, Ksa, of the matrix-fracture interface is roughly equal to the conductivity of the soil matrix (assuming a fracture spacing of 2 cm). For preferential flow to initiate in the present example, Ks a must be much less than K^ „, of the matrix. This conclusion is consistent with experimental studies that suggest that a soil aggregate can have a higher local bulk density (and hence lower conductivity) near its surface than in the aggregate center, in part because of the deposition of organic matter, fine-texture mineral particles, or various oxides and hydroxides on the aggregate exteriors or macropore walls. For example, Wilding and Hallmark (1984) noted that ped argillans can markedly reduce rates of diffusion and mass flow from ped surfaces into the soil matrix. Cutans, which consist of coatings with modified physical, chemical, or biological properties, often have also preferred orientations parallel to soil aggregate surfaces. Unsaturated fractured rock formations may exhibit similar features that is, fracture skins (Mocnch, 1984), or other types of coatings (Pruess and Wang, 1987) made up of fine clay particles, calcite, zeolites or silicates—which may reduce the hydraulic conductivity. Finally, preferential flow within the macropores or fractures themselves can also contribute to a lower effective Ka(h). Situations like this can restrict water and solute exchange between the two pore systems (notably imbibition into the matrix) to only a small portion of the total interface area (Hoogmoed and Bouma, 1980), even in capillary-size pores (Omoti and Wild, 1979). Hydrophobic fracture surfaces can similarly limit fluid exchange between the two pore systems. Application of the variably saturated dual-porosity model requires several hydraulic and other parameters that are not easily measured. Estimates for the Kfand A" m -functions (figure 6.6) may be obtained by assuming that Kf is primarily the conductivity function in the wet range, while Km is the conductivity in the dry range (Peters and Klavctter, 1988; Othmer et al., 1991; Durner, 1994). Obtaining accurate estimates for the hydraulic properties of the fracture pore system from the composite curves requires that the hydraulic functions be very well defined in the wet range. This problem is indirectly demonstrated by figure 6.6a, which was obtained by assuming that the fracture pore system comprises 5% of the porous medium.

Figure 6.9 Simulated distributions versus depth of (a) the pressure head, A, (b) the water transfer rate, F w , and (c) the total volumetric water content, 0, for different values of the fracture-matrix interface hydraulic conductivity, Ks_a (t = 0.02 days, a = 1 cm).

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 79

Notice that the retention function of the matrix differs only minimally from that of the composite medium. Hence, it may be very difficult, in practice, to estimate separate soil water-retention curves of the fracture and matrix pore systems by using bulk soil measurements that generally contain some noise. By contrast, it appears more promising to assess the contributions of macropores from carefully measured bulk hydraulic conductivity functions near saturation (e.g., Smettem and Kirby, 1990; Mohanty et al., 1997). Finally, we note that the dual-porosity model discussed here assumes applicability of the Richards equation, and hence of Darcy's law. This assumption may not be strictly correct for the fracture pore system. However, given the uncertainties in all of the physical and chemical processes related to preferential flow, the real issue may not necessarily be the validity of Darcy's law as such, but whether Darcy's law even if formally invalid—can still provide a useful qualitative description of the preferential-flow process. Alternative descriptions of the flow regime in fractures, such as Manning's equation for turbulent overland flow, kinematic wave theory, or simple gravity-flow models, may be too elaborate for routine use. Moreover, some of these approaches do not have provisions for flow to occur from the micropores back into the fractures—for example, at or near the bottom boundary of a coarse-textured soil horizon overlaying a fine-textured horizon.

Numerical Methods A large number of analytical solutions have been published for one- and multidimensional transport problems (e.g., Javandel et al., 1984; Leij et al. 1993; Toride et al., 1993). While useful for simplified analyses, analytical solutions are generally not available for more complex situations, such as for transient variably saturated flow or situations that involve nonlinear sorption or degradation, in which case numerical models must be employed. In this section, we give a brief review of recent advances in numerical methods for solving subsurface flow and transport problems. We will not address issues that pertain to the discretization of multiphase "black oil" or compositional simulators. A detailed discussion of discretization issues for multiphase compositional problems can be found in Unger et al. (1996). Numerical Solution of the Richards Equation A variety of numerical methods may be used to solve the variably saturated flow and transport equations (e.g., Huyakorn and Finder, 1983; Sudicky and Huyakorn, 1991). Early numerical variably saturated flow models generally used classical finite difference methods. Integrated finite differences (Narasimhan and Witherspoon, 1976), control-volume finite element techniques (Forsyth 1991; Therricn and Sudicky, 1996), and Galerkin finite element methods (Huyakorn et al., 1986; Simunek et al., 1994) became increasingly popular since the mid-1970s. Time and space discretization of the Richards equation using any of these methods leads to a nonlinear system of algebraic equations. These equations are most often linearized and solved using the Newton-Raphson or Picard iteration methods. Picard iteration

180

VADOSE ZONE HYDROLOGY

is widely used because of its ease of implementation, and because this method preserves symmetry of the final system of matrix equations. The Newton-Raphson iteration procedure is more complex and results in nonsymmetric matrices, but often achieves a faster rate of convergence and may be more robust than Picard iteration for highly nonlinear problems (Paniconi and Putti, 1994; Forsyth et al., 1995). In principle, the Picard scheme is linearly convergent, and therefore should converge more slowly than the quadratically convergent Newton-Raphson scheme. The basic approach for discretizing and solving the Richards equation depends upon the flow formulation being used—that is, the /z-based, the #-based, or the mixed formulation. Celia et al. (1990) suggested that numerical solutions based on the standard /j-based formulation of the Richards equation often yield poor results, characterized by large mass balance errors and incorrect estimates of the pressure head distributions in the soil profile. They solved the mixed formulation of the Richards equation using a modified Picard iteration scheme which possesses massconserving properties for both finite element and finite difference spatial approximations. Therrien and Sudicky (1996) also solved the mass-conservative mixed form of the Richards equations, but implemented the more robust Newton-Raphson linearization method and a highly efficient algorithm to construct the Jacobian matrix (Forsyth and Simpson, 1991). Milly (1985) earlier presented two mass-conservative schemes for computing nodal values of the water capacity in the /z-based formulation to force global mass balance. Several numerical schemes based on different types of pressure head transformations were recently also presented (Hills et al., 1989; Ross, 1990; Pan and Wierenga, 1995). Hills et al. (1989) showed that the 0-based form of the Richards equation can yield fast and accurate solutions for infiltration into very dry heterogeneous soil profiles. However, the $-based numerical scheme cannot be used for soils that have saturated regions. Kirkland et al. (1992) expanded the work of Hills by combining the #-based and A-based models to yield a transformation applicable also to variably saturated systems. They defined a new variable that is a linear function of the pressure head and water content in the saturated and unsaturated zone, respectively. More recently, Forsyth et al. (1995) proposed a robust and highly efficient algorithm in which variable substitution is used to switch between 9 or h as the primary variables when constructing the Jacobian matrix for NewtonRaphson iteration. The primary variable switch is made after each Newton iteration in different parts of the computational domain as a function of the state of the degree of saturation in those parts. Using this approach, and also by employing a monotone discretization (i.e., upstream weighting of relative permeabilities) that guarantees that saturations always remain in the physical range, they demonstrated that an order-of-magnitude execution speedup can be achieved for difficult problems that involve infiltration into dry, heterogeneous soils. They also pointed out that the method of Kirkland et al. (1992) is not necessarily monotone because of its partially explicit nature, and that mass balance errors can occur at the transition between the saturated and unsaturated zones. Upstream weighting of relative permeabilities is very much recommended over central weighting since the latter method can introduce oscillations (i.e., negative saturation values) for difficult problems, and thus can cause complete failure of the nonlinear iteration process (Forsyth, 1991; Therrien and Sudicky, 1996). Because of the self-sharpening properties of soil moisture fronts,

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 81

the use of upstream weighting in the numerical solutions of the Richards equation generally does not introduce excessive smearing of saturation fronts, unlike its use in solutions of the advection-dispersion equation. Numerical Solution of the Transport Equation Numerical methods for solving the advection-dispersion equation may be classified into three groups: (1) Eulerian, (2) Lagrangian, and (3) mixed Lagrangian-Eulerian methods. In the Eulerian approach, the transport equation is discretized by means of a usual finite difference or finite element method that uses a fixed grid system. For the Lagrangian approach, the mesh either deforms and moves along with the flow path, or the mesh is assumed to be stable in a deforming coordinate system. A two-step procedure is followed for a mixed Lagrangian-Eulerian approach. First, advective transport is considered, using a Lagrangian approach in which Lagrangian concentrations are estimated from particle trajectories. Subsequently, all other processes, including sinks and sources, are modeled using the standard Eulerian approach that involves any finite element or finite differences method, thus leading to the final concentrations. Standard finite difference and Galerkin or control-volume type finite element methods belong to the first group of Eulerian methods. Finite differences and finite elements methods provided the early tools for solving solute transport problems and, in spite of some limitations as discussed below, are still the most popular methods being used at present. Numerical studies have shown that both methods give good results for transport problems where dispersion is relatively dominant as compared with advective transport (e.g., as indicated by the grid Peclct number). However, both methods can lead to significant numerical oscillations and/or dispersion for advection-dominated transport problems. The Eulerian methods have been found to be very reliable and accurate when applied to quasi-symmetric problems when diffusion dominates the transport process. The advection term brings nonsymmetry into the governing solute transport equation and, as a result, compromises the success of Eulerian methods when applied to advection-dominated transport problems. By selecting an appropriate combination of relatively small space and time steps, it is still possible to virtually eliminate most or all oscillations. Alternatively, the spatial grid system may be refined using a "zoomable hidden fine-mesh" approach (Yeh, 1990), or by implementing local adaptive grid refinement (Wolfsberg and Freyberg, 1994). However, there is an additional computational cost with this approach, and the handling of natural grid irregularities due to material heterogeneity or other domain features can be problematic. Criteria for minimizing or eliminating oscillations and reducing numerical dispersion when solving the linear advection-dispersion equations are well known; that is, the product of the local Peclet (vAx/D) and Courant (vAf/Ax) numbers should be less than 2 (A/ is the time step and Ax is the nodal spacing). When small oscillations in the solution can be tolerated, this criterion can be increased to about 5 or 10. Monotonicity conditions and numerical smearing are also influenced by the type of temporal discretization being used. For example, while fully implicit time-weighting schemes are monotone (i.e., concentrations always fall within the physical range), they are more prone to

182

VADOSE ZONE HYDROLOGY

numerical dispersion than central-in-time (Crank-Nicolson type) weighting which is second-order correct. By comparison, monotonicity cannot be guaranteed with central weighting unless the grid Peclet and Courant criteria are appropriately satisfied. We refer to Unger et al. (1996) for a more thorough discussion of discretization strategies that involve both the linear and nonlinear forms of the transport equation in the context of multiphase compositional modeling. In particular, they discuss the use of flux limiters and total variation diminishing (TVD) schemes for reducing numerical dispersion in nonlinear multiphase compositional transport problems. Upstream weighting methods virtually eliminate numerical oscillations, even for purely advectivc transport, but a disadvantage is that they may create unacceptable numerical dispersion. Huyakorn and Nilkuha (1979) and Yeh (1986) used weighting functions that are different for the spatial derivatives than for other terms in the finite element solution of the transport equation. Their approach places greater weight on the upstream nodes within a particular element. Huyakorn and Nilkuha (1979) suggested, for this purpose, nonorthogonal basis functions, whereas Yeh (1986) used orthogonal functions. Petrov-Galerkin methods require the use of higher order weighting functions, which makes their implementation more difficult and more costly than classical Galerkin finite element methods. Another alternative for overcoming numerical dispersion is the use of higher order temporal and spatial approximation (e.g., van Genuchten and Gray, 1978). Such higher order approximations, however, are computationally more expensive and often produce numerical oscillations. While Lagrangian methods (or methods of characteristics) may substantially reduce or even eliminate problems with numerical oscillations (e.g., Neuman and Sorck, 1982), they can also introduce other problems, such as nonconservation of mass. Lagrangian methods are also relatively difficult to implement in two and three dimensions when an unstructured (nonrectangular) spatial discretization scheme is used. Instabilities that result from inappropriate spatial discretization sometimes occur during longer simulations as a result of a deformation of the stream function. Furthermore, nonrealistic distortions of the results may occur when modeling the transport of solutes that are undergoing certain sorplion/exchange or precipitation reactions. Mixed Eulerian-Lagrangian approaches have been reported by several authors (e.g., Molz el al., 1986; Sorek, 1988; Yeh, 1990, among others). In view of the different mathematical character of the diffusive (parabolic) and advectivc (hyperbolic) terms in the advcction-dispersion equation, the transport equation can be decomposed into a mixed problem that consists of a purely advection problem, followed by a diffusion-only problem. Advective transport then is solved with the Lagrangian approach, while all other terms of the transport equation are solved using Eulerian methods. The trajectories of the flowing particles may be obtained in a variety of ways. For example, Molz et al. (1986) used single-step reverse particle tracking in which the initial position of particles arriving at the end of a time step at fixed nodal points is calculated for each time step. The use of continuous forward particle tracking has similar disadvantages as the Lagrangian approach since complex geometric regions are, again, difficult to handle. To obtain good results, it may

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 83

be necessary to follow a large number of particles, thereby quickly leading to excessive computer time and memory. Still other solution methods exist, such as the use of a combination of analytical and numerical techniques. For example, Sudicky (1989) and Sudicky and McLaren (1992) modeled solute transport by using Laplace transforms with respect to time and Galerkin finite elements for the spatial domain. The use of Laplace transforms avoids the need for intermediate simulations (time-stepping) between the initial condition and the points in time for which solutions are needed, while also needing less stringent requirements for the spatial discretization. These features lead to computational efficiency, especially for large-time simulations. Recently, several methods have also been suggested that make use of local analytical solutions of the advection-dispersion equation in combination with finite differences (Li et al., 1992). We emphasize that combinations of analytical and numerical techniques have one important limitation. Because, for example, the Laplace transform eliminates time as an independent variable in the governing solute transport equation, all coefficients, such as water content, flow velocity, and retardation factors, must be independent of time. This limitation precludes the use of combination methods for solving coupled, transient variably saturated flow and transport problems typical of many field situations.

Matrix Equation Solvers Discretization of the governing partial differential equations for water flow and solute transport generally leads to a system of linear matrix equations: [A][x] = {b}

(6.32)

in which [x] is an unknown solution vector, {b} is the known right-hand side vector of the matrix equation, and [A] is a sparse banded matrix that is symmetric for water flow if the modified Picard procedure is used, but asymmetric for water flow if the Newton-Raphson method is used. Matrix [A] is generally asymmetric for solute transport, unless advection is not considered in the formulation. Technological breakthroughs in computer hardware and increased incentives to simulate complex coupled flow and transport problems in large three-dimensional systems has spurred the development and use of highly efficient and robust iterative matrix solvers. Robustness of the solver is essential to handle stiff matrices that result from extreme contrasts in material properties and, in the situation of variably saturated flow, severe nonlinearity. Traditionally, matrix equations have been solved by means of such direct methods as Gaussian elimination and LU decomposition. Although these methods usually take advantage of the banded nature of the coefficient matrices, they have several disadvantages as compared with iterative methods. For example, for two-dimensional problems, the operation count for a direct solver increases approximately by the square of the number of nodes, whereas for an iterative solver the operation count is typically 1.5 or less (Mendoza et al., 1991; VanderKwaak et al., 1995, among others). A similar reduction also holds for the

184

VADOSE ZONE HYDROLOGY

memory requirement since iterative methods do not require storage of nonzero matrix elements. Memory requirements, therefore, increase at a much smaller rate with the size and dimensionality of a problem when iterative solvers are used (Mendoza et al., 1991; VanderKwaak et al., 1995). Round-off errors also represent less of a problem for iterative methods as compared with direct methods. This is because round-off errors in iterative methods are self-correcting (Letniowski, 1989). Finally, for time-dependent problems, a reasonable approximation of the solution (i.e., the solution at the previous time step) exists for iterative methods, but not for direct methods (Letniowski, 1989). In general, direct methods are more appropriate for relatively small problems that involve a couple of thousand nodes, while iterative methods arc more suitable for the larger problems. This issue is of critical importance given that many research problems, as well as certain practical vadose zone field applications, may require discretizations that involve tens to hundreds of thousands of nodes. Many iterative methods have been used in the past for handling large sparse matrix equations. These methods include Jacobi, Gauss-Seidel, alternating direction implicit (ADI), successive overrelaxation (SOR), block successive ovcrrelaxation (BSSOR), successive line overrelaxation (SLOR), and strongly implicit procedures (SIP), among others (Letniowski, 1989). More powerful preconditioned accelerated iterative methods, such as the preconditioned conjugate gradient method (PCG) (Meijerink and van dcr Vorst, 1977; Kershaw, 1978; Behie and Forsyth, 1983), were introduced more recently. Sudicky and Huyakorn (1991) gave three advantages of the PCG procedure as compared with other iterative methods: (1) PCG can be readily modified for finite clement methods with irregular grids, (2) the method does not require arbitrary iteration parameters, and (3) PCG usually outperforms its iterative counterparts for situations that involve relatively stiff matrix conditions. The PCG methods can be used only for symmetric matrices. Since the system of linear equations that results from discretization of the solute transport equation is nonsymmetrical (the same is true when linearizing numerical solutions of the Richards equation using Newton-Raphson iteration), it is necessary to either formulate the transport problem such that a symmetric matrix results (Leismann and Frind, 1989), or use an extension of PCG for nonsymmetrical matrices. Examples for such an extension are the ORTHOM1N (generalized conjugate residual method, Behie and Forsyth, 1984), GMRES (generalized minimal residual method, Saad and Schultz, 1986), CGSTAB (conjugate gradient stabilized method, van der Vorst, 1992), or the conjugate gradient squared (Letniowski, 1989; Paniconi and Putti, 1994) procedures. Competitive iterative methods generally involve two operations: (1) initial preconditioning, and (2) iterative solution with a particular acceleration method—such as CGSTAB. Incomplete lower-upper (ILU) factorization (among other methods, such as incomplete Cholesky for symmetric matrices) can be used to precondition matrix [A]. This factorization leads to more easily inverted lower and upper triangular matrices by partial Gaussian elimination. The preconditioned matrix is subsequently repeatedly inverted using updated solution estimates, thus leading to a new approximation of the solution. More details about the CGSTAB and ORTHOMIN methods are given in the user's guides of the WATSOLV (VanderKwaak et al., 1995)

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

185

and ORTHOFEM (Mendoza et al., 1991). Letniowski (1989) also gave a comprehensive review of accelerated iterative methods, as well as preconditional techniques. The ORTHOMIN procedure is becoming increasingly popular in variably saturated flow and contaminant transport simulations (Gambolati et al., 1986; Kirkland et al., 1992; Simunek et al.. 1994; Therrien and Sudicky, 1996). Recent numerical experimentation for problems that involve difficult-to-solve variably saturated flow problems indicate that CGSTAB outperforms ORTHOMIN. This is because ORTHOMIN sometimes tends to stagnate and hence fails to satisfy a specified convergence criterion after many iterations.

Concluding Remarks The past few decades have produced tremendous advances in our ability to mathematically describe and simulate vadose zone flow and chemical transport processes. Careful laboratory and field experimentation has yielded much new information, not only on the form of fundamental constitutive relations, but also on the controlling effects of heterogeneities, fractures, and macropores on flow and transport at the field scale. Process-oriented deterministic and stochastic theories have achieved reasonable success in providing new qualitative and quantitative information on the hierarchical nature of heterogeneities and the scaling-up of relevant parameters and constitutive relations for use in large-scale simulators. The development and implementation of modern numerical algorithms for solving the nonlinear Richards equation in an efficient and robust fashion now makes it possible to routinely simulate large-grid, three-dimensional vadose flow problems on modern workstations. Similar strides in algorithm development have been made with regard to solutions of the solute transport equation and, for example, its coupling to multicomponent geochemical speciation models. One important key enabling us to handle increasingly larger scale three-dimensional flow and transport problems has been the implementation of highly efficient iterative sparse-matrix equation solvers, such as those based on ORTHOMIN and CGSTAB acceleration. In spite of the modeling advances, much remains to be done. For example, field testing of recently developed scale-up theories for application to heterogeneous field settings is generally lacking, and numerical models designed to predict vadose zone flow and chemical transport processes often yield only qualitative similarities to real-world field observations. Attempts to improve the predictive capabilities of recent models have typically involved the introduction of additional fitting parameters that are elusive and perhaps impossible to measure independently. This aspect is disconcerting given that practitioners, planners, and regulators are increasingly relying upon model predictions to establish far-reaching policies. It is our belief that a harmonious blend between laboratory research, field-scale experimentation, and modeling-based research is key to at least maintaining, and perhaps accelerating, the pace of advancement that we have seen over the last couple of decades.

186

VADOSE ZONE HYDROLOGY

References Alexander, M. and K.M. Scow, 1989, Kinetics of biodegradation in soil, in: B.L. Sawhney and K. Brown (eds.), Reactions and Movement of Organic Chemicals in Soils, Special Publication No. 22, Soil Science Society of America, Madison, WI, pp. 243-270. Bache, B.W. and E.G. Williams, 1971, A phosphate sorption index for soils, ./. Soil Sci., 27, 289 296. Barry, D.A., 1992, Modelling contaminant transport in the subsurface: theory and computer programs, in: H. Ghadiri and C.W. Rose (eds.). Modelling Chemical Transport in Soil: Natural and Applied Contaminants, Lewis Publishing, Chelsea, MI, pp. 105-144. Behie, A. and P.A. Forsyth, 1983, Comparison of fast iterative methods for symmetric systems, IMA J. Numer. Anal., 3, 41-63. Behie, A. and P.A. Forsyth, 1984. Incomplete factorization method for fully implicit simulation of enhanced soil recovery, SIAM J. Scientf. Slat. Comput., 5(3), 543561. Beven, K..T. and P. Germann, 1982, Macropores and water How in soils, Water Resour. Rex., 18, 1311-1325. Bolt, G.H. (ed.), 1979, Soil Chemistry, Physico-Chemical Models, Elsevicr Science, New York. Bond, W.J. and P.J. Wiercnga, 1990, Immobile water during solute transport in unsaturated sand columns, Water Resour. Res., 26, 2475-2481. Bresler, E. and G.J. Hoffman, 1986, Irrigation management for soil salinity control: theories and tests, So/7 Sci. Soc. Am. J., 50, 1552-1560. Bresler, E., B.L. McNeal, and D.L. Carter, 1982, Saline and Sodic Soils, Springer Verlag, Berlin. Bryant, S.L., R.S. Schechter, and L.W. Lake, 1986, Interactions of precipitation/ dissolution waves and ion exchange in flow through permeable media, AIChE J., 32(5), 751-764. Cardon, G.E. and J. Lctey, 1992a, Plant water uptake terms evaluated for soil water and solute movement models, Soil Sci. Soc. Am. J., 56, 1876-1880. Cardon, G.E. and J. Letey, 1992b, Soil-based irrigation and salinity management model, I. Plant water uptake calculations, Soil Sci. Soc. Am J., 56, 1881-1887. Cederberg, G.A., R.L. Street, and J.O. Leckie, 1985, A groundwater mass transport and equilibrium chemistry model for multicomponent systems. Water Resour. Res., 21(8), 1095-1104. Celia, M.A., E.T. Bouloutas, and R.L. Zarba, 1990, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26(7), 1483-1496. Cho, C.M., 1971, Convective transport of ammonium with nitrification in soil, Can. J. Soil Sci., 51(3), 339-350. Constantz, J., 1982, Temperature dependence of unsaturated hydraulic conductivity of two soils, Soil Sci. Soc. Am. J,, 46, 466-470. Dagan, G., 1993, The Bresler-Dagan model of flow and transport: recent theoretical developments, in: D. Russo and G. Dagan (eds.), Water Flow and Solute Transport in Soils, Springer Verlag, New York, pp. 13-32. Dane, J.H. and A. Klute, 1977, Salt effects on the hydraulic properties of a swelling soil, So/7 Sci. Soc. Am. J., 41(6), 1043-1049. Davidson, J.M. and J.R. McDougal, 1973, Experimental and predicted movement of three herbicides in water-saturated soil, /. Environ. Qual., 2, 428-433. DiGiulio, D.C., 1992, Evaluation of soil venting application. Report No. EPA/5401 S92/004, U.S. Environmental Protection Agency. Office of Research and Development.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

187

Durner, W., 1994, Hydraulic conductivity estimation for soils with heterogeneous pore structure, Water Resour. Res., 30(2), 211-223. Enfield, C.G., C.C. Harlin, Jr., and B.E. Bledsoe, 1976, Comparison of five kinetic models for orthophosphate reactions in mineral soils, Soil Sci. Soc. Am. J., 40, 243-249. Fava, A. and H. Eyring, 1956, Equilibrium and kinetics of detergent adsorption—a generalized equilibration theory, J. Phys. Chem., 65, 890-898. Feddes, R.A., P.J. Kowalik, and H. Zaradny, 1978, Simulation of Field Water Use and Crop Yield, Simulation Monograph, Pudoc, Wageningen, The Netherlands. Fitter, A.H. and S.D. Sutton, 1975, The use of the Freundlich isotherm for soil phosphate sorption data, /. Soil Sci., 26, 241-246. Forsyth, P.A., 1991, A control volume finite element approach to NAPL groundwater contamination, SIAM J. Scieniif. Slat. Comput., 12(5), 1029-1057. Forsyth, P.A. and R.B. Simpson, 1991, A two phase, two component model for natural convection in a porous medium. Int. J. Numer. Methods Fluids, 12, 655-682. Forsyth, P.A., Y.S. Wu, and K. Pruess, 1995, Robust numerical methods for saturaled-unsaturated flow with dry initial conditions. Adv. Water Resour., 18(1), 25-38. Freundlich, H., 1909, Kapillarchemie; eine Darstellung der Chemie der Kolloide und verwandter Gebiete, Akademische Verlagsgesellschaft, Leipzig, Germany. Gabcr, H.M., W.P. Inskeep, S.D. Comfort, and J.M. Wraith, 1995, Nonequilibrium transport of atrazine through large intact soil cores, Soil Sci. Soc. Am., 59, 60-67. Gambolati. G., F. Sartoretto, and F.A. Uliana, 1986, A conjugate gradient finite element method for large multiaquifer systems, Water Resour. Res., 22(7), 10031015. Gan, J., S.R. Yates, W.F. Spencer, M.V. Yates, and W.A. Jury, 1997, Laboratoryscale measurements and simulations of effect of application methods on soil methyl bromide emission, J. Environ. Qua!., 26, 310-317. Gaudct, J.P., H. Jegat, G. Vachaud, and P.J. Wierenga, 1977, Solute transfer, with exchange between mobile and stagnant water, through unsaturated sand, Soil Sci. Soc. Am. J., 41(4), 665-671. Gerke, H.H. and M.Th. van Genuchten, 1993, A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media, Water Resour. Res., 29(2), 305-319. Gerke, H.H. and M.Th. van Genuchten, 1996, Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media, Adv. Water Resour., 19(6), 343-357. Giles, C.H., T.H. MacEwan, S.N. Nakhwa, and D. Smith, 1960, Studies in adsorption. XI. A study of classification of solution adsorption isotherms, and its use in diagnosis of adsorption mechanisms and in measurement of specific surface areas of solids, /. Chem. Soc., 3973-3980. Glotfelty, D.E. and CJ. Schomburg, 1989, Volatilization of pesticides, in: B.L. Sawhney and K. Brown (eds.), Reactions and Movement of Organic Chemicals in Soils, Special Publication No. 22, Soil Science Society of America, Madison, WI, pp. 181-208. Gonzalez, J. and L. Ukrainczyk, 1999, Transport of Nicosulfuron in soil columns, J. Environ. QuaL, 28(1), 101 107. Grisak, G.E., J.F. Pickens, and J.A. Cherry, 1980, Solute transport through fractured media, 2. Column study of fractured till, Water Resour. Res., 16, 731-739. Gunary, D., 1970, A new adsorption isotherm for phosphate in soil, J. Soil Sci., 21, 72-77. Hendricks, D.W., 1972, Sorption in flow through porous media, in: Fundamentals of Transport Phenomena in Porous Media, Developments in Soil Science, 2, Elsevier, Amsterdam, The Netherlands, pp. 384-392.

188

VADOSE ZONE HYDROLOGY

Hillel, D., 1993, Unstable flow: a potentially significant mechanism of water and solute transport to groundwater, in: D. Russo and G. Dagan (eds.), Water Flow and Solute Transport in Soils, Springer Verlag, New York, NY, pp. 123-135. Hills, R.G., D.B. Hudson, I. Porro, and P.J. Wierenga, 1989, Modeling one-dimensional infiltration into very dry soils, 1. Model development and evaluation, Water Resour. Res., 25(6), 1259-1269. Hoffman, D.L. and D.E. Rolston, 1980, Transport of organic phosphate in soil affected by soil type, Soil Sci. Soc, Am. J., 44(1), 46 52. Hoogmoed, W.B. and J. Bouma, 1980, A simulation model for predicting infiltration into cracked clay soil, Soil Sci. Soc. Am. /., 44, 458-461. Hopmans, J.W. and J.H. Dane, 1986, Temperature dependence of soil water retention curves, Soil Sci. Soc. Am. J., 50, 562-567. Hornsby, A.G. and J.M. Davidson, 1973, Solution and adsorbed fluometuron concentration distribution in a water-saturated soil: experimental and prediction evaluation, Soil Sci. Soc. Am. Proc., 37, 823-828. Huyakorn, P.S. and K. Nilkuha, 1979, Solution of transient transport equation using an upstream finite element scheme, Appl. Math. Model., 3, 7-17. Huyakorn, P.S. and G.F. Finder, 1983, Computational Methods in Subsurface Flow, Academic Press, New York, NY. Huyakorn, P.S., E.P. Springer, V. Guvanasen, and T.D. Wadsworth, 1986, A threedimensional finite-element model for simulating water flow in variably saturated porous media, Water Resour. Res., 22, 1790-1808. Javandel, I., C. Doughty, and C.F. Tsang, 1984, Groundwater Transport: Handbook of Mathematical Models, Water Resources Monograph Series 10, American Geophysics Union, Washington, DC. Jennings, A.A., D.J. Kirkner, and T.L. Theis, 1982, Multicomponent equilibrium chemistry in groundwater quality models, Water Resour. Res., 18(4), 1089-1096. Jury, W.A. and K. Roth, 1990, Transfer Functions and Solute Transport Through Soil: Theory and Application, Birkhaeuser Publishing, Basel. Kcshaw, D.S., 1978, The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations, /. Comput. Phys., 26, 43 65. Kirkland, M.R., R.G. Hills, and P.J. Wierenga, 1992, Algorithms for solving Richards equation for variably saturated soils, Water Resour. Res., 28(8), 2049-2058. Kluitenberg, G.J. and R. Horton, 1990, Effect of solute application method on preferential transport of solutes in soil, Geoderma, 46, 283-297. Lai, S.-H. and J.J. Jurinak, 1971, Numerical approximation of cation exchange in miscible displacement through soil columns, Soil Sci. Soc. Am. Proc.. 35, 894— 899. Langmuir, I., 1918, The adsorption of gases on plane surfaces of glass, mica, and platinum, J. Am. Chem. Soc., 40, 1361-1403. Lapidus, L. and N.R. Amundson, 1952, Mathematics of adsorption in beds: VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns, /. Phys. Chem., 56, 984-988. Leenheer, J.A. and J.L. Ahlrichs, 1971, A kinetic and equilibrium study of the adsorption of carbaryl and parathion upon soil organic matter surfaces, Soil Sci. Soc. Am. Proc., 35, 700-705. Leij, F.J., N. Toride, and M.T. van Genuchten, 1993, Analytical solutions for nonequilibrium solute transport in three-dimensional porous media, /. Hydrol., 151, 193-228. Leismann, H.M. and P.O. Frind, 1989, A symmetric-matrix time integration scheme for the efficient solution of advection-dispersion problems, Water Resour. Res., 25(6), 1133-1139.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

189

Letniowski, F.W., 1989, An overview of preconditioned iterative methods for sparse matrix equations, Research Report CS-89-26, Faculty of Mathematics, University of Waterloo, Waterloo, ON, Canada. Li, S.-G., F. Ruan, and D. McLaughlin, 1992, A space-time accurate method for solving solute transport problems, Water Resour. Res., 28(9), 2297-2306. Lichtner, P.C., 1985, Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems, Geochim. Cosmochim. Ada, 49, 779800. Lindstrom, F.T., L. Boersma, and D. Stockard, 1971, A theory on the mass transport of previously distributed chemicals in a water saturated sorbing porous medium. Isothermal cases, Soil Sci., 112, 291-300. Lindstrom, F.T., R. Haque, V.H. Freed, and L. Boersma, 1967, Theory on the movement of some herbicides in soils, Environ. Sci. Technol., 1, 561-565. Liu, C.W. and T.N. Narasimhan, 1989, Redox-controlled multiple-species reactive chemical transport. 1. Model development, Water Resour. Res., 25(5), 869-882. Mangold, D.C. and C.-F. Tsang, 1991, A summary of subsurface hydrological and hydrochemical models, Rev. Geophys., 29(1), 51-79. McLay, C.D.A., K.C. Cameron, and R.G. McLaren, 1991, Effect of time of application and continuity of rainfall on leaching of surface-applied nutrients, Aust. J. Soil Res., 29(1), 1-9. Meijerink, J.A. and H.A. van der Vorst, 1977, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput., 31(137), 148-162. Mendoza, C.A., R. Therrien, and E.A. Sudicky, 1991, ORTHOFEM User's Guide, Version 1.02, Waterloo Centre for Groundwater Research, University of Waterloo, Waterloo, ON, Canada. Mercer, J.W. and R.M. Cohen, 1990, A review of immiscible fluids in the subsurface: properties, models, characterization and remediation, J. Contam. Hydro!,, 6, 107-163. Miller, C.W. and L.V. Benson, 1983, Simulation of solute transport in a chemically reactive heterogeneous system: model development and application, Water Resour. Res., 19(2), 381-391. Milly, P.C.D., 1985, A mass-conservative procedure for time-stepping in models of unsaturated flow, Adv. Water Resour., 8, 32-36. Moench, A.F., 1984, Double-porosity models for a fissured groundwater reservoir with fracture skin, Water Resour. Res., 20, 831-846. Mohanty, B.P., R.S. Bowman, J.M.H. Hendrickx, and M. Th. van Genuchten, 1997, New piece-wise continuous hydraulic functions for modeling preferential flow in an intermittent flood-irrigated field, Water Resour. Res., 33(9), 2049-2063. Molz, F.J., 1981, Models of water transport in the soil-plant system, Water Resour. Res., 17(5), 1245-1260. Molz, F.J.M., M.A. Widdowson, and L.D. Benefield, 1986, Simulation of microbial growth dynamics coupled to nutrient and oxygen transport in porous media, Water Resour. Res., 22, 1207-1216. Narasimhan, T.N. and P.A. Witherspoon, 1976, An integrated finite difference method for analyzing fluid flow in porous media, Water Resour. Res., 12(1), 57-64. Neuman, S.P. and S. Sorek, 1982, Eulerian-Lagrangian method for advection dispersion, in: K.P. Holz, U. Meisnerr, W. Zielke, C.A. Brebbia, G.F. Pinder, and W.G. Gray (eds.), Finite Elements in Water Resources, Proceedings of the 4th International Conference, Hannover, Germany, Springer-Verlag, New York, NY, pp. 14.41-14.68. Nielsen, D.R., M.Th. van Genuchten, and J.W. Biggar, 1986, Water flow and solute transport processes in the unsaturated zone, Water Resour. Res., 22(9), 89s108s.

1 90

VADOSE ZONE HYDROLOGY

Nkedi-Kizza, P. J.W. Biggar, Selim, M.Th. van Gcnuchlen, P.J. Wierenga, J.M. Davidson, and D.R. Nielsen, 1984, On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxisol, Water Resour. Res., 20(8), 1123-1230. Oddson, J.K., J. Letey, and L.V. Weeks, 1970, Predicted distribution of organic chemicals in solution and adsorbed as a function of position and time for various chemical and soil properties, Soil Sci. Soc. Am. Proc., 34, 412-417. Omoti, U. and A. Wild, 1979, Use of fluorescent dyes to mark the pathways of solute movement through soils under leaching conditions, 1. Laboratory experiments, Soil Sci., 128(4), 28-37. Othmer, H., B. Diekkriiger, and M. Kutilek, 1991, Bimodal porosity and unsaturated hydraulic conductivity, Soil Sci., 152(3), 139-150. Pan, L. and P.J. Wierenga, 1995, A transformed pressure head-based approach to solve Richards equation for variably saturated soils, Water Resour. Res., 31(4), 925 931. Paniconi, C. and M. Putti, 1994. A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems, Water Resour. Res., 30(12), 3357-3374. Parker, J.C. and P.M. Jardine, 1986, Effects of heterogeneous adsorption behavior on ion transport. Water Resour. Res., 22, 1334-1340. Parlange, J.-Y. and D.E. Hill, 1976, Theoretical analysis of wetting front instability in soils, Soil Sci., 122, 236-239. Peters, R.R. and E.A. Klavetter, 1988, A continuum model for water movement in an unsaturated fractured rock mass, Water Resour. Res., 24, 416-430. Pruess, K. and J.S.Y. Wang, 1987, Numerical modeling of isothermal and nonisothermal flow in unsaturated -saturated fractured rock a review, in: D.D. Evans and T.J. Nicholson (eds.), Flow and Transport Through Unsaturated Fractured Rock, American Geophysics Union, Washington, DC, pp. 11 22. Rao, P.S.C.. J.M. Davidson, and H.M. Selim, 1979, Evaluation of conceptual models for describing nonequilibrium adsorption-desorption of pesticides during steady flow in soils, Soil Sci. Soc. Am. J., 43(1), 22-28. Rogers, V.C.. 1978, Migration of radionuclide chains in groundwater, Nucl. Techno/., 40(3), 315-320. Ross, P.J., 1990, Efficient numerical methods for infiltration using Richards equation, Water Resour. Rex., 26(2), 279-290. Rubin, J. and R.V. James. 1973, Dispersion-affected transport of reacting solutes in saturated porous media: Galerkin method applied to equilibrium-controlled exchange in unidirectional steady water flow, Water Resour. Res.. 9(5), 13321356. Russo, D., 1993, Stochastic modeling of macrodispersion for solute transport in a heterogeneous unsaturated porous formation, Water Resour. Res., 29, 383-397. Saad, Y. and M.H. Schultz, 1986, A generalized minimum residual algorithm for solving nonsymmetric linear systems, SI AM J. Scientif. Slat. Comput., 1. 856869. Schweich, D. and M. Sardin, 1981, Adsorption, partition, ion exchange and chemical reaction in batch reactors or in columns—a review, J. Hydrol., 50, 1-33. Selim, H.M., J.M. Davidson, and R.S. Mansell, 1976, Evaluation of a two-site adsorption—desorption model for describing solute transport in soils, Proceedings of the Summer Computer Simulation Conference, National Science Foundation, Washington, DC. Shapiro. R.E. and M. Fried, 1959, Relative release and retentiveness of soil phosphates, Soil Sci. Soc. Am. Proc., 23, 195-198. Shikaze, S.G., E.A. Sudicky, and C.A. Mendoza, 1994, Simulation of dense vapor migration in discretely fractured geologic media, Water Resour. Res., 30(7), 1993-2009.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

1 91

Sibbesen, E. 1981, Some new equations to describe phosphate sorption by soils, /. Soil Sci., 32(1), 67-74. Simunek, J. and D.L. Suarcz, 1994, Two-dimensional transport model for variably saturated porous media with major ion chemistry, [Voter Resour. Res.. 30(4), 1115-1133. Simunek, J. and M.Th. van Genuchten, 1994, The CHAIN_2D code for simulating the two-dimensional movement of water, heat and multiple solutes in variably saturated porous media, Version 1.1, Research Report No. 136. U.S. Salinity Laboratory, USDA, ARS, Riverside, CA. Simunek, J., T. Vogel, and M.Th. van Genuchten, 1994, The SWMS_2D code for simulating water flow and solute transport in two-dimensional variably saturated media, Version 1.21, Research Report No. 132, U.S. Salinity Laboratory, USDA, ARS, Riverside, CA. Simunek, J., K. Huang, M. Sejna, and M. Th. van Genuchten, 1998, The HYDRUS1D software package for simulating the one-dimensional movement of water, heat and multiple solutes in variably-saturated media. Version 2.0. 1GWMCTPS-70, Int. Ground Water Modeling Center. Colorado School of Mines, Golden, CO. Sips, R., 1950, On the structure of the catalyst surface, II, /. Chem. Phys.. 18, 10241026. Smettem, K.R.J. and C. Kirby, 1990, Measuring the hydraulic properties of stable aggregated soil, /. Hydro/., 117, 1-13. Sorek, S., 1988, Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution, Transp. Porous Media, 3, 473^89. Stevenson, F.J. (ed.), 1982, Nitrogen in Agricultural Soils, Agronomy No. 22, American Society of Agronomy, Madison, WI. Suarez, D.L. and J. Simunek, 1996, Solute transport modeling under variably saturated flow conditions, in: P.C. Lichtner, C.I. Seefel, and E.H. Oelkers (eds.), Reactive Transport in Porous Media, Reviews in Mineralogy, Vol. 34, Mineralogy Society of America, Washington, DC, pp. 229 268. Sudicky, E.A., 1989, The Laplace transform Galerkin technique: a time-continuous finite element theory and application to mass transport in groundwater. Water Resour. Res., 25(8)/1833-1846. Sudicky, E.A., 1990, The Laplace transform Galerkin technique for efficient timecontinuous solution of solute transport in double-porosity media, Geoderma, 46, 209-232. Sudicky, E.A. and P.S. Huyakorn, 1991, Contaminant migration in imperfectly known heterogeneous groundwater systems. Reviews of Geophysics, 29, Supplement, U.S. National Report to the International Union of Geodesy and Geophysics, 1987 1990, pp. 240 253. Sudicky, E.A. and R.G. McLaren, 1992. The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations, Water Resour. Res., 28(2), 499-512. Sudicky, E.A., R.W. Gillham, and E.O. Frind, 1985, Experimental investigation of solute transport in stratified porous media 1. The nonreactive case, Water Resour. Res., 21(7), 1035-1041. Taylor, A.W. and W.F. Spencer, 1990, Volatilization and vapor transport processes, in: Pesticides in the Soil Environment, SSSA Book Series No. 2, Soil Science Society of America, Madison, WI, pp. 213-269. Therrien, R. and E.A. Sudicky, 1996. Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media, /. Contam. Hydro!., 23, 1-44. Toride, N., F.J. Leij, and M.T. van Genuchten, 1993, A comprehensive set of analytical solutions for nonequilibrium transport with first-order decay and zeroorder production, Water Resour. Res., 29(7), 2167-2182.

192

VADOSE ZONE HYDROLOGY

Unger, A.J.A., P.A. Forsyth, and E.A. Sudicky, 1996, Variable spatial and temporal weighting schemes for use in multi-phase compositional problems, Adv. Water Resour., 19(1), 1-27. Valocchi, A.J., Street, R.L., and P.V. Roberts, 1981, Transport of ion-exchanging solutes in ground-water: chromatographic theory and field simulation. Water Resour. Res., 17(5), 1517-1527. Vanclooster, M., P. Viaene, J. Diels, and K. Christiaens, 1994, WAVE, a mathematical model for simulating water and agrochemicals in the soil and vadose environment, Reference and User's Manual, Release 2.0, Institute for Land and Water Management, Katholieke Universiteit Leuven, Leuven, Belgium. VanderKwaak, J.E., P.A. Forsyth, K.T.B. MacQuarrie, and E.A. Sudicky, 1995, WATSOLV Sparse Matrix Iterative Solver Package User's Guide, Version 1.01, Waterloo Centre for Groundwater Research, University of Waterloo, Waterloo, ON, Canada. van der Vorst, H., 1992, A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, S1AM J. Scientif. Suit. Comput., 13, 631-644. van der Zee, S.E.A.T.M. and W.H. van Riemsdijk, 1994, Transport of reactive solutes in soils, in: M.Y. Corapcioglu (ed.), Advances in Porous Media, 2, Elsevier Science, B.V., Amsterdam, The Netherlands, pp. 1 105. van Genuchten, M.Th., 1981, Non-equilibrium transport parameters from miscible displacement experiments, Research Report No. 119, U.S. Salinity Laboratory, USDA, ARS, Riverside, CA. van Genucthen, M.Th., 1985, A general approach for modeling solute transport in structured soils, Proceedings of the 17th International Congress, Hydrogeology of Rocks of Low Permeability, Jan. 7-11, Tucson, AZ, Memoires Int. Assoc. Hydrogeol., 17(2), 513-526. van Genuchten, M.Th., 1987, A numerical model for water and solute movement in and below the root zone, Unpublished Research Report, U.S. Salinity Laboratory, USDA, ARS, Riverside, CA. van Genuchten, M.Th. and R.W. Cleary, 1979, Movement of solutes in soil; computer simulation and laboratory results, in: G.H. Bolt (ed.), Soil Chemistry B. Physico-Chemical Models, Elsevier, New York, NY, pp. 349-386. van Genuchten, M.Th, and F.N. Dalton, 1986, Models for simulating salt movement in aggregated field soils, Geoderma, 38, 165-183. van Genuchten, M.Th. and W.G. Gray, 1978, Analysis of some dispersion corrected numerical schemes for solution of the transport equation, Int. J. Numer. Methods Eng., 12, 387^104. van Genuchten, M.Th. and R.J. Wagenet, 1989, Two-site/two-region models for pesticide transport and degradation: theoretical development and analytical solutions, Soil Sci. Soc. Am. J., 53, 1303-1310. van Genuchten, M.Th., J.B. Kool, and J.C. Parker, 1987, Parameter estimation for various contaminant transport models, in: C.A. Brebbia and G.A. Keramidas (eds.), Reliability and Robustness of Engineering Software, Elsevier, New York, NY, pp. 273-295. van Genuchten, M.Th., J.M. Davidson, and P.J. Wierenga, 1974, An evaluation of kinetic and equilibrium equations for the prediction of pesticide movement through porous media, Soil Sci. Soc. Am. Proc., 38, 29-35. van Genuchten, M.Th., P.J. Wierenga, and G.A. O'Connor, 1977, Mass transfer studies in sorbing porous media, III. Experimental evaluation with 2,4,5,-T, Soil Sci. Soc. Am. J., 41, 278-285. Wagenet, R.J. and J.L. Hutson, 1987, LEACHM: Leaching Estimation And CHemistrv Model, a process-based model of water and solute movement, transformations, plant uptake and chemical reactions in the unsaturated zone, Continuum 2, Dept. of Agronomy, Cornell University, Ithaca, NY.

ADVANCES IN VADOSE ZONE FLOW AND TRANSPORT MODELING

193

Walsh, M.P., S.L. Bryant, R.S. Schechter, and L.W. Lake, 1984, Precipitation and dissolution of solids attending flow through porous media, AIChE J., 30(2), 317-328. Walter, A.L., E.G. Frind, D.W. Blowes, C.J. Ptacek, and J.W. Molson, 1994, Modeling of multicomponent reactive transport in groundwater. 1. Model development and evaluation, Water Resour. Res., 30(11), 3137-3148. Wang, D., S.R. Yates, J. Gan, and W.A. Jury, 1998, Temperature effect on methyl bromide volatilization: permeability of plastic cover films, J. Environ. Qual., 27(4), 821-827. Wang, J.S.Y., 1991, Flow and transport in fractured rocks, Rev. Geophys., 29, Supplement, 254-262. Wheatcraft, S.W. and J.H. Cushman, 1991, Hierarchical approaches to transport in heterogeneous porous media, Rev. Geophys., 29, Supplement, 261-267. Whisler, F.D., A. Klute, and R.J. Millington, 1968, Analysis of steady-state evaporation from a soil column, Soil Sci. Soc. Am. Proc., 32, 167-174. White, R.E., J.S. Dyson, Z. Gerstl, and B. Yaron, 1986, Leaching of herbicides through undisturbed cores of a structured soil, Soil Sci. Soc. Am. J., 50, 277283. Wilding, L.P. and C.T. Hallmark, 1984, Development of structural and microfabric properties in shrinking and swelling clays, in: J. Bouma and P.A.C. Raats (eds.), Proceedings of the JSSS Symposium on Water and Solute Movement in Heavy Clay Soils, Publication 37, International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands, pp. 1-18. Wolfsberg, A.V. and D.L. Freyberg, 1994, Efficient simulation of single species and multispecies transport in groundwater with local adaptive grid refinement, Water Resour. Res., 30, 2979-2991. Yates, S.R., F.F. Ernst, J. Gan, F. Gao, and M.V. Yates, 1996, Methyl bromide emissions from a covered field: II. Volatilization, /. Environ. Qua!., 25, 192-202. Yeh, G.T., 1986, Orthogonal-upstream finite element approach to modeling aquifer contaminant transport, Water Resour. Res., 22(6), 952-964. Yeh, G.T., 1990, A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations, Water Resour. Res., 26(6), 1133-1144. Yeh, G.T. and V.S. Tripathi, 1989, A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components, Water Resour. Res., 25(1), 93-108. Yeh, G.T. and V.S. Tripathi, 1991, A model for simulating transport of reactive multispecies components: model development and demonstration, Water Resour. Res., 27(12), 3075-3094. Zimmerman, R.W., G. Chen, T. Hadgu, and G.S. Bodvarsson, 1993, A numerical dual-porosity model with semianalytical treatment of fracture/matrix (low, Water Resour. Res., 29(7), 2127-2137. Zysset, A., F. Stauffer, and T. Dracos, 1994, Modeling of chemically reactive groundwater transport, Water Resour. Res., 30(7), 2217-2228.

7

Diffusion-Linked Microbial Metabolism in the Vadose Zone

J. E. WATSON R. F. HARRIS

Y. LIU W. R. GARDNER

Figure 7.1 is a schematic of nutrient and contaminant transformations and cycling in the vadose zone. As detailed in Harris and Arnold (1995), higher plants take up C, N, P, and S in their most oxidized forms and use, via photosynthesis, the Sun's energy and low-energy electrons from the oxygen in water to convert the oxidized forms of these essential elements into the relatively high energy reduced forms comprising plant biomass. Following plant death, the biomass residues enter the soil and are attacked by soil organisms as a source of food. The plant residues are depolymerized and the reduced, high-energy monomers are assimilated in part into soil organism biomass, and in part are used as electron donors to combine with the most thermodynamically efficient electron acceptors for dissimilatory energy generation to drive growth and maintenance reactions. In aerobic zones, oxygen is the preferred electron acceptor as long as it is nonlimiting. Death of soil organisms produces dead biomass which re-enters the biological reactor. Ultimately, via respiration in aerobic soils, all the reduced C, N, P, and S materials are released as their oxidized forms, and oxygen is reduced to water to complete the cycle. Ideally, the cycle is conservative, particularly from the standpoint of nonleakage of nutrients, such as nitrate, into the groundwater. Similarly, contaminants entering the vadose zone, either as a function of agronomic use or by accident, should ideally be integrated into the natural nutrient cycles and converted to harmless by-products for assimilation and dissimilation by soil organisms and higher plants (Liu, 1994). Management of nutrient and contaminant transformations by the soil organisms requires a thorough understanding of the ecophysiological and solute transport ground rules that control the nature and rates of transformation options available to the soil organisms.

DIFFUSION-LINKED MICROBIAL METABOLISM IN THE VADOSE ZONE

195

Figure 7.1 Nutrient and contaminant degradation and cycling in the vadose zone.

Tn models of chemical transport and transformation through the vadose zone, colonies of microorganisms are frequently treated as a homogeneous biofilm reactor (Grant and Rochettc, 1994). Often, modeling efforts are focused on environmental conditions external to the microbial colony. This consideration of the colony as a biofilm with relatively constant nutrient uptake rates ignores the growth differentiation that occurs as the colony develops. Much work in recent years, however, has enhanced the recognition of the geometric considerations of solute availability to

196

VADOSE ZONE HYDROLOGY

microorganisms. Wimpenny (1990), provides a detailed review of diffusion-limited growth of bacterial colonies. He identifies both molecular diffusion through the medium that surrounds the bacterial cell and molecular diffusion through the growing cell mass as two important diffusive processes that limit colony growth. One objective of the conference at which this work was presented was to bring together the physicist and microbiologist to consider transport processes at different scales; this chapter explores the implications of diffusive transport at the microbial scale. Most of the work in which the reaction kinetics in the biofilm arc considered uses Monod kinetics to describe the response of organisms to substrate concentration (e.g. Bader, 1982; Rittman, 1993; Buffiere et al, 1995). Conversely, microbiologists focus on Michaelis-Menten kinetics or zero-order kinetics for substrate concentrations greater than some measurable, kinctically meaningful, amount, since Monod kinetics are not appropriate for many circumstances; for instance, the case of oxygen kinetics under aerobic conditions (Rittman, 1993; Walter and Jordening, 1995). For this reason, we have considered Michaelis-Menten kinetics as the appropriate kinetic response function at low substrate concentrations. Using Michaelis-Menten kinetics, Harms and Zehnder (1994) attempted to obtain a modified Michaelis-Menten constant, which they termed Kt, for a bacterial cell suspended in an unstirred solution, and a second modified Michaelis-Menten constant, which they termed K,'att for a bacterial cell attached to a solid surface. The difference between the two modified terms was due to the different geometries (spherical for suspended cells and hemispherical for attached cells) of the substrate concentration gradient that forms around the cells as a result of their consumption of substrate. The modified constants were related to the Michaelis-Menten constant normally obtained from stirred solution studies by adding an appropriate term to account for the geometry of the substrate concentration isopleths around the cells. The calculations accounted for cell density. Experimental results presented by these authors demonstrated the approach to be not entirely satisfactory. The experimental K,>at,-v'd\ue exceeded the theoretical ,K,'ar,-value by factors of 2 (at the lowest cell density) to 8 (at the highest cell density). In spite of considering cell density in their formulation of the problem, the approach did not account for it very well. We suggest that these results offer a concrete example that approaches to simplify bacterial growth from accounting for individual cell responses as a function of the substrate concentration at a particular location within the colony cannot provide adequate insight into biofilm responses to changes in surrounding environmental conditions. Of particular concern is the common tactic of determining an "efficiency" term to relate bulk solution substrate concentrations to a kinetic response by a biofilm, since changes in bulk solution concentrations will necessarily change the overall, "averaged" biofilm kinetics, and consequently change the "efficiency" term. Our goal in this chapter is to emphasize the importance of considering a bacterial colony as a dynamic collection of cells that cannot be easily "parameterized" to account for observed responses under variable environmental conditions. We argue that determination of kinetic parameters in stirred batch culture can be used to predict experimental results in "nonstirred" conditions, and we present a framework of equations for integrating physiological and physical properties of bacterial colonies and the diffusion properties of substrates. The application of the equations

DIFFUSION-LINKED MICROBIAL METABOLISM IN THE VADOSE ZONE

1 97

is illustrated by evaluating the effect of physiological and substrate diffusion properties on the relative thickness of the substrate-unrestricted zone of an aerobic bacterial colony. Our objective is not so much to expand the theory of microbial growth kinetics in response to natural environments, but is rather more to emphasize the importance of recognizing microscale responses in the vadose zone.

Theory Physiological and Metabolic Properties of Bacterial Colonies Bacteria in the vadose zone are commonly associated with solid surfaces, where they grow as colonies from a few cells to millions of cells in size. The cells making up a colony are in different metabolic states depending on prevailing environmental conditions outside and within the colony. Three major zones of different metabolic states may be recognized based on substrate availability: (1) a zone in which the cells are substrate concentration (S")-unrestricted and are growing at their maximum specific growth rate (/Limax) with respect to prevailing environmental conditions, (2) a zone in which the cells are S-restricted and are growing at an S-dcpendent, reduced specific growth rate (0 < /A < ju, max ), and (3) a zone in which the cells are so Srestricted that they are unable to grow at all (ft — 0). Three basic cases may be recognized: case 1, a colony consisting of only substrate-unrestricted cells; case 2, a colony consisting of substrate-unrestricted and substrate-restricted growing cells; and case 3, a colony consisting of all three zones. Figure 7.2 includes two schematics of a case 3 bacterial colony growing on a porous medium with dissolved substrates that diffuse into the colony from the porous medium, and gaseous and/or dissolved substrates that diffuse into the colony from the surrounding atmosphere or aqueous medium. Case 3a represents the case for a dissolved substrate (concentration S) that diffuses from the porous medium into the colony ultimately becoming growth-limiting; and case 3b represents the case for a gaseous or dissolved substrate (concentration G) that diffuses from the surrounding atmosphere or aqueous medium into the colony ultimately becoming growth-limiting. The height locations (h), specific growth rates (ft), and substrate concentrations (S, G) that define the colony zones are identified directly in figure 7.2. For case 3a, the terminology is defined as follows: h0 the colony height (L) at the porous medium/colony interface. At this interface, 5 = S0, and G = Gso > G* h* the colony height (L) at 5*, and G = G,. > G* hc the colony height (L) at Sc, and G = GK. > G* hb the colony height (L) at S/,, and G = Gsh > G* where S0 is S at the 5-supply interface (porous medium/colony interface); G vo , G5-, Gsc, and Gsh are the G-values at S0, S*, Sc, and Sh, respectively; G* is the G-value below which G uptake rate limits growth rate (above G*, internal metabolism rather than G uptake limits growth rate); S* is the 5-value below which 5 uptake rate limits

1 98

VADOSE ZONE HYDROLOGY

Figure 7.2 Schematics of bacterial colonies on solid porous media showing zones of substrate-unrestricted growth (shaded), substrate-restricted growth (middle), and substrate-restricted no growth (third). The case for diffusion of the growth-limiting substrate from the solid phase is on the left (case 3a), and for diffusion from the atmosphere is on the right (case 3b). As exemplified by an aerobic bacterial heterotroph growing on glucose, ammonium, and inorganic phosphate, the basic equations for growth, exogenous maintenance, endogenous decay, death, and cryptic growth are listed in order below the schematics.

growth rate; Sc is the S-value below which S uptake rate (and thus S-driven growth rate) is zero; and Sh is the 5-value at the outer boundary of the colony (colony/ atmosphere interface). For case 3b (figure 7.2), G is used as a special cse for S, and the terms G0, G*, Gc and Gh are defined as for the analogous S-terms. To retain h/, as the top of the colony, the h terminology for case 3b is defined as follows: h0 is the colony height at Gh; h" is the colony height at G*; hc is the colony height at Gc; and hb is the colony height at G0. Mechanistically, as substrate diffuses into the colony, substrate consumption occurs with a progressive decline in substrate concentration with distance. Eventually, at h*, the substrate concentration reaches 5* or G*. From h* to hc, substrate uptake rate decreases with decreasing substrate concentration until, at /!,., it becomes zero.

Specific Rates of Biomass Change in the Zones The specific rate of biomass change (r, time"1) is a function of biomass gain related to growth on exogenous substrates (qxg — fji), loss due to endogenous decay (qxm) and death (qxj), and gain due to cryptic growth on dead cells (qxcg) (figure 7.2):

DIFFUSION-LINKED MICROBIAL METABOLISM IN THE VADOSE ZONE

199

The relative importance of the g t terms varies with metabolic zone. For example, for the nutrient-unrestricted zone, r ~ Mmax< since endogenous decay and death (and thus also cryptic growth on dead cells) are likely to be minimal. Alternatively, for the zone of zero 5-supported growth (^ = 0), r < 0 because qxm and qxl! will exceed q^.a unless there is a large amount of dead biomass input from a previous time. Specific Rates of Metabolism in the Zones As illustrated in the text of figure 7.2, the specific rates of substrate uptake and product formation (
For an individual qx reaction.

For a
For example, for the specific rate of OT consumption by one of the colony zones in the case 3a and 3b colonies represented in figure 7.2,

For the oxyen-restricted zones in the case 3b colony, alternate electron acceptors would be increasingly preferred by facultative anaerobes as oxygen became increasingly more restricted (Harris and Arnold. 1955). with related changes in all the mass balance biomass growth, decay, and maintenance reactions. The relationship between traditional dry weight-based specific rates of substrate consumption or product formation, and the colony volume-based metabolic rates (£>„., dry weight metabolite/volume wet colony/time) used in the diffusion equations, is given by

200

VADOSE ZONE HYDROLOGY

where SG is the specific gravity of the cells (dry weight cells/volume wet cells), px is the wet cell density of the colony (volume vvet cells/volume colony), WWD is the wet weight density of cells (wet weight cells/wet volume cells), and 0X is the cell water content (mass water in cells/volume of cells). A typical WWD for bacterial cells is 1.2 g wet cells/cm3 wet cells, and a typical water content is 0.7 g water/g vvet cells (i.e., 0.3 g dry cells/g wet cells), giving an SG of 0.36 g dry weight cells/cm3 wet cells (Harris, 1981). For S-unrestricted conditions, the specific rate of substrate uptake for growth and maintenance is dictated by the maximum specific growth rate:

where q* is the specific rate of substrate uptake for growth and maintenance at Mmax> As/x is the specific growth and maintenance requirement of X for S, Yx/s is the specific growth yield of X on S, q*/, is qs for ^ max growth, and Asb/K is the specific growth requirement of X for S. For S-restricted conditions, the specific rate of growth is dictated by the substrate uptake for growth and maintenance (qs):

For S < Sc, qs = 0, and equation (7.8) becomes

Relationship of Specific Rate of Substrate Consumption to Substrate Concentration For ,5-restricted conditions, the relationshp of qs to 5 may be represented by the Michaelis-Menten type kinetics (Harris, 1981; Button, 1985; Andrews and Harris, 1986). For negligible Sc,

where ^max is the maximum specific rate of S uptake, and Ks is the half-saturation coefficient for S uptake (S at which qs = 0.5<7STn;lx). Rearrangement of equation (7.10) for qs = q* and S = S*, gives

For the zone of zero 5-related growth,

The S*-modified Michaelis-Menten relationship (equations 7.10 and 7.11) docs not lend itself to development of analytical solutions of the diffusion equation for

DIFFUSION-LINKED MICROBIAL METABOLISM IN THE VADOSE ZONE

201

many situations. Little precision is lost, in view of the many other uncertainties, by replacing equation (7.11) by a linear relationship (Blackman, 1905). This is obtained by denning S** as S at the intercept of q*s and the 0.5 qsmmIKs line. This gives qs as zero order with respect to S for S > S**, as defined by equation (7.7), and first order for S < S**. For negligible 5C,

From equation (7.13) with qs = q* and S = S**,

Substrate Diffusion For this chapter, we will consider in depth only one-dimensional, three-dimensional, and cylindrical diffusion for the substrate-unrestricted zone. One-Dimensional Diffusion The vertical lines cross sectioning the colony diagrams in figure 7.2 identify the boundaries for the simple case of one-dimensional diffusion of substrate through the colony interface into the colony. As substrate diffuses into the colony and is consumed at the rate needed to support Amax> there is a progressive decline in 5 with distance until 5 reaches S* at a colony height of ti*. The following example focuses on a case 3a system for an aerobic heterotroph (Harris and Arnold. 1995) with the electron donor/carbon source considered as the ultimately growth-limiting substrate (S). For one-dimensional diffusion, the colony is, in principle, constrained to onedimensional growth. Growth into the agar is prevented. The assimilatory and dissimilatory electron donor sources are present at some initial concentration (S0) in the agar. Oxygen, the dissimilatory electron acceptor, is assumed to be in equilibrium with oxygen dissolved in the colony at the colony-atmosphere interface. It is assumed that no oxygen is available in the agar or from diffusion through the sides of the colony. Other essential nutrients are present in the agar medium as needed. The colony density is assumed to be constant. Diffusion Equations

The general equation describing one-dimensional substrate diffusion through the colony and simultaneous substrate uptake by the colony is given by

with general initial and boundary substrate conditions of

202

VADOSE ZONE HYDROLOGY

where S represents the concentration of substrate within the colony at some time t and some distance Z, measured from the colony substrate supply interface (i.e., the colony-agar interface, unless specified otherwise); Z is measured in the direction of decreasing substrate concentration; and D is the difusion coefficient for the substrate diffusing through the colony (Currier, 1961). The symbol Q(S) represents the substrate uptake rate per unit volume of colony, consistent with equation (7.6) for 2,, = Q,:

The time-dependent colony height is designated hh(i), with ha representing the height of one organism and the initial height of the colony. Substrate Profile If a steady-state solution to equation (7.15) exists (i.e., for the case dS/dl = 0), it can be obtained for the following boundary conditions:

From Kamke (1948, section 6.23.2) the steady-state form of equation (7.15), with Q(S) defined by equations (7.17), (7.10), and (7.11), can be integrated, subject to the boundary conditions described by equation (7.15), to yield

The negative sign was chosen from physical considerations (i.e., S decreases as Z increases). When S > S* throughout the entire colony, Q(S) is constant. Equation (7.16) can then be integrated to yield

where h/, is the colony height measured from the colony/substrate supply interface to the colony boundary, and S- is the substrate concentration at Z (usually taken as S0 at Z = 0). (It is worth repeating that the colony/substrate supply interface may be either the colony/agar interface or the colony/atmosphere interface, depending upon whether the substrate of interest is agar-supplied or atmosphere-supplied.) If hi represents the colony height when S/, = S*. hi can be calculated as

Equation (7.21) is the solution presented by Pirt (1975), with S* < S*)7 but is described by a Michaelis-Menten relationship in the portion of the colony where S < S*. Equation (7.2) is integrated as

DIFFUSION-LINKED MICROBIAL METABOLISM IN THE VADOSE ZONE

203

where S\ and h} represent the substrate concentration of interest and its corresponding location within the colony. For the portion of the colony where 5 > S*, an analytical solution can be obtained for equation (7.22); the integration must be carried out numerically for the portion of the colony where Michaelis-Menten kinetics apply (i.e., where Sc < S < S*). Alternatively, analytical solutions can be obtained from equation (7.22) for the zero-order (5 > S**) and first-order relationships (S < 5**) from the Blackman simplification [equations (7.13) and (7.14)]. Equation (7.22) can then be solved to find the approximate colony location /i] of some substrate concentration 5; > S^. for given boundary substrate concentrations.

Diffusion into a Hemispherical and a Concave Cylindrical Colony Equation (7.18) through (7.22) were integrated for the one-dimensional case in which oxygen diffuses from one face of a microbial colony. It is also of interest to consider the case of a hemispherical colony of organisms situated on a planar substrate for which the dissolved oxygen is maintained at a constant value at the outer perimeter of the colony. Diffusion is assumed be radially symmetric toward the center of the circular interface between the colony and the substrate. Although this is a case 3b system with oxygen as the ultimately growth-limiting substrate, for simplicity we will retain the generic 5 rather than G terminology for oxygen concentration. The solution for the three-dimensional analog to equation (7.21) is quite straightforward (Watson, 1982):

where amax is the maximum radius of a hemisphere at the center of which the concentration is reduced to S*. All other symbols have the same meaning as in equation (7.21). It is of interest to compare the maximum height of a cylindrical colony that is operating at a maximum metabolic rate with the maximum radius. Ths is done by taking the ratio of equation (7.23) to equation (7.21). This ratio gives the result a* = (3) 1/2 /4. One can also compare the total metabolic rate for the respective volumes of radius a* and height hi and a hemisphere of radius a*. This ratio is simply (3) 1/2 /2 or 0.866. Thus, it is obvious, given the approximate nature of all the assumptions necessary to evaluate the parameters in the equations, that the geometry is not very significant. We neglect here the zone beyond that of maximum uptake—that is, the zone in which reduced oxygen concentration reduces the rate of activity. Watson (1982) has shown that when S0 is that of a normal atmosphere, this zone is of the order of magnitude of the maximum uptake zone, though, of course, the total specific (per

204

VADOSE ZONE HYDROLOGY

unit volume) activity in this zone is significantly reduced, say, by roughly 75%. Thus, we can estimate the metabolic activity of a colony or colonies of microorganisms if we know the surface area covered. A more serious error is probably introduced by the assumptions that we must make about the density of the microbial colony.

Application Equation (7.21) was used to estimate the thickness of the zone (z*) in the colony within which the cells would grow exponentially before the substrate considered would limit the colony growth rate. For greater thicknesses, substrate would not be available at concentrations greater than S* to colony organisms farther from the substrate source. For case 3a (figure 7.2), the thickness of the S-unrestricted zone is equal to the height of the colony at S = S*—that is, z* = h*; for case 3b, z* = hb-h*. Table 7.1 presents the physiological and substrate diffusion properties controlling the thickness of the S-restricted zone, together with the corresponding z* values, for bacterial colonies growing on minimal agar culture media. The physiological mass balance properties represent those typical of an aerobic heterotrophic bacterial colony (Harris, 1981, 1982; Heijnen and Van Dijken, 1992; Harris and Arnold, 1995), as summarized in the text of figure 7.2. For simplicity, and consistent with current concepts (Heijnen and Van Dijken, 1992; Harris and Arnold, 1995), table 7.1 bacterial properties are confined to the growth reaction (i.e., exogenous maintenance, decay, death, and cryptic growth are assumed to be negligible), unless specified otherwise (e.g., table 7.1, no. 5). Equations (7.7) and (7.17) were used to obtain qs SGpx = Q(S) in equation (7.21); and equation (7.11) was used to derive S*. The bacterial properties reference on a typical N-mole based composition of C^vOi.sNPo.os . . . (total formula weight, 103.5 g), and, unless specified otherwise, a typical aerobic Yxfs of 0.5 g dry cells/g glucose independent of specific growth rate; the related molar /(^-values (derived as described by Harris and Arnold, 1995) are consistent with the growth reaction in the text of figure 7.2. Substrate affinity coefficients are consistent with Button (1985) and Tempest and Neijssel (1978). Substrate diffusion coefficients in water were obtained from Bruins (1929). The agar media composition is typical of a minimal glucose mineral salts medium that contains glucose at a relatively low level of 1 g/L, excess N as ammonium, and buffered by phosphate at a level vastly exceeding the assimilatory P needs for growth (Pirt, 1975). As shown in table 7.1, the thickness of the ^-unrestricted zone (z*) increases with decreasing specific growth rate. For example, for O2 with Sg = 8 mg/L, z* increases from 23 jj.ro. for the relatively fast-growing organism of /imax = 0.3 h"1 (doubling time of 0.69/0.3 = 2.3 h) to 74 /mi shown by the slow-growing organism of Mmax = 0-03 h~' (23 h doubling time). In all cases, oxygen will limit the colony growth rate before other substrates listed in table 7.1 become limiting. Growth yield data for the facultative anaerobe (table 7.1, no. 4) were obtained from Heijnen and Van Dijken (1992). The facultative anaerobe response illustrates the "Pasteur" effect (Pirt, 1975) of increased rate of glucose consumption that accompanies a shift from aerobic to anaerobic conditions, stemming from the organism's

Table 7.1 Physiological and Physical Properties Controlling the Thickness of the Substrate-Unrestricted Zone in Bacterial Colonies on Agar Media: One-Dimensional Diffusion Cell and Colony Properties

Substrate

Specific Growth Specific Maximum Specific Reaction Uptake Rale Speciiic Growth Yield Coefficicnl Of 5 at Hma» Growth Rale (}',,/] g dry (A,,,.,) mole (.?;> g 5/g dry cells-h l^mu>) 1'h cells/g .V w/mole .v

Substrate Diffusion Properties

Uptake Affinity Coefficient for S (K,)

'A/
/ytnole Sll.

/
Colony Cell Specific Cellular Gravity (.«?) Density Diffusion g dry cells/ (/\) cm* wet Coefficient in cm* wet cells/cm1 Water cells colony (/)c) cm~/h

ConcenMinimum Thickness tration at ConcenofSColony tration for Unrestricted .S-Supply Boundary Zone /<»» (S') tig S'/cnv (.S,,) /
System No.

Typical Aerobic Helfrotrc,ipluc G>oir;/i on Minimal Agar Media Glucose Oxygen Ammonium Phosphate

0.300

050

-1.148 -2541 -1.000 -0.080

0.600 0.236 0.052 0.023

0.70

10.0 1.0 1.0 1.0

1.802 0.032 0.018 0.097

0.36

0.7000

0.022 0.068 0.025 0.029

4.20 0.07 0.04 0.2.3

1000 8 300 3000

93 23 185 959

1

Glucose Oxygen Ammonium Phosphate

0.100

0.50

-1.148 -2.541 -1 000 -0.080

0.200 0.079 0.017 0.008

0.70

10.0 1.0 1.0 1.0

1.802 0.032 0.018 0.097

0.36

0.7000

0.022 0.068 0.025 0.029

4.20 0.07 0.04 0.23

1000 8 300 3000

161 40 320 1662

T

Glucose Oxygen Ammonium Phosphate

0.030

050

-1.148 -2.541 -1.000 -0.080

0.060 0.024 0.005 0.002

0.70

10.0 1.0 1.0 1.0

1.802 0.032 0.018 0.097

0.36

0.7000

0.022 0.068 0.025 0.029

4.20 0.07 0.04 0.23

1000 8 300 3000

295 74 584 3034

3

0.022

4.20

1000

93 63

4

4.20

1000

93 81 51

5

Aerobic and Perm enwrive Facltlldtive Anaerobe Glucose

0.300 0200

0.50 0.15

-1.148 -3.828

0.600 1.33.1

0.45 1.00

10.0

1.802

0.36

0.7000

Atnnu.iniuin A.\,*iiinitalii:ig find Dinilragen Fixing Azotobacter Glucose

0.300 0.200

0.50 0.25 0.10

-1.148 -2.297 -5.742

0.600 0.800 2.000

0..30 0.40 1.01)

10.0

1.802

0.36

07000

0.022

206

VADOSE ZONE HYDROLOGY

ecophysiological strategy of maintaining its /xma). relatively high, independent of aeration conditions. Mechanistically, in order to maintain /^max in the face of a decreased Yxfs associated with the lower energy of the anaerobic dissimilatory reaction, the q* must be increased in accordance with equation (7.7). In table 7.1 (no. 4), to better illustrate that qs may not always be fully expressed, q*/qimm 's set at 1 for the anaerobic condition. This gives
Table 7.2 Physiological and Physical Properties Controlling the Thickness of the Substrate-Unrestricted Zone in Bacterial Colonies in the Vadose Zone: One-Dimensional Diffusion Substrate Diffusion Properties

Cell and Colony Properties

Substrate

Specific Growth Specific Maximum Specific Reaction Uptake Rate Specific Growth Yield Coefficient of 5 at Mnxn Growth Rate ( }•',;,) g dry (A,,,J mole (
Uptake Affinity Coefficient for S (K,) ^irnole tf/?™, S.'L

/
Colony ConcenCell Specific Cellular Minimum tration at Thickness Diffusion ConcenColony of SGravity (SG) Density 1 g dry cells/ (pf J e m wet Coefficient in tration for S-Suppiy Unrestricted 1 1 cm wet cells/cm Water M nii s (>V*) Boundary Zone fig Stem (,$„) /fg 5/ctir (-') /jm cells colony (Do) cm'/h System No.

'^ymogcnous Soil Contiilivrn Glucose Oxygen Ammonium Phosphate

0.300

0.50

-1.148 - 2 541 -1.000 -0.080

0.600 0.236 0.052 0.023

0.70

1.0 1.0 1.0 0.10

1.802 0.032 0.018 0.010

0.36

0.022 0.068 0.025 0.029

4.20 0.07 0.04 0.02

100 8 10 0.10

19 23 34 5

1

0.7000

0.022 0.068 0.025 0.029

0.42 0.07 0.04 0.02

100 8 10 0.10

51 40 58 8

2

0.7000

AutoclnluJ/WU.T Soil Condition* Glucose Oxygen Ammonium Phosphate

0. 1 00

0.50

-1.148 -2.541 -1.000 -0.080

0.200 0.079 0.017 0.008

0.70

10.0 1.0 1.0 0.10

0.180 0.032 0.018 O.OU)

0..36

Ox rg<'» Rfldritinx

Glucose

0003

0.50

-2.541

0.002

0.70

I.I)

0032

0.36

0.7000

0.068

0.07

8

233

3

0.100

0.50

-2.541

0.079

0.10 0.90

1.0

0.032

0.36

0.7000

0.068

0.004 0.29

8

41 40

4

0 100

0.50

-2.541

0.079

0.70

10.0 0.1

0.320 0.003

0.36

0.7001)

0.068

0.75 0.01

8

39 41

5

0,100

050

-2.541

0.079

0.70

1.0

0.032

0.46 0.26

07000

0.068

0.07

8

3f> 48

6

0.100

0.50

-2.541

0.079

0.70

1.0

0.032

OJ6

09000 0.7000 O.SOOO 0.3000

0.068

0.07

8

21 40 62 94

7

0.100

0.50

-2.541

0.079

0.70

1.0

0.032

0.36

0.7000

0.068

0.07

8

40 20 12 1

8

0.8 0.08

208

VADOSE ZONE HYDROLOGY

Conclusions Mass balance kinetic equations for integrating the physiological and physical properties of bacterial colonies and the diffusion properties of substrates arc presented in this chapter. The cells that make up a colony are in different metabolic states depending on prevailing environmental conditions external to and within the colony. Three major zones of different metabolic states may be recognized based on substrate availability: (1) a zone in which the cells are substrate concentration (S)-unrestricted and are growing at their maximum specific growth rate with respect to prevailing environmental conditions, (2) a zone in which the cells are 5-restricted and arc growing at an 5-dependent, reduced specific growth rate, and (3) a zone in which the cells are so ^-restricted that they are unable to grow at all. Controlling physiological properties include molar empirical composition of living and dead biomass, specific rates of biomass growth, exogenous maintenance, endogenous decay, death, and cryptic growth. Metabolic rate equations involve specific rates of change of biomass and associated redox-based mass balance metabolic reactions. Substrate uptake is based on Michaelis-Menten kinetics modified to recognize that S uptake rate capability ( 9i-max) is unlikely to limit maximum specific growth rate (At max )» thereby allowing existence of a critical S(S*) above which the specific uptake rate („) properties on the relative thickness of the S-unrestricted zone (z*) of an aerobic bacterial colony. For one-dimensional diffusion, z* is relatively insensitive to g*/gr,smax ratio, Ks and SG, and most sensitive to/? v , At max and S0. The very low dissolved P concentrations that commonly prevail in soil identify that P could be a major factor that limits z* in aerobic vadose zones. Comparison of one- and three-dimensional diffusion equations for the Sunrestricted zone shows that geometry is not very significant and that the metabolic activity of a bacterial colony may be estimated from the surface area of the colony.

Acknowledgments This work was funded by the University of Arizona, Maricopa Agricultural Center (J. E. W., Western Regional Research Project W-45), the University of Wisconsin-Madison, College of Agricultural and Life Sciences (R. F. H., Hatch project 3581), and the University of California, Berkeley, College of Natural Resources (Y. L. and W. R. G.). Appreciation is extended to Scott Arnold for his contributions to figure 7.1.

References Andrews, J.A. and R.F. Harris, 1986, r- and K-selection and microbial ecology, Adv. Microbial Ecol., 9, 99-147. Bader, F.B., 1982, Kinetics of double-substrate limited growth, in Microbial population dynamics, pp. 1-32, edited by M.J. Bazin, CRC Press, Boca Raton, FL.

DIFFUSION-LINKED MICROBIAL METABOLISM IN THE VADOSE ZONE

209

Barber, S.A., 1984, Soil nutrient availability, John Wiley & Sons, New York. Blackman, F.F., 1905, Optima and limiting functions, Ann. Bot., 19, 281. Bruins, H.R., 1929, Coefficients of diffusion in liquids, in International critical tables of numerical data, physics, chemistry and technology, pp. 63-76, edited by E.W. Washburn, McGraw-Hill, New York. Buffiere, P., J.-P. Steyer, C. Fonade, and R. Moletta, 1995, Comprehensive modeling of methanogenic biofilms in fluidized bed systems: mass transfer limitations and multisubstrate aspects, Biotechnol. Bioeng., 48, 725-736. Button, O.K., 1985, Kinetics of nutrient-limited transport and microbial growth, Microbiol. Rev., 49, 270-297. Currier, J.A., 1961, Gaseous diffusion in the aeration of aggregated crumbs, Soil Sci., 92, 40^*5. Grant, R.F. and P. Rochette, 1994, Soil microbial respiration at different water potentials and temperatures: theory and mathematical modeling, Soil Sci. Soc. Am. J., 58, 1681-1690. Harms, H. and A.J.B. Zehnder, 1994, Influence of substrate diffusion on degradation of dibenzofuran and 3-chlorodibenzofuran by attached and suspended bacteria, Appl. Environ. Microbiol., 60, 2736-2745. Harris, R.F., 1981, Effects of water potential on microbial and activity, in Water potential relations in soil microbiology, pp. 23-95, edited by J.F. Parr, W.R. Gardner, and L.F. Elliot, American Society of Agronomy Special Publication 9, Madison, WI. Harris, R.F., 1982, Energetics of nitrogen transformations, in Nitrogen in agricultural soils, pp. 833-890, edited by F.J. Stevenson, J.M. Bremner, R.D. Hauck, and D.R. Keeney, Agronomy Monograph No. 22, American Society of Agronomy, Madison, WI. Harris, R.F. and S.M. Arnold, 1995, Redox and energy aspects of soil bioremediation, in Bioremediation: science and applications, pp. 55-87, edited by H.D. Skipper and R.F. Turco, Soil Science Society of America Special Publication 43, Madison, WI. Heijnen, J.J. and J.A. Van Dijken, 1992, In search of a thermodynamic description of biomass yields for the chemotrophic growth of microorganisms, Biotechnol. Bioeng., 39, 833-858. Kamke, E., 1948, Differential gleichungen: Losungsmethoden and losungen, Chelsea Publishing, New York. Liu, Y., 1994, Preferential water flow through root channels studied by NMR imaging, Ph.D. Thesis, University of California, Berkeley, CA. Pirt, S.J., 1975, Principles of microbe and cell cultivation, John Wiley & Sons, New York. Rittman, B.E., 1993, The significance of biofilms in porous media, Water Resour. Res., 29, 2195-2202. Tempest, D.W. and O.M. Neijssel, 1978, Eco-physiological aspects of microbial growth in aerobic nutrient limited environments, Adv. Microbial Ecol., 2, 105153. Walter, J. and HJ. Jordening, 1995, Kinetic model of disaccharide oxidation by Agrobacterium tumefaciens, Biotechnol. Bioeng., 48, 12-16. Watson, J.E., 1982, A mechanistic model of bacterial colony growth and activity on solid porous media, Ph.D. Thesis, University of Arizona, Tucson, AZ. Wimpenny, J.W.T., 1990, Diffusion-limited growth, in Microbial growth dynamics, pp. 65-83, edited by R.K. Poole, M.J. Bazin, and C.W. Keevil, Society for General Microbiology Special Publication 28, Oxford University Press, New York.

8

Persistence and Interphase Mass Transfer of Liquid Organic Contaminants in the Unsaturated Zone Experimental Observations and Mathematical Modeling

LINDA M. ABRIOLA KURT D. PENNELL WALTER ). WEBER, ]R. JOHN R. LANG MARK D. WILKINS

Surface and subsurface releases of organic chemicals have resulted in widespread contamination of groundwaters and soils. Frequently, such chemicals are introduced into the subsurface as nonaqueous-phase liquids (NAPLs), which are only slightly miscible with water. These organic liquids tend to migrate downward through the unsaturated soil zone, displacing the pore gases under the action of gravitational forces. During its migration, a portion of the NAPL will become entrapped in the soil pores due to capillary forces, creating zones of persistent contamination in the soil matrix. Organic liquid saturation in such zones may range from approximately 4% to 10% of the pore space (Wilkins et al., 1995). This entrapped NAPL may serve as a long-term source of contamination to the aqueous and gaseous pore fluids through subsequent dissolution and volatilization. Soil vapor extraction (SVE) has evolved over the past decade as an attractive in situ remediation technology for unsaturated soils contaminated by entrapped volatile organic compounds (VOCs). This technology involves the induction of gas flow within the porous medium to enhance volatilization of entrapped contaminants (Hutzlcr et al., 1989). Based upon the success of a number of feasibility studies and the ease of implementation, SVE remediation technologies are currently employed at approximately 18% of Superfund sites (Travis and Macinnis, 1992). An extensive review of the literature pertaining to SVE and related technologies is given in Rathfclder et al. (1995).

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

211

Although widely implemented, SVE systems are typically designed and installed with limited understanding of the processes that control their effectiveness. Clearly, the performance of SVE will be strongly influenced by contaminant volatility and effective gas-phase permeability (Pedersen and Curtis, 1991). Relatively little is known, however, about the physical and chemical processes that control contaminant vapor-phase mass transfer. The SVE systems characteristically exhibit large initial VOC recovery rates, followed by a rapid decline in effluent gas concentrations to a persistent low level (e.g., Crow et al., 1987; DiGiulio, 1992). Furthermore, a temporary increase in the produced gas organic concentration has often been observed following SVE shutdown periods (McClellan and Gilham, 1992). Such behavior suggests the presence of mass transfer limitations. Typically, the prolonged low effluent concentration "tailing" observed in field investigations has been attributed to macroscale heterogeneity in the distribution of permeabilities. Volatilization of contaminants is assumed to be limited by diffusion from less accessible, low-pemeability zones (Hochmuth et al., 1988; Johnson et al., 1990a, 1990b; Kearl et al.. 1991). Recent laboratory and controlled field experiments, however, suggest that effluent concentration tailing may also result from ratelimited mass transfer processes operative at the local or pore scale. Such processes include film transfer limitations between the entrapped organic residual or aqueous phases and the advective vapor phase (Berndtson and Bunge, 1991; Armstrong et al., 1994); gas flow bypassing of zones of high liquid saturation or low permeability (Ho and Udell, 1992); intra-aggregate diffusion (Brusseau, 1991; Gierke ct al., 1992); and rate-limited desorption (Farrell and Reinhard, 1994). The research investigations summarized herein represent a collaborative effort to examine mass transfer processes that affect organic liquid volatilization and organic vapor transport at the local or laboratory column scale. Research results have implications for the design of SVE and biovcnting remediation systems, as well as for the prediction of organic vapor transport under natural or induced flow conditions. The first part of this chapter presents a conceptual and mathematical framework for the quantification and assessment of multiphase mass transport processes in the vadose zone. That section is followed by a presentation and discussion of selected laboratory data that highlight particular research findings. A concluding section uses mathematical modeling to assess the utility of the presented conceptual model for the prediction of column-scale behavior. Modeling Framework A number of mathematical models have been presented in the literature for the description of SVE and related processes. The simplest models are designed to estimate the gas flow field through analytical (Massmann, 1989; Cho et al., 1993), quasianalytical (McWhorter, 1990), or numerical techniques (Welty et al., 1991; Gamliel and Abdul, 1993). Such models do not incorporate organic component transport; they are intended to serve as design tools for extraction well placement. In an effort to predict produced gas organic concentrations, another class of models couple steady-state single-phase gas flow with solutions of organic transport equations.

212

VADOSE ZONE HYDROLOGY

Again, analytical (Zaidel and Russo, 1993), semianalytical (Falta et al., 1993), and numerical (e.g., Wilson et al., 1988; Baehr et al., 1989; Johnson et al., 1990b; Massmann and Farrier, 1992; Benson et al., 1993) approaches have been implemented. In a contaminated unsaturated subsurface zone, however, three fluid phases are typically present. Thus, a multiphase modeling approach may be appropriate. Models that incorporate the complexities of multiphase flow, multicomponent transport, and interphase mass exchange have been developed to address this concern. Many of these models however, assume local thermodynamic equilibrium between contiguous phases (e.g., Forsyth and Shao, 1991; Falta et al., 1992; Hinckley et al., 1993; Sleep and Sykes, 1993), and are, thus, unable to adequately capture the tailing behavior discussed in the introduction to this chapter. Those three-phase models that do incorporate some interphase mass transfer rate limitations include Sleep and Sykes (1989), Rathfelder et al. (1991), Lingineni and Dhir (1992), and Abriola et al. (1997). The mathematical development that follows is presented from a multiphase perspective with particular emphasis on interphase mass exchange processes. It is a simplification of that presented in Abriola et al. (1997). For a more thorough discussion of existing SVE models, the reader is referred to Rathfelder et al. (1995). A conceptual model of pore fluid distribution in the vadose zone is shown in figure 8.1. Here, it has been assumed that water is the wetting phase, preferentially wetting the soil grains and occupying the smallest pores. The entrapped NAPL is the fluid of intermediate wettability, forming continuous films, coalesced lenses, or wedges on the air-water interfaces. Gas, as the nonwetting fluid, tends to occupy the central portion of the largest pore bodies and throats and is assumed to be the only mobile phase. Depending upon the pore structure heterogeneity and the wetting and entrapment cycle, it may also be hypothesized that a portion of the NAPL will become isolated from the gas phase, residing within pore throats or between aqueous-phase wedges. The conceptual schematic described above is consistent with experimental observations of three-phase fluid distributions in etched glass micromodels (Wilson et al., 1990) and natural sands (Hayden and Voice, 1993). In the presence of an entrapped organic liquid, the controlling mechanisms for volatile organic contaminant (VOC) migration are mass transfer to the aqueous and vapor phases. Under conditions of residual soil moisture (immobile water), the primary transport processes are gaseous-phase advection and diffusion. Direct mass transfer between the NAPL and gaseous phases will occur along the exposed residual NAPL surfaces. The organic, however, may also partition into the residual aqueous phase and sorb to the solid phase and water-gas interfaces. In the absence of a separate nonaqueous-phase liquid, water-gas partitioning will control mass transfer to the vapor phase. Transport of VOC in the multiphase system described conceptually above may be modeled by a coupled system of partial differential equations, incorporating mass and momentum balance relations. Balance equations may be written for each phase and each component within a phase. For simplicity in the presentation that follows, we will assume that the NAPL consists of a single organic component, that the NAPL and aqueous phases are immobile, and that there is no chemical or biological

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

21 3

Figure 8.1 Conceptual model of NAPL/vaporphase mass transfer processes. Arrows indicate potential direction of mass transfer under isothermal SVE conditions.

transformation of the organic. Four phases may coexist in the domain: solid (V), aqueous (n>), NAPL («), and gas (g). The mass balance equation for the gas phase can be written as (Abriola, 1989)

where <j> is the matrix porosity (unitless), Sg is the saturation of the gas phase (unitless); \g is the pore velocity of the gas phase (Lr1), p* is the mass density of the gas phase (ML~3), and £*£, is the net rate of mass transfer of organic component i to the gas phase from contiguous phase ft, per volume of the porous medium (ML~ J t~'). The gas-phase velocity is typically evaluated with a modified Darcy expression:

where qg is the specific discharge (Lt '); kg is the effective intrinsic permeability to the gas phase (L2), ng is the gas-phase dynamic viscosity (LM~'t~'), Pg is the gas-

214

VADOSE ZONE HYDROLOGY

phase pressure (ML~'t~ 2 ), g is the gravitational acceleration (Lt~ 2 ), z is the vertical coordinate (positive downward) (L), and krg is the relative permeability to the gas phase at saturation Sg (unitless). For fine textured soils and low gas pressures, kg may deviate significantly from the "true" or intrinsic permeability customarily used to compute the flow ofliquids in a porous medium, and it will vary with pressure. It may be computed from (Klinkenberg, 1941)

where k.^ is the true permeability (L2) and b is referred to as the Klinkenberg parameter. In the absence of experimental measurements, the Klinkenberg parameter may be estimated from empirical correlations (e.g., Heid et al., 1950). Mass balance equations for the immobile liquid phases (NAPL, aqueous) may be expressed with a simplified form of equation (8.1) as

where a = n or w and other notation is as defined above. Although an equation analgeous to (8.4) could also be written for the solid phase, it is typically assumed that the solid-phase volume fraction and density are not significantly altered by sorptive processes. Similarly, if one assumes that the organic compound is only slightly misciblc and one neglects water volatilization, the mass density and saturation of the aqueous phase will not vary appreciably and equation (8.4) need not be written for the aqueous phase. Transport of the organic component i within the mobile gas will be governed by the following balance equation:

where xgi represents the mole fraction of component;' in the gas phase (mol^/Eymol,), pg is the molar density of the gas phase (mol L~3), D^ is the effective diffusion/ dispersion tensor for component i in the gas phase (L 2 t~'), and Eg^ is the net molar transfer rate of component i to the gas phase from contiguous phase f), per volume of the porous medium (mol L~ 2 t"'). Equation (8.5) implicitly assumes that the nonadvective flux of component / can be represented by a Fickian expression. The usefulness of the Fickian approximation for the quantification of multicomponent diffusive processes has been examined in some recent studies (e.g., Thorstenson and Pollock, 1989; Baehr and Bruell, 1990; Amali and Rolston, 1993) through comparisons with more rigorous gas transport theories. Data and modeling studies conducted in our laboratories suggest that Pick's law prediction errors can be minimized through proper estimation of effective diffusion coefficients and expression of transport equations on a molar basis. Hence, equation (8.5) has been written as a molar balance equation. The interested reader is directed to Abriola et al. (1992) for further discussion on the evaluation of diffusion coefficients. Gas diffusive fluxes play a relatively minor role in the advection-dominated experimental systems examined in the next section and will not be discussed further herein.

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

215

An equation similar to (8.5) may be written to describe the molar balance of organic component / in the aqueous phase:

Here, advective fluxes have been neglected, since the phase has been assumed immobile. Note that D\t is a scalar representing molecular diffusion in the aqueous phase. A final balance equation expresses the molar balance of organic component i in the solid phase:

where,
where J is the net molar flux (mol L~ 3 t~ L ) of organic between the NAPL and gas phases and Af" is an overall mass transfer coefficient (t~'). Here, the concentration driving force has been approximated as the difference between x'gl, the mole fraction of component i in the vapor phase that is in thermodynamic equilibrium with the entrapped NAPL, and xg!, the molar fraction of the organic species in the bulk gas phase. Equilibrium concentrations may be estimated using Raoult's law and assuming ideal behavior of the organic and gas phases (Schwarzenbach et al., 1993). The extent of NAPL-vapor interphase mass transfer also depends upon the interfacial or contact area between the entrapped NAPL and the mobile gas phase. Thus, the molar rate of mass transfer per unit volume of the porous medium is given as

where a is the specific interfacial area between the NAPL and the gas phase (area per volume of porous medium) (L~'). This specific interfacial area is extremely difficult to quantify in practice. Thus, a lumped mass transfer coefficient, &*" (L t"1), is often employed to model mass transfer. Although few studies have attempted to measure

21 6

VADOSE ZONE HYDROLOGY

NAPL-gas mass transfer rates, similar linear driving force expressions have been employed to model NAPL-aqueous mass transfer in two-phase liquid flow systems (Pfannkuch, 1984; Miller et al, 1990; Powers et al.,1992, 1994a). Assuming that the rate of NAPL dissolution is controlled by resistance in the aqueous phase, an analogous linear driving force expression for this process may be given as

Equilibrium molar concentrations in equation (8.9b) may be estimated by employing Raoult's law. As noted in the introduction, the distribution and mobility of VOCs in the vadose zone may be strongly influenced by sorption processes. A key factor that governs both the magnitude of and the mechanisms responsible for VOC sorption in unsaturated porous media is the relative humidity or residual soil moisure content. In the absence of water, natural soils and clay minerals exhibit a sizable capacity to adsorb organic vapors, which is strongly correlated with solid specific surface area as determined by the nitrogen (N 2 )/Bruneaur-Emmett-Teller (BET) method (e.g., Rhue et al., 1988; Pennell et al., 1995). As the relative humidity (RH) of soil moisture content increases, VOCs are displaced from the sorbent surace, thus resulting in the suppression of organic vapor sorption (Call, 1957; Chiou and Shoup, 1985; Pennell et al. 1992). The reduction in organic vapor sorption in the presence of water is also accompanied by a change in the relation of vapor pressure to sorbed organic at equilibrium (adsorption isotherm). An increase in moisture content results in a shift from a BET (Type II) isotherm to an adsorption isotherm with a convex shape (Type III). This behavior has been widely attributed to the polar nature of water molecules, which effectively compete with relatively nonpolar organic vapor for sorption sites. Under natural conditions, the moisture contents of unsaturated soils typically exceed those required to achieve complete coverage of the solid surface with at least a monolayer of water. For example, in a soil with a bulk density of 1.60 g/ cm3 and specific surface area of 20 m2/g, a volumetric water content of 10% corresponds to a surface coverage of approximately 11 monolayers of water, assuming that the adsorbed water has a cross-sectional area of 0.105 nm 2 /molecule and exists in a hexagonal close packing. Although forced gas-phase advection could be expected to enhance soil drying, field studies provide no evidence of significant reduction in soil moisture content (Armstrong et al., 1994). Thus, the sorption of organic vapors on exposed mineral surfaces is unlikely to play a significant role in most natural and SVE systems. Although the effect of water on the magnitude of VOC sorption is well established, the specific mechanisms responsible for the sorption of organic vapors by hydrated soil materials remains a subject of considerable debate. From both an experimental and modeling perspective, the retention of organic vapors in the unsaturated zone, in the absence of a nonaqueous liquid phase, has often been assumed to result from two mechanisms: (1) dissolution into residual water and (2) aqueoussolid phase sorption processes (e.g., Chiou and Shoup, 1985; Jury et al., 1990). Typically, these processes are described mathematically using Henry's law constants

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

21 7

(KH) and liquid-solid distribution coefficients (Kd). respectively. However, this approach fails to account for the distinctly nonlinear adsorption isotherms (Type III) frequently observed for organic vapor sorption by hydrated solids. In addition, careful evaluation of organic vapor retention by soils and clay minerals has led to the discovery that the magnitude of VOC retention cannot be predicted based on Henry's law and independently measured values of Kj, particularly for soils and aquifer materials containing low levels of organic carbon (Pennell et al., 1992). These authors demonstrated that organic vapor sorption at the gas-liquid interface can contribute significantly to the overall retention of VOCs by hydrated soil materials. Similar observations were subsequently reported by Hoff et al. (1993), who found that adsorption at the gas-liquid interface was responsible for 50% of the observed sorption of alkanes by Borden aquifer material. Thus, at relative humidities typically encountered in the unsaturated zone (i.e., >90%), a multimechanistic explanation should be invoked for organic vapor retention. Retention mechanisms include (1) dissolution into residual water, (2) adsorption at the gas-liquid interface, and (3) solid-phase sorption from the aqueous phase. Each mechanism is discussed briefly below. The equilibrium dissolution of organic vapors into residual water can be described by Henry's law provided that the aqueous solution is dilute and that the adsorbed water possesses properties similar to those of bulk water. The aqueous solubility of most hydrophobic organic compounds is relatively small when expressed on a mole fraction basis, and, thus, the condition of a dilute ideal solution is usually met. In the intermediate relative humidity range (i.e., 30-80%), the second assumption may be questioned. Karger et al. (1971), however, reported that adsorbed water films on the order of 1.5-200 nm in thickness (5-40% water by weight) behave as bulk water with respect to hydrocarbon vapors. Similarly, Dorris and Gray (1981) showed that hydrocarbon sorption coefficients remained constant at water contents ranging from 3.8 (88% RH) to 47% by weight. Thus, the assumption of bulk water properties should be valid at relative humidities of approximately 90% and greater. The adsorption of sparingly soluble compounds at the gas-liquid interface can be estimated using the following form of the Gibbs equation (Cutting and Jones, 1955; Pennell et al., 1992):

where F is the surface excess (mol L~2), y is the surface tension (M t~ 2 ), and n is the chemical potential (M L2 t~ 2 mol" 1 ). For the low-pressure (dilute) systems found under natural soil conditions, the change in chemical potential may be related to the change in partial pressure:

where />,- is the partial pressure of the organic component, R is the gas constant, and T is the absolute temperature (degrees Kelvin). Under such conditions, the surface excess becomes

218

VADOSE ZONE HYDROLOGY

In practice, experimental data for the change in surface tension of bulk water with partial pressure are fit by a nonlinear least-squares regression procedure. The slope of this relationship is then used to calculate the surface excess as a function of partial pressure using equation (8.10c). Note, however, that the resulting surface excess is quantified per unit area of interface. Thus, the gas-liquid interfacial area must be known to express the surface excess on a soil volume or mass basis. These interfacial areas are extremely difficult to estimate. The retention of low-molecular-weight gases, such as methane and nitrogen, in packed columns has been used to determine the surface areas of water-coated solids (Okamura and Sawyer, 1973). Recent advances in the estimation of interfacial areas for multifluid soil systems may also prove useful for this purpose (Bradford and Leij, 1997). For the simulations presented later in this chapter, adsorption at the gas-liquid interface was neglected, due to lack of information on interfacial areas. A number of studies have explored the mass transfer of VOCs from residual water to a flowing gas phase. Gas-liquid interface sorption has typically been neglected in such investigations. Under advection-dominated conditions, laboratory and controlled field experiments have revealed that water-gas transfer may be rate-limited (e.g., Cho and Jaffe, 1990; Berndtson and Bunge, 1991; Gierke et al., 1992; McClellan and Gilham, 1992). While it is often difficult to conclusively ascertain the rate-limiting mechanism in such systems, laboratory and modeling investigations suggest that intraparticle or intra-aggregate diffusion or gas flow bypassing of immobile water zones will dominate any film transfer limitations (Brusseau, 1991; Gierke et al., 1992). Linear driving force (e.g., Cho et al., 1993; Armstrong et al., 1994) or spherical diffusion (e.g., Gierke et al., 1992) expressions have been employed to model mass transfer from inaccessible aqueous regions. For natural unsaturated soil systems, the pore level geometry is often not well characterized. Under such conditions, a linear driving force expression is an appropriate and flexible choice for modeling interphase mass exchange. Assuming, then, that the rate of aqueousgas phase mass transfer is controlled by resistance in the aqueous phase, an expression analogous to equations (8.9a) and (8.9b) may be written for this process:

where jc^* is the aqueous molar concentration of component / in equilibrium with the gas phase as estimated using Henry's law. The final and perhaps most significant process that contributes to the retention of organic components in two-phase aqueous-vapor systems is solid-phase sorption. A large literature exists on solid-phase sorption of aqueous-phase organic constituents. Any mechanism that influences the rate of desorption from the soil matrix will have the potential to substantially reduce the recovery of organic species during venting operations. Potential rate-limiting mechanisms include intrasoil organic matter diffusion (e.g., Nzedi-Kizza et al., 1989); diffusion within aqueous-phase-saturated intraparticle micropores (e.g., Ball and Roberts, 1991; Weber et al., 1991); desorption reaction rates (e.g., Weber et al., 1991); desorption hysteresis or nonideality (e.g.,

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

219

Brusseau and Rao, 1989); and contaminant aging (e.g., Steinberg et al., 1987). As with aqueous-gas mass transfer, many models that have been proposed to describe rate-limited desorption are based upon bicontinuum and pore diffusion concepts. In such models, the soil matrix is segmented into two compartments: an "accessible region," where desorption is governed by thermodynamic equilibrium, and a relatively "inaccessible region," where desorption is limited by diffusional processes. Note that a mathematically similar, although conceptually distinct, mass transfer model may also be developed for soil systems that have two types of sorption sites, each with a different reaction rate. Desorption from slow or diffusion-limited regions can be modeled most simply by a linear driving force expression similar to those presented above, describing diffusional resistances at interfaces. Thus, mass transfer between the solid and aqueous phases may be expressed as

Here, x^/ is the aqueous-phase mole fraction of the organic constituent /' in equilibrium with the solid-phase organic mass. The equilibrium concentration appearing in equation (8.12) must be evaluated with a measured equilibrium relation, known as a sorption isotherm. For many natural soils, which have a distribution of sorption site energies, sorption behavior may deviate from linearity with the aqueous-phase concentration. A general isotherm relation that can capture this nonlinearity is given by the Freundlich isotherm:

Here, Qei is the mass of organic constituent / sorbed per mass of the solid phase at equilibrium (A/ r A/j'), and both K^ and n arc empirical fitting parameters. Although the original development of the Freundlich model was largely empirical, subsequent theoretical analyses for sorption on heterogeneous surfaces (e.g., Carter et al., 1995) have revealed that K/*, is a measure of sorption capacity and n characterizes the cumulative magnitude and diversity of sorption energies.

Experimental Observations Several laboratory column venting experiments for the recovery of entrapped NAPLs have been documented in the literature (Hoag et al., 1984; Baehr et al.. 1989; Rainwater et al., 1989; Berndtson and Bunge, 1991; Kearl et al., 1991; Bloes et al., 1992; Hayden et al., 1994; Ho et al., 1994). Although a variety of media, fluids, and scales have been investigated in these studies, few experiments have been designed to systematically investigate mass transfer limitations and their dependence in macroscopically homogeneous porous media. To this end, a laboratory study was undertaken to quantify interphase mass transfer rates and to explore the properties that influence rate-limited mass transfer between an entrapped NAPL and a flowing gas phase for a range of sandy porous media and organic liquids. Initial NAPL removal rates from these experiments have been determined and are presented in Wilkins et al. (1995). A forthcoming publication will present the results of long-term

220

VADOSE ZONE HYDROLOGY

removal experiments in the same system. Representative data and analyses from these laboratory studies are used below to highlight important research results. Experiments were conducted in custom-designed soil columns, fabricated from aluminum and fitted with stainless steel endplates. A fluid emplacement procedure was developed to be representative of natural environmental conditions and to ensure uniform distributions of both water and NAPL residual saturations. This experimental protocol included uniform packing with air-dried sandy porous media; water imbibition and drainage to residual saturation; and NAPL injection and subsequent drainage to a residual level. Following entrapment, the columns were placed within a temperature-controlled volatilization apparatus. Purified nitrogen, nearly saturated with water vapor to maintain approximately 95% RH conditions within the column, was injected into the column at steady flow rates in an upflow mode. Effluent vapor-phase concentrations of the organic chemical were measured on-line by gas chromatography. For further details of the experimental procedure, the reader is referred to Wilkins et al. (1995). Characterization of the whole sands from which the size fractions used in the present work were taken is given in Weber et al. (1992). In the column experiments, residual aqueous phase and NAPL saturations ranged from 8% to 16% and 4% to 10%, respectively, for the natural sandy media examined. For uniform grain size media, larger residual saturations were retained in the sands of smaller mean pore size (grain diameter), consistent with capillary theory. With increasing variation of pore sizes (media gradation), entrapment of both fluids tended to increase. In general, entrapped NAPL residuals in the three-phase experimental systems were 2-3 times smaller than those measured in the same media under liquid-saturated (two-phase NAPL-water) conditions (Powers et al., 1992). These smaller residual saturations may be attributed in part to the lower interfacial tension between organic and air in comparison with organic and water and to the different NAPL entrapment geometry due to the intermediate wettability of the organic in the three-phase system. Representative measurements of column gas-phase effluent concentrations are plotted in figure 8.2 for volatilization of styrene from two uniform sandy media of differing grain sizes. Here, effluent concentrations have been normalized to equilibrium values. Each point represents a measurement under quasi-steady (stabilized concentration) conditions at a particular flow rate. Less than 10-15% of the NAPL was removed over the course of any particular experiment, limiting potential changes in NAPL-gas interfacial areas. Figure 8.2 reveals that NAPL-vapor phase mass transfer depends strongly on velocity, with deviations from local equilibrium increasing with velocity and ranging from 10% to 40% for gas-phase velocities typical of soil vapor extraction applications (vg = 0.25-1.5 cm/s). The figure also suggests a marked dependence of mass transfer rates on mean grain size, with increased deviations from local equilibrium at smaller grain sizes. Assuming a linear driving force representation of mass transfer [equation (8.9a)], an analytic solution to a simplified (quasi-steady) form of equation (8.5) was used to estimate lumped mass transfer coefficients from the experimental data (Wilkins et al., 1995). As anticipated from the above discussion, estimated mass transfer coefficients exhibited a strong dependence on velocity and mean grain size. No statistically

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

221

Figure 8.2 Quasi-steady volatilization; data represent styrene concentrations in the column effluent for volatilization in two uniform Wagner sand size fractions. (Data from Wilkins et al., 1995.)

significant correlation was found, however, with medium uniformity (gradation). This final observation is in marked contrast to results of NAPL dissolution column invesigations, where NAPL-aqueous mass transfer was shown to depend strongly on the soil uniformity index (£/, = <4oMo) (Powers et al., 1992). Based upon the column data for the complete suite of volatilization experiments, an empirical correlation was derived for the representation of the lumped mass transfer coefficient, k% (Wilkins et al., 1995). This correlation, presented in terms of dimensionless numbers, is given as

where Shn = kg0"(dsn)2/Dg is the modified Sherwood number, Pe = vgdi0/Dg is the Peclet number, and d0 — d50/dm is the normalized mean grain size. Here, dm = 0.05 cm and d$0 is the mean grain size of the medium. Figure 8.3 compares modified Sherwood numbers predicted from equation (8.14) with those determined from the experimental data for a range of porous media and organics. The figure reveals that the developed correlation provides an excellent representation of the data. Further verification of the applicability of this correlation to the volatilization of pure NAPLs entrapped in sandy media is given in Wilkins et al. (1995). The volatilization mass transfer correlation expression (8.14) may be compared to a corresponding correlation expression developed for dissolution mass transfer (Powers et al., 1992) to highlight similarities and differences in these phenomena.

222

VADOSE ZONE HYDROLOGY

Figure 8.3 Volatilization mass transfer correlation: model verification. (After Wilkins et al., 1995.) Data for volatilization of three organic liquid contaminants in a uniform quartz sand (Ottawa) and styrene volatilization in a range of graded (Wagner mix #1 and #2) and uniform Wagner sand soils. Numbers refer to U.S. standard sieve size fractions.

Explicit expressions for the lumped mass transfer coefficients developed directly from these correlations yield the following proportionalities: volatilization dissolution Note that the dependence of mass transfer on interstitial velocity is nearly identical in both expressions. This suggests that the flowing-phase fluid dynamics (gas or water) are similar in the three- and two-phase systems. In contrast, however, exponents associated with porous media properties are quite dissimilar. For dissolution, the mass transfer coefficient is inversely proportional to mean grain size, while, for volatilization, the mass transfer coefficient is directly proportional to d^. In addition, as noted above, no dependence on medium uniformity was found for volatilization mass transfer. These differences can be explained in terms of the conceptual model presented in figure 8.1. In the unsaturated systems examined, the mobile phase (gas) is the nonwctting phase, occupying the largest pores. As the mean grain size is reduced, the consequent increase in capillary forces will tend to increase residual liquid saturations, further restricting gas-phase flow and potentially limiting its access to the entrapped NAPL. In contrast, for NAPL dissolution, the flowing phase is the wetting phase. Here, a reduction in mean grain size will not decrease

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

223

pore accessibility. Tt will, however, tend to change the geometry of the entrapped NAPL, reducing mean ganglia size and increasing specific interfacial area. The observations of volatilization mass transfer summarized above suggest that NAPL entrapment geometry (NAPL presence as thin films) is comparatively unaffected by pore size or distribution. Close inspection of figure 8.3 also reveals that the magnitude of the interfacial tension between the organic liquid and the other fluid phases had no discernible influence on the interphase mass transfer. For the range of organics and porous media examined, the modified Sherwood number was found to be independent of spreading coefficient (Wilkins et al., 1995). For example, PCE, which has a negative spreading coefficient (—7.2 dyn/cm) behaved similarly to styrene, which has a positive spreading coefficient (7 dyn/cm). Recall that the lumped mass transfer coefficient incorporates the specific interfacial area between the NAPL and gas phases. Thus, these observations support the conclusion that this specific interfacial area is not sensitive to contaminant spreading characteristics. Further support for this conclusion can be found in the theoretical and experimental study of Blunt et al. (1994), who observed that both spreading and nonspreading organics may form thin films along water interfaces in three-phase water-wet porous media. The experiments described above explored the initial (quasi-steady) volatilization of entrapped NAPL under a variety of conditions. Figure 8.4a shows measurements of column effluent concentrations from a prolonged experiment for volatilization of entrapped styrene from a reasonably uniform size fraction (dso = 0.02 cm) of a sandy Michigan aquifer material (Wagner sand). In the figure, the log of the normalized effluent concentration is plotted versus the dimensionlcss pore volumes of introduced gas. (One pore volume is defined here as the total void volume of the column.) The cumulative percent of styrene mass removed during the experiment is also shown. This experiment was conducted at a fairly low pore velocity (vg = 0.1 cm/s) to ensure that equilibrium mass transfer occurred during the initial volatilization period. The figure reveals that removal of entrapped NAPL over extended periods of volatilization had a negligible influence on mass transfer rates. Equilibrium mass transfer was maintained until more than 99% of the entrapped NAPL mass was removed by volatilization. At this point, effluent concentrations exhibited a rapid decline (almost 2 orders of magnitude). A similar sharp decline in concentrations has been observed in other volatilization studies (Berndtson and Bunge, 1991; Bloes et al., 1992). These data suggest that the interfacial area remained relatively constant during volatilization of the entrapped styrene. The cumulative mass data shown in figure 8.4a suggest that the observed rapid decline in effluent concentrations coincided with the removal of the exposed freephase organic residual. Further examination of this figure reveals that the sharp concentration decrease was followed by a long period of "tailing" at low, but significant, concentration levels. To gain further insight into this tailing behavior, the gas flow was shut off (interrupted) for a period of 13 h. Recommencement of the nitrogen flow produced an effluent concentration "spike," reaching approximately 5% of the saturated vapor pressure for styrene. The appearance of this concentration spike indicates the presence of rate-limited transfer. In the absence of NAPL, such rate limitations could be the result of rate-limited mass transfer from the solid to

Figure 8.4(a) Transient volatilization experiment: styrene and Wagner 50-80 soil; arrows indicate axis approximate to data.

Figure 8.4(b) Transient styrene dissolution experiment in a Wagner sand mixture; arrows indicate axis appropriate to data. (After Powers et al., 1994a.)

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

225

aqueous phases [see equation (8.12)] and/or from the aqueous to gas phases [see equation (8.11)]. Using the measured sorptive capacity of the Wagner 50-80 sand [Kj = 6 (,ug styrene/g soil) (L aqueous phase/mg styrene)"; n = 0.73 in equation (8.13)], the measured aqueous-phase residual saturation (0.14), the medium porosity (0.38), and the Henry's law constant for styrene, a rough mass partitioning calculation for the column can be performed. This calculation assumes that the measured gas-phase concentration of 5% of its saturated value is at equilibrium with the other phases. Given this assumption, it is estimated that 0.144 mg, 0.133 mg, and 13 mg of styrene are present in the gas, aqueous, and solid phases, respectively. This simple calculation suggests that the primary source of long-term rate-limited volatilization in this system is the sorbed-phase contaminant. Figure 8.4b presents representative results from an analogous long-term styrene dissolution experiment in a two-phase (water-gas) flow system (Powers et al., 1994a). Here, the medium was a graded Wagner sand mixture. The aqueous effluent concentration pattern illustrated in figure 8.4b strongly contrasts with the vapor effluent pattern presented in figure 8.4a. Unlike observations from the volatilization experiment, in the dissolution experiment the transient interphase mass transfer rates appear to decrease significantly with the reduction of NAPL mass. In liquid-saturated systems, the residual NAPL is known to exist as isolated globules or interconnected ganglia. As the NAPL mass is removed during dissolution, the exposed interfacial area decreases, ultimately limiting the rate of mass transfer (Powers et al., 1994a, 1994b). However, as noted above, the unsaturated experiment results suggest that interfacial area remained relatively constant during volatilization, presumably due to its thin film configuration. The observations presented in figure 8.4a support the utility of the quasi-steady mass transfer correlation expression (8.14) for the description of transient volatilization mass transfer in uniform sandy media.

Mathematical Modeling A one-dimensional Galerkin finite element simulator was developed to solve the system of multiphase, multicomponent, flow and transport equations given by equations (8.1)-(8.7) above. Interphase mass exchange terms were represented using linear driving force expressions (8.9), (8.11), and (8.12) with equilibrium sorption represented by expression (8.13). This numerical model is an adaptation of the MISER (Michigan Soil Vapor Extraction Remediation model) soil vapor extraction/bioventing simulator (Lang et al., 1995; Abriola et al., 1997). In keeping with the laboratory observations of NAPL-gas mass transfer discussed above, the correlation expression given by equation (8.14) was employed to evaluate the lumped organicgas mass transfer coefficient. The developed simulator was used to explore the ability of the proposed mathematical model to predict or fit observed transient behavior in the styrene volatilization experiment presented in figure 8.4a. Model inputs included the measured initial entrapped aqueous and NAPL saturations, matrix porosity, the independently measured sorption isotherm, and experimental flow rates, as well as the gaseous diffusion coefficient and Henry's law constant for styrene under the experimental conditions.

226

VADOSE ZONE HYDROLOGY

No independent information, however, was available to quantify mass transfer coefficients for aqueous-gas, aqueous-solid, and NAPL-aqueous phase mass transfer. As an initial condition, it was assumed that all mass partitioning was in equilibrium with the pure NAPL phase. Note that, since the aqueous phase was thus assumed to be saturated with respect to the organic, the NAPL-aqueous mass transfer coefficient docs not influence simulation results. As mentioned in the mathematical development section ("Modeling Framework"), interface sorption was neglected in the simulator due to the lack of information on interfacial areas. This simplification reduced the number of required fitting parameters. Note that, for the experimental system under consideration, the effects of interface sorption would most likely be masked by the presence of NAPL since it is not expected that interface desorption will be significantly rate-limited relative to aqueous gas mass transfer. Neglecting this process effectively results in the lumping of sorbed interfacial mass with that of the free-phase organic liquid. All simulations presented below were conducted with a uniform discretization of Ax = 0.5 cm, for the 10-ctn column. An initial time-step size of 0.001 s was employed. Based upon the above discussion, specification of two mass transfer coefficients (aqueous-gas and aqueous-solid) was required. Figure 8.5 shows model predictions under conditions for which these estimated mass transfer coefficients are large — that is, neither aqueous-gas nor aqueous-solid mass transfer is rate-limiting. Here, styrene gas-phase concentration at the column effluent is plotted against fluid-phase pore volumes. The symbols represent the data, while the solid line is the model prediction. Observe that the use of the correlation (8.14) results in excellent effluent concentration predictions as long as NAPL is present in the system. The model also captures the timing of the rapid drop in concentration, which coincides with NAPL

Figure 8.5 Model simulation of styrene volatilization assuming equilibrium partitioning between the solid, aqueous, and gas phases.

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

227

disappearance. Measured data exhibited an even sharper falloff in concentration than predicted by the model. Following the disappearance of the NAPL, however, model predictions and observed behavior diverge. The equilibrium predictions, produced as a result of the large values of the estimated mass transfer coefficients, exhibit a much more rapid decline in concentrations than observed in the experiment. The small amount of tailing in the model simulations here is due to the nonlincarity of the sorption isotherm. Because the simulated system is in equilibrium, no recovery is predicted by the model during the 13 h shut-in period. Clearly, an equilibrium modeling approach fails to capture the significant features of the data. Figures 8.6a and 8.6b illustrate simulation results for a range of solid-aqueous mass transfer coefficients. In these simulations, the aqueous-gas mass transfer coefficient (k"g) was held constant at a value of 53.1/day, 2 orders of magnitude smaller than kg", the NAPL-gas mass transfer coefficient. This smaller value for k"ug was selected based upon the assumption that water-gas mass transfer may be more severely rate-limited than NAPL-gas mass transfer by diffusion through the aqueous phase at the interface. The assumed magnitude is consistent with the values of k"s reported by Imhoff and Jaffe (1994) for water-gas mass transfer under two-phase flow conditions in soil columns. It should be noted that, for the physical system examined in the present work, model predictions were relatively insensitive to the value of k'og within this 2 order of magnitude range. This is due to the fact that most of the mass is held on the solid. Inspection of figure 8.6 reveals that a solid-aqueous mass transfer coefficient of 3.056/day comes closest to reproducing the observed position of the concentration tail. When the solid-aqueous mass transfer coefficient is increased above this value (sec figure 8.6a), the simulator predicts that more mass is removed from the domain at earlier times than observed in the experiment. Also, the predicted concentration tends to fall off more rapidly than the measured data at later times. As the solid-aqueous mass transfer coefficient is decreased (see figure 8.6b), the simulated effluent concentration drops abruptly to a much lower level than the observed concentrations. In these simulated systems, more mass remains in the solid phase but concentrations fall rapidly due to the large mass transfer limitations. Although use of a solid-aqueous mass transfer coefficient of 3.056/day reproduces the initial tailing behavior of the observed data, the concentration recovery during the flow interrupt period is overestimated. In addition, subsequent tailing behavior is not matched as well as in the earlier time portion of the curve. The greater degree of "flattening" of the experimental measurement curve and its lower peak suggest that more severe rate-limitations may be present in the real system. The Wagner sand is a mixture of two primary components: a quartz fraction and a shale fraction (Weber et al., 1992). Each fraction is expected to have a distinct sorptive capacity and sorptive mass transfer behavior. Future work will explore the utility of a two-site desorption modeling approach for the simulation of the experiment observations.

228

VADOSE ZONE HYDROLOGY

Figure 8.6 Model simulations of styrene volatilization with varying solid-aqueous mass transfer coefficent: (a) 0.1/tf < C < ^g; (ft)C' < O.lfc"*Conclusions This chapter has provided an overview of ongoing collaborative research into NAPL volatilization and organic vapor transport at the laboratory column scale. A conceptual and mathematical framework was presented for the examination of multiphase transport in three-fluid systems. The presentation focused on the examination

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

229

of interphasc mass transfer limitations. Results of column volatilization experiments with entrapped NAPLs have revealed significant deviations from equilibrium behavior under conditions representative of soil vapor extraction applications, particularly in fine-grained media at high velocities. Analysis of the data indicate that a linear driving force expression can adequately capture NAPL volatilization behavior for a range of sandy media, organic compounds, and flow conditions. The mass transfer coefficient was found to be insensitive to NAPL mass removal over time or the NAPL spreading characteristics, suggesting that the specific interfacial contact area between the NAPL and gas phases exists as thin films that remain relatively stable during volatilization. Following NAPL removal, column experiments demonstrated that recovery of the remaining organic can be strongly rate-limited. Observed effluent concentrations in these experiments exhibited a marked tailing behavior. Simple mass balance calculations suggest that the remaining organic mass in the examined systems resided primarily on the solid phase. Thus, the strong tailing behavior is believed to be the result of desorption mass transfer limitations. A simple sequential linear driving force representation of aqueous-gas and solid-aqueous mass transfer failed to adequately capture system behavior. Additional modeling and experimental efforts must be directed toward the examination and quantification of sorption mass transfer limitations in such systems.

Acknowledgments Funding for this research was provided by the National Institute of Environmental Health Sciences under Grant No. ES04911. The content of this publication does not necessarily represent the views of this agency and no official endorsement should be inferred.

References Abriola, L.M. 1989, Modeling migration of organic chemicals in groundwater systems: a review and assessment, Environ. Health Persp., 83, 117-143. Abriola, L.M., C.-S. Fen, and H.W. Reeves, 1992, Numerical simulation of unsteady organic transport in porous media using the dusty gas model, Proceedings of the IAH Conference on Subsurface Contamination by Immiscible Fluids, Calgary, Alberta, Canada, April 1990, A. A. Balkema, Rotterdam, 195-202. Abriola, L.M., J.R. Lang, and K.M. Rathfelder, 1997. Beta Version Documentation for: Michigan Soil-Vapor Extraction Remediation (MISER) Model — A Computer Program to Model Bioventing of Organic Chemicals in Unsaturated Geological Material, EPA 600R97099, R. S. Kerr Environmental Research Laboratory, Environmental Protection Agency, Ada, OK, 1997. Amali, S. and D.E. Rolston, 1993, Theoretical investigation of multicomponent volatile inorganic vapor diffusion: steady-state fluxes. J. Environ. Qual., 22, 825-831.

230

VADOSE ZONE HYDROLOGY

Armstrong, J.E., E.G. Frind, and R.D. McClellan, 1994, Nonequilibrium mass transfer between the vapor, aqueous, and solid phases in unsaturated soils during vapor extraction, Water Resour. Res., 30(2), 355-368. Baehr, A.L. and C.J. Bruell, 1990, Application of the Stefan-Maxwell equations to determine limitations of Pick's law when modeling organic transport in sand columns, Water Resour. Res., 26(6), 1155-1163. Baehr, A.L., G.E. Hoag, and M.C. Marley, 1989, Removing volatile contaminants from the unsaturated zone by inducing advective air-phase transport, J. Contam. Hydrol., 4, 1-26. Ball, W.P. and P.V. Roberts, 1991, Long-term sorption of halogenated organic chemicals by aquifer material. 1. equilibrium, Environ. Sci. Techno!., 25(7), 1223-1236. Benson, D.A., P. Huntley, and P.C. Johnson, 1993, Modeling vapor extraction and general transport in the presence of NAPL mixtures and nonideal conditions, Ground Water, 31(3), 437-445. Berndtson, M.J. and A.L. Bunge, 1991, A mechanistic study of forced aeration for in-place remediation of vadose zone soils, Proceedings of the Petroleum Hydrocarbons and Organic Chemicals in Ground Water, National Water Well Association, Houston, TX, 249-263. Bloes, M.B., K.M. Rathfelder, and D.M. Mackay, 1992, Laboratory studies of vapor extraction for remediation of contaminated soil, in Subsurface Contamination by Immiscible Fluids, A. A. Balkema, Rotterdam, 255-262. Blunt, M.J., D.H. Fenwick, and D. Zhou, 1994, What determines residual oil saturation in three-phase flow?, SPE/DOE 9th Symposium on Improved Oil Recovery, Tulsa, OK, April, 1994, 371-380. Bradford, S.A. and F.J. Leij, 1997, Estimating interfacial areas for multi-fluid soil systems, /. Contam. Hydro!., 27, 83-105. Brusseau. M.L., 1991, Transport of organic chemicals by gas advection in structured or heterogeneous porous media: development of a model and application to column experiments, Water Resour. Res., 27(12), 3189-3199. Brusseau, M.L. and P.S.C. Rao, 1989, Sorption nonideality during organic contaminant transport in porous media CRC Crit. Rev. Environ. Contr., 19(1), 33-99. Call, F., 1957, The mechanism of sorption of ethylene dibromide on moist soils, /. Sci. Food Agric., 8, 630-639. Carter, M.C., J.E. KLilduff, and W.J. Weber, Jr., 1995, Site energy distribution analysis of preloaded adsorbents, Environ. Sci. Techno!., 29, 1773—1780. Chiou, C.T. and T.D. Shoup, 1985, Soil sorption of organic vapors and effects of humidity on sorptive mechanism and capacity, Environ. Sci. Techno!., 19, 11961200. Cho, J.H. and P.R. Jaffe, 1990, The volatilization of organic compounds in unsaturated porous media during infiltration, /. Contam. Hydro!., 6, 387 410. Cho, J.H., P.R. Jaffe, and J.A. Smith, 1993, Simulating the volatilization of solvents in unsaturated soils during laboratory and field infiltration experiments, Water Resour. Res., 29(10), 3329-3342. Crow, W.L., E.R. Anderson, and E. Minugh, 1987, Subsurface venting of hydrocarbon emanating from hydrocarbon product on groundwater, Ground Water Man. Rev., 7(1), 51-57. Cutting, C.L. and D.C. Jones, 1955, Adsorption of insoluble vapors on water surfaces, Part I, /. Chem. Soc., 4067-4075. DiGiulio, D.C. 1992, Ground Water Issue — Evaluation of Soil Venting, EPA/540/S92/004, Environmental Protection Agency, Washington, DC. Dorris, G.M. and D.G. Gray, 1981, Adsorption of hydrocarbons on silica-supported water surfaces, J. Phys. Chem., 85, 3628-3635. Falta, R.W., K. Pruess, I. Javandel, and P.A. Witherspoon, 1992, Numerical modeling of steam injection for the removal of nonaqueous phase liquids from

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

231

the subsurface 2. Code validation and application, Water Resour. Res., 28(2), 451-465. Falta, R.W., K. Pruess, and D.A. Chesnut, 1993, Modeling advective contaminant transport during soil vapor extraction, Ground Water, 31(6), 1011-1020. Farrell, J. and M. Reinhard, 1994, Desorption of halogenated organics from model solids, sediments, and soil under unsaturated conditions: 2. Kinetics, Environ. Sci. Techno!., 28(1), 63-72. Forsyth, P.A. and B.Y. Shao, 1991, Numerical simulation of gas venting for NAPL site remediation, University of Waterloo Report, Ontario. Gamliel, A. and A.S. Abdul, 1993, Numerical investigations of optimal well spacing and the effect of screen length and surface sealing on gas flow toward an extraction well, J. Contain. Hydro!., 12, 171-191. Gierke, J.S., N.J. Hutzler, and D.B. McKenzie, 1992, Vapor transport in unsaturated soil columns: implication for vapor extraction, Water Resour. Rex., 28(2), 323-335. Hayden, N.J. and T.C. Voice, 1993, Microscopic observation of a NAPL in a threefluid phase soil system, J. Contam. Hydro!., 12, 217-226. Hayden, N.J., T.C. Voice, M.D. Annable, and R.B. Wallace, 1994, Change in gasoline constituent mass transfer during soil venting, /. Environ. Eng., 120(6), 15981614. Heid, J.G., J.J. McMahon, R.F. Nielsen, and ST. Yuster, 1950, Study of the Permeability of Rocks to Homogeneous Fluids, American Petroleum Institute, New York, 230-246. Hinckley, R.E., J.E. Killough, J. D'Sa, and G. Hertfelder, 1993, Infiltration and remediation modeling of in-situ NAPL transport using a three-phase, threedimensional simulator, Proceedings of Petroleum Hydrocarbons and Organic Chemicals in Ground Water, National Water Well Association, Houston. TX, 709-727. Ho, C.K. and K.S. Udell, 1992, An experimental investigation of air venting of volatile liquid hydrocarbon mixtures from homogeneous and heterogeneous porous media, J. Contam. Hydrol., 11, 291-316. Ho, C.K., S.-W. Liu, and K.S. Udell, 1994, Propagation of evaporation and condensation fronts during multicomponent soil vapor extraction, J. Contam. Hydro!., 16, 381^01. Hoag, G.E., C.J. Bruell, and M.C. Marley, 1984, A study of the mechanisms controlling gasoline hydrocarbon partitioning and transport in groundwater systems, NTIS Publication No. PB85-242907, October. Hochmuth, D.P., K.S. Udell, E.G. Lappala, and J.L. Jasperse, 1988, Soil venting of volatile organic chemicals from low permeability soils at a site in Santa Clara County, CA., presented at American Institute of Chemical Engineers, 1988 Summer National Meeting, Session 2, Ground Water Control and Treatment II, Denver, CO. Hoff, J.T., R. Gilham, D. Mackay, and W.Y. Shiu, 1993, Sorption of organic vapors at the air-water interface in a sandy aquifer material, Environ. Sci. Technoi, 27(13), 2789-2794. Hutzler, N.H., B.E. Murphy, and J.S. Gierke, 1989, State of Technology Review: Vapor Extraction Systems, EPA/600/2-89-024, Environmental Protection Agency, Washington, DC., 87. Imhoff, P.T. and P.R. Jaffe, 1994, Effect of liquid distribution on gas-water phase mass transfer in an unsaturated sand during infiltration, J. Contam. Hydrol., 16, 359-380. Johnson, P.C., M.W. Kemblowski, and J.D. Colthart, 1990a, Quantitative analysis for the cleanup of hydrocarbon contaminated soils by in-situ soil venting, Ground Water, 28(3), 413^29.

232

VADOSE ZONE HYDROLOGY

Johnson, P.C., C.C. Stanley, M.W. Kemblowski, D.L. Byers, and J.D. Colthart, 1990b, A practical approach to the design, operation and monitoring of in situ soil-venting systems, Ground Water Man. Rev., 10(2), 159-178. Jury, W.A., D. Russo, G. Striele, and H.E. Abd, 1990, Evaluation of volatilization by organic chemicals residing below the soil surface, Water Resour. Res., 26(1), 13-20. Karger, B.L., P.A. Sewell, R.C. Castells, and A. Hartkopf, 1971, Gas chromatographic study of the adsorption of insoluble vapors on water, J. Colloid Interface Sci., 35, 328-339. Kearl, P.M., N.E. Korte, T.A. Gleason, and J.S. Beale, 1991, Vapor extraction experiments with laboratory soil columnst implications for field programs, Waste Mgmt., 11, 231-239. Klinkenberg, L.J., 1941, The permeability of porous media to liquids and gases in drilling and production practice, American Petroleum Institute, New York, 200-213. Lang, J.R., K.M. Rathfelder, and L.M. Abriola, 1995, Multiphase, multicomponent numerical model of bioventing with nonequilibrium mass exchange, In Situ Aeration: Air Sparging, Bioventing, and Related Remediation Processes, Hinchee et al., ed., Proceedings of the Third International In Situ and On-Site Bioreclamation Symposium, San Diego, CA, Vol. 2, Battelle Press, 447—453. Levenspiel, O., 1972, Chemical Reaction Engineering, John Wiley, New York. Lingineni, S. and V.K. Dhir, 1992, Modeling of soil venting processes to remediate unsaturated soils, J. Environ. Eng., 118(1), 135-152. Massmann, J.W., 1989, Applying groundwater flow models in vapor extraction system design, J. Environ. Eng., 115(1), 129-149. Massmann, J.W. and D.F. Farrier, 1992, Effects of atmospheric pressures on gas transport in the vadose zone, Water Resour. Res., 28(3), 777-791. McClellan, R.D. and R.W. Gilham, 1992, Vapour extraction of trichlorethylene under controlled conditions at the Borden site, Subsurface Contamination byImmiscible Fluids, A. A. Balkema, Rotterdam, 89-96. McWhorter, D.B., 1990, Unsteady radial flow of gas in the vadose zone, J. Contam. Hydro!., 5, 297-314. Miller, C.T., M.M. Poirier-McNeill, and A.S. Mayer, 1990, Dissolution of trapped nonaqueous phase liquids: mass transfer characteristics, Water Resour. Res., 26, 2783-2796. Nzedi-Kizza, P., M.L. Brusseau, P.S.C. Rao, and A.G. Hornsby, 1989, Nonequilibrium sorption during displacement of hydrophobic organic chemicals and 45Ca through soil columns with aqueous and mixed solvents, Environ. Sci. Techno!., 23(7), 814-820. Okamura, J.P. and D.T. Sawyer, 1973, Gas chromatographic studies of sorptive interactions of normal and halogenated hydrocarbons with water-modified soil, silica, and chromosorb W, Anal. Chem., 45, 80-84. Pedersen, T.A. and J.T. Curtis, 1991, Soil Vapor Extraction Technology — Reference Handbook, EPA/540/2-91/003, Environmental Protection Agency, Washington, DC. Pennell, K.D., R.D. Rhue, P.S.C. Rao, and C.T. Johnston, 1992, Vapor-phase sorption of p-xylene and water on soils and clay minerals, Environ. Sci. Techno!., 26(4), 756-763. Pennell, K.D., S.A. Boyd, and L.M. Abriola, 1995, Surface area of soil organic matter reexamined, Soil Sci. Soc. Am. J., 59, 1012-1018. Pfannkuch, J.O., 1984, Determination of the contaminant source strength from mass exchange processes at the petroleum-groundwater interface in shallow aquifer systems, Proceedings of Petroleum Hydrocarbons and Organic Chemicals in Ground Water, National Water Well Association, Dublin, OH, 111-129.

LIQUID ORGANIC CONTAMINANTS IN THE UNSATURATED ZONE

233

Powers, S.E., L.M. Abriola, and W.J. Weber, Jr., 1992, An experimental investigation of nonaqueous phase liquid dissolution in saturated subsurface systems: steady state mass transfer rates, Water Resour. Res., 28(10), 2691-2705. Powers, S.E., L.M. Abriola, and W.J. Weber, Jr., 1994a, An experimental investigation of nonaqueous phase liquid dissolution in saturated subsurface systems: transient mass transfer rates, Water Resour. Res., 30(2), 321-332. Powers, S.E., L.M. Abriola, J.S. Dunkin, and W.J. Weber, Jr., 1994b, Phenomenological models for transient NAPL-water mass transfer processes, J. Contain. Hydro!., 16, 1-33. Rainwater, K., M.R. Zaman, B.J. Claborn, and H.W. Parker, 1989, Experimental and modeling studies of in situ volatilization: vapor-liquid equilibrium or diffusion-controlled processes?, Proceedings of Petroleum Hydrocarbons and Organic Chemicals in Ground Water, National Water Well Association, Houston. TX, 357-371. Rathfelder, K.M., W.W.-G. Yeh, and D. Mackay, 1991, Mathematical simulation of soil vapor extraction systems: model development and numerical examples, J. Contam. Hydro!., 8, 263-297. Rathfelder, K.M., J.R. Lang, and L.M. Abriola, 1995, Soil vapor extraction and bioventing: applications, limitations, and future research directions, Rev. Geophys., Supplement, 1067-1081, July. Rhue, R.D., P.S.C. Rao, and R.E. Smith, 1988, Vapor-phase sorption of alkylbenzenes and water on soils and clays, Chemosphere, 17, 727-741. Schwarzenbach, R.P., P.M. Gschwend, and D.M. Imboden, 1993, Environmental Organic Chemistry, John Wiley, New York. Sherwood, T.K., R.L. Pigford, and C.R. Wilke, 1975, Mass Transfer, McGraw-Hill, New York. Sleep, B.E. and J.F. Sykes, 1989, Modeling the transport of volatile organics in variably saturated media, Water Resour. Res., 25(1), 81-92. Sleep, B.E. and J.F. Sykes, 1993, Compositional simulation of groundwater contamination by organic compounds. 1. Model development and verification, Water Resour. Res., 29(6), 1697-1708. Steinberg, S.M., J.J. Pignatello, and B.L. Sawhney, 1987, Persistence of 1,2-dibromoethane in soils: entrapment in intraparticle micropores, Environ. Sci. Techno!., 21(12), 1201-1208. Thorstenson, D.C. and D.W. Pollock, 1989, Gas transport in unsaturated zones: multicomponent systems and the adequacy of Pick's laws, Water Resour. Res., 25(3), 377^09. Travis, D.D. and J.M. Macinnis, 1992, Vapor extraction of organics from subsurface soils is it effective?, Environ. Sci. Techno!., 26(10), 1885-1887. Weber, W.J., Jr., 1972, Physicochemical Processes for Water Quality Control, John Wiley, New York. Weber, W.J., Jr., P.M. McGinley, and L.E. Katz, 1991, Sorption phenomena in subsurface systems: concepts, models and effects on contaminant fate and transport, Water Res., 25(5), 499-528. Weber, W.J., Jr., P.M. McGinley, and L.E. Katz, 1992, A distributed reactivity model for sorption by soils and sediments. 1. Conceptual basis and equilibrium assessments, Environ. Sci. Techno!., 26(10), 1955-1962. Welty, C., C.J. Joss, A.L. Baehr, and J.A. Dillow, 1991, Use of a three-dimensional air-flow model coupled with an optimization algorithm to aid in the design of soil venting systems. Proceedings of Petroleum Hydrocarbons and Organic Chemicals in Ground Water, National Water Well Association, Houston, TX, 221-231. Wilkins, M.D., L.M. Abriola, and K.D. Pennell, 1995, An experimental investigation of rate-limited nonaqueous phase liquid volatilization in unsaturated porous media: steady state mass transfer, Water Resour. Res., 31(9), 2159-2172.

234

VADOSE ZONE HYDROLOGY

Wilson, D.J., A.N. Clarke, and J.H. Clarke, 1988, Soil clean up by in-situ aeration. I. Mathematical modeling. Sep. Sci. Tech., 23(10/11), 991-1037. Wilson, J.L., S.H. Conrad, W.R. Mason, W. Peplinski, and E. Hagan, 1990, Laboratory investigations of residual liquid organics from spills, leaks, and the disposal of hazardous wastes in groundwater, Report EPAI600/6-90/004, Environmental Protection Agency, Washington, DC. Zaidel, J. and D. Russo, 1993, Analytical models of steady state organic species transport in the vadose zone with kinetically controlled volatilization and dissolution, Water Resour. Res., 29(10), 3343-3356.

9

Coupling Vapor Transport and Transformation of Volatile Organic Chemicals

YASSAR H. EL-FARHAN KATE M. SCOW DENNIS E. ROLSTON

Importance of VOC Vapor Transport and Fate Volatile organic chemicals (VOCs) are the most prevalent group of organic goundwater contaminants and originate primarily from industrial sources (Westerick et al., 1984). Many VOCs are aliphatics, of which a number are halogenated, and aromatics, which may or may not be chlorinated. As a class, these chemicals are highly volatile, many are relatively insoluble, and some have densities greater than that of water. The high volatility of these chemicals has supported a belief that fluxes of these materials from soil to the atmosphere arc so great that their persistence in soil is short-lived and the probability of groundwater contamination is small. However, groundwater monitoring data show that this is not the case and that many of these chemicals are posing potential threats to human health and the environment through contamination of water supplies (U.S. EPA, 1980). Even though VOCs are so widespread in the environment, our ability to adequately predict their transport and transformation in soil and the vadose zone is greatly lacking. This problem is further compounded by the fact that most sites are not contaminated with single compounds, but with mixtures of VOCs. As will be discussed later, the presence of other VOCs greatly complicates our ability to predict the behavior, both physical and biological, of a given chemical. Microbial communities play a pivotal role in the duration of contaminants from natural and managed environments and thus in reducing human exposure to toxins. A broad range of bioremediation approaches exist for contaminated soils and vadose material (Nelson et al., 1987, 1988; Marker and Kim 1990; Gibson and Sayler, 1992) and range from unmanaged to highly engineered systems. The unmanaged biodegradation of pollutants by indigenous microbial communities is increasingly becoming a remediation option in certain cases and is called "passive" or "intrinsic"

236

VADOSE ZONE HYDROLOGY

bioremediation. Biostimulation usually involves additions of nutrients, electron acceptors, or cosubstrates to enhance the activity of indigenous microbial communities. Understanding and quantifying the factors that control biodegradation rates by vadose microbial communities is essential for developing realistic pollutant transport models and useful in estimating the requirements or analyzing the response of microorganisms involved in bioremediation. Microorganisms in soil are intimately associated with their environment and strongly influenced by physical processes at the pore, column, and field scale (Scow, 1993). In fact, it is impossible to predict rates of biodegradation in porous media, particularly under transient conditions, without consideration of the mass transfer processes that are tightly coupled, spatially and temporally, with microbial processes. More research has concerned groundwater aquifers than the vadose zone, perhaps because groundwater is much more significant than soil in terms of human exposure to toxic chemicals. Focusing primarily on groundwater systems, however, is somewhat short-sighted because the sources of groundwater contaminants are frequently hazardous waste or former dump sites situated in surface soils or the vadose zone. These locations are active sources of VOCs and will often replenish groundwater aquifers that have been thought to be "successfully" treated by costly methods, such as pump and treat. Unsaturated systems are scientifically challenging because, with the presence of air-filled pores, there is greater complexity to the physical system and more phases in which a chemical can be present. Large fluxes in the vapor phase may result in contamination much further from the source than if transport occurred only in the liquid phase. Also, there is the potential for vadose environments to support high rates of aerobic biodegradation. The purpose of this chapter is to review the major physical and biological processes that govern the fate and transport of VOCs in soil and the vadose zone (e.g., Babiuk and Paul, 1970; Chiou and Shoup, 1985; Garbarini and Lion, 1986; Fliermans et al., 1988; Brusseau and Rao, 1989; Harmon et al, 1989; AlvarezCohen and McCarty, 1991; Bekins et al., 1993). Laboratory investigations of the diffusion, sorption and biodegradation of VOCs in California soils are described. Also presented is a study of the coupled processes of biodegradation and mass transfer of toluene and trichloroethylene (TCE) during transient diffusion through soil.

Background on Fate Processes Physical Processes

Convection Convection or mass flow of VOC vapors in the subsurface may occur due to barometric pressure changes, temperature effects, wind, water infiltration, density-driven flow, and vacuum extraction. Each of these processes results in pressure gradients that are the driving forces for flow. Assuming incompressible flow, the

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

237

steady-state transport equation for convection of gases is similar to Darcy's law for water flow:

where Jc is the convenience vapor flux, ka is the air permeability, P is the pressure above or below atmospheric, and z is the spatial coordinate. Temperature effects likely play a minor role below the upper few centimeters of the soil surface. Also, convective transport in the subsurface due to barometric pressure changes is generally considered to be small in relation to diffusive transport. However, for fairly coarse porous media with a relatively high air permeability, "fresh" air may migrate several meters into the subsurface during typical barometric pressure cycles (Mezzanine and Farrier, 1992). Although effects due to barometric pressure fluctuations may not be very large in most soils, natural fluctuations in barometric pressure are being considered as a passive soil vapor extraction method to remove contaminant gases from the vadose zone (Weidner et al., 1995). Fluctuations of air pressure at the soil surface due to wind cause mixing of air near the surface soil that enhances gas transport over that due to diffusion (Scotter ct al., 1967). The effects of wind influence transport only in the upper few centimeters of soil. Infiltration of water from rainfall and irrigation forces soil air and any chemical vapor ahead of the wetting front. Thus, convective transport may be substantial during the short times of infiltration events, The vapors of many of the nonaqueous-phase liquids (NAPLs) that exist within the vadose zone are much denser than air. These dense vapors cause convective flow, which can result in contaminant movement to much greater depths than would occur due to normal diffusion and movement of the liquid NAPL (Johnson et al., 1992). Density-driven flow is a significant transport mechanism for VOCs, particularly in coarse-grained materials. One of the most common methods for remediation of contaminated sites is by vacuum extraction, where a vacuum is applied to extraction wells within the unsaturated zone (Brauns and Wchrle, 1992; McClcllan and Gillham, 1992). The convective velocity of vapors is great near the wells and decreases with distance away from wells. It is obvious that this remediation technique results in substantial convective transport that must be considered in simulation models. Diffusion—Cos Phase For many circumstances and applications, vapor diffusion is the major mechanism of gas transport. The diffusion of gases in the vadose zone has often been assumed to be adequately modeled by Pick's law:

where Jg is diffusive flux density, Dp is the soil-gas diffusivity, Cg is the chemical concentration in the gas phase, and z is the spatial coordinate. This equation is applicable to systems where the flux of a species can be assumed to be independent

238

VADOSE ZONE HYDROLOGY

of the flux of others, and inherently assumes a low concentration for that species in the bulk gas phase (Amali and Rolston, 1993). However, liquid mixtures of organic chemicals introduced into the soil environment can involve compounds with vapor pressures high enough to form a significant portion of the contaminated soil gas (Baehr and Bruell, 1990). At these high vapor pressures, the flux of each species may be dependent on the flux of other species. To deal with the flux interdependence of the diffusing species, the general multicomponent diffusion equations that arise from the gas kinetic theory should be used. Neglecting pressure diffusion in the vertical direction, the general multicomponent equations reduce to the well-known Stefan-Maxwell equations (Amali and Rolston, 1993):

where y is the mole fraction, J is the molar flux, £>,; is the binary diffusion coefficient, p is total gas pressure, R is the universal gas constant, T is temperature in degrees Kelvin, z is the spatial coordinate, i and j represent different gas species, and s is the total number of gases making up the mixture. If the total mole fraction of the chemical vapors exceeds 0.05 (Amali and Rolston, 1993), the steady-state fluxes should be determined from the Stefan-Maxwell equations. However, from laboratory transport studies of VOC mixtures, Amali et al. (1996) showed that during transient diffusion, the effects of VOC dissolution in water and sorption on soil overshadowed the multicomponent diffusion effects. Thus, during transient diffusion, Pick's law (with a nonlinear sorption isotherm) adequately described concentration profiles and VOC fluxes. At steady state, the Stefan-Maxwell equations are needed. Diffusion—Liquid Phase

Besides diffusion of VOCs through the gas phase of soil, chemicals must also diffuse through water films or water-filled pores to reach adsorption sites or locations where biodegradation of the chemical occurs. Brusseau (1991) and McCoy and Rolston (1992) have developed models that consider mass transfer from the gas phase to the water and sorbed phases during gaseous advection of organic chemicals, but do not consider biodegradation. They have shown that for some chemicals and soil conditions, sorption may be limited by mass transfer constraints. However, for diffusion only (no convection) in the gas phase, mass transfer limitations on sorption may be expected to be small or negligible for many of the VOCs unless very large water-filled aggregates are present. For packed soil columns, Petersen et al. (1994) observed no evidence of mass transfer limitations for diffusion of toluene and TCE through sterile soil with air-filled porosities as low as 0.12. Biodegradation may also be limited by mass transfer or diffusion through the water-filled pores of aggregates from the interior of the aggregate to the exterior solution. Since the interiors of aggregates are often inaccessible to aerobic microorganisms, either due to the presence of small pores or to oxygen and substrate

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

239

limitations within the aggregate (Schmidt et al., 1985; Steinberg et al., 1987; Scow and Alexander, 1992; Scow, 1993), the diffusion of dissolved and sorbed VOC from the interior of aggregates to the sites of biodegradation at or near the outer surfaces of aggregates may limit transformation rates. Scow and Hutson (1992) developed a model that describes the biodegradation of chemicals under mass transfer limitations due to sorption and diffusion in spherical aggregates. Based on this model, Chung et al. (1993) proposed a modified Thiele modulus that includes the effect of sorption and biodegradation for evaluating whether mass transfer limitations are important for biodegradation. The modified Thiele modulus, <j>, is

where R is the radius of aggregates, e is the porosity of aggregates, K is the equilibrium adsorption constant, k is the first-order biodegradation rate constant, and De is the effective liquid diffusion coefficient. For 0 < 1, intraparticle diffusion resistance does not significantly affect biodegradation. For the soil conditions of the experiments to be described later in this paper,

240

VADOSE ZONE HYDROLOGY

component partitioning relationships will likely suffice to describe VOC dissolution in water and sorption on soil. There are examples in the literature (Pignatello, 1990a, 1990b) that show very slow desorption of sorbed VOCs from soil, particularly the soil organic matter. However, for the conditions of the experiments described later on in this chapter, we are mostly concerned with processes during the period of adsorption because rates of biodegradation are relatively fast. Thus, for modeling purposes, we ignore the possible slow desorption mechanism. Biological Processes Biodegradation of VOCs

Microorganisms, as a group, employ a variety of metabolic pathways that result in the transformation or biodegradation of VOCs. These include aerobic and anaerobic processes in which the VOC serves as an electron donor, anaerobic processes in which the VOC serves as an electron donor or acceptor, and cometabolic processes in which the VOC is broken down by enzymes that are induced for the breakdown of other compounds. A considerable amount of research has been conducted on the biodegradation of specific VOCs, including toluene (Goldsmith and Balderson, 1988; Alvarez and Vogel, 1991; Chang et al., 1993); TCE (Oldcnhuis et al., 1989; Ensley, 1991), naphthalene (Mihelcic and Luthy, 1988), and 1,2-dichloroethane (Hartmans et al., 1992; van den Wijngaard et al., 1992). The particular metabolic pathway involved in biotransformation of a VOC may be of great environmental importance. Some microbial pathways may convert pollutants to equally or more toxic metabolites, as can occur in the anaerobic degradation of chlorinated aliphatics (Parsons et al., 1984; Wilson et al., 1986). Much of the existing information on pathways and rates is for pure cultures or enrichment cultures of bacteria and may not be applicable to environmental conditions where biodegradation is frequently controlled by factors other than an organism's metabolic capabilities. There have been fewer studies of the biodegradation of VOCs by indigenous populations in aquifer or subsurface media (Lanzarone and McCarty, 1990; Alvarez et al., 1991) or soil (Fan and Scow, 1993). Many VOCs in the environment are found in mixtures. Although the kinetics of biodegradation of the various chemicals present in mixtures are sometimes simply additive, many VOCs show strong interactions, as discussed below, which may significantly alter their kinetics when another chemical is present. Cometabolism The presence or absence of other carbon/energy sources is an important determinant of the biodegradation of certain VOCs (Scow et al., 1989; Fan and Scow, 1993). One of the best examples of this phenomenon is the biodegradation of TCE. Just over a decade ago, it was believed that TCE could not be biodegraded (Bouwer et al., 1981). It is now well established that TCE can be degraded by methanogens (Bouwer and McCarty, 1984), methanotrophs (Little et al., 1988) nitrifying bacteria (Ensley, 1991), and by certain species of bacteria able to degrade aromatic compounds (Ensley, 1991). The

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

241

latter group includes Pseudomonas cepacia (Nelson et al., 1986; Folsom et al., 1990), P. mendocina (Winter et al., 1989), and P. putida (Wackett and Gibson, 1988). The mono- or dioxygenase enzymes that catalyze the first step in toluene or phenol metabolism are implicated in the breakdown of TCE (Ensley, 1991). An advantage of these aerobic pathways is that they do not appear to promote the formation of the undesirable metabolites, such as dichloroethylene and vinyl chloride, that are potential dehalogenation products of anaerobic degradation of TCE (Vogel and McCarty, 1985; Wilson et al., 1986). Repression The presence of one chemical may repress or stimulate the biodegradation of another chemical in a mixture, as has been observed for mixtures of benzene, xylene, toluene, and ethyl benzene (Alvarez and Vogel, 1991; Chang et al., 1993; Criddle, 1993) and in TCE's requirement for a cosubstrate (Ensley, 1991). Toluene also strongly represses the biodegradation of low concentrations of dichloromethane (K. M. Scow, unpublished data). Toxicity Some pollutants and/or their metabolites are toxic to the microbial populations that degrade them and this may ultimately result in termination of biodegradation activity. One of best known of the more toxic VOCs is TCE, which is frequently shown to be toxic to the organisms involved in its cometabolism (Wackett and Gibson, 1988; Wackett and Householder, 1989; Broholm et al., 1990; Oldenhuis et al., 1991). The toxicity is apparently due to the formation of a toxic metabolite, possibly TCE epoxide, which binds to the cell's membrane and disables its metabolic activity. Biodegradation of Toluene and TCE by Indigenous Populations in Soil

Extensive studies have been conducted on the aerobic biodegradation of toluene and TCE by indigenous microbial populations in Yolo silt loam, as well as other soils (Fan and Scow, 1993; Mu and Scow, 1994) and vadose sediments (Fuller et al., 1995). Trichloroethylene can be degraded by soil and vadose zone microbial communities in the presence, but not the absence, of toluene as a cosubstrate. Most of the TCE that disappeared from the headspace was mineralized to carbon dioxide rather than to volatile metabolites. At concentrations of 1 ng TCE/mL soil solution and 20/xg toluene/tnL, a lag period of 60-80 h was observed prior to degradation (Fan and Scow, 1993). Population measurements were performed to determine whether the number of organisms able to degrade TCE is a subset of the population able to degrade toluene, or whether the sizes of the two populations are equivalent. A most probable number (MPN) method was developed to estimate the population size of microorganisms able to degrade TCE and toluene in Yolo silt loan (Mu and Scow, 1994). The initial populations of toluene and TCE degraders in Yolo soil before exposure to the chemicals were 4.0 and 1.9 x 103 cells/g soil, respectively; approximately 0.004% of the total eulturable (on tripticase soy agar) microbial population. After exposure to 20 ng toluene and 1 /zg TCE/g soil, populations increased to 7.3 and 6.8 x 107

242

VADOSE ZONE HYDROLOGY

cells/g soil, respectively (approximately 25% of total population). Measurement of toluene degraders throughout the degradation of 20/u.g of toluene and 1 /ug TCE/g soil showed population growth to be simultaneous with the disappearance of both chemicals. Thus, the lag period was found to be due to the slow growth of initially very small populations able to degrade these chemicals. The lag period for both chemicals decreased with increasing number of times of exposure to the two chemicals. The rate and extent of removal of TCE is dependent on the initial concentrations of both TCE and its cosubstrate, toluene. In Yolo silt loam, at a concentration of 1 /ug TCE/mL soil solution, approximately 60% of TCE is degraded with 20 /Mg toluene/mL. At the same TCE concentration, with more toluene present, there is a greater rate and extent of removal of TCE; 100//g toluene/mL supported removal of TCE to below the detection limit. At 20 fj,g toluene/mL and various initial TCE concentrations, there was an inverse relationship between TCE concentration and (1) percent of TCE degraded, (2) the rate of toluene degradation. Too high a TCE concentration (60 /Ltg/mL) resulted in little or no degradation of either TCE or toluene. Unlike what has been reported for pure cultures of bacteria, continual exposure of soil populations to high concentrations of TCE did result in the termination of toluene and TCE degradation. Biodegradation of TCE and toluene by indigenous microbial communities in vadose zone samples from Lawrence Livermore National Laboratories required the addition of nutrients (Fuller et al., 1995). Added nitrogen was essential and phosphorus further enhanced the rate. Inoculation of vadose samples with a bacterial species able to degrade toluene and TCE did not enhance the rate of degradation above that of the indigenous populations. Vadose zone samples from an uncontaminated area showed more biodegradation activity than did samples from a dieselcontaminated site.

Coupling Biodegradation and Mass Transfer Background and Model Development In order to predict the fate of chemicals during subsurface transport, understanding physical, chemical, and biological processes in the subsurface environment is essential. Kinetic studies are important in predicting rates of biodegradation in the field and useful in evaluating the efficacy of treatment methods (Alexander and Scow, 1989). Biodegradation in highly heterogeneous environments, such as soil and groundwater, can be complicated and difficult to predict. For example, what controls the rate of degradation: mass transfer of the chemical or the properties of the microbial population able to degrade the chemical? Is the chemical the sole carbon and energy source or is it cometabolized? If so, what compound(s) serve(s) as the secondary carbon source: indigenous compounds or other chemicals in the waste stream? Some of these questions are explored below in a discussion of the equations used to describe the biodegradation of organic chemicals in well-mixed conditions, as well

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

243

as consideration of a model that couples biodegradation kinetics with expressions of mass transfer. Experiments were performed in Yolo soil under transient concentration conditions to measure how diffusive mass transfer affects biodegradation rates of toluene in soil and to describe the kinetics of biodegradation under transient conditions. Reaction and mass transfer parameters obtained from the experiments described previously were used as input parameters, and model simulations were compared with experimental data. Biodegradation Kinetics Chemical consumption by microorganisms can be described using one of two techniques: (1) chemical disappearance curves in closed systems, or (2) relating microbial populations and their growth to chemical consumption. While both techniques involve obtaining information from batch experiments, the latter offers better flexibility for describing various degradation curves. The most common equation that characterizes chemical degradation rates from chemical disappearance curves is known as the Michaelis-Menten equation:

where Fmax is the maximum rate of chemical disappearance (\/T), Km(M/V) is the concentration at which the disappearance rate is half of the maximum rate, C is the concentration (M/V\ and t is time. This equation, developed to describe enzyme kinetics, is applicable only to a static microbial population (i.e., a constant number of microbial cells, and thus a constant amount of enzyme). Though some batch experiments may have a constant microbial population, this condition is unlikely in field sites, rendering equation (9.5) practically inapplicable. Relating microbial growth to chemical disappearance rate was proposed by Monod in 1942. He related the chemical disappearance rate to microbial growth by

where A is a proportionality constant (to be discussed below) and «ceils is the number of microbial cells per unit volume (cells/ V). The Monod second equation relates specific microbial growth rate to chemical concentrations as follows:

where // is the specific growth rate (\/T\ /imax is the maximum specific growth rate (1/T), and Ks the half-saturation constant (the concentration at which /z is half Mmax)- We can combine equations (9.6) and (9.7) to give

Equations (9.7) and (9.8) can be used together to describe chemical degradation rates while accounting for microbial population changes. Parameter A is related to the

244

VADOSE ZONE HYDROLOGY

total amount of enzyme present and to the inverse of the yield (Y). which represents the fraction of the degraded chemical that is converted into biomass. A quick investigation of the dimensionality of the two sides of equation (9.8) shows the dimensions of A to be mass of chemical/cell when «ceu is reported in units of cells/unit volume, or mass of chemical/cell mass when ncen is reported in units of cell mass. A commonly used form of equation (9.8) is

where B is the biomass (Cell mass/unit volume), and Y is the yield coefficient (cell mass/chemical mass). Working with closed batch cultures in which degraded chemical mass is converted into biomass, Simkins and Alexander (1984) combined equations (9.7) and (9.9) and derived

where Q is the initial concentration in the system and X0 is the initial microbial biomass in the system in equivalent substrate mass units. They also examined conditions under which equation (9.10) reduces to other more familiar degradation functions such as zero and first order. Use of this equation is not appropriate for the transient conditions modeled in our experimental systems. If biodegradation of a substrate is due to the activity of several distinct microbial populations—for example, different pseudomonad species using different metabolic reactions—then each reaction is described by a separate Monod expression [equation (9.9)] with unique parameters to describe each reaction. With the assumption that there are no interactions among the different reactions, a summation of these reactions is used to describe the net disappearance of the substrate Q (Celia et al., 1989; Chen et al., 1992), shown in equation (9.11), where / represents the reaction of interest (with n possible reactions). If biodegradation of the substrate via a single reaction is limited not only by substrate concentration (C,), but also by other nutrients, such as oxygen, the effect of such nutrients is described by a function similar in form to the Michaelis-Menten equation and specific to each nutrient (Celia et al., 1989; Chen et al., 1992). Thus, the result is a set of additive terms that represent the degradation rate of the substrate as influenced by the concentration of limiting nutrients;

where II represents the multiplication of terms j — 1 to m, which designate other nutrients that influence the reaction. The sum of all of these terms will give the expression for the overall degradation rate of Q. Note here that similar steps must be taken to convert the growth rate equation [equation (9.7)], to be able to incorporate multiple compound dependency of the growing microorganisms. It is evident at this point of the discussion that a full description of even simple chemical reactions can quickly become mathematically complex, and physically

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

245

impractical. This difficulty is typically avoided by ensuring that other nutrients are not limiting, therefore enabling the use of equation (9.9). In our study, we assumed that toluene degradation was limited only by toluene concentration. Finally, in order to prevent uncontrolled microbial growth, using equation (9.7), and as a logical progression in the conceptual modeling of microbial population growth, microbial decay is often incorporated into equation (9.7) when modeling microbial kinetics. If one assumes that microbial populations decay exponentially, the rate of decay can be represented by a decay constant multiplied by microbial population. Such a term would be subtracted from equation (9.7) to give (written using microbial biomass, B)

where b is the microbial decay constant (\/T}.

Physical Transport Experiments were conducted where VOC vapors were allowed to diffuse through a soil column while undergoing sorption, dissolution, and biodegradation. The governing one-dimensional transport equation for Fickian transient diffusion is

where C is the gas-phase concentration (g VOC/cm3 air), e is the air-filled porosity (cm3 air/cm3 soil), Dp is the soil-gas diffusivity (cm3 air/cm soil/min), / is time (min), and x is distance (cm). The sink term in the above equation includes the processes explained above that take place during transport. Each process, and its measured parameters, is discussed below. Sorption is calculated using an equilibrium, linear adsorption isotherm given by

where Kd is the solid/aqueous partition coefficient (cm3/g). For TCE and toluene, Kd is equal to 0.58 and 0.87, respectively, for the Yolo silt loam used in the experiments. The linearity of the isotherm was established in batch experiments and is believed to hold during transport. The assumption of equilibrium conditions is justified from batch experimental results, and, more important, due to the relatively slow transport during diffusion. Partitioning into water is calculated by equilibrium, Henry's law partitioning using

where KH is Henry's coefficient, with values equal to 0.261 and 0.397, for toluene and TCE, respectively, at 25°C. Using the equilibrium and the linearity assumptions for both sorption and dissolution, we are able to rewrite equation (9.13) as

246

VADOSE ZONE HYDROLOGY

where R is the retardation factor defined as

where 9 is the soil-water content (cm3 water/cm3 soil) and pb is the bulk density (g soil/cm3). During the first part of this study, sterilized soil columns were used during chemical diffusion experiments. This resulted in the establishment of a relationship between the effective diffusion coefficient (Dp) and the air-filled porosity. The resulting relationship (Petersen et al., 1994) is given by

where Z>0 is the chemical diffusion coefficient in air (cm2 air/min), u — 0.12, and v = 1.23. For TCE, £>0 = 5.01 cm2/min; for toluene, D0 = 4.58 cm2/min. Coupling Transport and Biodegradation Chemical transport and biodegradation experiments were conducted using unsaturated soil columns. Transient concentration conditions were maintained throughout the duration of these experiments; thus, the collected data would reflect the various coupled processes described above. Initially, equation (9.5) was used to represent the sink term in equation (9.16) when modeling chemical transport. The model was unable to reproduce the data, since there were changes in the microbial population that could not be described by such a simple model. The set of equations used to model toluene biodegradation, biomass growth, and transport are equations (9.9), (9.12), and (9.16), respectively. These equations can be combined to describe coupled transport and biodegradation to give

and

As evident from the previous two equations, we are assuming that no additional compounds are limiting. This assumption was verified to be true for oxygen, which most likely would limit biodegradation at high toluene concentrations.

Experimental Apparatus The apparatus used in this study is the two-chamber diffusion cell shown in figure 9.1 (Glauz and Rolston, 1989). The apparatus consists of a soil column with air cham-

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

247

Figure 9.1 A schematic of the two-chamber diffusion apparatus.

bers attached at either end. One of the chambers (the inlet chamber) is equipped with a piston mechanism used to separate the soil column from the inlet chamber in order to establish initial conditions. Magnetic stirrers are placed inside both chambers to maintain well-mixed gas conditions throughout the experiment. Initially, the piston is pushed against the soil column, and chemical vapors are injected into the inlet chamber. The vapors are allowed to mix and equilibrate to C0 in the inlet chamber. The experiment is started by pulling the piston back and allowing the gas to diffuse through the soil column and into the exit chamber. Gas samples were taken from the inlet and exit chambers, and from column sampling ports placed at 2.5, 5, 10 and 15 cm from the inlet chamber. Gas samples from the end chambers were taken using a 1-mL gas-tight syringe (Hamilton Company, Reno, NV) and analyzed using a Hewlett Packard 5890A gas chromatograph (GC) (Hewlett Packard Company, Palo Alto, CA) equipped with Flame lonization Detector (FID) and a 10-ft packed column 20% SP-2100, 0.1% Carbowax 1500, 100/120 mesh Supelcoport (Supelco Inc., Bellefonte, PA) run isothermally at 140°C. Gas samples from the soil column were taken using a 50-//.L Hamilton gas-tight syringe and analyzed with a SRI GC (SRI Co., Torrance, CA), equipped with an FID and a 30m fused silica capillary column, 0.53mm inside diameter, and a 3.0/^m film thickness (Supelco) run isothermally at 100°C. The effective inlet chamber length was 721 cm, and the effective exit chamber length was 323 cm (effective length is equal to chamber volume/cross-sectional area of the soil column). Chamber sizes were decided using the error analysis from Glauz and Rolston (1989) with the idea that chemical concentrations in the inlet chamber would decrease gradually over the duration of the experiment. The soil column was 20 cm in length, and 7.6 cm in diameter. Preparation of the soil column was carried out as follows: 7-cm columns were attached to either end of the soil column and the entire column was packed to a bulk density of 1.3 g/cm3 with air-dry Yolo silt (see table 9.1)—the same soil used in the biodegradation batch experiments described earlier. Enough water was added uniformly to either end of the packed soil

248

VADOSE ZONE HYDROLOGY

Table 9.1. Characteristics of the Soil and the Two Chemicals Used in the Experiments Characteristic Surface area (m2/g) Organic carbon (%) EC (milli-mhos/cm) pH Sand (%) Silt (%) Clay (%) Water content (cm3/cm3) Molecular weight (g/mol) Diffusion coefficient in aira (cm2/min) Henry's constant" (KH) Partition coefficient" (Kd, cm3/g)

Yolo Silt Loam

TCE

Toluene

80.60 1.05 0.77 7.9 33 49 18 20 131.4 5.01 0.397 0.58

92.3 4.83 0.261 0.87

"Constants were obtained from Petersen et al. (1994)

to bring it to a volumetric water content (0) of approximately 25%. The column was allowed to equilibrate in a cold room (4°C) for 12-16 weeks, at which time the two extra end columns were cut off and discarded, while the middle column was used in the experiment. Uniformity of packing was checked using gamma attenuation measurement. In addition, uniformity of water content in the discarded columns was checked at the end of the equilibrium period, as was the soil column itself at the end of experiments. Soil-liquid and liquid-vapor partition coefficients were determined using the Equilibrium Partitioning In Closed Systems method (EPICS) (Petersen et al., 1994). Results and Discussion Experiments were conducted for two initial toluene to TCE concentration ratios in the inlet chamber (20:1 and 40:1). These ratios are based on the liquid-phase concentration of both compounds. In order to minimize the lag period associated with biodegradation, air at 100% relative humidity and 40 mg toluene/L was flushed through each soil column immediately prior to each experiment to increase the initial density and enzyme activity of toluene-degrading populations. Figures 9.2 and 9.3 show the concentration change with time and distance for toluene and TCE, respectively, for the 20:1 experiment. Similarly, figures 9.4 and 9.5 show the toluene and TCE data for the 40:1 experiment. In both experiments, toluene concentrations initially increase then decrease at the column ports, conceivably reflecting shifts in the processes that control concentrations breakthrough. During the increasing concentration phase, diffusive transport supplies the chemical in excess of the rate it is being consumed, causing the concentrations to increase. The decrease in concentration demonstrates that toluene is being consumed faster than it is being supplied by diffusion. The relationship between biodegradation and mass transfer changes throughout the course of an experiment. Initially, the diffusive flux is very large

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

249

Figure 9.2 Variation of toluene concentrations with time at the different sampling points in the apparatus for the 20:1 toluene to TCE ratio experiment. due to the large concentration gradient across the column, and the impact of biodegradation appears to be small in comparison. As time progresses, the diffusive flux quickly decreases, becoming small relative to the degradation rate. In other words, these two processes change simultaneously, thus making attempts to resolve transport versus rate limitations very difficult. Data from the column ports are a direct representation of processes that occur at that point of the column, while data from the inlet and outlet chambers represent an integration of the coupled processes throughout the column. Therefore, to be able to understand the coupled processes that occur at each point, model simulations were fitted to data from the column.

Figure 9.3 Variation of TCE concentrations with time at the different sampling points in the apparatus for the 20:1 toluene to TCE concentration ratio experiment.

250

VADOSE ZONE HYDROLOGY

Figure 9.4 Variation of toluene concentrations with time at the different sampling points in the apparatus for the 40:1 toluene to TCE ratio experiment. The equations used to describe the transport and biodegradation of the primary substrate (toluene) [equations (9.19) and (9.20)] require five biological parameters in order to define the shape of the Monod growth curves. These parameters are the maximum specific growth rate (/imax), the yield coefficient (7), the half-saturation coefficient (Ks), the initial biomass (BQ), and the microbial decay/die-off rate (b). In order for the equations to hold, these parameters must not vary significantly over the duration of the experiment. An attempt was made to independently determine as many parameters as possible. We assumed that /^max and Ks values of 3.22 (±0.76) and 1.95 (±1.71), respectively, obtained from batch experiments with similar toluene to TCE ratios, were applicable to the column. A value of 0.35 for the yield coefficient Y was obtained directly from batch experiments where microbial populations were

Figure 9.5 Variation of TCE concentrations with time at the different sampling points in the apparatus for the 40:1 toluene to TCE concentration ratio experiment.

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

251

quantified. Two parameters remained undetermined: the decay rate constant (b) (for which we have no value estimates) and the initial biomass in the column (B0). Both parameters were fitted to data collected at each port by solving equations (9.19) and (9.20) using an iterative finite difference scheme and using a general-purpose optimization code for minimizing the root-mean-square error (Clausnitzer and Hopmans, 1995). Figure 9.6a shows the model fits to column data from the 20:1 experiment. The fitted values obtained for each port for b and BQ are shown in figure 9.7a. As might be expected, the decay rate did not vary significantly across the column, whereas the initial biomass decreased with distance from the inlet chamber. Similarly, figures 9.6b

Figure 9.6 Comparison of fitted model results to toluene concentration data at the different column ports for (a) the 20:1 experiment; (b) the 40:1 experiment.

252

VADOSE ZONE HYDROLOGY

Figure 9.7 Initial biomass and decay rate values fitted to toluene concentration port data for (a) the 20:1 experiment; (b) the 40:1 experiment.

and 9.7b show the model fits to data from the 40:1 experiment, and the distribution of the fitted parameters across the column, respectively. Again, little variability is observed in the decay constant, while the initial biomass again decreased with distance. Variation in B0 within the column may be attributed to a small concentration gradient that existed across the soil column during the preacclimation period. Another possibility is the existence of other biological interactions between the toluene and TCE further along the column, such as competitive inhibition. At high TCE to toluene ratios, as discussed previously, the apparent degradation of toluene would decrease. Since the fitted model does not yet account for such interactions, the existing model would compensate for it by fitting a lower biomass at regions where competitive inhibition may be occurring. This hypothesis will be tested when the model is modified to incorporate the effects of TCE on toluene. The distribution of B0 for both experiments was fitted with a linear, an exponential, and a power equation. In the 40:1 experiment, two linear equations were developed; one from 0 to 5 cm and another from 5 to 20 cm. These fitted distributions were

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

253

then used in the numerical model in order to obtain results that could be compared with the inlet chamber data. The average of the decay rate was used during those comparison simulations. Model fits to the inlet chamber data, for both experiments, are presented in figures 9.8a and 9.8b for the 20:1 and 40:1 experiments, respectively. Both the linear and exponential distributions provide better fits to the data, reflecting their more reasonable representation of the initial biomass (S0) distribution across the column. The poor fits of the power distribution were due to overestimation of the initial biomass close to the inlet chamber, where most of the degradation was occurring. In summary, all parameters, other than B0, used to fit data from both experiments were the same. The variation in B0 between the two experiments (run with two different columns) can be attributed to the slightly higher concentration of toluene in the air used for flushing the 20:1 over 40:1 column during the time prior to each

Figure 9.8 Simulated inlet chamber concentrations using an average decay rate value and various equations to represent the initial biomass distribution for (a) the 20:1 experiment; (b) the 40:1 experiment.

254

VADOSE ZONE HYDROLOGY

experiment. It should be noted, however, that the difference in biomass was small relative to the changes reported in batch systems before and after addition of toluene. Also, the variability associated with biomass measurement techniques is similar to the variability observed between the two experiments. Trichloroethylene concentrations in the soil column follow a trend similar to that of toluene. At depths closer to the inlet chamber, the concentrations increase then decrease with time. However, the decrease in concentration is not as sharp as that experienced by toluene. This may be explained by the cometabolic nature of TCE degradation. Only a small fraction of enzyme produced to degrade toluene reacts with TCE molecules. Examining figures 9.2 to 9.5, we can see good correlation between the termination of TCE degradation and the depletion of toluene at each of the column ports. No significant degradation of TCE occurs when toluene concentrations become very low. As discussed earlier for batch systems, the ratio of toluene to TCE strongly influences the kinetics. Thus, the various ratios of toluene to TCE concentration that occur throughout the column cause their interactions to be highly complex. Because the diffusion coefficient of TCE is larger than that of toluene, some TCE will diffuse to regions where toluene is not yet available to induce degradation. At the end closer to the inlet chamber, the toluene to TCE concentration ratios are largest; thus, strong interactions between TCE and toluene are unlikely. However, concentration levels at the 10- and 15-cm ports show that toluene to TCE ratios are close to 1. At these ratios, batch experiments have shown considerable reduction in toluene biodegradation. The mechanism underlying this inactivation is not yet fully understood, although it appears to function as a competitive inhibition system with TCE outcompeting toluene for the oxygenase enzyme. This would ultimately result in a decrease in total enzyme activity. The concentrations of TCE at the end of each experiment leveled off, indicating that the system was reaching equilibrium. Concentration gradients across the column were very small, and TCE consumption ceased in response to the depletion toluene. The concentration of TCE after equilibrium was reached was lower for the 40:1 experiment than for the 20:1. This would be expected because higher levels of toluene would result in greater overall removal of TCE.

Conclusions The results obtained from this work enable us to reach the following conslusions: Incorporation of microbial population changes is essential when modeling transient transport of a chemical that is used as a substrate for microbial growth. Parameters that describe microbial growth in batch experiments can be used to sufficiently describe microbial population dynamics when substrate degradation is coupled with its transport. The initial biomass concentration within the column is the main parameter that varied among the data sets. This variability may be a reflection of the

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

255

method of preacclimation, in addition to the presence of any substrate interactions not described by the model. The TCE degradation across the column was related to the presence and degradation of toluene, and terminated as soon as toluene was depleted from the system. In order to model TCE transport and degradation, degradation models that deal with dual substrate utilization need to be incorporated in the transport model.

References Alexander, M. and K.M. Scow, 1989, Kinetics of biodegradation in soil, in Reaction and Movement of Organic Chemicals in Soils, Soil Science Society of America Special Symposium Publication 22, pp. 243-269, Soil Science Society of America, Madison, WI. Alvarez, P.J.J. and T.M. Vogel, 1991, Substrate interactions of benzene, toluene, and para-xylene during microbial degradation by pure cultures and mixed culture aquifer slurries, Appl. Environ. Microbiol, 57, 2981-2985. Alvarez, P.J.J., P.J. Anid, and T.M. Vogel, 1991, Kinetics of aerobic biodegradation of benzene and toluene in sandy aquifer material, Biodegradation 2, 43-51. Alvarez-Cohen, L. and P.L. McCarty, 1991, Effects of toxicity, aeration, and reductant supply on trichloroethylene transformation by a mixed methanotrophic culture, Appl. Environ. Microbiol., 57, 228-235. Amali, S. and D.E. Rolston, 1993, Theoretical investigation of multicomponent volatile organic vapor diffusion: steady-state fluxes, /. Environ. QuaL, 22, 825-831. Amali, S., L.W. Petersen, D.E. Rolston, and P. Moldrup, 1994, Modeling multicomponent volatile organic and water vapor adsorption on soils, /. Hazard. Mater. 36, 89-108. Amali, S., D.E. Rolston, and T. Yamaguchi, 1996, Transient multicomponent gasphase transport of volatile organic chemicals in porous media, J. Environ. QuaL, 25, 1041-1047. Babiuk, L.A. and E.A. Paul, 1970, The use of fluorescein isothiocyanate in the determination of the bacterial biomass of a grassland soil, Can. J. Microbiol., 16, 57-62. Baehr, A.L. and C.J. Bruell, 1990, Application of the Stefan-Maxwell equations to determine limitations of Fick's law when modeling organic vapor transport in sand columns, Water Resour. Res. 26, 1155-1163. Bekins, B.A., E.M. Godsy, and D.F. Goerlitz, 1993, Modeling steady-state methanogenic degradation of phenols in groundwater, J. Contam. Hydro!., 14, 279294. Bouwer, E.J. and P.L. McCarty, 1984, Modeling of trace organics biotransformation in the subsurface, Groundwater, 22, 433-440. Bouwer, E.J., B.E. Rittman, and P.L. McCarty, 1981, Anaerobic degradation of halogenated 1- and 2-carbon organic compounds, Environ. Sci. Technol., 15, 596-599. Brauns, J. and K. Wehrle, 1992, Some aspects of air flow through unsaturated soil by vapor extraction, in Subsurface Contamination by Immiscible Fluids, Weyer, K.U. (Ed.), pp. 73-80, A.A. Balkema, Rotterdam. Broholm, K., B.K. Jensen, T.H. Christensen, and L. Olsen, 1990, Toxicity of 1,1,1trichloroethane and trichloroethene on a mixed culture of methane-oxidizing bacteria, Appl. Environ. MicriobioL, 56, 2488-2493.

256

VADOSE ZONE HYDROLOGY

Brusseau, M.L., 1991, Transport of organic chemicals by gas advection in structured or heterogeneous porous media: development of a model and application to column experiments, Water Resour. Res., 27, 3189-3199. Brusseau, M.L. and P.S.C. Rao, 1989, Sorption during organic contaminant transport in porous media, CRC Crit. Rev. Environ. Contr., 19, 33-99. Celia, M.A., J.S. Kindred, and I. Herrera, 1989, Contaminant transport and biodegradation 1. A numerical model for reactive transport in porous media, Water Resour. Res., 25, 1141-1148. Chang, M.-K., T.C. Voice, and C.S. Criddle, 1993, Kinetics of competitive inhibition and cometabolism in the biodegradation of benzene, toluene, and p-xylene by two Pseudomonas isolates, Biotechnol. Bioeng., 41, 1057-1065. Chen, Y.-M., L.M. Abriola, P.J.J. Alvarez, P.J. Anid, and T.M. Vogel, 1992, Modeling transport and biodegradation of benzene and toluene in sandy aquifer material: compactions with experimental measurements, Water Resour. Res., 28, 1833-1847. Chiou, C.T. and T.D. Shoup, 1985, Soil sorption of organic vapors and effects of humidity on sorptive mechanism and capacity, Environ. Sci. Technol., 19, 11961200. Chung, G.-Y., B.J. McCoy, and K.M. Scow, 1993, Criteria to assess when biodegradation is kinetically limited by intraparticle diffusion and sorption, Biotechnol. Bioeng., 41, 625-632. Clausnitzer, V. and J.W. Hopmans, 1995, LM-OPT, General-purpose optimization code based on the Levenberg-Marquardt algorithm, V. 1.0 for UNIX, Land, Air, & Water Resources Paper No. 100032, University of California, Davis. Criddle, C.S., 1993, The kinetics of cometabolism, Biotechnol. Bioeng., 41, 10481056. Ensley, B.D., 1991, Biochemical diversity of trichloroethylene metabolism, Annu. Rev. Microbiol, 45, 283-299. Fan, S. and K.M. Scow, 1993, Biodegradation of trichloroethylene and toluene by indigenous microbial populations in soil, Appl. Environ. Microbiol., 59, 19111918. Fliermans, C.B., T.J. Phelps, D. Ringelberg, A.T. Mikell, and D.C. White, 1988, Mineralization of trichloroethylene by heterotrophic enrichment cultures, Appl. Environ. Microbiol., 54, 1709-1714. Folsom, B.R., P.J. Chapman, and P.H. Pritchard, 1990, Phenol and trichloroethylene degradation by Pseudomonas cepacia G4: kinetics and interactions between substrates, Appl. Environ. Microbiol., 56, 1279-1285. Fuller, M.E., D.Y. Mu and K.M. Scow, 1995, Biodegradation of trichloroethylene and toluene by indigenous microbial populations in vadose sediments, Microb. Ecol. 29, 311-325. Garbarini, D.R. and L.W. Lion, 1986, Influence of the nature of soil organics on the sorption of toluene and trichloroethylene, Environ. Sci. Technol., 20, 1263-1269. Gibson, D.T. and G.S. Sayler, 1992, Scientific foundations of bioremediation: current status and future needs, A Report from the American Academy of Microbiology, Washington, DC. Glauz, R.D. and D.E. Rolston, 1989, Optimal design of two-chamber, gas diffusion cells, Soil Science Soc. Am. J., 53, 1619-1623. Goldsmith, J.C.D. and R.K. Balderson, 1988, Biodegradation and growth kinetics of enrichment isolates on benzene, toluene, and xylene, Water Sci. Technol., 20, 505-507. Marker, A.R. and Y. Kim, 1990, Trichloroethylene degradation by two independent aromatic-degrading pathways in Alcaligenes eutrophus IMP 134, Appl. Environ. Microbiol., 56, 1179-1181. Harmon, T.C., W.P. Ball, and P.V. Roberts, 1989, Nonequilibrium transport of organic contaminants in groundwater, in Reactions and Movement of Organic

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

257

Chemicals in Soil, SSSA Special Publication 22, SSSA, ASA, Sawhney, B.L. and Brown, K. (Eds.), pp. 405-437, Madison, WI. Hartmans, S., A. Kaptein, J. Tramper, and J.A.M. de Bont, 1992, Characterization of a Mycobacterium sp. and a Xanthobacter sp. for the removal of vinyl chloride and 1,2-dichloroethane from waste gases, Appl. Microbiol. Biotechnol, 37, 796801. Hill, T.L., 1946, Theory of multimolecular adsorption from a mixture of gases, J. Chem. Phys., 14, 268-275. Johnson, R.L., K.A. McCarthy, M. Perrott, and C.A. Mendoza, 1992, Densitydriven vapor transport: physical and numerical modeling, in Subsurface Contamination by Immiscible Fluids, Weyer, K.U. (Ed.), pp. 19-27, A.A. Balkema, Rotterdam. Lanzarone, N.A and P.L. McCarty, 1990, Column studies on methanotrophic degradation of trichlorethene and 1,2-dichloroethane, Groundwater, 28, 910-919. Little, C.D., A.V. Palumbo, S.E. Herbes, M.E. Lidstrom, R.L. Tyndall, and P.J. Gilmer, 1988, Trichloroethylene biodegradation by a methane-oxidizing bacterium, Appl. Environ. Microbiol., 54, 951-956. Massmann, J. and D.F. Farrier, 1992, Effects of atmospheric pressure on gas transport in the vadose zone, Water Resour. Res., 28, 777-791. McClellan, R.D. and R.W. Gillham, 1992, Vapor extraction of trichloroethylene under controlled conditions at the Borden site, in Subsurface Contamination by Immiscible Fluids, Weyer, K.U. (Ed.), pp. 89-96, A.A. Balkema, Rotterdam. McCoy, B.J. and D.E. Rolston, 1992, Convective transport of gases in moist porous media: effect of absorption, adsorption, and diffusion in soil aggregates, Environ. Sci. Techno!., 26, 2468-2476. Mihelcic, J.R. and R.G. Luthy, 1988, Microbial degradation of acenaphthene and naphthalene under denitrification conditions in soil-water systems, Appl. Environ. Microbiol., 54, 1188-1198. Mu, D.Y. and K.M. Scow, 1994, Effect of trichloroethylene (TCE) and toluene concentrations on TCE and toluene biodegradation and the population-density of TCE and toluene degraders in soil, Appl. Environ. Microbiol., 60, 2661-2665. Nelson, M.J.K., S.O. Montgomery, E.J. O'Neill, and P.H. Pritchard, 1986, Aerobic metabolism of trichloroethylene by a bacterial isolate, Appl. Environ. Microbiol., 52, 383-384. Nelson, M.J.K., S.O. Montgomery, W.R. Mahaffey, and P.H. Pritchard, 1987, Biodegradation of trichloroethylene and involvement of an aromatic biodegradative pathway, Appl. Environ. Microbiol., 53, 949-954. Nelson, M.J.K., S.O. Montgomery, and P.H. Pritchard, 1988, Trichloroethylene metabolism by microorganisms that degrade aromatic compounds, Appl. Environ. Microbiol., 54, 604-606. Oldenhuis, R., R.L.J.M. Vink, D.B. Janssen, and B. Witholt, 1989, Degradation of chlorinated aliphatic hydrocarbons by Methylosinus trichosporium OB3b expressing soluble methane monooxygenase, Appl. Environ. Microbiol., 55, 2819-2826. Oldenhuis, R., J.Y. Oedez, J.J. van der Waarde, and D.B. Janssen, 1991, Kinetics of chlorinated hydrocarbon degradationn by Methylosinus trichosporium OB3b and toxicity of trichloroethylene, Appl. Environ. Microbiol., 57, 7-14. Ong, S.K. and L.W. Lion, 199la, Mechanisms for trichloroethylene vapor sorption onto soils minerals, /. Environ. Qual, 20, 180-188. Ong, S.K. and L.W. Lion, 1991b, Effects of soil properties and moisture on the sorption of trichloroethylene vapor. Water Res., 25, 29-36. Parsons, F., P.R. Wood, and J. DeMarco, 1984, Transformations of tetrachloroethylene and trichloroethylene in microcosms and groundwater, /. Am. Water Works Assoc., 76, 56-59. Petersen, L.W., D.E. Rolston, P. Moldrup, and T. Yamaguchi, 1994, Volatile organic vapor diffusion and adsorption in soils. J. Environ. Qual., 23, 799-805.

258

VADOSE ZONE HYDROLOGY

Petersen, L.W., P. Moldrup, Y.H. El-Farhan, O.H. Jacobsen, T. Yamaguchi, and D.E. Rolston, 1995, The effect of moisture and soil texture on the adsorption of organic vapors, J. Environ. Qual., 24, 752-759. Pignatello, J.J., 1990a, Slowly reversible sorption of aliphatic halocarbons in soils. I. Formation of residual fractions, Environ. Toxicol. Chem., 9, 1107-1115. Pignatello, J.J., 1990b, Slowly reversible sorption of aliphatic halocarbons in soils. II. Mechanistic aspects, Environ. Toxicol. Chem., 9, 1117-1126. Rao, P.S.C., R.A. Ogwanda, and R.D. Rhue, 1989, Adsorption of volatile organic compounds on anhydrous and hydrated sorbents: equilibrium adsorption and energetics, Chemosphere, 18, 2177-2191. Rhue, R.D., K.D. Pennell, P.S.C. Rao, and W.H. Reve, 1989, Competitive adsorption of alkylbenzene and water vapors on predominantly mineral surfaces, Chemosphere, 18, 1971-1986. Rijnaarts, H.H.M., A. Bachmann, J.C. Jumelet, and A.J. Zehnder, 1990, Effect of desorption and intraparticle mass transfer on the aerobic biomineralization of a-hexachlorocyclohexane in a contaminated calcareous soil, Environ. Sci. Technol, 24, 1349-1354. Schmidt, S.K., S. Simkins, and M. Alexander, 1985, Models for the kinetics of biodegradation of organic compounds not supporting growth, Appl. Environ. Microbiol., 50, 323-331. Scotter, D.R., G.W. Thurtell, and P.A.C. Raats, 1967, Dispersion resulting from sinusoidal gas flow in porous materials, Soil Sci., 104, 306-308. Scow, K.M., 1993, Effect of sorption-desorption and diffusion processes on the kinetics of biodegradation of organic chemicals in soil, in Sorption and Degradation of Pesticides and Organic Chemicals in Soil, D. Linn (Ed.), pp. 73-114, Soil Science Society of America Special Publication 32, Madison, WI. Scow, K.M. and M. Alexander, 1992, Effects of diffusion on the kinetics of biodegradation: experimental results with synthetic aggregates, Soil Sci., Soc. Am. J., 56, 128-134. Scow, K.M. and J. Hutson, 1992, Effect of diffusion and sorption on the kinetics of biodegradation: theoretical considerations, Soil Sci. Soc. Am. J., 56, 128-134. Scow, K.M., S.K. Schmidt, and M. Alexander, 1989, Kinetics of biodegradation of mixtures of substrates in soil, Soil Biol. Biochem., 21, 703-708. Simkins, S. and M. Alexander, 1984, Models for mineralization kinetics with the variables of substrate concentration and population density, Appl. Environ. Microbiol., 47, 1299-1306. Steinberg, S.M., J.J. Pignatello, and B.L. Sawhney, 1987, Persistence of 1,2-dibromoethane in soils: entrapment in intraparticle micropores, Environ. Sci. Technol., 21, 1201-1208. Thibodeaux, L.J., K.C. Nadler, K.T. Valsaraj, and D.D. Reible, 1991, The effect of moisture on volatile organic chemical gas-to-particle partitioning with atmospheric aerosols, competitive adsorption theory predictions, Atmos. Environ., 25A, 1649-1656. U.S. EPA (U.S. Environmental Protection Agency), 1980, Ambient water quality criteria for trichloroethylene, Publication 440/5-80-073, National Technical Information Services, Springfield, VA. Valsaraj, K.T. and L.J. Thibodeaux, 1988, Equilibrium adsorption of chemical vapors on surface soils, landfills and landfarms—a review, J. Hazard. Mater., 19, 79-99. van den Wijngaard, A.J.K., K.W.H.J. van der Kamp, J. van der Ploeg, B. Kaxemier, R. Pries, and D.B. Janssen, 1992, Degradation of 1,2-dichloroethane by Ancylobacter aquations and other facultative methylotrophs, Appl. Environ. Microbiol., 58, 976-983.

COUPLING VAPOR TRANSPORT AND TRANSFORMATION OF VOCS

259

Vogel, T.M. and P.L. McCarty, 1985, Biotransformation of tetrachlorethylene to trichloroethylene, dichloroethylene, vinyl chloride, and carbon dioxide under methanogenic conditions, Appl. Environ. Microbiol., 49, 1080-1083. Wackett, L.P. and D.T. Gibson, 1988, Degradation of trichloroethylene by toluene dioxygenase in whole-cell studies with Pseudomonas putida Fl, Appl. Environ. Microbiol., 54, 1703-1708. Wackett, L.P. and S.R. Householder, 1989, Toxicity of trichloroethylene to Pseudomonas putida Fl is mediated by toluene dioxygenase, Appl. Environ. Microbiol., 55, 2723-2725. Weidner, J.R., W.C. Downs, and A.J. Sondrup, 1995, Passive soil vapor extraction at Hill Air Force Base, Utah, Abstracts of AGU Spring Meeting, P. SI 13, American Geophysical Union, Washington, DC. Westerick, J.J., J.W. Mello, and R.F. Thomas, 1984, The groundwater supply survey, /. Am. Water Works Assoc., 76, 52-56. Wilson, B.H., G.B. Smith, and J.F. Rees, 1986, Biotransformations of selected alkylbenzenes and halogenated aliphatic hydrocarbons in methanogenic aquifer material: a microcosm study, Environ. Sci. Technol., 20, 997-1002. Winter, R.B., K.M. Yen, and B.D. Ensley, 1989, Efficient degradation of TCE by a recombinant Escherichia coli, Bio/Technology, 7, 282-285.

10

Evaporation Use of Fast-Response Turbulence Sensors, Raman Lldar, and Passive Microwave Remote Sensing

MARC B. PARLANCE JOHN D. ALBERTSON WILLIAM E. EICHINGER

A. T. CAM ILL T. J. JACKSON G. KIELY G. G. KATUL

Since evaporation represents some 60% of precipitation over land surfaces, it is crucial for hydrologic purposes to know with some degree of certainty the magnitude of the water vapor flux into the atmosphere. Actual evaporation (E) from drying land surfaces is often formulated, in hydrology, as a fraction of some measure of potential evaporation (Ep), which can be written as a bulk transfer relationship:

where CE is the bulk mass transfer coefficient for water vapor, u is the mean wind speed at reference height z above the surface, p is the density of the air, q is the mean specific humidity at z, and q*s is the saturation specific humidity at the temperature of the surface (Ts) (Brutsaert, 1982, 1986). Alternatively, Ep is sometimes defined using the Penman (1948) equation,

where Qne (= Rne — Ge) is the available energy (expressed in the same units as evaporation), Rne is the net radiation, Ge is the soil heat flux, A = dq* jdT taken at the air temperature (T"fl), q* is the saturation specific humidity at the same temperature, y = cp/Le is the psychrometric constant, cp is the specific heat of the air at constant pressure, and Le is the latent heat of vaporization (Brutsaert, 1986).

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

261

The second term on the right-hand side of equation (10.2), in particular CE, can be formulated in a universal way based upon Monin and Obukhov (1954) similarity theory as opposed to making use of empirical wind functions (e.g., Penman, 1948; Dorenbos and Pruitt, 1975). The use of Monin-Obukhov similarity theory with the Penman equation was suggested by Brutsaert (1982) and tested critically by Katul and Parlange (1992). The Penman-Brutsaert formulation was found to be very robust, even under conditions of local advection when Ep exceeds Qne (Katul and Parlange, 1992). When the surface is no longer wet, evaporation can be estimated as

where /3 is an empirical reduction factor (ranging from 0 to 1), often denned as a function of near-surface soil moisture content (e.g., Crago and Brutsaert, 1992). This formulation is also the basis for crop coefficient models for E, used in irrigation management and scheduling, where ft is a crop- and season-specific reduction parameter (Dorenbos and Pruitt, 1975). Another popular means for estimating actual evaporation is based upon a resistance factor, r, to account for the surface control on evaporation:

note that when the surface is wet, r = 0 and equation (10.4) reduces to equation (10.2) (e.g., Thorn, 1972; Monteith 1973). Notice that ft and r are related through

(see Brutsaert, 1986). To use either equation (10.3) or equation (10.4) in a real situation, ft or r must be specified for the region of interest. Any measure of ft or r should reflect the aridity of the Earth's surface at the spatial scale for which E is desired. Data availability in practical applications is typically limited to local measures of surface dryness from, say, gravimetric soil moisture samples, neutron probe access tubes, or time domain reflectometry (TDR) installations (see chapter 11, this volume). Since it is well known that soil moisture and vadose zone transport rates and properties vary considerably in nature (e.g., Nielsen et al., 1973; Biggar and Nielsen, 1976; Parlange et al., 1992), any measure of surface aridity at a point in the field is not likely to be appropriate for use with ft or r for field or regional scales (0~ 1-10 km). One tool that holds promise for obtaining appropriate measures of near-surface soil moisture at field scales is passive microwave remote sensing (see chapter 12, this volume). To address the appropriateness of passive microwave measurements to specify near-surface soil moisture for flux calculations with equation (10.3), experiments were carried out at a bare soil field at the University of California (UC) at Davis Campbell Tract field site. An S-band radiometer was mounted on a fixed platform (boom truck), and soil moisture estimates for the top 2cm over a 3m x 4m surface area of a bare soil field were obtained every 20 min. While there certainly is a mismatch of scales between that of the soil moisture measurement and the spatial extent of the irrigated field (150m x 130m), it serves as an exploratory

262

VADOSE ZONE HYDROLOGY

test of the approach. Coincident field-scale evaporation measurements were made using eddy correlation instrumentation. This consisted of a three-dimensional sonic anemometer (see Stull, 1988; Kaimal and Finnigan, 1994) collocated with a krypton hygrometer to derive E (= p(w'q')), where {.) is the time-averaging operator, w' is the fluctuation of the vertical wind velocity, and q is the fluctuation of the specific humidity about their time-average values. In addition, mean (20 min) micrometeorological measurements of wind speed, air temperature, and humidity were taken so that Ep could be defined using equation (10.2) in the Penman-Brutsaert formulation (Katul and Parlange, 1992). In figure 10.1, a plot of ft (= E/Ep) versus passive microwave estimated soil moisture content is presented. Various functions that have been presented in the literature (e.g. Barton, 1979; Lee and Pielke, 1992; Noilhan and Planton, 1989) are given, in addition to a best fit line. Clearly, if one is to apply this approach to obtain E in practice, some preliminary site-specific empirical work must be carried out to establish the ft versus soil moisture content function for the application of equation (10.3). In addition, it is unlikely, in practice, that soil moisture observations will be available throughout the course of a day, so some scheme will be necessary to derive daily evaporation from simple one-time-ofday measurements of soil moisture. One approach is to recognize that there is a natural similarity between the diurnal structures of E and Qne. With the often reasonable assumption that the Bowen ratio (H/LeE) remains constant over the daytime, it is straightforward to obtain a daily flux estimate (see Brutsaert and Sugita, 1992; Nichols and Cuenca, 1993). Nevertheless, the surface aridity measures, r and ft, are clearly site-specific and scale-specific, with unique dependence on the type of remote

Figure 10.1 Soil aridity function, ft, versus near-surface soil moisture measured from passive microwave remote sensing.

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

263

sensing platform and instrumentation used (and the inherent areal and depth averaging of soil moisture content). Obviously, much more work must be carried out before the evaporation formulations often presented in hydrology can be used in practice at these larger scales. It is worthwhile noting that an alternative strategy to these empirical site-specific surface resistance formulations is to infer the field- or regional-scale aridity from the state of the atmosphere. Most of these approaches are based on hypothetical energy balance arguments due to Bouchet (1963); various evaporation equations for nonsaturated surfaces have been derived from Bouchet's hypothesis (e.g., Morton, 1969; Fortin and Seguin, 1975; Brutsaert and Strieker, 1979). The Brutsaert and Strieker approach, known as the advection aridity model, has the main advantage that only meteorological parameters are needed and no measures of surface aridity, such as soil moisture or stomatal resistance, are necessary. The accuracy of this model is known to deteriorate under conditions of strong local advection (e.g., Parlange and Katul, 1992a); however, useful extensions to the advection-aridity model have been developed and tested to correct for this pathology (Parlange and Katul, 1992b). The revised model has been tested with measurements taken at the UC Davis Campbell Tract, but clearly more validation research is needed to further establish the generality of the approach. It is somewhat remarkable that the evaporation literature, in the fields of soil hydrology and atmospheric science, is so heavily impacted with papers that present variations on the Penman-Monteith resistance-type models and various new multilayer resistance formulations. These so-called advanced or sophisticated models of evaporation involve networks of resistances (see Shuttleworth, 1993), which include a collection of nonphysical fitting parameters. Nevertheless, as a general rule, all of these models are soil- and plant-specific, involve numerous tunable coefficients, and appear to be useful mainly for simulation purposes as opposed to actual hydrologic practice. In predictive models, these parameters are typically "tuned" to make the results appear realistic, rather than receiving their values from some physical understanding of the system. Furthermore, when the number of parameters becomes large with respect to the dimension of the physical system, it becomes an elusive task to invert for the parameter values from observations of the system response (such as with actual observations of evaporation). When faced with such a problem, modelers would do well to heed Occam's razor, which, in recognition of the need for parsimony in the description of physical systems, states that "what can be done with fewer [parameters] is done in vain with more" (New Columbia Encyclopedia, 1975). Since the surface resistance approaches in hydrology are of questionable usefulness for obtaining accurate estimates of actual evaporation, we focus on improvements for the description of transport processes in the atmospheric boundary layer (ABL). The ABL is that layer of the atmosphere directly above the Earth's surface, in which the effects of the surface (friction, evaporation, heating, and cooling) are felt directly on time scales of less than a day. The daytime ABL, or convective boundary layer, is subdivided into two layers. The lower layer, or atmospheric surface layer (ASL), occupies the first 10% of the ABL—extending some 100m above the land surface and possessing a structure defined largely by surface fluxes. The rest of the ABL is known as the outer region or mixed layer and is affected by both surface

264

VADOSE ZONE HYDROLOGY

fluxes and entrainment of the free atmosphere air from above. In figure 10.2, a schematic of the ABL is presented (Albertson et al., 1996). Since the characteristic horizontal length-scales in the atmosphere are orders of magnitude greater than those of surface soils, some useful parameterizations of surface evaporation may be obtained from consideration of the structure and processes of the ABL (Brutsaert, 1986; Parlange et al., 1995). The key feature of the ABL is its ability to quickly mix and integrate spatially in such a way as to reflect surface conditions for a ratio of vertical to horizontal scales on the order of 1:100. Hence, ASL measurements (i.e., first 100m above the surface) can be used to study surface flux processes integrated over distances of up to 10km upwind (e.g., Kustas and Brutsaert, 1987; Brutsaert and Parlange, 1992; Parlange and Brutsaert, 1993; Sugita and Brutsaert, 1993; Parlange and Katul, 1995). We focus this chapter on some recent advances in making use of the integrating power of the atmosphere to obtain field- or regional-scale surface fluxes. To show the response of the ASL to surface flux processes, we first present a Raman lidar (light detection and ranging) image of the growth of an internal boundary layer (IBL) over an individual wet field and compare the observation with an analytical solution due to Sutton (1934). This example is useful in its demonstration of how the atmosphere

Figure 10.2 Schematic of the structure of the daytime atmospheric boundary layer.

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

265

naturally integrates over the characteristic length-scales of soils at the land surface. Then, a new one-step (noniterative) dissipation method to obtain the fluxes of sensible heat and water vapor is presented; this technique is proving to be highly robust and reliable in practice. Finally, a very useful one-point Bowen ratio method is presented that is based upon some simple scaling laws for the turbulent fluctuations of temperature and humidity in the ASL. What is particularly useful about this approach over a traditional Bowen ratio/energy budget (BREB) station is that it circumvents the need to obtain the available energy (Qne) and the gradients of scalars in the surface layer. The available energy is typically measured at different scales from the atmospheric measurements of temperature and humidity gradients, and hence the BREB approach can be fraught with error. The results presented here provide some approaches to improve the reliability of flux estimates in the ABL while simplifying the instrumentation needs. These techniques provide observations of actual field-scale evaporation that may be used to deduce simpler models and to identify parameters such as the soil aridity function, /3.

The Internal Boundary Layer from Lidar We consider the development of the internal boundary layer when there is a step change in surface water content from a relatively dry surface to a wet surface in the direction of the mean wind with no significant change in surface roughness. This is a situation found in irrigated agricultural regions—for example, in the California Central Valley and many parts of the southwestern United States. The theory used to describe this situation is due to Sutton (1934) and is discussed in great detail by Brutsaert (1982). The key points are outlined here. This theory was further developed by Frost (1946) and others, who recast the result into more practical forms. The essential governing equation is taken as a balance between the horizontal advection and the divergence of the vertical turbulent flux of water vapor, namely,

where x is the direction along the land surface aligned with the mean wind (x = 0 is the dry-wet surface interface), u is the mean horizontal wind velocity in the .x-direction, and z is the vertical coordinate (z = 0 at the land surface). The key simplifying assumptions to obtain equation (10.6) are steady state, negligible horizontal gradients of turbulence (fluctuation moments), and negligible mean wind velocities in the vertical and lateral directions. The turbulent flux (w'q) can be closed with A'-theory as a turbulent analogy to Pick's equation:

where Kv is the turbulent "eddy" diffusivity, which under neutral stability conditions can be defined with a power function:

266

VADOSE ZONE HYDROLOGY

where the constants, b and n, are defined from Reynolds' analogy of the similarity of momentum and mass transport for neutral stability flows as m — 1/7, n — 1 — m, and b — ul/m, where w* (= [—r0/p]1/7) is the friction velocity and r0 is the surface shear stress. The boundary conditions are

where qa is the specific humidity of the ambient air (above the internal boundary layer), qs is the specific humidity at the wet land surface, and qas is the specific humidity at the surface before entering the wetted patch. The specific humdity is written as a normalized concentration,

so that the transport equation is written

From the boundary conditions, the similarity variable

gives the solution

where P(v, x) is the incomplete gamma function and v = m/(\ + 2m). Because x is a function only of x, equation (10.12) can be used to determine the shape of the IBL by drawing a line of constant concentration, x- Rearranging the equation, the thickness of the vapor blanket as a function of fetch x is

where c is determined from equation (10.13). To test this solution, a lidar experiment was carried out at the UC Davis Campbell Tract facility in August 1991. The site consists of an irrigated patch of about 150m x 130m (see figure 10.3) within a bare soil field of 500m x 500m with an average momentum roughness length (z0} of 0.002m. A sprinkler irrigation system was used to saturate the cross-hatched area shown in figure 10.3. Evaporation measurements were available from a circular (6-m diameter) weighing lysimeter located in the irrigated section of the field. A vapor blanket (i.e., IBL) was measured using a solar-blind Raman lidar development at Los Alamos National Laboratory (Eichinger et al., 1993). The principle of the Raman lidar is based on the techniques pioneered by Cooney (1970). A pulse of high-energy laser beam is emitted by the lidar system, and the Raman-shifted return light from both atmospheric nitrogen and water vapor is collected using a telescope and then digitized. The ratio of the return water vapor signal to the return nitrogen

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

267

Figure 10.3 Plan view of lidar experimental layout for internal boundary layer experiment.

signal is directly proportional to the absolute water vapor content in the atmosphere, and requires only a correction for differential ozone absorption at the two return wavelengths. The time elapsed from the pulse until the return defines the distance along the beam. The details of this particular lidar system are given in Eichinger et al. (1993). The laser source was placed 3 m above the land surface and the scanning system positions the mirror assembly to align into the predominant wind direction (see figure 10.3). The water vapor profile is measured taking vertical scanning angle ranges from —4 to 2°, with a resolution of 0.1°. The water vapor concentration was sampled every 1.5m along the laser beam at each scanning angle. Each vertical scan took approximately 60s to complete and 10 scans were done in succession and averaged to create the vapor blanket time-averaged image in figure 10.4. The atmospheric stability was quantified using the Obukhov length,

where k (— 0.4) is the von Karman constant and g is the gravitation acceleration. The friction velocity «* = {—u'w') l / 2 was calculated from direct measurement of the Reynolds stress (u'w'} with a three-dimensional sonic anemometer, the sensible heat flux H (= pcp(0'w')) was obtained using a one-dimensional sonic anemometer and fast-response thermocouple, and E was measured with the lysimeter. The observed L-value was —56m, implying that the atmosphere was under near-neutral stability; accordingly, the power m was set equal to 1/7. A comparison plot of the Sutton

268

VADOSE ZONE HYDROLOGY

Figure 10.4 Vertical cross section of water vapor mixing ratio (g/kg) over the irrigated field during the lidar experiment. Sutton's (1934) analytic solution is drawn with a solid line for comparison.

solution for the vapor blanket height is given in figure 10.4, starting at the dry-wet interface where the wind is blowing from right to left in figure 10.4. Though it is difficult to declare a close match of the model and the field data, the comparison certainly supports the order of magnitude result of the adjustment of the atmosphere to a sharp discontinuity in surface humidity conditions. Further work on this problem is under way using large eddy simulation (LES) (Albertson, 1996; Albertson and Parlange, 1999a,b) and should provide further information on the effect of surface patchiness for a wide range of atmospheric stabilities. Nevertheless, the important feature is to note that measurements taken within the vapor blanket (i.e., well inside the IBL) are useful to quantify the flux of water vapor (or other scalars) for the field in which one desires to know the evaporation rate.

Flux-Dissipation Formulation Flux-dissipation methods require some of the same type of fast-response turbulence instrumentation as used in deriving eddy correlation fluxes. The main advantages of using flux-dissipation measurements is that they do not require the precise orientation and alignment of the sensors that is central to eddy correlation (Brutsaert, 1982), and that fluctuations in the streamwise component of the velocity are needed rather

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

269

than the vertical component. The results presented below suggest, indeed, that the method is becoming a practical tool. Turbulent Kinetic Energy

Our focus here is on the use of the flux-dissipation method to obtain in one step (no iteration) the sensible and latent heat fluxes. For completeness, we first present results on the scaling of the mean dissipation rate of turbulent kinetic energy €. The turbulent kinetic energy (TKE) budget equation (per unit mass) with the Boussinesq approximation for a stationary flow and horizontal homogeneity is given as

where e [= (u 2 + v 2 + w 2)/2] is the TKE, £ is the dissipation rate of e by viscous action, and p' is the fluctuating component of the pressure. If equation (10.16) is nondimensionalized by ul/kz, the dimensionless dissipation can be written as

Various experimental results have been published for the behavior of 0e versus z/L (e.g., McBean et al., 1971; Wyngaard and Cote, 1971; McBean and Elliot, 1975; Champagne et al., 1977; Frenzen and Vogel, 1992). One recent extension of the scaling of various turbulence measures in the ASL was brought out in the work of Kader and Yaglom (see Kader, 1988; Kader and Yaglom, 1990). They subdivide the ASL into three separate layers (see figure 10.2). The lowest layer is the dynamic sublayer (DSL), where buoyant action is negligible compared with mechanical production. The uppermost layer, which is predominantly affected by buoyant production, is termed the free convective sublayer (FCSL). The middle layer is the dynamicconvective sublayer (DCSL), where both mechanical and buoyant forces play important roles. From order-of-magnitude analysis (Kader, 1992), the stability (or dimensionless height) limits of the sublayers are

Estimates of 6 can be obtained from inertial subrange scaling (Kolmogorov, 1941) of turbulence measurements. An attractive technique under this class of approaches involves using the third-order structure function, the averaged cubed velocity difference over lag r, Dmu(r) — ((u(x + r) — u(x))3}, which scales in the inertial subrange as

From dimensional analysis and application of the third-order structure function equation (10.19), estimates of 06, the dimensionless dissipation for TKE, is given (Albertson et al., 1997) as

270

VADOSE ZONE HYDROLOGY

This is a formal scaling form of the TKE dissipation rate for the three-sublayer model of Kader and Yaglom. A simplified form is available for temperature and humidity dissipation rates.

Sensible and Latent Heat Fluxes from Inertial Dissipation Scaling The temperature variance budget equation (written for (l/2){# 2 )) for steady and horizontally homogeneous flow is

where €e is the mean dissipation rate of the temperature variance. This can be nondimensionalized by u*@l/kz where

and the dimensionless dissipation rate of temperature variance is given as

The mean dissipation rate of temperature variance can be determined from the mixed third-order structure function,

which is defined to scale in the inertial subrange as

Note that no empirical constants are used in equation (10.25) (Monin and Yaglom, 1975; Frisch, 1995). Kiely et al. (1996) fit a three-sublayer model to extensive field data for the dimensionless dissipation of temperature variance,

The important result is that the dimensionless dissipation rate scales with a single convective power law over an extended range of — z/L (see figure 10.5). This provides

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

271

Figure 10.5 Dimensionless dissipation rate of temperature variance versus the stability parameter. Each point represents the time-averaged dissipation rate from thirdorder structure function analysis over a 20-min averaging period. The solid line is the convective scaling form of equation (10.26).

a very useful simplification for the calculation of H from estimates of the dissipation rate of temperature variance. That the free convective scaling can be applied for — z / L > 0 has been noted before; for example, the standard deviation of temperature fluctuations is known to scale convectively (e.g., Albertson et al., 1995) over a wide range of stability. With the convective scaling, the sensible heat flux can be determined from

where, in practice, the dissipation rate is estimated with application of the third-order structure function and Taylor's (1938) hypothesis from single lag values of the structure function; that is,

where T (— r/u) is a time lag corresponding to a value of r that falls in the inertial subrange. Note that the structure function can be computed in the field with a standard data logger from a single time lag T since the third-order structure function is sufficiently smooth to determine the intercept with a known slope and one point on the line (in a log-log framework). Similar to equation (10.27), the evaporative flux may be determined from

272

VADOSE ZONE HYDROLOGY

which is obtained from the same free convective scaling for the dimensionless dissipation rate for water vapor variance,

Experiments took place during the summer of 1994 at the UC Davis Campbell Tract and the dry Owen's Lake bed in Owen's Valley in southeastern California. The fastresponse equipment included a one-dimensional sonic anemometer with a fine wire (0.0127-mm diameter) thermocouple and a krypton hygrometer operating at 10 Hz, with eddy covariances taken over 20-min averaging periods, so that direct measurements of the vertical fluxes of sensible and latent heat were obtained. A three-dimensional sonic anemometer was used to record the three velocity components at 21 Hz. Instantaneous air temperature was also measured from the speed of sound recorded by the three-dimensional sonic anemometer. We should note that the flux comparisons presented here were not used in fitting the 0e and 4>f(> functions—they were fit from an independent data set. The sensible heat flux comparison is given in figure 10.6. Amazingly, the model estimates match the eddy correlation measurements to within the 10% stated accuracy range for eddy correlation (Albertson et al., 1996). Very good comparison (see figure 10.7) was found for LeE derived from equation (10.29) versus the eddy correlation measurement for this 1 day at the UC Davis Campbell Tract (Albertson et al., 1996). Though the results remain somewhat limited in terms of number of field sites and surface characteristics, they are most encouraging. Further experimental efforts regarding the suitability of the free convective formulation of the inertial flux dissipation models are under way. Note that using the third-order structure function to obtain the dissipation rates requires no empirical constants and the calculation of the dissipation for the scalars does not require prior estimation of the dissipation rate for momentum as is required with the Fourier power spectra approach.

Figure 10.6 Comparison of the sensible heat flux predictions from the dissipation rates calculated by the mixed third-order structure function method with the measured sensible heat fluxes from eddy correlation. Each point represents a 20-min averaging period.

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

273

Figure 10.7 Comparison of the latent heat flux predictions from the dissipation rates calculated by the mixed third-order structure function method with the measured fluxes from eddy correlation. Each point represents a 20-min averaging period.

A One-Point Bowen Ratio Method The traditional BREB station requires the Bowen ratio to be estimated from mean gradients of temperature and humidity:

where the subscripts 1 and 2 refer to the two heights in the ASL at which the mean scalar values are measured. The operation to measure the gradients is not always trivial in practice. First of all, the lower temperature-humidity sensor height must be out of the roughness wake layer of the canopy (Parlange et al., 1995), while the upper sensor height position is constrained in that it must reflect the same type of land surface as the bottom sensor (i.e., inside the blanket). At the same time, the sensors should be separated sufficiently such that a reliable temperature or humidity difference is obtained. To calculate the latent LeE or sensible heat flux, the available energy (Rn — G} must be measured and partitioned based on the observed Bowen ratio Bo:

The measurement of both the soil heat flux and net radiation, especially for sparse canopies (e.g., Kustas and Daughtry, 1990), is not a simple task. Many of the commercially available net radiometers are subject to error and, due to soil and plant heterogeneity, the heat flux into the land surface is difficult to extrapolate from a soil heat budget by using a few heat flux sensors and temperature probes. A simple Bowen ratio alternative is presented here, based on the use of free convective Monin-Obukhov formulations for the standard deviations of the temperature ot and humidity aq fluctuations:

274

VADOSE ZONE HYDROLOGY

where Q* (= (w'q')/u*) is a humidity scale. In figure 10.8, the normalized standard deviation of temperature is plotted versus —z/L. The data presented in figure 10.8 were obtained at the Owen's Valley experimental site (Albertson et al., 1995). Assuming similarity between temperature and humidity—that is, c is the same in equations (10.33) and (10.34)—the Bowen ratio is straightforward to obtain:

If H is estimated from the free convective second-moment model (Albertson et al., 1995),

then LeE can be obtained from equation (10.35). This formulation was tested using data collected at Owen's Valley dry lake bed. The latent heat flux is the smallest term in the energy budget at Owen's Valley and, as such, this presents an extreme test of the formulation. The daily evaporation from Owen's Valley in the summer is approximately 0.5 mm/day. In figure 10.9, the sensible heat flux obtained from the free convective model, equation (10.36), is compared with eddy correlation H measurements (r2 = 0.88). In figure 10.10, the latent heat flux derived from the one-point Bowen ratio is plotted versus the eddy correlation measured LeE (r2 = 0.83). Notice the latent heat flux is an order of magnitude less than the sensible heat fluxes. Again, like the flux dissipation results, more analysis and testing of this method is necessary in the future. This is an interesting alternative to eddy correlation flux measurements, since there is no need for any velocity measurements—thus greatly simplifying field operations.

Figure 10.8 Normalized standard deviation of temperature as function of the stability parameter, —z/L. The free convection model is regressed to the data and shown with a solid line.

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

275

Figure 10.9 Comparison of sensible heat flux estimates derived from equation (10.36) with eddy correlation measured values. A one-to-one line is shown for the eddy correlation measurements.

Concluding Summary The ability to obtain reliable evaporation estimates, especially under land surface limited conditions, is key to a wide array of hydrologic problems. The atmospheric boundary layer provides a natural integration of field- or regional-scale fluxes into the atmosphere as shown by the Raman-lidar scan of the internal vapor blanket. The ABL approaches presented here on the flux-dissipation and one-point Bowen ratio method appear very promising. It is reasonable to expect that long-term monitoring of evaporation might be accomplished through use of these methods. As an example of the value of excellent evaporation information, one important hydrologic aspect that makes the link between evaporation and soil hydrology concerns the measurement of field- or regional-scale desorption from evaporation measurements at daily

Figure 10.10 Comparison of latent heat flux estimates derived from the one-point Bowen ratio approach, equation (10.35), with eddy correlation measured values. A one-to-one line is shown for the eddy correlation measurements.

276

VADOSE ZONE HYDROLOGY

time scales. Apparently, Gardner (1959) was the first to apply the desorption assumption for soil evaporation:

where De is the desorptivity and t is the time elapsed since commencement of drying. Hence, the measure of daily evaporation provides a useful physical measure of a soil hydraulic property under water-limited soil conditions (e.g., Black et al., 1969; Parlange et al., 1993; Brutsaert and Chen, 1995). Tremendous opportunities exist for improving connections between vadose zone water transport processes (chapter 4, this volume) and the atmosphere through remote sensing (e.g., chapter 12, this volume) and developments in turbulence, such as large eddy simulation (e.g., Albertson, 1996; Albertson and Parlange, 1999a,b). Improvements in computers and field instrumentation will present further opportunities to deepen our understanding of land-atmosphere interaction.

References Albertson, J.D., 1996, Large Eddy Simulation of Land-Atmosphere Interaction, Ph.D. Thesis, University of California, Davis. Albertson, J.D., M.B. Parlange, G.G. Katul, C.-R. Chu, H. Strieker, and S. Tyler, 1995, Sensible heat flux from arid regions: a simple flux-variance method, Water Resour. Res., 31, 969-973. Albertson, J.D., G. Kiely, and M.B. Parlange, 1996, Surface fluxes of momentum, heat, and water vapor, in: Remote Sensing of Processes Governing Energy and Water Cycles in the Climate System, E. Raschke (Ed.), NATO ASI Series 1: Global Environmental Change, Springer-Verlag, New York, pp. 59-82. Albertson, J.D., M.B. Parlange, G. Kiely, and W.E. Eichinger, 1997, The average dissipation rate of turbulent kinetic energy in the neutral and unstable atmospheric surface layer, J. Geophys. Res., 102, 13, 423^32. Albertson, J.D. and M.B. Parlange, 1999a, The integrative power of the atmospheric boundary layer over complex terrain, Adv. Water Res. (in press). Albertson, J.D. and M.B. Parlange, 1999b, A large eddy simulation of the neutral atmospheric boundary layer over patchy terrain, Water Resour. Res. (in press). Barton, I.J., 1979, A parameterization of the evaporation from nonsaturated surface, /. Appl. MeteoroL, 18, 43-47. Biggar, J.W. and D.R., Nielsen, 1976, Spatial variability of the leaching characteristics of a field soil, Water Resour. Res., 12, 78-84. Black, T.A., W.R. Gardner, and G.W. Thurtell, 1969, The prediction of evaporation, drainage, and soil water storage for a bare soil, Soil Sci. Soc. Am. Proc., 33, 655-660. Bouchet, R.J., 1963, Evapotranspiration reelle, evapotranspiration potentielle, et production agricole, Ann. Agron., 14, 743-824. Brutsaert, W., 1982, Evaporation into the Atmosphere: Theory, History and Applications, D. Reidel, Norwell, MA. Brutsaert, W., 1986, Catchment scale evaporation and the atmospheric boundary layer, Water Resour. Res., 22, 39S-45S. Brutsaert, W. and M.B. Parlange, 1992, The unstable surface layer above forest: regional evaporation and heat flux, Water Resour. Res., 28, 3129-3134. Brutsaert, W. and D. Chen, 1995, Desorption and the two stages of drying of natural tallgrass prairie, Water Resour. Res., 31, 1305-1313.

EVAPORATION: MEASURING ATMOSPHERIC VAPOR FLUX

277

Brutsaert, W. and H. Strieker, 1979, An advection-aridity approach to estimating actual regional evaporation, Water Resour. Res., 15, 443-450. Brutsaert, W. and M. Sugita, 1992, Application of self-preservation in the diurnal evolution of the surface energy budget to determine daily evaporation, /. Geophys. Res., 97D, 18377-18382. Champagne, F.H., C.A. Friehe, J.C. LaRue, and J.C. Wyngaard, 1977, Flux measurements, flux estimation techniques, and fine-scale turbulence measurements in the unstable surface layer over land, /. Atmos. Sci. 34, 515-530. Cooney, J., 1970, Remote measurements of atmospheric water-vapor profiles using the Raman component of laser backscatter, /. Appl. MeteoroL, 9, 182-184. Crago, R.D. and W. Brutsaert, 1992, A comparison of several evaporation equations, Water Resour. Res., 28, 951-954. Dorenbos, J. and W.O. Pruitt, 1975, Crop Water Requirements, Irrigation and Drainage Paper No. 24, FAO (United Nations), Rome. Eichinger, W., D. Cooper, M. Parlange, and G. Katul, 1993, The application of a scanning, water-Raman lidar as a probe of the atmospheric boundary layer, IEEE Trans. Geosci. Remote Sensing, 31, 1, 70-79. Fortin, J.P. and B. Sequin, 1975, Estimation de 1'ETR regional a partir de 1'ETP locale: utilisation de la relation de Bouchet a differentes echelles de temps, Ann. Agron., 26, 537-554. Frenzen, P. and C.A. Vogel, 1992, The turbulent kinetic energy budget in the atmospheric surface layer: a review and an experimental reexamination in the field, Boundary-Layer MeteoroL, 60, 49-76. Frisch, U., 1995, Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, New York. Frost, R., 1946, Turbulence and diffusion in the lower atmosphere, Proc. R. Soc. London, A186, 20-35. Gardner, W.R., 1959, Solution of the flow equation for the drying of soils and other porous media, Soil Sci. Soc. Am. Proc., 23, 183-187. Kader, B.A., 1988, Three-level structure of an unstably stratified atmospheric surface layer, Izv. Atmos. Ocean. Phys., 24, 907-919 (English translation). Kader, B.A., 1992, Determination of turbulent momentum and heat fluxes by spectral methods, Boundary-Layer MeteoroL, 61, 323-347. Kader, B.A. and A.M. Yaglom, 1990, Mean fields and fluctuation moments in unstably stratified turbulent boundary layers, /. Fluid Mech., 212, 637-662. Kaimal, J.C. and J.J. Finnigan, 1994, Atmospheric Boundary Layer Flows, Oxford University Press, New York. Katul, G.G. and M.B. Parlange, 1992, A Penman-Brutsaert model for wet surface evaporation, Water Resour. Res., 28, 121-126. Kiely, G., J.D. Albertson, M.B. Parlange, and W.E. Eichinger, 1996, Scaling the average dissipation rate of temperature variance in the atmospheric surface layer, Boundary-Layer MeteoroL, 77, 267-284. Kolmogorov, A.N., 1941, The local structure of turbulence in incompressible viscous fluid for very large Reynolds number, Dokl. Akad. Nauk SSSR, 30, 301-303. Kustas, W.P. and W. Brutsaert, 1987, Budgets of water vapor in the unstable boundary layer over rugged terrain, J. Climate Appl. MeteoroL, 26, 607-620. Kustas, W.P. and C.S.T. Daughtry, 1990, Estimation of the soil heat flux net radiation ratio from spectral data, Agric. Forest MeteoroL, 49, 205-223. Lee, T.J. and R.A. Pielke, 1992, Estimating the soil surface specific humidity, /. Appl. MeteoroL, 31, 480-484. McBean, G.A. and J.A. Elliott, 1975, The vertical transport of kinetic energy by turbulence and pressure in the boundary layer, J. Atmos. Sci., 32, 753-766. McBean, G.A., R.W. Stewart, and M. Miyake, 1971, The turbulent energy budget near the surface, J. Geophys. Res., 76, 6540-6549.

278

VADOSE ZONE HYDROLOGY

Monin, A.S. and A.M. Obukhov, 1954, Basic laws of turbulent mixing in the ground layer of the atmosphere, Tr. Geofiz. Inst. Akad. Nauk SSSR, 151, 163-187. Monin, A.S. and A.M. Yaglom, 1975, Statistical Fluid Mechanics Vol. 77, J. Lumley (Ed.), MIT Press, Cambridge, MA. Monteith, J.L., 1973, Principles of Environmental Physics, Elsevier, New York. Morton, F.I., 1969, Potential evaporation as a manifestation of regional evaporation, Water Resour. Res., 5, 1244-1255. New Columbia Encyclopedia, 1975. Nichols, W.E. and R.H. Cuenca, 1993, Evaluation of the evaporative fraction for parameterization of the surface energy balance, Water Resour. Res., 29, 36813690. Nielsen, D.R., J.W. Biggar, and K.T. Erh, 1973, Spatial variability of field-measured soil-water properties, Hilgardia, 42, 215-259. Noilhan, J. and S. Planton, 1989, A simple parameterization of land surface processes for meteorological models, Mon. Wea. Rev., 117, 536-549. Parlange, M.B. and W. Brutsaert, 1993, Regional shear stress of broken forest from radiosonde wind profiles in the unstable surface layer, Boundary-Layer Meteorol., 64, 355-368. Parlange, M.B. and G.G. Katul, 1992a, Estimation of the diurnal variation of potential evaporation from a wet bare surface, /. Hydrol., 132, 71-89. Parlange, M.B. and G.G. Katul, 1992b, An advection-aridity evaporation model, Water Resour. Res., 28, 127-132. Parlange, M.B. and G.G. Katul, 1995, Watershed scale shear stress from tethersonde wind profile measurements under near neutral and unstable atmospheric stability, Water Resour. Res., 31, 961-968. Parlange, M.B., G.G. Katul, R.H. Cuenca, M.L. Kavvas, D.R. Nielsen, and M. Mata, 1992, Physical basis for a time series model of soil water content, Water Resour. Res., 28, 2437-2446. Parlange, M.B., G.G. Katul, M.V. Folegatti, and D.R. Nielsen, 1993, Evaporation and the field scale soil water diffusivity function, Water Resour. Res., 29, 12791286. Parlange, M.B., W.E. Eichinger, and J.D. Albertson, 1995, Regional evaporation into the atmospheric boundary layer, Rev. Geophys., 33, 99-124. Penman, H.L., 1948, Natural evaporation from open water, bare soil, and grass, Proc. R. Soc. London Ser., A, 193, 120-145. Shuttleworth, W.J., 1993, Evaporation, in: Handbook of Hydrology, D.R. Maidment (Ed.), McGraw-Hill, New York, chapter 4. Stull, R., 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Press, Dordrecht. Sugita, M. and W. Brutsaert, 1990, Regional surface fluxes from remotely sensed skin temperature and lower boundary layer measurements, Water Resour. Res., 26, 2937-2944. Sutton, O.G., 1934, Wind structure and evaporation in a turbulent atmosphere, Proc. R. Soc. London, A146, 701-722. Taylor, G.I., 1938, The spectrum of turbulence, Proc. R. Soc., A, CLXIV, 476-490. Thorn, A., 1972, Momentum, mass and heat exchange of vegetation, Quart. J. R. Meteorol. Soc., 97, 414-^28. Wyngaard, J.C. and O.R. Cote, 1971, The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer, /. Atmos. Sci., 28, 190201.

11 Emerging Measurement Techniques for Vadose Zone Characterization

JAN W. HOPMANS JAN M. H. HENDRICKX JOHN S. SELKER

Variables and parameters required to characterize soil water flow and solute transport are often measured at different spatial scales from those for which they are needed. This poses a problem since results from field and laboratory measurements at one spatial scale are not necessarily valid for application at another. Herein lies a challenge that vadose zone hydrologists are faced with. For example, vadose zone studies can include flow at the groundwater-unsaturated zone as well as at the soil surface-atmosphere interface at either one specific location or representing an entire field or landscape unit. Therefore, vadose zone measurements should include techniques that can monitor at large depths and that characterize landsurface processes. On the other end of the space spectrum, microscopic laboratory measurement techniques are needed to better understand fundamental flow and transport mechanisms through observations of pore-scale geometry and fluid flow. The Vadose Zone Hydrology (VZH) Conference made very clear that there is an immediate need for such microscopic information at fluid-fluid and solid-fluid interfaces, as well as for methodologies that yield information at the field/landscape scale. The need for improved instrumentation was discussed at the ASA-sponsored symposium on "Future Directions in Soil Physics" by Hendrickx (1994) and Hopmans (1994). Soil physicists participating in the 1994-1999 Western Regional Research Project W-188 (1994) focused on "improved characterization and quantification of flow and transport processes in soils," and prioritized the need for development and evaluation of new instrumentation and methods of data anlysis to further improve characterization of water and solute transport. The regional project documents the critical need for quantification of water flow and solute transport in heterogeneous, spatially variable field soils, specifically to address preferential and accelerated contaminant transport. Cassel and Nielsen (1994) describe the contributions in computed tomography (CT) using x-rays or magnetic resonance imaging

280

VADOSE ZONE HYDROLOGY

(MRI) as "an awakening," and they envision these methodologies to become an integral part of vadose zone research programs. The difference in size between measurement and application scales poses a dilemma for the vadose zone hydrologist. In many laboratory and field studies, the measurement scale is not directly related to either the larger application scale (as for modeling purposes) or to the microscopic scale at which the fundamental processes take place. For example, soil parameters obtained from centimeter-scale measurements are included in numerical models with a grid or element size 10 times as large, with the numerical results extrapolated to field-scale conditions. Alternatively, when considering the pore-size scale, measurements representative at the centimeter-scale might be too large to gain a better fundamental understanding of flow and transport. Rather than applying identical measurement techniques for either of the two applications with different objectives, in this chapter we emphasize the need for instrumentation and techniques for specific spatial scales with associated objectives. Consequently, we chose to categorize measurement techniques as they apply to the various spatial scales. Without rigid boundaries, the spatial domain is divided into three measurement scales: (1) the microscale, (2) the laboratory column and field-plot scale, and (3) the field and landscape scale. The microscale includes those measurements that potentially can be applied to infer pore-scale geometry and processes. Arbitrarily, we defined that scale at the size of millimeters or smaller. Presented methodologies in the field/landscape category apply to measurement techniques by which soil characteristics are directly or indirectly obtained so that flow/ transport processes can be inferred that apply to areas of land and not to points (Bouma et al., 1996). We loosely define the field/landscape scale to be equal to the size of a field or larger (soil map unit, watershed). Measurement techniques in between those scale sizes belong to the second category. In this chapter, it is not the intention to present proven technologies. These can be found in various excellent references, such as Methods of Soil Analysis edited by Klute (1986), Soil Analysis: Physical Methods edited by Smith and Mullins (1991), Handbook of Vadose Zone Characterization and Monitoring edited by Wilson et al. (1995), and Vadose Zone Hydrology by Stephens (1995). We have not included a treatise on remote sensing techniques, since its application to the field and landscape scale is presented in chapter 12 of this book. Our objective is to introduce the reader to innovative techniques in soil and vadose zone research across spatial scales, some of which might need further development by the scientist to be successful in VZH. In many instances, we view these methods as an opportunity and challenge, which, if exploited to the fullest extent, can provide additional clues to fundamental mechanisms of flow and transport at both the microscopic and the landscape scale. We present the emerging vadose zone measurement techniques as they apply to the three selected spatial scales. For each of these three categories, we will present a brief summary of their physical basis and their operation, and include references for the most recent developments with general statements on why and how these methodologies might overcome the limitations of traditional methodologies, as well as the constraints of these new methods to date. Moreover, we will present specific examples, particularly if little or no soils literature is available. No doubt our list of

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

281

references is incomplete, and we ask for the reader's understanding if we have missed a key reference or measurement technique.

Microscale The current understanding of water flow and contaminant transport in soils has been limited by existing measurement technologies. For example, the majority of established soil water measurement methods require an instrument to be inserted at or near the region of interest, thereby disturbing the environment being measured. Second, their operation allows for a limited number of "point" measurements, with each measurement being representative for a soil volume that may be too small or too large, depending on the research objective. Therefore, measurements or results need to be scaled up or down so that the data can be interpreted properly for the scale of interest. In the application of the conceptual description of flow and transport, we are limited to the macroscopic approach, because parameters can be measured only at the centimeter scale or larger. Macropore and bypass flow are suggested as mechanisms by which accelerated breakthrough of contaminants occurs, and their study requires measurements at the microscale. To better understand mechanical dispersion, diffusion, chemical and physical adsorption, degradation, the role of immobile soil water regions, and other dynamic systems requires pore-size scale measurements. Various contributions in this issue (e.g., chapters 1, 2, and 8) emphasize the need to study fluid-fluid interfaces in the characterization of flow and transport and mass transfer between fluids. Noninvasive, nondestructive measurement techniques have been used in the past 7 years to spatial scales of millimeters to micrometers. These methods allow observations of changing fluid-phase content and solute concentration, which with increasing sophistication resolves increasingly smaller features of the pore space (Anderson and Hopmans, 1994). Here, we present a current review of the concepts and operation of the most promising microscopic measurement technologies in vadose zone research. These include electromagnetic (EM) radiation techniques, nuclear magnetic resonance (NMR), and other microscopic methods. The EM methods are categorized by those methods that employ radiography and those based on the principle of tomography. Although both methods make use of the attenuation of electromagnetic energy by the porous medium, radiography yields integrative information across the thickness of the medium (two-dimensional), whereas tomography makes use of reconstruction algorithms that resolve the internal distribution of phase content or density (three-dimensional). Both methods are used across a spectrum of frequencies (light, x-rays, and y-rays). Radiography In a radiographic measurement, electromagnetic radiation is passed through the investigated medium, with the transmitted portion quantified using a detection device. For a parallel, monoenergetic beam of x-rays or y-rays, the distribution of

282

VADOSE ZONE HYDROLOGY

transmitted radiation through the medium is a function of the adsorption characteristics, and is denned by Lambert-Beer's law:

where 7X is the transmitted radiation intensity, I0 k is the incident electromagnetic radiation intensity, and i^[ is the linear attenuation coefficient, with the subscript X (wavelength of radiation) indicating the frequency dependency of the attenuation parameter and the validity of equation (11.1) for monochromatic radiation. The linear attenuation coefficient is a function of the absorbing material, including its density, and X indicates the thickness of the medium between the source and detector. The linear attenuation coefficient is the sum of various type of interactions of the EM-radiation with the absorbing material. These are photoelectric absorption, Compton scattering, pair production, and Rayleigh scattering. Photoelectric absorption is a function of the density of the medium, atomic and mass numbers, and wavelength of the EM-radiation. It is most pronounced at the lower energies (25 keV for soft tissue and 500 keV for lead), and increases rapidly with the third to fourth power of the atomic number of the absorber. The Compton scatter in soils is dominating at higher energies (> lOOkeV) and relatively independent of atomic number (Hubbell, 1969). Rayleigh scattering can be important for very low energy x-rays but is of only minor importance in the typical energy range of interest. Pair production is only present at energy levels beyond our applications (> 1 MeV). Thus, EM-absorption is dependent on bulk density, fluid content, and chemical composition, and radiography therefore offers possibilities to determine spatial and temporal distributions of fluid saturations and solute concentrations in multifluid soil systems. Equation (11.1) includes the spatial dependence of the mass attenuation coefficient, reflecting the fact that the fluid- or solid-phase absorption characteristics may vary with space. In radiography, however, 7X is determined from the average attenuation along the pathlength (thickness) of the investigated medium, so that, for monochromatic radiation, equation (11.1) becomes

with X denoting the total travel path or thickness of the medium. For a medium consisting of solid, water, and gas phases, and denoting the mass absorption coefficient, n, as the ratio of the linear attenuation coefficient and density, Lambert-Beer's equation can be rewritten as

where /xs and /XH, denote the mass attentuation coefficients of soil and water, respectively, and the attenuation of the gas phase is neglected. Thus, in using the radiographic technique, the collected attenuation data represent an integrated average across the soil sample. When using dual-energy gamma sources, each with different mass absorption coefficients, the above equation is applied to each source, after which the two equations can be solved to yield estimates of volumetric water content

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

283

(9) and soil bulk density (p). Based on consideration of half-life, self-absorption, and distinct attenuation coefficients, radioactive sources that are used are 241Am (60keV) and 137Cs (662 keV). An extensive reference on the use of multiple sources is provided by Schiegg (1990). A combination of pulse-height analyzers and detectors are used to discriminate and count photons in the appropriate energy spectra. The early literature (e.g., Corey et al., 1971) described the experimental requirements. Later applications improved calibration, automation, and error analysis of such dual-energy gamma radiation systems (e.g., Hopmans and Dane, 1986), or applied dual-energy gamma radiation to measure solute concentrations (Grismer et al., 1986; Oostrom et al., 1992, 1995) and fluid saturation in multiphase systems (Dane et al., 1992). Using the dual-gamma radiation technique, fluid and porous medium properties can be determined noninvasively and nondestructively. Measurements yield average values over the transmission length or sample thickness, thereby allowing two-dimensional visualization of fluid contents and media density. Optimal sample thickness varies with absorption characteristics and photon intensity, but is generally between 5 and 10 cm. Spatial resolution is controlled by the collimation, and is generally between 1 and 10mm. Rapid measurements and simple calculations allow for almost immediate results. Despite the fact that most sources emit polychromatic x-rays, which are subject to preferential absorption of the lower energy photons, it is assumed that their attenuation is governed by Lambert-Beer's law of absorption as well. The first application of x-ray radiography is credited to Rontgen in 1895 (Seliger, 1995). Tidwell and Glass (1994) applied this technique to image spatial and temporal distribution of fluid saturation. Their technique records the light output through the x-ray-exposed film on a charge-coupled device (CCD) camera, which is then digitized into a 512 x 512 points array, yielding a spatial resolution of approximately 8 pixels per centimeter in their experiments. Liquid water was doped with a 10% KI solution, thereby increasing the sensitivity of transmitted x-ray intensity to degree of fluid saturation. In addition to the exponential absorption, visible light is scattered and refracted at fluid fluid and fluid-solid interfaces. Therefore, in the visible light transmission method (Tidwell and Glass, 1994), the intensity of the transmitted light is a function of the refractive indices of the light-absorptive phases. Imaging of the light transmission technique (Glass et al., 1989) is experimentally identical to the x-ray absorption technique, with the x-ray film replaced by the 1-cm thick silica sand medium. However, the physical basis of their measurements are quite different. Whereas the attenuation of x-rays is used to infer fluid distribution, the light technique uses the property that light transmission is increased as the water saturation increases. Both the x-ray method and the light transmission technique provide quantitative liquid saturation information with an accuracy of 5% saturation. The speed of the light transmission measurement makes it especially suitable for transient flow experiments. Both methods have demonstrated their potential in detecting preferential flow mechanisms in heterogeneous and fractured media in thin slab systems (Nicholl et al., 1994). The light transmission technique is limited since it requires a translucent porous medium with a thickness less than 1 cm.

284

VADOSE ZONE HYDROLOGY

Computed Tomography Classic radiography projects a three-dimensional distribution of attenuation coefficients as a shadow on a two-dimensional plane. Therefore, it does not provide information on the variation in attenuation along the beam direction. A major breakthrough in the 1970s, the introduction of x-ray transmission computed tomography (CT or CAT) in the medical sciences, allowed nondestructive cross-sectional imaging (Hounsfield, 1973). Using a collimated x-ray source and detector array, a series of one-dimensional attenuation projections are obtained at a prescribed set of angles through the test object. These projections are analyzed using a reconstruction algorithm to yield a two-dimensional map of attenuation coefficients. Three-dimensional representations are constructed by stacking individually obtained cross-sectional maps. Computed tomography is based on the assumption that, for each detector, the logarithm of the ratio of emitted to detected photon intensity is equal to the line integral over the respective beam path through the two-dimensional distribution of linear attenuation coefficients [equation (11.1) for monochromatic radiation]. By measuring a sufficient number of these line integrals through variation of incident angle, the distribution of attenuation values (/x' as a function of position) can be obtained. However, CT x-ray radiation is usually not monochromatic, but instead consists of a spectrum of photon energies (i.e., wavelengths). The polychromatic nature of x-rays causes a deviation from the exponential attenuation predicted by Lambert-Beer's law because the lower energy portion of the emitted spectrum is being attenuated more strongly than the higher energy portion as the beam passes through the object, an effect known as "beam-hardening." A typical beam-hardening artifact is the presence of elevated attenuation values near the circumference of the measured object. The problem can be reduced by selective filtering of the lower energy photons. Scanners differ in number and size of sources and detectors, and type of source collimation (pencil beam, fan, or cone beam), but have developed toward higher spatial resolution and faster scanning times. A CT image plots the two- or three-dimensional spatial distribution of attenuation coefficients, with the average mass attenuation equal to the sum of the weighted mass attenuation coefficients of the constituent elements. The spatial resolution is controlled by the size of the smallest possible volume elements or voxels. Voxel size is determined by many factors, including source and detector size, source photon energy and flux, detected photon flux, and acquisition time. Since medical scanners are primarily designed for investigation of living tissue, these use relatively low energy levels (120keV) and low photon fluxes. Consequently, their spatial resolution is limited (500-1000/xm). Industrial applications are not constrained by dose restrictions, and therefore can use x-ray systems with higher energies (x-ray computed microtomography, CMT). Smaller source beam diameters and new developments in detection technology have increased the maximum spatial resolution to 5-15 /zm. Other developments, such as the introduction of cone-beam imaging and two-dimensional detectors that allow acquisition of full three-dimensional data sets with a single object rotation, have greatly decreased the scanning time of three-dimensional objects.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

285

The CT technique was quickly adopted by the oil industry to improve oil recovery and identification of drilling sites, and was first introduced in soils by Petrovic et al. (1982). Follow-up studies (e.g., Anderson et al., 1988; Hopmans et al., 1992) have shown that linear relationships exist between attenuation values and the soil's dry bulk density and volumetric water content, whereas Vinegar and Wellington (1987) and Steude et al. (1989) demonstrated the application of CT to the monitoring of transport and breakthrough of solutes. At the same time, it has also been shown that x-ray CT can be successfully applied to image the geometry of macropores and plant roots. Recent work has demonstrated the potential for using CT in the characterization of root geometry (Tollner et al., 1994; Heeraman et al., 1997). A review of CT applications can be found in Anderson and Hopmans (1994). Examples of the use of y-ray CT in porous media are presented by Brown et al. (1993) and Phogat et al. (1991). The large advantage of y- over x-ray sources is that they are monochromatic. On the other hand, photon fluxes are much lower, thereby requiring proportionally larger acquisition times. The dual-energy gamma CT system as introduced by Phogat et al. (1991) allows the imaging of the spatial distributions of two soil characteristics by the independent scanning that uses two y-ray sources (137Cs and 169Yb). For example, it allows simultaneous measurement of the three-dimensional distribution of volumetric water content and soil density or chemical concentration and fluid content. Although the use of cone-beam geometry in x-ray CT has further increased the spatial resolution, the three-dimensional images obtained from cone-beam scanners are distorted. This is caused by the decreasing photon intensity as the x-ray beam increases in size while passing through the medium. Synchrotron radiation sources, on the other hand, produce parallel x-ray beams and can be made nearly monochromatic. These two properties together eliminate the distortion effects as caused by the cone-shaped beam geometry, as well as beam-hardening because of the near-constant energy of the synchrotron x-rays. Their high brightness (ensures high photon flux density) has now provided a means to measure at a spatial resolution of 1 /-tm or better, whereas scanning times have been reduced to seconds rather than minutes, thereby providing opportunities to study transient flow and transport problems. Xray imaging using the synchrotron is also referred to as x-ray tomographic microscopy (XTM), because of the microscopic spatial resolution. Results from using XTM in porous media have been presented by Spanne et al. (1994a, 1994b) using the Brookhaven National Synchrotron Light Source X26 beamline, and by Liu et al. (1993) at the Cornell High Energy Synchrotron Source (CHESS) to measure rapidly changing soil water contents in preferential flow fields. Kinney et al. (1994) present a clear overview of the recent advances in XTM with examples obtained at the Stanford Synchrotron Radiation Laboratory. The advantages of using synchrotron x-ray sources will generate new opportunities, especially with the availability of new sources, such as the Advanced Photon Source at Argonne National Laboratory. As an example, we report on the use of x-ray CMT to study multiphase and solute transport in porous media at 15-/um spatial resolution. The experiments were carried out at Scientific Measurement Systems (SMS), Inc., in Austin, Texas. Instead of the traditional two-dimensional measurement systems that use a single or linear detector array, yielding spatial information within the same two-dimensional plane, this sys-

286

VADOSE ZONE HYDROLOGY

tern uses a microfocus x-ray source and cone-beam x-ray imaging in combination with a two-dimensional detector. It allows three-dimensional measurements by employing a three-dimensional image-reconstruction method. Cone-beam CT allows acquisition of a full three-dimensional data set with a single object rotation (figure 11.1). Using the cone-beam system with geometric magnification, spatial resolution has been improved to the 10-/um voxel size with 15/xm x 15/mi detectors arranged in a 1000 x 1000 array. A 4.5-mm diameter plastic vial was packed with 500-/xm glass beads at a bulk density of 1.4gcm~ 3 . A single scan lasted approximately 20 min and provided attenuation information for a 0.3-mm-thick slice within the glass-bead column. Histograms were analyzed to separate phases with distinct attenuation values. Additional software allows the visualization of isoattenuation surfaces in three dimensions, an example of which is presented in figure 11.2, which show the spatial arrangement of the dry glass beads. Subsequently, the flow cell was flushed with water and CC14 was infiltrated in the water-saturated glass-bead medium and the spatial distribution of each of these phases in the pore space was visualized by subtracting the glass-bead image from the fluid scans. These static experiments confirmed the CMT capabilities at the 15-/^m resolution. In a dynamic experiment, the breakthrough of a 100-mg/mL Nal solution was scanned for an initially water-saturated glass-bead pack (porosity = 0.47). A 90-min pulse was moved through the 2-cm-long system at a steady flow rate of 100/xL/h. Scans were performed continuously at 20-min intervals over a 5-h period, 20mm below the inflow boundary. Each scan covered the same 0.45-mm-thick vertical range and consisted of 30 individual 15-/Mm slices. Information on the three-dimensional spatial arrangement of the iodide was obtained with a spatial resolution of 15 /zm. For quantitative analysis, the top horizontal cross-section was divided into 16 segments by imposing a rectangular grid. The breakthrough curves for all segments are presented in figure 11.3. The overall mass balance using the segment-average pore

Figure 11.1 Schematic representation of cone-beam CT. Microfocal scanning system.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

287

Figure 11.2 Outline of three-dimensional air-glass interfaces in a dry glass-beads porous medium, as obtained from CT. velocities inferred from the peak travel time for each individual segment was 85%. It was clear from these images that even under ideal experimental conditions, pores were extremely selective in their contributions to flow and transport. Further work using a parallel-beam geometry in combination with an areal detector will analyze the breakthrough through a centimeter-thick section, thereby allowing instant threedimensional visualization of these preferential flow paths, as well as improved estimates of the three-dimensional pore-water velocity distribution. Continued develop-

Figure 11.3 Sixteen breakthrough curves (cross-sectional segments), with each curve representing breakthrough for about 1.0mm 2 .

288

VADOSE ZONE HYDROLOGY

ment of CT systems will likely increase the spatial resolution to less than 1 /^m. However, data interpretation and subsequent quantification is constrained by the volume-averaging at any scale. That is, each voxel contains information on the average attenuation of the voxel. Only if the voxel contains a single phase and a single chemical component can we infer microgeometry of phase distributions. It should be noted, therefore, that even at higher spatial resolutions the geometry of phase interfaces will be difficult to interpret. Accurate determination of interfacial shapes and areas will become possible as the spatial resolution becomes orders of magnitude smaller than characteristic sizes of the individual phase elements. Magnetic Resonance Microscopy (MRM) Nuclear magnetic resonance (NMR) is widely applied for chemical analysis in the laboratory and in the medical field. Theoretical work and laboratory experiments (Andreyev and Martens 1960; Prebble and Currie, 1970; Semenov, 1987) have shown that NMR can be used to infer liquid water content. Paetzold et al. (1987) concluded from their laboratory experiments that the NMR signal is a linear function of volumetric water content and is not affected by clay mineralogy, soil organic matter, or texture, thereby providing evidence that the NMR signal is uniquely related to liquid water content in soils. Recent developments in nuclear magnetic resonance imaging (NMRI) have emerged that can provide spatial resolutions in the 10-400//m range, superior to medical scanners. Applications have included determination of root geometry, porous media structure, root water extraction, flow through porous media, degree of water binding, and chemical characteristics. Although predominantly used to identify the presence and state of water (proton NMR), other isotopes that might be observed include 31 P, 13C, 15N, 35C1, and 39K. Using current NMRI technologies, a test object is placed in a static magnetic field with a strength between 1 and 7 T. A radiofrequency pulse (RF) is then generated perpendicular to the static magnetic field, causing an additional varying magnetic field, and tipping the spinning nuclei in the direction of the RF field. After each RF pulse, the nuclei realign with the static magnetic field, releasing energy. This energy decay is quantified as a function of the frequency of the imposed RF field. Each isotope is associated with an energy peak at a particular frequency (Callaghan, 1991). The magnitude of the peak is indicative of the mass of the isotope contained in the test sample (spectroscopy). In NMRI, magnetic gradients may be imposed in all three spatial directions, thereby yielding information on the spatial distribution of the specific isotope. Using the highest strength magnetic fields, the spatial resolution attainable is close to those possible by x-ray CT. Problems can arise in porous media if paramagnetic components, such as iron, are present in the test sample (Rogers and Bottomley, 1987). By using strong magnetic field gradients and a spin echo sequence method (Liu et al., 1994; MacFall and Johnson, 1994), the signal-to-noise ratio is improved, thereby reducing the distortions caused by ferromagnetic particles. Applications have predominantly been in the characterization of root architecture (Liu et al., 1994; MacFall and Johnson, 1994) and preferential flow (Posadas et al., 1996), achieving a spatial resolution of 100/zm or lower.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

289

To decrease scanning times, gradient-recalled echo (GRE), fast-spin echo (FSE), and echo-planar imaging (EPI) and doping procedures have been developed, which are especially useful in three-dimensional applications. In applying these new techniques, Li et al. (1994a, 1994b) and Merrill and Jin (1994) inferred indirectly local velocities for laminar and turbulent flow with a spatial resolution in the micrometer to millimeter range with a temporal resolution of about 1 s, whereas Mansfield and Issa (1994) estimated localized fluid flow velocities in a water-saturated sandstone. Improvements in hardware and measurement protocols are expected that will allow direct velocity measurements in opaque porous media. Other Microscopic Technologies Fiber-optic sensors of 1-3 mm in total diameter use the fluorescence intensity of a tracer to directly estimate concentration and to infer transport characteristics in soils. For example, Meredith and Ghodrati (1994) monitored the displacement of pyranine (a fluorescent water tracer) using fiber-optic probes. After insertion of the probe in the soil, light is filtered to the desired frequency and focused onto the central fiber of a bifurcated fiber-optic probe. The radiation emitted by the fluorescence of the tracer is collected by surrounding fibers and detected by a photomultiplier tube. After calibration of the sensor to the particular fluorescent tracer, sensor response is related to tracer concentration. This technology is used for in situ monitoring of pollutant concentrations (Koglin et al., 1995). Meredith and Ghodrati (1994) demonstrated that such fiber-optic systems can be multiplexed, so that high-frequency observations at multiple locations can lead to the capture of breakthrough curves at small spatial scales, such as in macropores. Micromodels are transparent physical models of a pore space network that allow direct observation of actual pore-scale behavior of processes such as multiphase flow, and colloid and bacterial transport. They are created by etching a pore network pattern onto two glass plates, which are then fused together (Chatzis, 1982; Buckley, 1991; Conrad et al., 1992). Although the network is two-dimensional, the pores have a complex three-dimensional structure, including pore wedges, composed of corners of the pore bodies, and pore throats where the glass plates meet. Conventional micromodels have pore sizes that vary from 0.1 mm to a few millimeters while Wan and Wilson (1994a, 1994b) created models with pore sizes from 4 to 400 nm in diameter, so that a microscope is needed to observe flow and transport processes inside the micromodels. Micromodels are not quantitative tools but help us to understand and validate concepts and assumptions. For example, Conrad et al. (1992) used them to test the hypothesis that the preferential wetting of an organic liquid to spread at the water-gas interface in water wet soils would influence its behavior in the vadose zone. Organic liquids with a propensity for spreading formed a film along the water-gas interface and behaved as a continuum, while those without spreading propensity coalesced into isolated pockets and tiny lenses that float at the water-gas interface. Conrad et al. (1992) used etched glass micromodels to study the mechanism of entrapment of organic liquids. Wan and Wilson (1994b) observed transport of colloids in a micromodel and their behavior at the water-gas interface. They found preferential sorption of colloid particles onto the water-gas interface.

290

VADOSE ZONE HYDROLOGY

This suggests that a stationary water-gas interface can retard colloid transport in the vadose zone while a moving interface, such as during infiltration or near a fluctuating water table, can enhance colloid mobility. Obviously, such observations have important implications for the way we approach problems related to contaminant movement and aquifer remediation. Photomicrographs produced by optical and scanning electron microscopy allowed examination and pore-level scale observation of capillary trapping of organic liquids (isolated blobs). Lu et al. (1994) used a microscope coupled with a CCD camera to visualize capillary rise and drainage in a 1-nim diameter glass-bead media for both water and ethanol, and used their observations to explain the hysteresis phenomenon. A miniature ion-specific electrode was developed by Hamza and Aylmore (1991), allowing the study of the accumulation of sodium near plant roots. Such microelectrodes make possible the accurate, repetitive, and nondestructive local measurements, with an electrode tip size of about 2/Ltm. Photoluminescent volumetric imaging (PVI) was introduced by Montemagno and Gray (1995) to visualize and quantify interfacial areas between fluid phases. This technique was applied to a porous medium system with both transparent quartz beads and immiscible fluids with equal optical refractive indices. Planar areas of the multiphase system are excited by a laser light, thereby illuminating fluorescent material, which accumulates at the fluid-fluid interface only. Using a CCD camera and the scanning of multiple planar sections, a three-dimensional distribution of fluid-fluid interfaces was obtained. Using a similar fluorescence imaging technique, Rashidi et al. (1996) were able to quantify microscopic pore geometry, fluid velocities, and solute concentrations in a saturated glass-bead medium. Microscopic pore-water velocities within a section of a 4.5-cm diameter cylinder containing 0.31-cm plastic beads, saturated with a liquid with an equal refractive index as the beads, were determined by tracking the movement of 6.5-^im diameter latex microspheres in the fluid. Although tomographic studies allow visualization of the spatial arrangement of soil particles, soil pores, water content, fluid interfaces, and water velocities, tensiometric measurements are needed to infer magnitude and direction of the driving forces at the microscopic scale. The original microscopic pressure probe was presented by Husken et al. (1978) for the measurement of turgor pressure (positive) in plant root cells. Using the same technology, a capillary probe was designed to measure capillary pressures in porous media (Heeraman et al., 1994). The probe consists of a 1-mm glass capillary with a 5-/u,m outside diameter tip, connected to a minimum displacement pressure transducer. Rigid tubing between the capillary and the transducer, and complete water filling of the measurement system, resulted in fast response time and minimum exchange of water between the water-filled pores and the capillary. The pressure measurement range of this microtensiometer is controlled by the air-entry value of the capillary (e.g., a 10-/im inside diameter tip corresponds with 150-cm capillary pressure), and the size of the water-filled pores. The capillary probe is inserted in surfacial water-filled pores with the help of a microscope. The microtensiometer has been successfully tested in the range of 040-cm capillary pressure by variation of the macroscopic capillary pressure through application of vacuum to an initially water-saturated 0.5-mm diameter glass-bead medium.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

291

Laboratory Column and Field-Plot Scale Many of the current measurement types apply to this measurement scale. An excellent review of many of these methodologies is presented in the Special Publication of ASA, Advances in Measurement of Soil Physical Properties: Bringing Theory into Practice by Topp et al. (1992). In this chapter, we continue to review the most current developments in instrumentation for the measurement of soil moisture, soil water potential, and soil solution concentration. Time Domain Reflectometry The ability to accurately measure water content in time and space is central to the study of vadose zone hydrology. The measurement of water content using time domain reflectometry (TDR), although long standing (e.g., Fellner-Feldegg, 1969), has rapidly grown in popularity with the advent of affordable TDR systems as it allows continuous automated measurement at multiple locations with a precision sufficient for most applications. Time domain reflectometry depends upon the measurement of travel time of an electromagnetic wave down a wave guide that is either inserted or laid on the soil surface (Selker et al., 1993; Maheshwarla et al., 1995). Increasing travel time is increased with the square root of increase in the real component of the dielectric that surrounds the probe. Since the mineral portion of porous media typically has constant dielectric (between 2-5) at frequencies > 50 MHz (Hoekstra and Delaney, 1974; Campbell, 1990), and liquid water in such media has a dielectric of 70-80 (temperature-dependent), variation in signal travel time along the probes is attributed to variations in water content. Typical accuracy of TDR measurements is equal or better than 2 vol.% (Roth et al., 1990). With the travel times of signals along TDR probes being in the order of nanoseconds, the precise measurement of this travel time has only been economically feasible in the last 15 years with the advent of inexpensive dedicated TDR oscilloscopes. The specific implementation of the TDR method has been intimately tied to the characteristics of the measurement tools. In particular, the Tektronix 1502 series TDR meters, which were designed for field evaluation of signal line integrity, have been the primary instrument employed in TDR moisture measurement. A key determinant of spatial resolution in TDR is the rise-time of the device; approximately 2 x 10~'°s for the Tektronix 1502 series. This dictates the minimum probe length that can be used. The change in travel time along a probe, A/, for a change in travel velocity from v\ to ?;2 is given by

where L is the probe length, with the factor 2 coming from the fact that two-way travel time is observed. Solving for L, we may calculate the minimum probe length for a given ability to measure A?, and a given tolerance in velocity change. For example, when considering a dry soil-water system with a dielectric of 10, one can ask what minimum probe length allows determination of a change of 2% in volumetric moisture content. This would create a change in dielectric of about 1.5, and, applying the relationship between wave velocity, the velocity of light (3 x 10 8 ms~ 1 ),

292

VADOSE ZONE HYDROLOGY

and the dielectric constant, one can compute that the minimum desirable probe length is approximately 12cm. Measurement accuracy can be increased or the probe length decreased when using a faster TDR system. Kelly et al. (1995) determined that probes as short as 0.02m could be used with a TDR system which had a 25 ps rise-time. The physical limitations of the frequency dependence of the dielectric of water become significant at these time scales. The period of molecular resonance of water is of the order of 20 ps. The real dielectric of water drops dramatically for signals with periods in this range, while the complex component (which is an energyloss term) climbs (Merabet and Bose, 1988). The combined loss of propagation delay and energy for single components with periods <40ps obviates any advantage of operating at frequencies in excess of about 10 GHz. In addition to considerations of length, issues of spacing, conductor diameter, and number of wave guides are all significant in determining the sampling volume and sensitivity of the device (Knight, 1992; Whalley, 1993). An additional limitation experienced in the application of TDR has been signal loss due to bulk conductivity of the porous media, which essentially shorts out the signal sent down the TDR probe (Arcone, 1986). The loss of signal strength due to the electrical conductivity of the media can be exploited to provide estimates of soil solution salinity, as demonstrated by Dalton et al. (1984) and many others. Signalloss difficulties are also encountered using ground-penetrating radar (GPR) methods in fine-textured media, as will be described later in this chapter. The signal-loss problem can, in part, be mitigated through the use of minimum-length insulated probes (e.g., Kelly et al., 1995), but it requires individual calibration curves for each probe geometry. In addition, high-conductivity conditions reduces signal energy due to eddy currents established within the media, thereby limiting the range of applicability of the insulated probes to solutions with concentration of smaller than 1 M total salinity, about 25 times greater than can be accommodated by uninsulated probes. The TDR methods are well established in vadose zone monitoring, yet there are various areas where significant enhancements can be achieved. One recent advancement is the development of a multilevel shorting-diode TDR probe (Hook et al., 1992), described in chapter 13 of this book. It allows the monitoring of a linear moisture profile with the installation of a single probe. Another opportunity for enhancement of TDR methods lies in the interpretation of wave forms. At present, most TDR signals are interpreted with an empirical relationship between moisture content and travel time as developed by Topp et al. (1980). More recently, authors have derived physically based methods to interpret the signals (Herkelrath et al., 1991; Heimovaara, 1993; Whalley, 1993), thereby allowing a more clear distinction between dielectric effects on the signal by the solid and liquid phase of the soil matrix. At this time, explicit electromagnetic models for signal propagation are being developed that predict the exact shape of the reflected wave form. These models can be used in a forward modeling mode, but the ultimate objective is to estimate phase contributions by inverse modeling using the full TDR trace as the basis of estimation of moisture content and soil conductivity, which will make more complete use of the wave form obtained from a TDR system.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

293

Measurement of moisture content using TDK will continue to grow in the research community, but rapid adoption in the commercial sector has been hampered by the relatively high cost of TDR systems and the requirement of careful signal interpretation. New products have reduced these concerns, with increasingly robust signal interpretation software and more affordable meters. The TDR method has yet to be packaged into a system that is broadly accessible to individuals in the commercial sector. Nevertheless, TDR is continuing to grow in popularity in the measurement of moisture content within the vadose zone. Competing methods of moisture content measurement through sensing of the soil dielectric are under development or being marketed. However, as shown by Hoekstra and Delaney (1974) and Campbell (1990), these measurements must be made at frequencies greater than 50 MHz to obtain a calibration that is independent of soil type. Soil Water Potential Measurements Water movement through unsaturated media is controlled by gradients in potential, which are typically dominated by gravity and hydraulic pressure. While determination of gravity potential is simply a matter of measuring elevation, measurement of soil water pressure potential in unsaturated media continues to present significant practical difficulties. Three pressure measurement approaches have been implemented widely: (1) direct measurement in a body of water isolated from the soil by a rigid porous membrane (tensiometer), (2) indirect measurement of pressure via measurement of the energy state of a calibrated media (e.g., gypsum block), and (3) indirect measurement of pressure via measurement of relative humidity of the vapor phase (psychrometer). Each of these methods has been revisited in recent years. Some of the interesting recent improvements in tensiometers have been directed toward reduction of the response time and increasing the range of pressures over which they can be used. Reduction of response time has been achieved through careful de-airing of the filling solution (water), and the application of solid-state pressure transducers, both of which have reduced response times to 1 s or less (Selker et al., 1992). It has long been known that pure water can support negative pressures in excess of 1 bar while remaining in the liquid state. Recent experimental studies have shown that the maximum attainable value is greater than 140 bar (Zheng et al., 1991), yet liquid-filled tensiometers are widely assumed to fail at 1 bar, due to the dissolution of gas from the water in the tensiometer filling solution. Recent studies by Miller and Salehzadeh (1993) and Tamari et al. (1993) present tensiometers that measure pressures in excess of 1 bar through removal of dissolved gas by stripping of the dissolved air. These techniques are feasible for both laboratory and field measurements, as shown by Morrison and Szecsody (1987). When tensiometric measurements are required, soil solution samples are often of interest as well. Morrison and Szecsody (1987) introduced the notion of utilizing a single porous cup device for the joint application of solution sampling and soil water potential measurement. Tokunaga (1992) explored the same concept further and provided an explicit method to determine the time required for each measurement to maintain independence. Tokunaga (1992) went on further to demonstrate the application of such a device under several field conditions. Essert and Hopmans

294

VADOSE ZONE HYDROLOGY

(1994) present yet another device, where a single probe allows the simultaneous measurement of soil water potential and extraction of soil solution. This was achieved by dividing the traditional tensiometer into two separate compartments. The concept of combined solution sampling and pressure measurement was pushed one step further by Baumgartner et al. (1994), who devised a porous stainless steel TDR probe that allows the simultaneous measurement of pressure and moisture content and extraction of soil solution samples. Indirect measurement of low soil-water pressure potentials is still carried out through observation of the energy state of a calibrated media, such as an gypsum block. New commercial devices have become available in recent years that claim to be increasingly stable and reproducible. However, the advances in this area are not sufficient to allow application of these devices in a reliable quantitative manner. A novel optical sensing method was introduced by Gary et al. (1989) in which the opacity of a porous block was measured using a light-emitting diode-phototransistor pair. This technique is based on the dependence of light transmission of the block on fluid saturation (Hoa, 1981). The method was tested for both water (in fritted glass) and oil (in porous polyethylene). New technologies for psychrometric measurement of soil water pressure potential were introduced through the adoption of techniques developed for analysis of food products. In particular, Gee et al. (1992) introduced the use of a chilled mirror psychrometer which greatly expedites the measurement of humidity for laboratory samples. Soil Solution Extraction in the Vadose Zone The recent blossoming of the interest in vadose zone hydrology has largely been due to the need to understand contaminant transport to groundwater and aquifers. The critical need in this area has been driven by the ability to accurately monitor the quantity and quality of vadose zone percolate. Traditionally, three methods have been widely employed in this effort: weighing lysimetry, pan lysimetry, and suctioncup lysimetry. Each has been fraught with difficulties: weighing lysimeters, while yielding satisfactory data in most cases, are prohibitive in cost for most applications; pan lysimeters are disruptive to the soil environment; and suction-cup lysimeters do not measure water flux, and thus do not suffice in many applications. Until recently, pan lysimeters were used in either a zero-tension passive collection mode, or in an active-tension collection mode using a porous plate. The zero-tension mode has been shown to significantly undersample vadose water (e.g., Jamison and Fox, 1992), whereas the collected water misrepresents the quality and quality of the true recharge due to undersampling of matrix flow (Steenhuis et al., 1995). The active collection mode provides continuous vacuum to the device, but the magnitude of the vacuum needs continuous adjustment to match temporal variations in soil water pressure potential. In many circumstances, this degree of monitoring and control prohibits its use in many field settings. The recent introduction of wick pan samplers, whereby soil water is extracted through the application of tension through a hanging wick, has provided a costeffective and alternative method of soil solution sampling. The concept of the technique was introduced by Brown et al. (1986), and has been refined through extensive

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

295

laboratory and field experiments in the past few years. Key advantages are that the samplers operate in a passive mode, and that the applied tensions are designed to match a broad range of soil water fluxes. Recent advances in the wick sampler technique include wick-selection design equations (Boll et al., 1992; Knutson and Selker, 1994; Rimmer et al., 1995a), wick preparation methods (Knutson et al., 1994), wick influence on sample concentration due to dispersion (Boll et al., 1992; Poletica et al., 1992; Knutson and Selker, 1996), and laboratory experiments that evaluate wick performance (Rimmer et al., 1995b). Field evaluations of wick samplers have shown that they are most effective in soils when significant transport occurs with water at pressures of —0.1 to —1.5m pressure, which covers a broad range of soil types from sandy to silt loam (Boll et al., 1991; Holder et al., 1991). Sampling from clayey soils is not improved through use of wicks (Steenhuis et al., 1995) in comparison to zero-tension samplers. Although the development of wick samplers adds an important new set of capabilities, they are still expensive to build and instal. There is still a great need for additional reliable and cost-effective methods for the measurement of solute concentration and water flux in the vadose zone. In Situ Measurement of Vadose Zone Hydraulic Characteristics In recent decades, the importance of the multiscale structure of the hydraulic properties of vadose zone materials has been widely documented. At negative pressures, features of textural interfaces and fissures cause drastic reduction in unsaturated permeability, while at near-zero pressure macroporosity can greatly increase permeability. Thus, the ability to measure hydraulic properties of vadose materials in situ at realistic negative pressures has been recognized as an area in need of attention. The use of controlled infiltration under tension to determine unsaturated water retention and transport properties has been considered for decades; however, only in the past few years have experimental and analytical tools been improved to make the technique practical in the field. With regard to necessary instrumentation, the automated tension infiltrometer (TI), as described by Ankeny et al. (1988), has allowed for convenient measurement of infiltration rate as a function of both time and suction pressure. These measurements are typically made at a series of tensions and often with two sizes of circular sources. The measurements require access to a horizontal soil surface, thereby limiting application of this technique to the first few meters of the vadose zone, although a down-hole tension infiltrometer design has also been developed (Sisson and Honeycutt, 1994). The key to the recent wide use of such techniques is the availability of methods to indirectly estimate accurate values of the unsaturated flow parameters from these infiltration studies. There has been a blossoming of inversion schemes by which the unsaturated conductivity function can be obtained from TI data (e.g., Warrick, 1992; Smettem et al., 1994). At present, the most widely accepted method uses the steadystate rate of infiltration using Wooding's solution for steady infiltration from a circular source (Wooding, 1968). It is clear that the next improvement in TI interpretation will be the ability to obtain both the sorptivity and hydraulic conductivity functions from transient infiltration (Simunek and van Genuchten, 1996), a process

296

VADOSE ZONE HYDROLOGY

that holds the promise of significantly increasing the utilization of site-specific hydraulic properties by reducing the experimental time required to obtain reliable values. Heat-Pulse Probe Physical, chemical, and biological processes in soils are a function of temperature, and soil thermal properties are needed to predict temperature regimes. A dual-probe heat-pulse technique was presented by Bristow et al. (1994) to measure, simultaneously from one set of measurements, both the thermal diffusivity and volumetric heat capacity. The dual probe consists of thin needle-like heater and temperature sensor probe which are mounted parallel with 6mm separation. A heat pulse is applied, and the sensor temperature response is recorded. The maximum temperature rise and the time to maximum temperature rise are put into an analytical solution for the temperature distribution around an instantaneously heated infinite line source, thereby explicitly yielding values for the soil thermal diffusivity. Not only can the thermal conductivity be determined from thermal diffusivity and heat capacity measures, but Bristow et al. (1993) also showed that the same measurements can be used for water content monitoring, especially if one is interested in changes in water content only. Error analyses (e.g., Kluitenberg et al., 1995) have shown that the distance between the heater and temperature-sensing probe is a particularly sensitive parameter in obtaining accurate results. Rigid needles are required to minimize changes in mutual probe position while inserting the heat pulse into soils. Bristow and Kluitenberg (1995) showed that a simple modification of the dual probe provides a measure of the soil electrical conductivity as well. If indeed successful, the dualprobe heat-pulse technique might be the instrument of the future for general flow and transport studies, in both the laboratory and in the field, because of its simple, accurate, and versatile design. Other Methods Keller and Lowry (1990) introduced the SEAMIST™ system to sample fluids and vapors from uncased boreholes in the vadose zone. A long balloon-shaped impermeable liner is guided into the borehole by inflating it with air. The positive air pressure ensures good contact between the borehole wall and the liner and prevents collapse of the borehole. Liquid samples are taken with absorbent wicks that are pressed against the borehole wall. Vapors can be sampled in a similar manner or by pulling samples from discrete ports on the membrane via tubes to surface collectors. Keller and Travis (1993) evaluated the performance of different absorber materials and found that sufficient volumes of fluids can be obtained within a reasonable time for many soils. While retrieving the membrane through a line or tether, its outside is turned inside. It is therefore ideal for use in contaminated boreholes since fluid and gas samplers, as well as sensors, are not contaminated while in use, and exposure of workers or instruments to hazardous chemicals is minimized (Koglin et al., 1995). Cone penetrometer technology has been a standard method to evaluate soil strength properties in foundation and road subgrades. Penetrometers have been

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

297

used in soil science to relate soil resistance to root growth, crop yields, and soil physical properties (Bradford, 1986). Penetrometer technology varies from simple pocket penetrometers to heavy truck-mounted cone penetrometer systems that can reach depths of approximately 50m in unconsolidated sediments. The merit of this technology for vadose zone hydrology is its use as an access device for insertion of sensors, such as the four-electrode salinity probe (Rhoades and Van Schilfgaarde, 1986), soil gas samplers (Cronk and Vovk 1993), or to estimate the soil hydraulic parameters of unsaturated soils (Gribb, 1996). The Site Characterization and Analysis Penetrometer System program (SCAPS) integrated cone penetrometer technology with advanced sensors, such as fiber-optic chemical sensors and y-ray counters that provide real-time data regarding lithology, groundwater depth, water quality, and contaminant concentrations (Koglin et al., 1995). Merging cone penetrometer technology with the large suite of chemical sensors may change how we will conduct field investigations. The obvious limitation of cone penetrometer technology is its inapplicability to consolidated geologic materials.

Field/Landscape Scale A wide variety of existing and emerging techniques is available for monitoring vadose zone processes at the field scale. In this section, we will discuss new techniques or new applications of existing techniques in vadose zone hydrology. We classified the different techniques into five categories: lysimetry, isotope hydrology, noninvasive techniques, cross-borehole techniques, and remote sensing. The latter will not be discussed here since recent developments in remote water content measurements from airplanes or satellites are presented in chapter 12 of this book. Lysimetry Lysimeters consist of enclosed blocks of disturbed or undisturbed soil, with or without vegetation, that are hydrologically isolated from the surrounding soil in order to assess or control various terms of the water balance. Nonweighing lysimeters are relatively easy to construct but provide a direct measurement of deep percolation only. They are, therefore, widely used in recharge studies through deep vadose zones in humid and arid climates (Pruitt and Angus, 1960; Mukammal et al., 1971; Stichler et al., 1984; Gee et al., 1994). Weighing lysimeters are more complex to build, but provide direct measurements of both the deep percolation and evapotranspiration. A recent example is the construction of large lysimeters at the University of Arizona in Tucson (P.J. Wierenga, 1996, personal communication; Young et al., 1996). The three lysimeters at Tucson are 2.5m in diameter and 4m deep. They are heavily instrumented with tensiometers, TDK probes, neutron probes, thermocouples, and solution samplers. This allows for detailed measurements of subsurface flow and transport processes, in addition to evapotranspiration. Furthermore, because of the physical separation of the weighing lysimeter from the surrounding soil, this type of device is well suited for studies that involve toxic chemicals and microbes.

298

VADOSE ZONE HYDROLOGY

Lysimeters are expensive research instruments that yield important data to understand the water balance of field soils. However, they do not necessarily represent the regional water balance. They are typically filled with disturbed soils that generally have different water contents from the surrounding area, and a single lysimeter represents only a single location within the landscape. Moreover, in arid regions, it takes several years for a lysimeter filled with dry disturbed soils to reach equilibrium with its environment. Because lysimeters are so effective for the study of flow and transport mechanisms in the vadose zone, this oldest hydrological tool has remained in vogue until the present day and must not be overlooked. New applications are presented continuously in the literature. For example, Jones and Serne (1995) used lysimeters to study leaching of radioactive material from solid waste through unsaturated sediments. Poletika et al. (1995) investigated transport of pesticides and pathogenic viruses through undisturbed soil. Maloszewski et al. (1995) examined water movement and isotopic effects in household refuse dumps and sewage sludge. Hendrickx and Dekker (1991) and Yao and Hendrickx (1996) examined the development of unstable wetting fronts in lysimeters. A truly innovative application of the weighing lysimeter concept is presented by Van der Kamp and Maathuis (1991), who analyzed 20 years of practically continuous water-level records in 49 wells located in the province of Saskatchewan, Canada. A strong, albeit not perfect, correlation was detected between water content changes in the vadose zone and water pressure changes in deep confined aquifers. The analysis demonstrated that groundwater pressures in deep confined aquifers could be used as a measure of areal soil water accumulation. This is especially true for thin aquifers between thick compressible aquitards under a climatic regime with distinct wet and dry seasons. Thus, they postulate that deep confined aquifers can act as large-scale, weighing lysimeters. Bardsley and Campbell (1994) conducted a field experiment in New Zealand to test the aquifer lysimeter hypothesis. Their 5m-thick confined alluvial sand aquifer appears to behave as a true lysimeter that weighs not only the daily variation of water storage in the vadose zone but the seasonal variation as well. Given the difficulty of measuring areal evapotranspiration at the landscape scale, this idea merits serious consideration. Isotope Hydrology Isotopes are defined as atoms whose nuclei contain the same number of protons but differing numbers of neutrons (Hoefs, 1987). In general, light isotopes react more readily than heavy ones, so that "fractionation" occurs. Through evaporation, lighter isotopes will become enriched in the vapor phase and depleted in the residual liquid phase. The process of diffusion also contributes to isotopic enrichment since the lighter isotope is more mobile than the heavier one. Measurement of isotope concentrations in the water and vapor phase thus allows estimation of the amount of evaporated water. Field studies in the 1980s have demonstrated how 2 H (deuterium) and 18O depth profiles can be used to estimate depth of evaporation fronts, depth and timing of water uptake by vegetation (Barnes and Allison, 1983, 1988), and to identify sources of water exposed to evaporation (Walker and Richardson, 1991). For example,

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

299

Komor and Emerson (1994) used differences in isotopic signature between the vadose zone and groundwater to conclude that recharge water was little affected by evaporation, as could be caused by water moving downward through preferential flow paths. Using stable isotopes analyses, root water uptake rates and spatial patterns were examined by Thorburn et al. (1993). These examples demonstrate the potential application of stable isotopes to improve our knowledge of root water uptake and its influence on the water flow regime in the vadose zone. Other effective vadose zone isotopes include 3 H (tritium) and 36C1, both of which entered the atmosphere by nuclear testing during the 1950-1970 era, and were deposited at the soil surface through precipitation. Haynes et al. (1987) used tritium levels of shallow groundwater (0.6-1.3m below soil surface) in the hyperarid Darb el Arba'in Desert between the Nile Valley and the border with Libya for detection of the first nuclear-age recharge. Rainfall in this area is extremely low and the frequency of significant rain is estimated to vary from 20 to 40 years. Due to its relatively short half-life of 12.4 years, bomb tritium has virtually ceased to be a useful tracer in the Southern and most of the Northern Hemisphere. Chlorine-36 occurs naturally at low levels and has a half-life of 3 x 105 years. Due to the mixing processes in the atmosphere, its natural fallout depends on the latitude. For example, in Southern Australia, the 36C1 fallout is 25 atoms m~ 2 s~ ] (Lai and Peters, 1967). For a precipitation of 300 mm/year and a chloride concentration in the rainfall of 4mgL~ 1 , the total chloride fallout is 1.2gm~ 2 year"1, yielding a 36C1/C1 ratio of 40 x 10~ 15 . Nuclear weapons testing during the 1950s produced deposition rates several orders of magnitude higher than either pre- or postbomb production rate. The magnitude of this pulse has been modeled (Bentley et al., 1982) using rainfall concentrations, but radionuclide fallout is highly variable in both space and time. Moreover, measurements have been scarce, so that detailed information of bomb fallout patterns is presently not available. This lack of information is also partly attributed to the difficulty in measuring natural levels of 36C1. However, with the development of accelerated mass spectrometry in the last decade, it is now a routine measurement. There have been few soil 36C1 soil studies (Norris et al., 1987; Phillips et al., 1988; Scanlon, 1992; Cook et al., 1994). Phillips et al. (1988) and Walter et al. (1991) found that recharge estimates obtained with 36C1 and Cl are consistent, while Cook et al. (1994) found considerable differences between the two methods. Its high cost and high variability in fallout makes 36C1 less attractive, but it is useful in some vadose zone studies (Phillips et al., 1990; Fabryka-Martin et al., 1993; Phillips, 1995). Although isotope hydrology is accepted as a separate subdiscipline in hydrology, vadose zone hydrologists have made "surprisingly infrequent use of isotopic methods" (Phillips, 1995). Only under conditions when proven hydrological methods fail has the stable isotope technique been used to study water movement in the vadose zone. For example, environmental tracers, such as chloride and isotopes, have been used as the predominant techniques for recharge and discharge studies under arid and semiarid conditions (chapter 13 in this book). The simple and inexpensive chloride mass balance method is now a standard technique for estimation of longterm recharge rates in rainfed and irrigated areas (Allison et al., 1994; Phillips, 1994; Hendrickx and Walker, 1997).

300

VADOSE ZONE HYDROLOGY

Although isotopic measurements are point observations, the general application is at the field-plot scale. Isotopic signatures at a point location are often the result of vadose zone water movement during many years or decades. The measurement has become quite robust for short-term fluctuations of the water balance, and contains valuable information about the long-term mean soil water fluxes within a hydrological landscape unit. For example, Phillips (1994) compared chloride profiles from six different arid regions within the western United States, and found that despite variations in climate, vegetation, and soil properties among the locations, chloride displacements were similar for all sites, indicating similar water extraction efficiencies between vegetations. Walker et al. (1991) analyzed chloride profiles to assess the effect of native Eucalyptus vegetation removal on recharge rate. More research is needed on the potential of isotope and environmental tracer profiles to enhance our understanding of long-term water balances at the landscape and even regional scales (e.g., Melamed et al., 1977; Allison and Hughes, 1983). Noninvasive Techniques Noninvasive geophysical techniques have been successfully used for many decades by geophysicists studying the Earth's crust and hydrogeologists exploring aquifers. Their application to vadose zone hydrology is relatively recent. Improvements in electronics allowed geophysical sensors to detect signals at the short time intervals required to explore shallow vadose zones. In this section, we will present three established and two emerging geophysical methods. The former include electromagnetic induction, electrical resistivity, and seismic reflection and refraction; the latter include ground-penetrating radar and nuclear magnetic resonance. Since the principles of these methods are presented in excellent references such as Burger (1992), Telford et al. (1990), and Ward (1990), we will limit this section to a succinct description of the method with relevant examples of hydrological and environmental applications. Electromagnetic Induction Although various methods are available (Telford et al., 1990; Ward, 1990), we constrain our discussion to electromagnetic induction equipment that transmits and receives continuously at a single frequency. Examples include the ground conductivity meters EM38 and EM31 (Geonics Limited, Mississauga, Ontario) with penetration depths of 1.5 and 6.0m, respectively, both of which are commonly used in shallow environmental surveys. Using the electromagnetic induction technique, the effect of a conducting soil profile on a time-varying electromagnetic field is measured, and used to derive the apparent electrical conductivity of the profile (McNeill, 1980). An alternating current in a transmitter coil causes a primary magnetic field that induces small currents in the conductive soil that, in turn, generate a secondary magnetic field. Both magnetic fields are detected by a receiver coil; their ratio is a unique function of the apparent electrical conductivity. The secondary magnetic field has an amplitude and phase that differ from the primary field. Differences arise not only from the properties of the soil (such as salt or water content), but also from the

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

301

spacing of the coils and their orientation relative to the soil surface, as well as their distance from the soil surface at the time of measurement. Electromagnetic induction has been used to map contaminant plumes that migrate from landfills under different hydrogeological conditions (McNeill et al., 1990). The method has also been used for subsurface detection and mapping of industrial wastes such as metal hydroxide sludge (Hankins et al., 1991), low-level radioactive waste (Nyquist and Blair, 1991), organics (Barton and Ivanhenko, 1991), and hydrocarbons that result from gasoline spills (Valentine and Kwader, 1985). In agriculture, the electromagnetic induction method is widely used for mapping soil salinity in irrigated lands (Hendrickx et al., 1992; Rhoades, 1993) and in riparian areas under natural vegetation (Sheets et al., 1994). Other applications are the measurement of soil water content (Kachanoski et al., 1990; Sheets and Hendrickx, 1995), detection of brine seepage from oil-field evaporation ponds (Hendrickx et al., 1994), and measurement of salinity of coal mine spoils (Hendrickx et al., 1994). Lesch et al. (1995a, 1995b) describe a statistical methodology for the prediction of field-scale spatial salinity conditions from electromagnetic induction data. Although developed for agriculture, their method has a wide applicability for environmental electromagnetic induction surveys at different scales. Lesch et al. (1995c) provide a software package to implement their methodology. While electromagnetic induction is very versatile, only the apparent electrical conductivity of the soil profile is measured. The user needs to combine hydrogeological information with sound statistical procedures and a basic understanding of the geophysics to arrive at a meaningful interpretation of the electrical conductivity measurements. The great strengths of the method are (1) no contact is needed between the instrument and the soil surface, thereby eliminating contact errors; (2) measurement speed is sufficient to collect regional/landscape-scale information, and (3) its horizontal resolution can be about 0.3m with the EM38. Its weakness is the lack of vertical resolution. Although combining EM38 and EM31 readings in both the horizontal and vertical mode does yield some indication of apparent electrical conductivity changes with depth, the vertical resolution is limited. Therefore, an electromagnetic induction survey is often complemented with electrical resistivity measurements that provide better vertical resolution.

Electrical Resistivity

Using the electrical resistivity technique, a direct current is introduced into the ground through two surface electrodes, while the apparent electrical resistance between two other surface electrodes is measured. Repeated measurements with increasing distance between the two latter electrodes yield the apparent electrical resistivity as a function of depth. Electrical resistivity is probably the most common method applied to delineate groundwater aquifers or to detect the extent of contamination plumes (Burger, 1992). Its application for the determination of salinity depth profiles of agricultural soils is described by Rhoades and van Schilfgaarde (1986). This method gives excellent vertical resolution of hydrogeological layers with different apparent electrical conductivities. However, the loss of contact between the

302

VADOSE ZONE HYDROLOGY

electrodes and a dry soil may cause poor data, and the electrical resistivity method is time-consuming as it requires insertion of electrodes into the soil.

Seismic Reflection and Refraction Seismic methods measure the velocity of sound propagation through the subsurface (Burger, 1992). Since the acoustic properties of geologic materials differ from their electrical properties, seismic techniques yield information distinct from that provided by electrical conductivity and resistivity methods. A seismic source is placed at the soil surface and the velocity of the acoustic waves is measured with geophones. In a layered profile, the waves will be transformed into reflected waves and refracted waves at the layer interface. If the sound velocity of the top layer exceeds that of the bottom layer, the refracted waves will continue to travel downward and the geophone will detect only reflected waves. If the velocity of the bottom layer exceeds that of the top layer, a refracted wave travels partly through the faster bottom layer before entering the top layer again. Therefore, its arrival time at the geophone is earlier than that of the reflected wave. The seismic reflection technique uses the arrival time of the reflected wave for subsurface exploration. This technique is often cumbersome in shallow profiles since the reflected wave is obscured by other waves. The seismic refraction technique uses the arrival time of the refracted wave. Since no other waves interfere with the latter one, refraction data are relatively easy to analyze. However, a shortcoming of the refraction technique is that the bottom layer must have a higher velocity than the top layer for successful application. This constraint is mitigated in many hydrologic investigations, as velocities generally increase with depth due to increased soil water content and/or the presence of a water table. Water table depths have been measured with seismic refraction (Birch, 1976) and reflection (Birkelo et al., 1987) techniques. Experimental data suggest that the seismic method is especially sensitive for estimation of the depth of the capillary fringe (Birkelo et al., 1987; Bonnet and Meyer, 1988).

Ground-Penetrating Radar Ground-penetrating radar (GPR) probes the subsurface environment using bursts of microwave energy. Reflections of the applied signal are recorded in terms of their strength and time of travel. Reflections are caused by changes in the dielectric constant of the subsurface, and therefore the method is very sensitive to positions of wetting fronts and textural interfaces where abrupt changes in water content might occur. The signal can penetrate to approximately 20 m. Ground-penetrating radar is used to assist in the visualization of the stratigraphy of the upper vadose zone, as well as in the mapping of buried objects for undocumented waste-site characterization. The device can be used in a continuous mode by moving it across the soil surface, as well as in a discrete mode by placing a set of antenna in an array of evenly spaced positions. In current instruments, the signal is both digitally recorded for postprocessing, and printed in the field for immediate interpretation.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

303

Ground-penetrating radar has been used to characterize the bedding of soil to assist in locating water-quality sampling devices (Kung and Donohue, 1991; Kung et al., 1991). The GPR technique has proven successful for observing the movement of water in unsaturated soil (Vellidis et al., 1990), defining geologic features (Collins et al., 1990; Beres and Haeni, 1991), and mapping of surface soil water content (Chanzy et al., 1996), and has proven effective in the development of soil surveys and soils data sets (Rebertus et al., 1989; Capece and Campbell, 1990). Recently, GPR has been shown to be effective in delineating subsurface contamination (Scaife and Annan, 1991), although application in the detection and characterization of light nonaqueous-phase liquids (LNAPL) plumes appears to be unlikely to be successful due to the low dielectric contrast provided by such materials (Redmond et al., 1994). A comprehensive treatment of recent applications of GPR to a variety of subsurface characterization problems may be found in the proceedings of the GPR'94. International Symposium (Waterloo Centre for Groundwater Research, 1994). Nuclear Magnetic Resonance As has been described in the microscopic measurements section ("Microscale"), nuclear magnetic resonance (NMR) measurements require a strong magnetic field, as well as an alternating magnetic field perpendicular to that static magnetic field. To measure water content in the vadose zone using surface measurements, no strong external magnetic field can be generated to depths of several tens of meters or more. Instead, the natural existing Earth's magnetic field is utilized. For practical purposes, this magnetic field is homogeneous to a depth of approximately 60 m. The alternating magnetic field perpendicular to the Earth's magnetic field is generated by an electromagnetic dipole at the surface. The protons of the water molecules in the ground will absorb energy from the component of the alternating field perpendicular to the Earth's magnetic field at the resonance frequency of the spinning protons. The nonintrusive NMR measurements using the Earth's magnetic field are recorded by placing a magnetic dipole consisting of a square 100-m x 100-m wire loop on the ground surface (Semenov, 1987). This magnetic dipole is the source for the exciting field and serves as the antenna for the NMR signal. A radiofrequency (RF) pulse is induced through the square loop with a frequency equal to the proton resonance frequency in the Earth's magnetic field. After the exciting pulse is switched off, an electromotive force is observed in the receiver coil. It was shown that the NMR signal depends on the water content distribution and on the product of current amplitude and duration (Semenov, 1987). Through measurements at various locations at the soil surface, a three-dimensional image of water content distribution can be obtained. Although the application of NMR for detection of subsurface water was first proposed by Varian (1962), application of this technique in field tests was only successfully demonstrated in 1978 by Semenov et al. (1989). Continued development resulted in the "hydroscope," which was capable of noninvasive groundwater detection, as well as the measurement of depth of occurrence, thickness, and water content of aquifers. Schirov et al. (1991) concluded that the hydroscope is applicable to Australian conditions and can be used to measure the volume of subsurface water,

304

VADOSE ZONE HYDROLOGY

but that it needs improvement for the measurement of the depth and porosity of the water-containing strata. In Israel, Goldman et al. (1994) combined the NMR method with the time domain electromagnetic (TDEM) method, which is particularly useful for the detection of saline groundwater. Their feasibility study showed that the combined method holds great promise for the noninvasive delineation of aquifers and the simultaneous evaluation of water quality. Their data also indicated the potential of their approach for vadose zone measurements. The studies in Israel and Australia confirmed that (1) the theoretical concepts of the NMR technique are sound, (2) the equipment is operational, and (3) the equipment and analysis can be greatly improved using new computational and electronic technologies. The major limitations of the present technology are caused by interferences from ambient electromagnetic noise of power lines. Moreover, all of the referenced studies have been qualitative in nature. Cross-Borehole Techniques Cross-borehole tomography allows three-dimensional characterization and monitoring of the vadose zone. In this technique, geophysical measurements are made between two boreholes. In the seismic cross-hole method, a seismic source is placed in one borehole and geophones are placed at various depths in the other borehole to obtain travel-time data for a number of ray paths between source and geophones. Using travel-time tomography, seismic velocities between the two boreholes can be estimated. Changes in those velocities indicate changes of intrinsic geological properties and/or water content. The process is analogous to CAT scans with two key differences. First, the number of sources and detectors is limited in hydrogeological applications. Second, whereas EM radiation follows a straight path through the object, seismic rays are curved when crossing geologic boundaries. In seismic travel-time tomography, the vertical plane between the two boreholes is divided into a number of rectangular cells. Each cell is assumed to have its own characteristic sound wave velocity or "slowness" (reciprocal of velocity). The travel time of a ray path crossing a number of cells is determined from the sum of the distance-slowness products of these cells. The objective of seismic tomography is to estimate cell velocities that will result in travel times that agree with the measured travel times (Lines, 1995). This is an inverse problem, and much progress has been made for its solution in the 1980s as a result of active research programs by major oil companies interested in improved characterization of existing oil fields (Rector, 1995; Hyndman and Gorelick, 1996). Contact problems between the borehole wall and the geophones and damage of the borehole by the source have often resulted in poor data quality. However, recent technological developments in the oil industry have largely overcome these obstacles, making more applications in the vadose zone likely. Electrical resistance tomography (Ramirez et al., 1993) appears a more obvious choice for detection of vadose zone water, as more information is available on the variables that determine the apparent electrical conductivity of soils (e.g., Rhoades et al., 1990). Data for cross-borehole electrical resistivity tomography are obtained by installing electrodes in each of the two boreholes at different depths. Because current paths are dependent on the resistivity distribution, the inverse problem is highly

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

305

nonlinear and uniqueness problems may arise. For details on the inversion procedure, see LaBrecque and Ward (1990), Daily et al. (1992), and Ramirez et al. (1993). Daily et al. (1992) demonstrated its potential for vadose zone studies by electrical resistivity measurements of two infiltration experiments in complex sediments. Tomography of the electrical resistivity measurements showed that the infiltration pattern was highly irregular because of preferential flow. Borehole induction logs and high-frequency electromagnetic logs both verified the results of the electrical resistivity tomography. The dry borehole conditions inherent to the vadose zone characterization creates contact problems between the borehole wall and the geophysical devices used. Therefore, there is a need to develop methods that do not require physical contact. Examples are borehole radar (e.g., Sandberg et al., 1991; Soonawala et al., 1990) and electromagnetic tomography (e.g., Alumbaugh and Morrison, 1995a, 1995b).

Discussion

Having gone through this exercise of reviewing new technologies for measurements in the vadose zone, we were impressed with ongoing new developments that are becoming available only recently. For example, microscopic techniques offer a broad spectrum of opportunities in vadose zone research, especially in combination with noninvasive measurements (e.g., x-ray CT and NMR), to study spatial and temporal distributions of fluid phases and their interfaces. Using such systems, models of preferential flow (macro versus matrix flow and film flow) or accelerated breakthrough (mobile versus immobile soil solution, and inter- and intra-aggregate solute transport) could be verified experimentally. The various microscopic techniques might allow simultaneous measurements of physical, chemical, and biological processes—for example, to study the interactions between plant roots and soil water and other soil environmental variables using a combination of ion-specific microelectrodes, CT, and microtensiometric measurements. Also, at the field-scale, the application of noninvasive techniques offers tremendous opportunities to enhance our understanding of flow and transport at the landscape and regional scale, and to study the interfacial processes near the groundwater table and the land surface. Nevertheless, there is a pressing need for continued development of established measurement methods, such as TDR, tensiometric designs, and in situ field measurements of soil moisture, pressure, and soil solution concentration. In particular, we note the need for making TDR more accessible to the user, the promise of using inverse methodologies to infer in situ soil hydraulic characteristics, and the possibilities of the dual-probe heat-pulse technique. However, in the development or application of any of these exciting new measurement techniques, we must note that the measurements in themselves serve little purpose. It is so easy to overemphasize the measurement and the data collection, without realizing the meaning and implications of the data values. That is, when collecting data, we must have an objective in mind to test a hypothesis. Data are obtained to better understand vadose zone processes and to validate models that conceptualize these processes. The vadose zone hydrologist should collaborate with

306

VADOSE ZONE HYDROLOGY

others such that various types of measurements are taken at more than one spatial scale, so that the physics, chemistry, and biology can be integrated for a better understanding of the relationships between flow and transport processes at the micro- and laboratory scale and how these can be applied to the field scale.

Acknowledgments We acknowledge the constructive comments by Volker Clausnitzer, Tony Cahill, Fred Phillips, Peter Wierenga, and John Wilson for their partial review of this manuscript.

References Allison, G.B. and M.W. Hughes. 1983. The use of natural tracers as indicators of soil-water movement in a temperate semi-arid region. J. Hydrol. 60: 157-173. Allison, G.B., G.W. Gee, and S.W. Tyler. 1994. Vadose-zone techniques for estimating groundwater recharge in arid and semiarid regions. Soil Sci. Soc. Am. J. 58: 6-14. Alumbaugh, D.L. and H.F. Morrison. 1995a. Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry. Geophysics 60: 846-870. Alumbaugh, D.L. and H.F. Morrison. 1995b. Monitoring subsurface changes over time with crosswell electromagnetic tomography. Geophys. Prospecting 43: 873-902. Anderson, S.H. and J.W. Hopmans. 1994. Tomography of Soil-Water-Root Processes. Soil Science Society of America Special Publication Number 36. American Society of Agronomy, Madison, WI. Anderson, S.H., CJ. Gantzer, J.M. Boone, and R.J. Tully. 1988. Rapid nondestructive bulk density and soil-water content determination by computed tomography. Soil Sci. Soc. Am. J. 52: 35^0. Andreyev, S.V. and B.K. Martens. 1960. Soil moisture determination by the method of nuclear magnetic resonance. Soviet Soil Sci. 10: 1129-1132. Ankeny, M.D., T.C. Kaspar, and R. Horton. 1988. Design for an automated tension infiltrometer. Soil Sci. Soc. Am. J. 52: 893-896. Arcone, S. 1986. Conductivity limitations in single-reflection time-domain reflectometry. J. Phys. E: Sci. Instrum. 19: 1067-1069. Bardsley, W.E. and D.I. Campbell. 1994. A new method for measuring near-surface moisture budgets in hydrologic systems. J. Hydrol. 154: 245-254. Barnes, C.J. and G.B. Allison. 1983. The distribution of deuterium and 18O in dry soils, 1. Theory. J. Hydrol. 60: 141-156. Barnes, C.J. and G.B. Allison. 1988. Tracing of water movement in the unsaturated zone using stable isotopes of hydrogen and oxygen. J. Hydrol. 100: 143-176. Barton, G.J. and T. Ivanhenko, 1991. Electromagnetic-terrain-conductivity and ground-penetrating-radar investigation at and near the Ciba-Geigy Superfund Site, Ocean County, New Jersey: quality control and quality assurance plan and results. In Proceedings of the Symposium on the Application of Geophysics to Engineering and Environmental Problems, March 11-14, 1991. Baumgartner, N., G.W. Parkin, and D.E. Elrick. 1994. Soil water content and potential measured by hollow time domain reflectometry probe. Soil Sci. Soc. Am. J. 58: 315-318. Bentley, H.W., P.M. Phillips, S.N. Davis, S. Gifford, D. Elmore, L. Tubbs, and H.E. Gove. 1982. The thermonuclear 36C1 pulse in natural water. Nature (London) 300: 737-740.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

307

Beres, M. and P.P. Haeni. 1991. Application of ground penetrating radar methods in hydrogeologic studies. Ground Water 29(3): 375-386. Birch, F.S. 1976. A seismic ground water survey in New Hampshire. Ground Water 14: 94-100. Birkelo, B.A., D.W. Steeples, R.D. Miller, and M. Sophocleous. 1987. Seismic reflection study of a shallow aquifer during a pumping test. Ground Water 25: 703709. Boll, J., J.S. Selker, B.M. Nijssen, T.S. Steenhuis, J. Van Winkle, and E. Jolles. 1991. Water quality sampling under preferential flow conditions. In Lysimeters for Evapotranspiration and Environmental Measurements. Proceedings of the ASCE International Symposium on Lysimetry, Honolulu, HI, July 23-25, 1991. American Society of Civil Engineers, New York, NY, pp. 290-298. Boll, J., J.S. Selker, and T.S. Steenhuis. 1992. Fiberglass wicks for sampling water and solutes in the vadose zone. Soil Sci. Soc. Am. J. 56: 701-707. Bonnet, G. and M. Meyer. 1988. Seismic refraction tests above the water table. J. Geotech. Eng. 114: 1183-1189. Bouma, J.H., W.G. Booltink, and P.A. Finke. 1996. Use of soil survey data for modeling solute transport in the vadose zone. J. Environ. Qual. 25: 519-526. Bradford, J.M. 1986. Penetrability. In A. Klute (ed.), Methods of Soil Analysis, Part I, Physical and Mineralogical Methods, 2nd edn, American Society of Agronomy, Madison, WI, pp. 463-478. Bristow, K.L. and G.J. Kluitenberg. 1995. Soil water and solute analysis using modified dual-probe heat-pulse probes. Agronomy Abstracts, American Society of Agronomy, Seattle, WA, November 13-18, 1994, p. 208. Bristow, K.L., G.S. Campbell, and K. Calissendorf. 1993. Test of a heat-pulse probe for measuring changes in soil water content. Soil Sci. Soc. Am. J. 57: 930-934. Bristow, K.L., G.J. Kluitenberg, and R. Horton. 1994. Measurement of soil thermal properties with a dual-probe heat-pulse technique. Soil Sci. Soc. Am. J. 58: 1288-1294. Brown, G.O., M.L. Stone, and J.E. Gazin. 1993. Accuracy of gamma ray computerized tomography in porous media. Water Resour. Res. 29(2): 479-486. Brown, K.W., J.C. Thomas, and M.W. Holder. 1986. Development of a Capillary Wick Unsaturated Zone Water Sampler. Cooperative Agreement CR812316-01 0. U.S. EPA, Environmental Monitoring Laboratory, Las Vegas, NV. Buckley, J.S. 1991. Multiphase displacements in micromodels. In N.R. Morrow (ed.), Interfacial Phenomena in Petroleum Recovery, Marcel Dekker, New York, pp. 157-189. Burger, H.R. 1992. Exploration Geophysics of the Shallow Subsurface. PrenticeHall, New York. Callaghan, P.T. 1991. Principles of Nuclear Magnetic Resonance Microscopy. Clarendon Press, Oxford. Campbell, J.E. 1990. Dielectric properties and influence of conductivity in soils at one to fifty megahertz. Soil Sci. Soc. Am. J. 54: 332-341. Capece, J.C. and K.L. Campbell. 1990. Using Ground Penetrating Radar to Develop Soil Data Sets. ASAE Paper Number 902640, presented at the 1990 International Winter Meeting of the ASAE, December 18-21, 1990. Gary, J.W., J.F. McBride, and C.S. Simmons. 1989. Electro-optical detection of liquid in translucent porous material. Soil Sci. Soc. Am. J. 53(5): 1591-1595. Cassel, D.K. and D.R. Nielsen. 1994. Introduction: the realization of a dream. In S.H. Anderson and J.W. Hopmans (eds.), Tomography of Soil-Water-Root Processes. SSSA Special Publication Number 36. American Society of Agronomy, Madison, WI. Chanzy, A., A. Tarussov, A. Judge, and F. Bonn. 1996. Soil water content determination using a digital ground-penetrating radar. Soil Sci. Soc. Am. J. 60: 13181326.

308

VADOSE ZONE HYDROLOGY

Chatzis, I. 1982. Photofabrication technique of two-dimensional glass micromodel. PRRC Report 82-12, New Mexico Institute of Mining and Technology, Socorro, NM. Collins, M.E., W.E. Puckett, G.W. Schellentrager, and N.A. Yust. 1990. Using ground penetrating radar for micro-analysis of soils and karst features on the Chiefland limestone plain in Florida. Geoderma 47: 159-170. Conrad, S.H., J.L. Wilson, W.R. Mason, and W.J. Peplinski. 1992. Visualization of residual organic liquid trapped in aquifers. Water Resour. Res. 28: 467^78. Cook, P.O., I.D. Jolly, F.W. Leaney, G.R. Walker, G.L. Allan, L.K. Fifield, and G.B. Allison. 1994. Unsaturated zone tritium and chlorine-36 profiles from southern Australia: their use as tracers of soil water movement. Water Resour. Res. 30: 1709-1719. Corey, J.C., S.F. Peterson, and M.A. Wakat. 1971. Measurement of attenuation of Cs and Am gamma rays for soil density and water content determinations. Soil Sci. Soc. Am. J. 35: 215-219. Cronk, G.D. and M.A. Vovk. 1993. Conjunctive use of cone penetrometer testing and hydropunch™ sampling to evaluate migration of VOCs in groundwater. Proceedings of the Seventh National Outdoor Action Conference and Exposition, National Ground Water Association, Dublin, OH, p. 459. Daily, W., A. Ramirez, D. LaBrecque, and J. Nitao. 1992. Electrical resistivity tomography of vadose water movement. Water Resour. Res. 28: 1429-1442. Dalton, F.N., W.N. Herkelrath, D.S. Rawlins, and J.D. Rhoades. 1984. Timedomain reflectometry: simultaneous measurement of soil water content and electrical conductivity with a single probe. Science 224: 989-990. Dane, J.H., M. Oostrom, and B.C. Missildine. 1992. An improved method for the determination of capillary pressure-saturation curves involving TCE, water and air. J. Contam. Hydrol. 11: 69-81. Essert, S.J. and J.W. Hopmans. 1994. Development and testing of a combined tension-solution probe. Agronomy Abstracts, American Society of Agronomy, Seattle, WA, November 13-18, 1994. Fabryka-Martin, J.T., S.J. Wightman, W.J. Murphy, M.P. Wickham, M.W. Caffee, G.J. Nimz, J.R. Southon, and P. Sharma. 1993. Distribution of chlorine-36 in the unsaturated zone at Yucca Mountain: an indicator of fast transport paths. In FOCUS 93: Site Characterization and Model Validation, Proceedings of Conference, Las Vegas, Nevada, September 26-29, 1993. Fellner-Feldegg, H. 1969. The measurement of dielectric in the time domain. J. Phys. Chem. 73: 616-623. Gee, G.W., M.D. Campbell, G.S. Campbell, and J.H. Campbell. 1992. Rapid measurement of low soil water potentials using a water activity meter. Soil Sci. Soc. Am. J. 56: 1068-1070. Gee, G.W., P.J. Wierenga, B.J. Andraski, M.H. Young, M.J. Payer, and M.L. Rockhold. 1994. Variations in water balance and recharge at three western desert sites. Soil Sci. Soc. Am. J. 58: 63-72. Glass, R.J., T.S. Steenhuis, and J.-Y. Parlange. 1989. Mechanisms for finger persistence in homogeneous unsaturated porous media: theory and verification. Soil Sci. 148: 60-70. Goldman, M., B. Rabinovich, M. Rabinovich, D. Gilad, I. Gev, and M. Schirov. 1994. Application of the integrated NMR-TDEM method in ground water exploration in Israel. J. Appl. Geophys. 31: 27-52. Gribb, M.M. 1996. Parameter estimation for determining hydraulic properties of a fine sand from transient flow measurements. Water Resour. Res. 32(7): 19651974. Grismer, M.E., D.B. McWorther, and A. Klute. 1986. Monitoring water and salt movement in soils at low solution contents. Soil Sci. 141: 163-171.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

309

Hamza, M. and L.A.G. Aylmore. 1991. Liquid ion exchanger microelectrodes used to study soil solute concentrations near plant roots. Soil Sci. Soc. Am. J. 55(4): 954-958. Hankins, J.B., R.M. Danielson, and P.A. Gregson, 1991. Delineation of metal hydroxide sludge disposal areas using electromagnetics and ground-penetrating radar. In Proceedings of the 1991 FOCUS Conference on Eastern Regional Ground Water Issues, Portland Marriott at Sable Oaks, Portland, ME, October 29-31,1991. National Water Well Publishing, Dublin, OH, pp. 675-691. Haynes, C.V., Jr., P.J. Mehringer, D.L. Johnson, H. Haas, A.B. Muller, El Sayed El Zaghloul, A. Swedan, and T.A. Wyerman. 1987. Evidence for the first nuclearage recharge of shallow ground water, Arba'in Desert, Egypt. Natl. Geog. Res. 3: 431-438. Heeraman, D.A., J.W. Hopmans, and T.C. Hsiao. 1994. Pore water pressure measurement using a micro-tensiometer. Agronomy Abstracts, American Society of Agronomy, Seattle, WA, November 13-18, 1994, p. 207. Heeraman, D.A., J.W. Hopmans, and V. Clausnitzer. 1997. Three-dimensional imaging of plant roots in situ with x-ray computed tomography. Plant Soil. 189: 167-179. Heimovaara, T.J. 1993. Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci. Soc. Am. J. 57: 1410-1417. Hendrickx, J.M.H. 1994. Future directions and opportunities in field instrumentation. Agronomy Abstracts, American Society of Agronomy, Seattle, WA, November 13-18, 1994, p. 252. Hendrickx, J.M.H. and L.W. Dekker. 1991. Experimental evidence of unstable wetting fronts in homogeneous non-layered soils. In: T.J. Gish and A. Shiromohammadi (eds.), Proceedings of ASAE National Symposium on Preferential Flow, Chicago IL, December, 1991, pp. 22-31. Hendrickx, J.M.H. and G.R. Walker. 1997. Precipitation recharge. In I. Simmers et al. (eds.), Recharge of Phreatic Aquifers in Arid and Semi-Arid Areas. Heise Verlag. Hendrickx, J.M.H., B. Baerends, Z.I. Raza, M. Sadiq, and M. Akram Chaudhry. 1992. Soil salinity assessment by electromagnetic induction on irrigated land. Soil Sci. Soc. Am. J. 56: 1933-1941. Hendrickx, J.M.H., C.D. Grande, B.A. Buchanan, and R.E. Bretz. 1994. Electromagnetic induction for restoration of saline environments in New Mexico. In R.K. Bhada, A. Ghassemi, T.J. Ward, M. Jamshidi, and M. Shahinpoor. (eds.) ECM Series on Environmental Management & Intelligent Manufacturing, Vol. 1, Waste-Management: From Risk to Remediation. ECM Press, Albuquerque, NM. pp. 247-265. Herkelrath, W.N., S.P. Hamburg, and F. Murphy. 1991. Automatic, real-time monitoring of soil moisture in a remote field area with time domain reflectometry. Water Resour. Res. 27: 857-864. Hoa, M.T. 1981. A new method allowing the measurement of rapid variations in water content in sandy porous media. Water Resour. Res. 17: 41-48. Hoefs, J. 1987. Stable Isotope Geochemistry. Springer-Verlag, New York. Hoekstra, P. and A. Delaney. 1974. Dielectric properties of soils at UHF and microwave frequencies. J. Geophys. Res. 79: 1699-1708. Holder, M., K.W. Brown, J.C. Thomas, D. Zabcik, and H.E. Murray. 1991. Capillary-wick unsaturated zone pore water sampler. Soil Sci. Soc. Am. J. 55: 1195-1202. Hook, W.R., N.J. Livingston, Z.R. Sun, and P.B. Hook. 1992. Remote diode shorting improves measurement of soil water by time domain reflectometry. Soil Sci. Soc. Am. J. 56: 1384-1391.

310

VADOSE ZONE HYDROLOGY

Hopmans, J.W. 1994. Developments in laboratory measurements: an opportunity of improved understanding. Agronomy Abstracts, American Society of Agronomy, Seattle, WA, November 13-18, p. 235. Hopmans, J.W. and J.H. Dane. 1986. Calibration of a dual-energy gamma radiation system for multiple point measurements in a soil. Water Resour. Res. 22(7): 1109-1114. Hopmans, J.W., T. Vogel, and P.D. Koblik. 1992. X-ray tomography of soil water distribution in one-step outflow experiments. Soil Sci. Soc. Am. J. 56(2): 355362. Hounsfield, G.N. 1973. Computerized transverse axial scanning tomography. Part I: description of the system. Br. J. Radiol. 46: 1016-1022. Hubbell, J.H. 1969. Photon cross sections, attenuation coefficients, and energy absorption coefficients from lOkeV to 100 GeV. U.S. Department of Commerce, NSRDS-NBS 29, Washington, DC. Husken, D.E., E. Steudle, and U. Zimmerman. 1978. Pressure probe technique for measuring water relations of cells in higher plants. Plant Physiol. 61: 158-163. Hyndman, D.W. and S.M. Gorelick. 1996. Estsimating lithologic and transport properties in three dimensions using seismic and tracer data: the Kesterson reservoir. Water Resour. Res. 32: 2659-2670. Jamison, J.M. and R.H. Fox. 1992. Estimation of zero-tension pan lysimeter collection efficiency. Soil Sci. 153: 85-94. Jones, T.L. and RJ. Serne. 1995. Contaminant release from solidified radioactive wastes buried in unsaturated sediments: lysimeter study. J. Environ. Qual. 24: 1063-1073. Kachanoski, R.G., E. De Jong, and I.J. Van Wesenbeeck. 1990. Field scale patterns of soil water storage from non-contacting measurements of bulk electrical conductivity. Can. J. Soil Sci. 70: 537-541. Keller, C. and W. Lowry. 1990. A new vadose zone fluid sampling system for uncased holes. In Proceedings of the Fourth National Outdoor Action Conference, National Ground Water Association, Dublin, OH, pp. 3-10. Keller, C. and B. Travis. 1993. Evaluation of the potential utility of fluid absorber mapping of contaminants. In Proceedings of the Seventh National Outdoor Action Conference and Exposition, Association of Ground Water Scientists and Engineers, Las Vegas, NV, pp. 421^136. Kelly, S.F., J.S. Selker, and J.L. Green. 1995. Using short soil moisture probes with high-bandwidth time domain reflectometry instruments. Soil Sci. Soc. Am. J. 59: 97-102. Kinney, J.H., D.L. Haupt, M.C. Nichols, T.M. Breunig, G.W. Marshall, Jr., and S.J. Marshall. 1994. The x-ray tomographic microscope: 3-dimensional perspectives of evolving microstructures. Nucl. Instrum. Methods Phys. Res., Sect. A 347: 480-486. Kluitenberg, G.J., K.L. Bristow, and B.S. Das. 1995. Error analysis of heat pulse method for measuring soil heat capacity, diffusivity, and conductivity. Soil Sci Soc. Am. J. 59: 719-726. Klute, A. (ed.) 1986. Methods of Soil Analysis, Part 1. Physical and Mineralogical Methods, 2nd edn. American Society of Agronomy, Madison, WI. Knight, J.H. 1992. Sensitivity of time domain reflectometry measurements to lateral variations in soil water content. Water Resour. Res. 28: 2345-2352. Knutson, J.H. and J.S. Selker. 1994. Unsaturated hydraulic conductivities of fiberglass wicks and designing capillary pore-water samplers. Soil Sci. Soc. Am. J. 58: 721-729. Knutson, J.H. and J.S. Selker. 1996. Fiberglass wick sampler effects to measurement of solute transport in the vadose zone. Soil Sci. Soc. Am. J. 60: 420-424.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

311

Knutson, J.H., S.B. Lee, W.Q. Zhang, and J.S. Selker. 1994. Fiberglass wick preparation for use in passive capillary wick soil-pore-water samplers. Soil Sci. Soc. Am. J. 57: 1474-1476. Koglin, E.N., E.J. Poziomek, and M.L. Kram. 1995. Emerging technologies for detecting and measuring contaminants in the vadose zone. In L.G. Wilson, L.G. Everett, and S.J. Cullen (eds.), Handbook of Vadose Zone Characterization and Monitoring. Lewis, Boca Raton, FL. Komor, S.C. and D.G. Emerson. 1994. Movements of water, solutes, and stable isotopes in the unsaturated zones of two sand plains in the upper Midwest. Water Resour. Res. 30: 253-267. Kung, K.-J.S. and S.V. Donohue. 1991. Improved solute-sampling protocol in a sandy vadose zone using ground penetrating radar. Soil Sci. Soc. Am. J. 55: 1543-1545. Kung, K.-J.S., J. Boll, J.S. Selker, W.F. Ritter, and T.S. Steenhuis. 1991. Use of ground penetrating radar to improve water quality monitoring in the vadose zone. In Preferential Flow, Proceedings of the National Symposium, ASAE, 1991, pp. 142-149. LaBrecque, D.J. and S.H. Ward. 1990. Two-dimensional cross-borehole resistivity model fitting. In S.H. Ward, Geotechnical and Environmental Geophysics, Vol. Ill, Geotechnical Society of Exploration Geophysicists, Tulsa, OK, pp. 51-74. Lai, D. and B. Peters. 1967. Cosmic-ray produced radioactivity on earth. In Fluegge, S. (ed.), Handbook of Physics, vol. 46(2). Berlin, Springer, pp. 551-612. Lesch, S.M., D.J. Strauss, and J.D. Rhoades. 1995a. Spatial prediction of soil salinity using electromagnetic induction techniques: 1. Statistical prediction models: a comparison of multiple linear regression and cokriging. Water Resour. Res. 31: 373-386. Lesch, S.M., D.J. Strauss, and J.D. Rhoades. 1995b. Spatial prediction of soil salinity using electromagnetic induction techniques: 2. An efficient spatial sampling algorithm suitable for multiple linear regression model identification and estimation. Water Resour. Res. 31: 387-398. Lesch, S.M., J.D. Rhoades, D.J. Strauss, K. Lin, and M.A.A. Co. 1995c. The ESAP User Manual and Tutorial Guide, Version 1.0. Research Report No. 138. U.S. Salinity Laboratory, United States Department of Agriculture, ARS, Riverside, CA. Li, T.-Q., J.D. Seymour, R.L. Powell, M.J. McCarthy, K.L. McCarthy, and L. Odberg. 1994a. Visualization of flow patterns of cellulose fiber suspensions by NMR Imaging. J. Am. Ind. Chem. Eng. 40(8): 1408-1411. Li, T-Q., J.D. Seymour, R.L.Powell, K.L. McCarthy, L. Odberg, and M.J. McCarthy. 1994b. Turbulent pipe flow studied by time-averaged NMR imaging: measurements of velocity profile and turbulent intensity. Magn. Reson. Imag. 12(6): 923-934. Lines, L.R. 1995. Cross-borehole seismology. A tool for enhanced reservoir characterization. Geotimes 40: 11-13. Liu, Y., B.R. Bierck, J.S. Selker, T.S. Steenhuis, and J.-Y. Parlange. 1993. High intensity x-ray and tensiometer measurements in rapidly changing preferential flow fields. Soil Sci. Soc. Am. J. 57: 1188-1192. Liu, I.-Wen, Y., L. J. Waldron, and S.T.S. Wong. 1994. Application of nuclear magnetic resonance imaging to study preferential water flow through root channels. In S.H. Anderson and J.W. Hopmans (eds.), Tomography of Soil-WaterRoot Processes, SSSA Special Publication Number 36. American Society of Agronomy, Madison, WI, pp. 135-148. Lu, T.X., J.W. Biggar, and D.R. Nielsen. 1994. Water movement in glass bead porous media. 1. Experiments of capillary rise and hysteresis. Water Resour. Res. 30(12): 3275-3281.

312

VADOSE ZONE HYDROLOGY

MacFall, J.S. and G.A. Johnson. 1994. Use of magnetic resonance imaging in the study of plants and soils. In S.H. Anderson, and J.W. Hopmans (eds.), Tomography of Soil-Water-Root Processes. SSSA Special Publication Number 36. American Society of Agronomy, Madison, WI, pp. 99-113. Maheshwarla, S.V., R. Venkatasubramanian, and R.F. Boehm. 1995. Comparison of time domain reflectometry performance factors for several dielectric geometries: theory and experiments. Water Resour. Res. 31: 1927-1933. Maloszewski, P., H. Moser, and P. Trimborn. 1995. Isotope hydrology investigations in large refuse lysimeters. J. Hydrol. 167: 149-166. Mansfield, P. and B. Issa. 1994. Studies of fluid transport in porous rocks by echoplanar MRI. Magn. Reson. Imag. 12(2): 275-278. McNeill, J.D. 1980. Electromagnetic terrain conductivity measurement at low induction numbers. Technical Note TN-6, Geonics Ltd, Mississauga, Ontario, Canada. McNeill, J.D., M. Bosnar, and F.B. Snelgrove, 1990. Resolution of an electromagnetic borehole conductivity logger for geotechnical and ground water applications. Technical Note TN-25, Geonics Ltd, Mississauga, Ontario, Canada. Melamed, D., Hanks, R.G., and Willardson, L.S. 1977. Model of salt flow in soil with a source-sink term. Soil Sci. Soc. Am. J. 41: 29-33. Merabet, M. and T.K. Bose. 1988. Dielectric measurements of water in the radio and microwave frequencies by time domain reflectometry. J. Phys. Chem. 92: 61496150. Meredith, C.E. and M. Ghodrati. 1994. A multi-channel optic system for characterization of solute transport in soil. Agronomy Abstracts, American Society of Agronomy, Seattle, WA, November 13-18, 1994, p. 251. Merrill, M.R. and Z. Jin. 1994. Velocity measurements in natural porous rocks. Magn. Reson. Imag. 12(2): 345-348. Miller, E.E. and A. Salehzadeh. 1993. Stripper for bubble-free tensiometry. Soil Sci. Soc. Am. J. 57: 1470-1473. Montemagno, C.D. and W.G. Gray. 1995. Photoluminescent volumetric imaging: a technique for the exploration of multiphase flow and transport in porous media. Geophys. Res. Lett. 22(4): 425-428. Morrison, R.D. and J.E. Szecsody. 1987. A tensiometer and pore water sampler for vadose monitoring. Soil Sci. 144(5): 367-372. Mukammal, E.I., G.A. McKay, and V.R. Turner. 1971: Mechanical balance electrical readout weighing lysimeter. Bound. Layer Meteorol. 2: 207-217. Nicholl, M.J., R.J. Glass, and S.W. Wheatcraft. 1994. Gravity driven infiltration instability in initially dry nonhorizontal fractures. Water Resour. Res. 30(9): 2533-2546. Norris, A.E., K. Wolfsberg, S.K. Gifford, H.W. Bentley, and D. Elmore. 1987. Infiltration at Yucca Mountain traced by 36C1. Nucl. Instrum. Methods Phys. Res. B29: 361-371. Nyquist, J.E. and M.S. Blair. 1991. A geophysical tracking and data logging system: description and case history, Geophysics, LVI(7): 1114-1121. Oostrom, M., J.H. Dane, O. Guven, and J.S. Hayworth. 1992. Experimental investigation of dense solute plumes in an unconfined aquifer model. Water Resour. Res. 28(9): 2315-2326. Oostrom, M., J.H. Dane, B.C. Missildine, and R.J. Lenhard. 1995. Error analysis of dual-energy gamma radiation measurements. Soil Sci. 160(1): 28-42. Paetzold, R.F., A. De los Santos, and G.A. Matzkanin. 1987. Pulsed nuclear magnetic resonance instrument for soil-water content measurement: sensor configurations. Soil Sci. Soc. Am. J. 51: 287-290. Petrovic, A.M., J.E. Siebert, and P.E. Riecke. 1982. Soil bulk density analysis in three dimensions by computed tomographic scanning. Soil Sci. Soc. Am. J. 46: 445-450.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

31 3

Phillips, P.M. 1994. Environmental tracers for water movement in desert soils of the American Southwest. Soil Sci. Soc. Am. J. 58: 15-24. Phillips, P.M. 1995. The use of isotopes and environmental tracers in subsurface hydrology. Rev. Geophys. Supplement: 1029-1033. Phillips, P.M., J.L. Mattick, T.A. Duval, D. Elmore, and P.W. Kubik. 1988. Chlorine-36 and tritium from nuclear-weapons fallout as tracers for long-term liquid and vapor movement in desert soils. Water Resour. Res. 24: 1877-1891. Phillips, P.M., S.N. Davis, and P. Kubik. 1990. A proposal to use chlorine-36 for monitoring the movement of radionuclides from nuclear explosions. Ground Water Monitor. Rev. 10: 106-113. Phogat, V.K., L.A.G. Aylmore, and R.D. Schuller. 1991. Simultaneous measurement of the spatial distribution of soil water content and bulk density. Soil Sci. Soc. Am. J. 55: 908-915. Poletika, N.N., K. Roth, and W.A. Jury. 1992. Interpretation of solute transport data obtained with fiberglass wick soil solution samplers. Soil Sci. Soc. Am. J. 56: 1751-1753. Poletika, N.N., W.A. Jury, and M.V. Yates. 1995. Transport of bromide, simazine, and MS-2 coliphage in a lysimeter containing undisturbed, unsaturated soil. Water Resour. Res. 31: 801-809. Posadas, D.A.N., A. Tannus, H. Panepucci, and S. Crestana. 1996. Magnetic resonance imaging as a non-invasive technique for investigation of 3-D preferential flow occurring within stratified soil samples. Comput. Electron. Agric. 14(4): 255-267. Prebble, R.E. and J.A. Currie. 1970. Soil water measurement by a low-resolution nuclear magnetic resonance technique. J. Soil Sci. 21: 272-288. Pruitt, W.O. and D.E. Angus. 1960. Large weighing lysimeter for measuring evapotranspiration. Trans. Soc. Agric. Eng. 3: 13-18. Ramirez, A., W. Daily, D. LaBrecque, E. Owen, and D. Chesnut. 1993. Monitoring an underground steam injection process using electrical resistance tomography. Water Resour. Res. 29: 73-87. Rashidi, M., L. Peurrung, A.F.B. Tompson, and T.J. Kulp. 1996. Experimental analysis of pore-scale flow and transport in porous media. Adv. Water Resour. 19(3): 163-180. Rebertus, R.A., J.A. Doolittle, and R.L. Hall. 1989. Landform and stratigraphic influences on variability of loess thickness in nothern Delaware. Soil Sci. Soc. Am. J. 53: 843-847. Rector, J.W. Ill 1995. Crosswell methods: where are we, where are we going? Geophysics 60: 629-630. Redmond, J.D., S.M. Ryck, and A.P. Annan. 1994. Detection of LNAPL Plumes with GPR: theoretical modeling and surveys of a controlled spill. In GPR '94: Proceedings of the 5th International Conference on Ground Penetrating Radar, Waterloo Centre for Groundwater Research, Waterloo, Canada, June 12-16, 1994, pp. 1283-1294. Rhoades, J.D. 1993. Electrical conductivity methods for measuring and mapping soil salinity. Adv. Agron. 49: 201-251. Rhoades, J.D. and J. van Schilfgaarde. 1986. Solute content. In A. Klute, (ed.), Methods of Soil Analysis, Part I. Physical and Mineralogical Methods, 2nd edn. American Society of Agronomy, Madison, WI, pp. 985-1006. Rhoades, J.D., P.J. Shouse, W.J. Alves, N.A. Manteghi, and S.M. Lesch. 1990. Determining soil salinity from soil electrical conductivity using different models and estimates. Soil Sci. Soc. Am. J. 54: 46-54. Rimmer, A., T.S. Steenhuis, and J.S. Selker. 1995a. One-dimensional model to evaluate the peformance of wick samplers in soils. Soil Sci. Soc. Am. J. 59: 88-92. Rimmer, A., T.S. Steenhuis, J.S. Selker, and G.J. Albrecht. 1995b. Wick samplers: an evaluation of solute travel times. Soil Sci. Soc. Am. J. 59: 235-243.

314

VADOSE ZONE HYDROLOGY

Rogers, H.H. and P.A. Bottomley. 1987. In situ nuclear magnetic resonance imaging of roots: influence of soil type, ferromagnetic particle content, and soil water. Agron. J. 79: 957-967. Roth, K., R. Schulin, H. Fluhler, and W. Attinger. 1990. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resour. Res. 26: 2267-2273. Sandberg, E.V., O.L. Olsson, and L.R. Falk. 1991. Combined interpretation of fracture zones in crystalline rock using single-hole, crosshole tomography and directional borehole-radar data. The Log Analyst 32: 108-119. Scaife, I.E. and A.P. Annan. 1991. Ground penetrating radar: a powerful, high resolution tool for mining engineering and environmental problems. Proceedings of the 93rd CIM General Meeting, April 29 - May 1, 1991, PEMD #59. Scanlon, B.R. 1992. Evaluation of liquid and vapor water flow in desert soils based on chlorine-36 and tritium tracers and nonisothermal flow simulations. Water Resour. Res. 28: 285-297. Schiegg, H.O. 1990. Laboratory setup and results of experiments on two-dimensional multiphase flow in porous media. Report #PNL-7453. Batelle Pacific North West Laboratories. Schirov, M., A. Legchenko, and G. Creer. 1991. A new direct non-invasive ground water detection technology for Australia. Explor. Geophys. 22: 333-338. Seliger, H.H. 1995. Roentgen, Wilhelm, Conrad and the glimmer of light. Phys. Today. 48: 25-31. Selker, J., P. LeClerq, J.-Y. Parlange, and T.S. Steenhuis. 1992. Fingered flow in two dimensions. 1. Measurements of matric potential. Water Resour. Res. 28: 25132521. Selker, J.S., L. Graff, and T. Steenhuis. 1993. Noninvasive time domain reflectometry moisture probe. Soil Sci. Soc. Am. J. 57(4): 934-936. Semenov, A.G. 1987. NMR hydroscope for water prospecting. Proceedings of the Seminar on Geotomography, Indian Geophysical Union, Hyderabad, India, pp. 66-67. Semenov, A.G., M.D. Schirov, A.V. Legchenko, A.I. Burshtein, and A.Ju. Pusep. 1989. Device for measuring parameters of an underground mineral deposit. GB Patent 2198540. Sheets, K.R. and J.M.H. Hendrickx. 1995. Non-invasive soil water content measurement using electromagnetic induction. Water Resour. Res. 31: 2401-2409. Sheets, K.R., J.P. Taylor, and J.M.H. Hendrickx. 1994. Rapid salinity mapping by electromagnetic induction for determining riparian restoration potential. Restoration Ecol. 2: 242-246. Simunek, J. and M.Th. van Genuchten. 1996. Estimating unsaturated hydraulic properties from tension disc infiltrometer data by numerical inversion. Water Resour. Res. 32(9): 2683-2696. Sisson, J.B. and T.K. Honeycutt. 1994. Tension Bore Hole Permeameter Annual Report. Report INEL-94/0107, October 1994, Idaho National Engineering Laboratory. Smettem, K.R.J., J.-Y. Parlange, P.J. Rose, and R. Haverkamp. 1994. Three-dimensional analysis of infiltration from the disc infiltrometer. I. A capillary-based theory. Water Resour. Res. 30: 2925-2929. Smith, K.A. and C.E. Mullins (eds.). 1991. Soil Analysis: Physical Methods. Marcel Dekker, New York. Soonawala, N.M., A.L. Holloway, and D.K. Tomsons. 1990. Geophysical methodology for the Canadian nuclear fuel waste management program. In S.H. Ward, Geotechnical and Environmental Geophysics, Vol. I: Geotechnical Society of Exploration Geophysicists, Tulsa, OK, pp. 309-331.

MEASUREMENT TECHNIQUES FOR VADOSE ZONE CHARACTERIZATION

315

Spanne, P., K.W. Jones, L. Prunty, and S.H. Anderson. 1994a. Potential applications of synchrotron computed microtomography to soil science. In S.H. Anderson and J.W. Hopmans (eds.), Tomography of Soil-Water-Root Processes. SSSA Special Publication Number 36. American Society of Agronomy, Madison, WI, pp. 43-57. Spanne, P., J.F. Thovert, C.J. Jacquin, W.B. Lindquist, K.W. Jones, and P.M. Adler. 1994b. Synchrotron computed microtomography of porous media: topology and transports. Phys. Rev. Lett. 73(14): 2001-2004. Steenhuis, T.S., J. Boll, E. Jolles, and J.S. Selker. 1995. Field evaluation of wick and gravity pan samplers. In L. Everett, S. Cullen, and L. Wilson (eds.), Vadose Zone Characterization and Monitoring: Principles, Methods and Case Studies. Lewis Press, Chelsea, MI. Stephens, D.B. 1995. Vadose Zone Hydrology. Lewis Publishers, London. Steude, J.S., C.P. Sullivan, R.C. Chancy, M. McKee, and L.E. O'Shea. 1989. Tracer experiments in saturated sand by computed tomography and inductively coupled plasme. In K. Hoddinott and R.O. Lamb (eds.), Proceedings of the Symposium on Physio-Chemical Properties of Soil, Rock, and Related Materials, St. Louis, MO, June 29, 1989. American Society of Testing and Materials, Philadelphia, PA, pp. 171-184. Stichler, W., H. Moser, and M. Schroeder, 1984. Measurements of seepage velocity in a sand lysimeter by means of 18O content. In P. Udluft et al. (eds.), Recent Investigations in the Zone of Aeration, Proceedings of Symposium, Technical University of Munich, Munich, Vol. 1, pp. 191-204. Tamari, S., J.-C. Gaudu, and T. Simonneau. 1993. Tensiometric measurement and metastable state of water under tension. Soil Sci. 156: 149-155. Telford, W.M., L.P. Gledart, and R.E. Sheriff. 1990. Applied Geophysics, 2nd edn. Cambridge University Press, New York. Thorburn, P.J., T.J. Hatton, and G.R. Walker. 1993. Combining measurements of transpiration and stable isotopes of water to determine ground water discharge from forests. J. Hydrol. 150: 563-587. Tidwell, V.C. and R.J. Glass. 1994. X-ray and visible light transmission for laboratory measurement of two-dimensional saturation fields in thin-slab systems. Water Resour. Res. 30(11): 2873-2882. Tokunaga, T. 1992. The pressure response of the soil water sampler and possibilities for simultaneous soil solution and tensiometry. Soil Sci. 154: 171-176. Tollner, E.W., E.L. Ramseur, and C. Murphy. 1994. Techniques and approaches for documenting plant root development with X-ray computed tomography. In S.H. Anderson, and J.W. Hopmans (eds.), Tomography of Soil-Water-Root Processes. SSSA Special Publication Number 36. American Society of Agronomy, Madison, WI, pp. 115-133. Topp, G.C., J.L. Davis, and A.P. Annan. 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour. Res. 16: 574-582. Topp, G.C., W.D. Reynolds, and R.E. Green. 1992. Advances in Measurement of Soil Physical Properties: Bringing Theory into Practice. SSSA Special Publication Number 30. American Society of Agronomy, Madison, WI. Valentine, R.M. and T. Kwader, 1985. Terrain conductivity as a tool for delineating hydrocarbon plumes in a shallow aquifer—a case study. In proceedings of the NWWA Conference on Surface and Borehole Geophysical Methods in Ground Investigations, 1985, Fort Worth, Texas. February 12-14. National Water Well Publishing, Dublin, OH, pp. 52-63. Van der Kamp, G. and H. Maathuis. 1991. Annual fluctuations of ground water levels as a function of loading by surface moisture. J. Hydrol. 127: 137-152. Varian, R.H. 1962. Ground liquid prospecting method and apparatus. US Patent 3.019.383.

31 6

VADOSE ZONE HYDROLOGY

Vellidis, G., M.C. Smith, D.L. Thomas, and L.E. Asmussen. 1990. Detecting wetting front movement in a sandy soil with ground penetrating radar. Trans. ASAE 33(6): 1867-1874. Vinegar, H.J. and S.L. Wellington. 1987. Tomographic imaging of three-phase flow experiments. Rev. Sci. Instrum. 58: 96-107. Walker, C.D. and S.B. Richardson. 1991. The use of stable isotopes of water in characterizing the source of water in vegetation. Chem. Geol. 94: 145-158. Walker, G.R., I.D. Jolly, and P.G. Cook. 1991. A new chloride leaching approach to the estimation of diffuse recharge following a change in land use. J. Hydrol. 128: 49-67. Wan, J. and J.L. Wilson. 1994a. Visualization for the role of the gas-water interface on the fate and transport of colloids in porous media. Water Resour. Res. 30(1): 11-23. Wan, J. and J.L. Wilson. 1994b. Colloid transport in unsaturated porous media. Water Resour. Res. 30(4): 857-864. Ward, S.H. (ed.). 1990. Geotechnical and Environmental Geophysics, Vols. I, II, and III. Society of Exploration Geophysicists, Tulsa, OK. Waterloo Centre for Groundwater Research. 1994. GPR '94: Proceedings of the 5th International Conference on Ground Penetrating Radar, June 12-16, 1994. Waterloo Centre for Groundwater Research, Waterloo, Canada. Warrick, A.W. 1992. Models for disc infiltrometers. Water Resour. Res. 28: 13191327. Whalley, W.R. 1993. Considerations on the use of time-domain reflectometry (TDR) for measuring soil water content. J. Soil Sci. 44: 1-9. Western Regional Research Project W-188. 1994. Improved Characterization and Quantification of Flow and Transport Processes in Soils. U.S. Department of Agriculture, Washington, DC. Wilson, L.G., L.G. Everett, and S.J. Cullen (eds.). 1995. Handbook of Vadose Zone Characterization and Monitoring. Lewis Publishers, Boca Raton, FL. Wooding, R.A. 1968. Steady infiltration from a circular pond. Water Resour. Res. 4: 1259-1273. Yao, T. and J.M.H. Hendrickx. 1996. Stability of wetting fronts in homogeneous soils under low infiltration rates. Soil Sci. Soc. Am. J. 60: 20-28. Young, M.H., P.J. Wierenga, and C.A. Mancino. 1996. Large weighing lysimeters for water use and deep percolation studies. Soil Sci. 161: 491-501. Zheng, Q., D.J. Durben, G.H. Wolf, and C.A. Angell. 1991. Liquids at large negative pressures: water at the homogenous nucleation limit. Science 254: 829-832.

12

Microwave Observations of Soil Hydrology

T. J. JACKSON E. T. ENGMAN T. ]. SCHMUGGE

The upper few centimeters of the soil are extremely important because they are the interface between soil science and land-atmosphere research and are also the region of the greatest amount of organic material and biological activity (Wei, 1995). Passive microwave remote sensing can provide a measurement of the surface soil moisture for a range of cover conditions within reasonable error bounds (Jackson and Schmugge, 1989). Since spatially distributed and multitemporal observations of surface soil moisture are rare, the use of these data in hydrology and other disciplines has not been fully explored or developed. The ability to observe soil moisture frequently over large regions could significantly improve our ability to predict runoff and to partition incoming radiant energy into latent and sensible heat fluxes at a variety of scales up to those used in global circulation models. Temporal observation of surface soil moisture may also provide the information needed to determine key soil parameters, such as saturated conductivity (Ahuja et al., 1993). These sensors provide a spatially integrated measurement that may aid in understanding the upscaling of essential soil parameters from point observations. Some specific issues in soil hydrology that could be addressed with remotely sensed observations as described above include (Wei, 1995): (1) criteria for soil mapping based on spatial and temporal variance structures of state variables, (2) identifying scales of observation, (3) determining soil physical properties within profiles based on surface observations, (4) quantifying correlation lengths of soil moisture in time and space relative to precipitation and evaporation, (5) examining the covariance structure between soil water properties and those associated with water and heat fluxes at the land-atmosphere boundary at various scales, and (6) determining if vertical and horizontal fluxes of energy and matter below the surface can be ascertained from surface soil moisture distributions. In this chapter, the basis of microwave remote sensing of soil moisture will be presented along with the advantages and disadvantages of different techniques. Currently available sensor systems will be described. It should be noted that there

31 8

VADOSE ZONE HYDROLOGY

are no satellite systems in operation that are truly capable of providing reliable soil moisture measurements. Finally, some recent research highlights that utilize different microwave techniques and platforms will be described.

Microwave Remote Sensing A general advantage of microwave sensors (as opposed to visible and infrared) is that observations can be made under conditions of cloud cover. In addition, these measurements are not dependent on solar illumination and can be made at any time of the day. There are two basic approaches used in microwave remote sensing: passive and active. Passive methods measure the natural thermal emission of the land surface at microwave wavelengths using very sensitive detectors. Active methods or radars send and receive a microwave pulse. The power of the received pulse is compared with that of the pulse sent to obtain the backscattering coefficient. The backscattering coefficient is then related to the characteristics of the target. In the next section, common elements of the two approaches are presented, followed by descriptions of the individual techniques. The microwave region of the electromagnetic spectrum comprises the wavelengths between 1 and 100cm. Within this region, there are various bands that are protected. These bands are often referred to by a lettering system. Some of the relevant bands that are used are: K (~ 0.8cm), X (~ 3cm), C (~ 5cm), S (~ 10cm), L (~ 20cm), and P (~ 50cm). Fundamental Basis From Fresnel Reflection to Soil Dielectric Properties

By assuming that the target being observed is a plane surface with surface geometric variations much less than the wavelength, only refraction and absorption of the media need to be considered. This permits the use of the Fresnel reflection equations. These equations predict the surface reflectivity as a function of the indices of refraction of the target and the viewing angle based on polarization of the sensor (horizontal or vertical). The indices of refraction are related to the square roots of the dielectric constants of the two media at the surface of the target. If the sensor provides a measure of reflectivity, and the viewing angle and polarization are denned, it should be possible to estimate the index of refraction. For a bare soil land surface, the target consists of an interface of air and soil. Since the dielectric constant of air is a known value, the reflectivity provides a measurement of the dielectric constant of the medium (soil). The Fresnel equations apply when the two media at the interface each have uniform dielectric properties. This is certainly valid for air; however, for soil this will rarely be true. One of the significant issues that has been addressed in recent research is the validity of the Fresnel assumptions for soil surfaces. These results will be presented in a later section.

MICROWAVE OBSERVATIONS OF SOIL HYDROLOGY

31 9

From Dielectric Constant to Volumetric Soil Moisture The dielectric constant of soil is a composite of the values of its components: air, soil, and water. Although the dielectric constant is a complex number, for most soil mixtures the imaginary part is small and can be ignored for computational purposes without introducing significant error. Values of the real part of the dielectric constant for air and soil particles are 1 and 5, respectively. Water has a value of about 80 at the longer wavelengths considered here ( > 5 cm). The basic reason that microwave remote sensing is capable of providing soil moisture information is this large dielectric difference between water and the other components. Since the dielectric constant is a volume property, the volumetric fraction of each component is involved. The computation of the mixture dielectric constant has been the subject of several studies and there are different theories as to the exact form of the mixing equation (Ulaby et al., 1986). A simple linear weighting function is typically used. The dielectric constant of water mentioned above is that of free water in which the molecules are free to rotate and align with an electrical field. It has been recognized for some time that not all the water present in soil satisfies this condition. Schmugge (1980) suggested that some water in the soil had different properties and that for a given soil this was associated with soil texture in much the same way that general procedures are used to estimate 15-bar and ^-bar moisture contents based on texture (Rawls et al., 1993). Schmugge proposed that the initial water added to the soils below a "transition" moisture had the dielectric properties of frozen water (real part of the dielectric constant = 3). Figure 12.1 shows the predicted relationship between

Figure 12.1 Relationship between volumetric soil moisture and the dielectric constant based on Wang and Schmugge (1980) for a sandy loam soil.

320

VADOSE ZONE HYDROLOGY

soil moisture and dielectric constant for one soil type based on the model proposed by Wang and Schmugge (1980). The important aspect of this figure concerns the slower rate of change in the dielectric constant at lower soil moisture. Dobson et al. (1985) developed a more elaborate description of this relationship, stating that the initial moisture is bound to the soil particle surfaces (not free to align with the electrical field). The most important parameter in determining this bound water fraction is the specific surface area of the soil, which is primarily dependent on the clay fraction and type. However, it is not well known exactly how many layers of water molecules are fully or partially immobilized and how the dielectric constant changes with the layer. Dobson et al. (1985) suggested a value of the real part of the dielectric constant of 15; however, as noted in Schanda (1987), there is little to justify the choice of any particular value. Dobson et al. (1985) did test their approach against laboratory measurements, with good results. In a recent study, Peplinski et al. (1995) examined the effect of clay type on the dielectric constant as a function of water content. Very significant effects were found that were attributed to the change in the specific surface area of the soil. The above discussion leads to the conclusion that four components need to be considered in computing the dielectric constant of soil: air, soil particles, bound water, and free water. To interpret the data correctly, it will be necessary to have knowledge of the soil texture. Based on an estimate of the mixture dielectric constant derived from the Fresnel equations and soil texture, it is possible to then estimate volumetric soil moisture.

Contributing Depth of the Soil and Microwave Wavelength There are well-known theories that describe the reflection and refraction that results from a soil profile with uniform or varying properties (Njoku and Kong, 1977; Wilheit, 1978). The computations involve a nonlinear weighting that decays with depth. Predicting the profile properties from a single microwave measurement is not possible. However, numerous field studies (Jackson and Schmugge, 1989) and modeling efforts have shown that a near-surface layer dominates. These results suggest that the contributing depth is approximately a quarter of the wavelength (based on a range of wavelengths from 2 to 21 cm).

Passive Microwave Methods Passive microwave remote sensing utilizes highly sensitive radiometers that measure the natural radio thermal emission at a particular wavelength. The measurement provided is the brightness temperature, TB, that includes contributions from the atmosphere, reflected cosmic radiation, and the land surface. Atmospheric contributions are negligible at wavelengths > 5 cm (the microwave region of interest here). Cosmic radiation has known values and is easily incorporated into computations. Therefore, TB is essentially dependent on the land surface condition.

MICROWAVE OBSERVATIONS OF SOIL HYDROLOGY

321

The brightness temperature of an isothermal surface is equal to its emissivity multiplied by its physical temperature. If we independently estimate physical temperature, emissivity can be determined. Microwave emissivity varies between 0.6 and 0.95 for most land surfaces. At these wavelengths, the reflectivity is equal to 1 minus the emissivity, which then provides the linkage to the Fresnel equations and soil moisture. For natural conditions, varying degrees of vegetation will be encountered and this affects the microwave measurement. Vegetation attenuates the sensitivity of the interpretation algorithm to soil moisture changes and increases the possibility of significant error. The attenuation increases as wavelength decreases. This is an important reason for using longer wavelengths. As described in Jackson and Schmugge (1989), at longer wavelengths it is possible to correct for vegetation using a vegetation water content-related parameter. An algorithm for estimating surface soil moisture from TB based on the inversion of the Fresnel equations has been presented in Jackson (1993). This algorithm incorporates soil texture, surface roughness, and temperature. It also includes corrections for vegetation. It has been applied in a number of ground and aircraft studies using L (21 cm) and S (11 cm) band radiometers, with very good results (Jackson et al., 1995, 1997). A problem with passive microwave methods is spatial resolution. For a given antenna size, the footprint size increases as wavelength and altitude increase. For realistic satellite designs at the L-band, this might result in footprints as large as 100km. Recent research has focused on the use of synthetic-aperture thinned array radiometers that could decrease the footprint size for satellites down to 10km (Le Vine et al., 1994).

Active Microwave Methods A fixed-position active microwave sensor that measures the sent and received power is called a scatterometer. These instruments measure the backscattering coefficient (cr°). Through theory described in Ulaby et al. (1986), the backscattering coefficient can be related to the surface reflectivity. As described for the passive methods, these results can then be used to determine surface soil moisture. For active techniques, the step between the measurement of the backscattering coefficient and the surface reflectivity is a bit more involved. The geometric properties of the soil surface and any vegetation have a greater effect on these measurements, and simple correction procedures are difficult to develop. The signals sent and received by a radar are usually linearly polarized, either horizontal (H) or vertical (V). Combinations possible are HH, VV, HV and VH. More advanced multipolarization systems can make all of these measurements simultaneously. For bare soils, all models that relate the backscattering coefficient to soil moisture require at least two soil parameters: the dielectric constant and the surface height standard deviation (rms). This means that in order to invert these models, the rms must be determined accurately.

322

VADOSE ZONE HYDROLOGY

For a given sensor configuration of wavelength and viewing angle, different results are obtained at different polarizations but still depend on these same two variables. Therefore, most approaches to determining soil moisture with active microwave methods utilize dual-polarization measurements. With two independent measurements of two dependent variables, it is possible to solve for both the dielectric constant and the rms. Algorithms incorporating this approach are presented in Oh et al. (1992), Dubois et al. (1995), and Shi et al. (1997). Although an adequate model that accounts for vegetation has not been proposed, some modeling efforts have focused on particular types of vegetation (Lin et al., 1994) to develop soil moisture algorithms. Active microwave sensors on aircraft and spacecraft typically employ syntheticaperture radar (SAR) techniques, which utilize the motion of the platform to synthesize larger antennas. Exceptional spatial resolutions with footprints on the order of 20m can be achieved from satellite altitudes.

Current and Near-Future Sensor Systems To a large degree, research and application that utilize microwave sensors are dependent on the instruments currently available. As the needs for soil moisture studies have developed, some new instruments have emerged to satisfy the need. However, soil moisture is a small voice in the crowd asking for new satellites. Therefore, for the most part, we must take what we can get, which is generally a nonoptimal system that limits the research and development that can be accomplished. Current and near-future microwave sensors that operate from ground, aircraft, and satellite platforms are described in the following sections.

Ground-Based Platforms The advantages of ground-based systems include the small footprints (a few meters) and the ability to control and measure the target and to collect data continuously. These systems are ideally suited to the study of the fundamental relationships between microwave observables and target variables, as well as observing timedependent hydrologic processes, such as evaporation and infiltration. The USDA currently operates a dual-wavelength (11-cm and 21-cm single polarization) passive microwave system installed on a boom truck. This system is capable of obtaining either automatic continuous observations over a single target or moving from one target to another to collect specific data sets (Jackson et al., 1997; Schmugge et al., 1998; Jackson et al., 1998). A similar system that includes a 21cm sensor and a number of shorter wavelengths is operated by a French research organization who have focused much of their research on soil moisture-related studies (Wigneron et al., 1993, 1998). There are several other systems in operation; however, these generally do not include a long wavelength or they are involved in other types of research.

MICROWAVE OBSERVATIONS OF SOIL HYDROLOGY

323

Truck-based active microwave systems are operated by several groups. These include a NASA Goddard Space Flight Center multipolarization system with wavelengths of 3, 6, and 18cm (O'Neill et al., 1994). Similar systems currently used in soil moisture-related research include those described by Sofko et al. (1989), Oh et al. (1992), and Benallegue et al. (1995).

Aircraft Platforms Aircraft-based microwave instruments are especially useful in studies that require the mapping of large areas. They can also serve as prototypes of future satellite sensors. In most cases, they will offer better spatial resolution than satellite systems, as well as more control over the frequency and timing of coverage. In the case of passive microwave systems, there are no appropriate satellite systems available for soil moisture studies. Therefore, all large-area research must utilize aircraft sensors. In recent years, NASA has supported two aircraft L-band (21 cm) radiometers: the pushbroom microwave radiometer (PBMR) and the electronically scanned thinned array radiometer (ESTAR). The PBMR was in operation since 1983 in soil moisture studies and has contributed significantly to large-area soil moisture research (Schmugge et al., 1992). It collected data for four footprints simultaneously along a flightline and utilized conventional antenna technology. The ESTAR instrument doubles the number of footprints to eight, which makes it a more efficient mapping instrument. It also is a prototype for a new synthetic-aperture antenna technology that can solve the high-altitude/spatial resolution problem described earlier (Le Vine et al., 1994). Although several other sensors are capable of flying on aircraft, these either operate at shorter wavelengths or provide data for a single footprint. Of the currently operating active microwave aircraft systems, two of the most widely used for soil moisture-related studies are the AIRSAR operated by NASA's Jet Propulsion Lab (Dubois et al., 1995) and the Canadian Centre for Remote Sensing C/X-band airborne SAR (Livingston et al., 1988). The AIRSAR flies on a DC-8 aircraft and provides multipolarization data at wavelengths of 5.66, 23.98, and 68.13cm (C-, L-, and P-band, respectively). It is very efficient for mapping large areas and provides exceptional spatial resolution. The Canadian system is a multipolarization X- and C-band SAR.

Satellite Systems Satellite-based sensors offer the advantages of large-area mapping and long-term repetitive coverage. Revisit time can be a critical problem in studies that involve rapidly changing conditions, such as surface soil moisture. With very wide swaths, it is possible to obtain twice-a-day coverage with a polar-orbiting satellite. For most satellites, especially if viewing angle is important, the revisit time can be much longer. Optimizing the time and frequency of coverage is a critical problem for soil moisture studies.

324

VADOSE ZONE HYDROLOGY

Currently, all passive microwave sensors on satellite platforms operate at very short wavelengths (<1.5cm). Of particular note is the SSM/I package on the Defense meteorological satellites (Hollinger et al., 1990). These satellites have been in operation continuously since 1987 and provide the following combinations of wavelength and polarizations: 0.3cm H and V, 0.8cm H and V, 1.3cm V, and 1.5cm H and V. The system was designed for estimating atmospheric parameters primarily over oceans and not land surface conditions. Therefore, interpreting the data to extract surface information will require accounting for atmospheric effects on the measurement. The atmospheric correction and the shallow contributing depth of soil for these short wavelengths make the data of limited value. Spatial resolution is 70km at the longest wavelength and 15km for the shortest. The SSM/I utilizes conical scanning, which provides measurements at the same viewing angle at all beam positions on a swath. This makes data interpretation more straightforward and simplifies image comparisons. These satellites have a polar orbit that provides two passes a day, roughly 12 h apart, over most areas. Close to the poles, there will be daily twice-a-day coverage. As latitude decreases, the coverage becomes intermittent. For instance, in the central United States there might be several days with twicea-day coverage followed by a day to two of no data or a single pass. This potential gap in coverage is offset to a degree by the fact that there are currently three different satellites in operation with slightly different local coverage times. This also means that there could be coverage at up to six times a day. Although it is not designed for soil moisture studies, under limited conditions (basically no vegetation) the SSM/I satellite sensors can provide some very interesting information on soil hydrology. The results described by Heymsfield and Fulton (1992) and Teng et al. (1993) are good examples of its application. There are two planned multiple-wavelength satellite systems that will include Cband (~ 5 cm) microwave radiometers: Priroda and the Advanced Microwave Scanning Radiometer (AMSR). Priroda is a Russian system that was launched and installed on the Mir space station in 1995. This will be a research mission with limited data availability. The AMSR is currently planned for launch by both the United States and Japan. At present, there are three operational radar satellites. The ERS-1 was launched by the European Space Agency in 1991 and provides C-band VV synthetic aperture radar (SAR) data. Although numerous investigations have been conducted that attempt to utilize ERS-1 data, there have been few reported results in the area of soil moisture estimation. This is due to the limitations of using a single short wavelength and a single polarization SAR with an exact repeat cycle of 35 days. With this kind of temporal coverage, the data will be of little value in process studies. The ERS-2 was launched in 1995 to provide continuing coverage and, at the present time, data may be obtained from both satellites. The JERS-1 is operated by the Japanese and provides L-band HH SAR data and also has a long repeat cycle. Some improvement may be provided by the Canadian RADARSAT sensor launched in 1995. This satellite has a C-band HH SAR with a more frequent revisit interval. A multifrequency-multipolarization SAR called SIR-C/X-SAR was flown on the space shuttle in 1994. This instrument included X-, C-, and L-band radars. Two missions, one in April and the other in October, provided a large amount

MICROWAVE OBSERVATIONS OF SOIL HYDROLOGY

325

and variety of observations for selected test sites, some of which focused on soil moisture.

Recent Research Verification of the Fresnel Inversion Model

As described in an earlier section, the passive microwave measurement is an integrated response of the near-surface profiles of moisture and temperature. To derive surface soil moisture it is necessary to invert a model that describes the relationship between soil moisture and emissivity. The Fresnel model is especially useful in this regard; however, it requires that certain assumptions on the homogeneity of the surface layer are valid. This was recently addressed in a study reported by Jackson et al. (1997). Soil moisture observations averaged over several depths (0-1, 0-3, 0-5, and 0-15 cm) were made concurrent with microwave observations obtained with the truck-mounted USDA system described previously. Brightness temperature values were converted to emissivity using soil temperatures. Comparisons of the observed and predicted emissivity and volumetric soil moisture at four depths (1, 3, 5, and 15cm) for the bare soil are shown in figure 12.2. The lines in figure 12.2 are based on the Fresnel equation for a uniform profile of the specified soil moisture. Based on simple visual analysis, for S-band the Fresnel model corresponds to the observations falling between the 1-cm and 3-cm soil moistureemissivity data (we will call this 2cm). At the L-band, the 5-cm soil moisture matches the model best. This confirms previous studies at 1.4 GHz that have suggested that the L-band response corresponds to the 5-cm soil layer, and also provides new information at the S-band. For the bare sandy loam soil and environment being studied, it appears that a very simple Fresnel-based inversion algorithm would work very well in estimating soil moisture for these layers. The ability to use a physically based algorithm gives us more confidence in the extrapolation of the procedure to other areas. Additional experimental verifications are planned. Diurnal Patterns

Passive microwave radiometry experiments have typically employed a single daily observation of the land surface, usually at high spatial resolution and often at a single wavelength. There exists the potential of new information about land surface parameters by increasing the temporal resolution, decreasing the spatial resolution, and by using multifrequency sensor packages. The availability of new ground-based sensors that are capable of automated continuous monitoring have created the opportunity to observe the dynamics of the surface layer of the soil. Figure 12.3, from Jackson et al. (1997), presents radiometer and soil temperature data collected over a bare soil. This data series was initiated with relatively wet soil conditions. At the outset, the tracking of the L- and S-band responses follow the expected pattern for drying. There is a match in the general pattern of the soil temperatures and the two brightness temperatures. It is interesting to note that there is an offset between

Figure 1 2.2 Observed and predicted soil moisture and emissivity for a bare sandy loam soil using truck-based measurements, H polarization, and 10° viewing angle: (A) Lband; (B) S-band.

Figure 12.3 Diurnal microwave brightness temperature and soil temperature observations for a bare sandy loam soil, H polarization, and 10° viewing angle.

328

VADOSE ZONE HYDROLOGY

the daily peak values of the four curves. A unique aspect of this particular data set was that we were able to observe the TB changes that occurred during and after a rainfall event on the second day. The rapid increase in 7^ (30 K) following the rain is quite large. This change occurred at night and is due only to the drainage of the surface layer. There is obviously some valuable information on soil properties, such as saturated hydraulic conductivity (Ahuja et al., 1993) and a third bar moisture content of both the surface and the profile, imbedded in these data that might be extractable. The relative influence of the thermal temperature of the soil column, as determined using in situ profiles recorded by a meteorological station, was insignificant compared with the more dominant moisture effect. It is quite clear in these data sets that the time of day is a critical parameter in the design of a sensor system that collects data once a day. Large-Area Multitemporal Mapping Washita'92 was a large-scale study of remote sensing and hydrology conducted over the Little Washita watershed in southwest Oklahoma (Jackson et al., 1995). Data collection during the experiment included passive microwave observations using an L-band electronically scanned thinned array radiometer (ESTAR), radar data using the AIRSAR, and surface soil moisture observations at sites distributed over the area. Data were collected over a 9-day period in June, 1992. The watershed was saturated with a great deal of standing water at the outset of the study. During the experiment, there was no rainfall and the surface soil moisture observations exhibited a drydown pattern over the period. Significant variations in the level and rate of change in surface soil moisture were noted over areas dominated by different soil textures. The ESTAR data were processed to produce brightness temperature maps of a 740km2 area on each of 8 days during the 9-day period. Gray-scale images for each day are shown in figure 12.4. These data exhibited significant spatial and temporal patterns. Spatial patterns were clearly associated with soil textures (see figure 12.5) and temporal patterns with drainage and evaporative processes. Relationships between the ground-sampled soil moisture and the brightness temperatures were consistent with previous results. An aspect of spatial scaling of soil moisture sensing was investigated using this data set. All of the soil moisture samples collected on a given day were averaged for the study area. This same procedure was used for the brightness temperature, which was then converted to an cmissivity estimate by normalizing with the averaged soil temperature data. This results in one pair of emissivity and soil moisture data for each of the 8 days. When compared with the Fresnel-based predicted relationship, there was very good agreement, indicating that the data-interpretation algorithms apply within this region and that largescale averaging (740km 2 ) does not degrade their predictive ability. Figure 12.6 shows the observed and predicted values for the Washita'92 study, as well as the results for the truck-based L-band observations described in the Fresnel model section. During the same experiment described above, the AIRSAR was also flown over the study site a total of seven times. At the present time, the soil moisture algorithms

Figure 1 2.4 Brightness temperature images of the Washita'92 study area (L-band, H polarization).

Figure 12.5 Generalized soil texture image of the Washita'92 study area.

330

VADOSE ZONE HYDROLOGY

Figure 12.6 Observed and predicted soil moisture for (A) truck-based measurements and (B) Washita'92 averaged data.

available, even those that utilize multipolarization data, can only be used for bare soils and lightly vegetated conditions. The investigators (Dubois ct al., 1995) recognized this and masked out areas that did not satisfy the algorithm conditions by using vegetation information derived from visible/near infrared satellite data. They applied the soil moisture algorithm for selected dates to generate soil moisture images similar to the passive microwave results described above. As a by-product of this procedure, they were also able to produce surface roughness images. They have also applied this same algorithm to data collected during the imaging radar experiments on the shuttle in 1994.

Summary and Future Directions Surface soil moisture can be measured using microwave sensors. The ability to monitor surface soil moisture over extended time periods and areas could provide valuable new information on soil parameters and processes related to hydrology. Depending on the platform and the sensor, the scale of application could range from a few meters to the globe. There are limitations on microwave-based soil moisture sensing. At the present time, it is recognized that at some level of biomass the vegetation will mask the signal from the soil. The use of longer wavelengths can minimize this effect. Passive and active microwave sensors each have advantages and disadvantages. The spatial resolution of passive instruments will limit the range of applications when used on a satellite. Sensitivity to other surface features could limit the usefulness of active systems. Selecting the best system will require tradeoffs and prioritizing applications. It may be that the optimal sensor system would include both an active

MICROWAVE OBSERVATIONS OF SOIL HYDROLOGY

331

and a passive instrument. This would allow a range of applications and the synergism of the two types of measurements to provide new information. Important research issues that need to be addressed include the diurnal aspects of observation, extracting hydrologic process and state information on infiltration and evaporation, integrating microwave surface observations with meterological measurements and process models, and relating the surface observation to the profile soil moisture. The problem of profile estimation is the most important. There are several possible solutions that might work, ranging from simple regression (Jackson, 1980) to integrated water and radiative transfer modeling (Entekhabi et al., 1994), as well as methods that utilize a combination of modeling and a priori information (Reutov and Shutko, 1986). Wide-scale research and application will continue to be severely hampered by the currently available and planned satellite instruments. All of these instruments have been designed for some other purpose. Although the optimal systems for soil moisture are known, the priority is not high within the current space agency programs. Discipline groups, such as soil science and hydrology, must be more aggressive with these agencies to make them recognize the need for appropriate long-wavelength microwave sensors in space.

References Ahuja, L.R., O. Wendroth, and D.R. Nielson, 1993, Relationship between the initial drainage of surface soil and average profile saturated hydraulic conductivity, Soil Science Society of America Journal, 5, 19-25. Benallegue, M.O., O. Taconet. D. Vidal-Madjar, P. Lancelin, G. Laurent, and F. Baudin, 1995, The use of radar backscattering signals for measuring soil moisture and surface roughness, Remote Sensing of Environment, 53, 61-68. Dobson, M.C., F.T. Ulaby, M.T. Hallikainen, and M.A. El-Rayes, 1985, Microwave dielectric behavior of wet soil—part II: dielectric mixing models, IEEE Transactions on Geoscience and Remote Sensing, GE-23, 35 46. Dubois, P.C., J. van Zyl, and E.T. Engman, 1995. Measuring soil moisture with imaging radars, IEEE Transactions on Geoscience and Remote Sensing, 33, 915-926. Entekhabi, D., H. Nakamura, and E.G. Njoku, 1994, Solving the inverse problem for soil moisture and temperature profiles by sequential assimilation of multifrequency remotely sensed observations, IEEE Transactions on Geoscience and Remote Sensing, 32, 438^48. Heymsfield, G.A. and R. Fulton, 1992, Modulation of SSM/I microwave soil radiances by rainfall. Remote Sensing of Environment, 29, 187-202. Hollinger, J.P., J.L. Peirce, and G.A. Poc. 1990, SSM/I instrument evaluation, IEEE Transactions on Geoscience and Remote Sensing, 28, 781-790. Jackson, T.J., 1980, Profile soil moisture from surface measurements, Journal of the Irrigation and Drainage Division of the ASCE, 106, 81-92. Jackson, T.J., 1993, Measuring surface moisture using passive microwave remote sensing, Hydrological Processes, 7, 139-152. Jackson, T.J. and T.J. Schmugge, 1989, Passive microwave remote sensing system for soil moisture: some supporting research, IEEE Transactions on Geoscience and Remote Sensing, 27, 225 235.

332

VADOSE ZONE HYDROLOGY

Jackson, T.J., D.M. Le Vine, C.T. Swift, T.J. Schmugge, and F.R. Schiebe, 1995, Large area mapping of soil moisture using the ESTAR passive microwave radiometer in Washita'92. Remote Sensing of Environment, 53, 27-37. Jackson, T.J., P.E. O'Neill, and C.T. Swift, 1997, Passive microwave observation of diurnal soil moisture, IEEE Transactions on Geoscience and Remote Sensing, 35, 1210-1222. Jackson, T.J., T.J. Schmugge, P.E. O'Neill, and M.B. Parlange, 1998, Soil water infiltration observation with microwave radiometers, IEEE Transactions on Geoscience and Remote Sensing, 36, 1376-1383. Le Vine, D.M., A.J. Griffis, C.T. Swift, and T.J. Jackson, 1994, ESTAR: a synthetic aperture microwave radiometer for remote sensing applications, Proceedings of the IEEE, 82, 1787-1801. Lin, D.S., E.F. Wood, S. Saatchi, and K. Beven, 1994, Soil moisture estimation over grass covered areas using AIRSAR, International Journal of Remote Sensing, 15, 2323-2343. Livingston, C.E., A.L. Gray, R.K. Hawkins, and R.B. Olsen, 1988, CCRS C/X band airborne SAR: a research and development tool for the ERS-1 time frame, IEEE Aerospace and Electronic Systems, 3, 11-20. Njoku, E.G. and J. Kong, 1977, Theory for passive microwave remote sensing of near-surface soil moisture, Journal of Geophysical Research, 82, 3108-3118. Oh, Y., K. Sarabandi, and F.T. Ulaby, 1992, An empirical model and an inversion technique for radar scattering from bare soil surfaces, IEEE Transactions on Geoscience and Remote Sensing, 30, 370-381. O'Neill, P.E., N.S. Chauhan, T.J. Jackson, D.M. Le Vine, and R.H. Lang, 1994. Microwave soil moisture prediction through corn in Washita'92, Proceedings of the International Geoscience and Remote Sensing Symposium, IEEE No. 94CH3378-7, 1585-1587. Peplinski, N.R., F.T. Ulaby, and M.C. Dobson, 1995, Dielectric properties of soils in the 0.3-1.3-GHz range, IEEE Transactions on Geoscience and Remote Sensing, 33, 803-807. Rawls, W.J., T.J. Gish, and D.L. Brakensiek, 1993, Estimating soil water retention from soil physical properties and characteristics, Advances in Soil Sciences, 16, 213-234. Reutov, E., and A. Shutko, 1986, Prior-knowledge based soil moisture determination by microwave radiometry, Soviet Journal of Remote Sensing, 5, 100-125. Schanda, E., 1987, Microwave modelling of snow and soil, Journal of Electromagnetic Waves and Applications, 1, 1-24. Schmugge, T.J., 1980, Effect of texture on microwave emission from soils, IEEE Transactions on Geoscience and Remote Sensing, GE-18, 353-361. Schmugge, T.J., T.J. Jackson, W.P. Kustas, and J.R. Wang, 1992, Passive microwave remote sensing of soil moisture: results from HAPEX, FIFE and MONSOON'90, ISPRS Journal of Photographic and Remote Sens., 47, 127143. Schmugge, T.J., T.J. Jackson, P.E. O'Neill, and M.B. Parlange, 1998, Observations of coherent emissions from soils, Radio Science, 33, 267-272. Shi, J., J. Wang, A. Hsu, P. O'Neill, and E.T. Engman, 1997, Estimation of bare soil moisture and surface roughness parameters using L-band SAR measurements, IEEE Transactions on Geoscience and Remote Sensing, 35, 1254-1266. Sofko, G.J., J.M. Koeler, M.J. McKibben, A.G. Whacker, M.R. Hinds, R. Brown, and B. Brisco, 1989, Ground microwave operations, Canadian Journal of Remote Sensing, 15, 14-27. Teng, W.L., J.R. Wang, and P.C. Doraiswamy, 1993, Relationship between satellite microwave radiometric data, antecedent precipitation index, and regional soil moisture, International Journal of Remote Sensing, 14, 2483-2500.

MICROWAVE OBSERVATIONS OF SOIL HYDROLOGY

333

Ulaby, F.T., R.K. Moore, and A.K. Fung, 1986, Microwave remote sensing: active and passive, Vol. Ill, from theory to application, Artech House, Dedham, MA. Wang, J.R. and T.J. Schmugge, 1980, An empirical model for the complex dielectric permittivity of soils as a function of water content, IEEE Transactions on Geoscience and Remote Sensing, GE-18, 288-295. Wei, M. (ed.), 1995, Soil moisture: report of a workshop held in Tiburon, California 25-27 January 1994, NASA Conference Publication 3319. Wilheit, T.T., 1978, Radiative transfer in a plane stratified dielectric, IEEE Transactions on Geoscience and Remote Sensing, GE-16, 138-143. Wigneron, J.P., Y. Kerr, A. Chanzy, and Y.Q. Jin, 1993, Inversion of surface parameters from passive microwave measurements over a soybean field, Remote Sensing of Environment, 46, 61-72. Wigneron, J.P., T. Schmugge, A. Chanzy, J.C. Calvet, and Y. Kerr, 1998, Use of passive microwave remote sensing to monitor soil moisture, Agronomie, 18, 27-43.

13

Water and Solute Transport in Arid Vadose Zones Innovations in Measurement and Analysis

SCOTT W. TYLER BRIDGET R. SCANLON GLENDON W. GEE GRAHAM B. ALLISON

Understanding the physics of flow and transport through the vadose zone has advanced significantly in the last three decades. These advances have been made primarily in humid regions or in irrigated agricultural settings. While some of the techniques are useful, many are not suited to arid regions. The fluxes of water and solutes typically found in arid regions are often orders of magnitude smaller than those found in agricultural settings, while the time scales for transport can be orders of magnitude larger. The depth over which transport must be characterized is also often much greater than in humid regions. Rather than relying on advances in applied tracers, arid-zone researchers have developed natural-tracer techniques that are capable of quantifying transport over tens to thousands of years. Techniques have been developed to measure the hydraulic properties of sediments at all water contents, including the very dry range and at far greater depths. As arid and semiarid regions come under increased development pressures for such activities as hazardous- and radioactive-waste disposal, the development of techniques and the understanding of water and solute transport have become crucial components in defining the environmental impacts of activities at the landsurface.

Motivation for Research In the past, the movement of water and solutes through the unsaturated zones of arid and semiarid regions was largely ignored, either for the sake of expediency or from a lack of knowledge or misperceptions regarding the extent of water movement. In the High Plains of the United States, water extraction from the Ogallala aquifer pro-

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

335

ceeded at a rapid rate throughout the 20th century, with little attention paid to the rate of replenishment from natural recharge. As withdrawals began to exceed recharge, water levels dramatically declined and are now necessitating changes in the economic base for this large portion of the agricultural United States. At Hanford, Washington, large amounts of radioactive waste from nuclear weapons production were disposed of at or near the landsurface under the premise that there was no movement of water within the unsaturated zone to transport the contaminants to the underlying aquifer. Transport has occurred, however, and current cost estimates for cleanup of contaminated soils and groundwater exceed $70 billion. In large portions of Australia, clearing native vegetation for cultivated agriculture and pastureland was for many years viewed as "greening the desert," and the economic benefits of this development are well documented. However, the replacement of deep-rooted native vegetation by crops and pasture species has resulted in a dramatic increase in recharge. With generally flat-lying topography and very large accumulations of salts in the soils, this increase in recharge has resulted in salinization of large land areas because of rising water tables. The economic and social consequences of such large-scale land degradation are only beginning to be realized.

Issues to Be Addressed In each of the examples above, a lack of fundamental understanding of the processes of water and solute transport in arid and semiarid regions has led to significant environmental and economic impacts. In this work, we focus our attention on recent developments in the study of unsaturated-zone hydrology. This work is motivated by global needs (e.g., economic, social, and environmental) to understand and quantify the fluxes of water and solutes in the unsaturated zone. We also share a universal concern about groundwater contamination and the development of waste-disposal facilities in arid regions. We begin with a discussion of definitions and the differences between humid- and arid-region water flux and transport. We follow this with a discussion of several emerging technologies and methods that have shown promise in quantifying the low water fluxes commonly found in many unsaturated zones. This review should be considered a mark in time, as new approaches are constantly being developed. We present three examples of studies that have not only improved our understanding of the physics of the unsaturated zone, but have also raised questions about our current conceptual models. We conclude with our thoughts on the directions of future research needs. Definitions Before we begin our discussions, it is important to define clearly the terminology, which has often led to confusion between the disciplines. In this work, we define infiltration to be that portion of precipitation (or irrigation) that passes across the Earth—atmosphere interface. Within the root zone, water flux varies significantly with time and has been termed residual flux (Phillips, 1994). Net infiltration is defined as the water flux at any point below the zone of active evapotranspiration. This zone

336

VADOSE ZONE HYDROLOGY

can range in thickness from a few centimeters in unvegetated sand dunes to tens of meters under deep-rooted trees and shrubs. At any one location, the net infiltration may not be uniform in the vertical dimension due to lateral transport (transport adjacent to an ephemeral wash or wadi) or to temporal variations in either precipitation or evapotranspiration demand. The temporal scale may range from days in the case of irrigated lands to tens of thousands of years in response to climatic shifts. Recharge is defined as the flux of water from the unsaturated zone to the saturated zone that serves to replenish the aquifer. As with net infiltration, recharge is likely to be spatially and temporally variable. Water in the unsaturated zone moves in response to gradients in potential energy along flow paths governed by the hydraulic properties of the medium. In the last four decades, we have seen that vadose zones are naturally heterogeneous, and therefore flow velocities and water fluxes may vary significantly. The presence of large voids, variously defined as macropores, fractures, or preferential pathways, only adds to this variation in velocity. In this work, we define the term preferential flow to include any portion of the soil, at the continuum scale or larger, where flow velocities or water fluxes are significantly above the mean value for a given domain. We therefore group such features as washes or depressions (where net infiltration may be larger than in surrounding areas) with smaller features such as root tubules and fractures. Such features can produce a continuum of scales of flow velocities, and whether they are an important phenomenon will be determined by the problem of interest. Conversely, we define piston-like flow to indicate a velocity or flux field characterized by a small variance. In the strict sense, piston-like flow refers to uniform displacement of solute or water without any mixing. True piston-like flow never occurs because of mixing as a result of molecular diffusion and microscopic water velocity variations; therefore, we use the term piston-like flow instead of piston flow. Once again, we do not define a scale for those phenomena; instead, the scale of piston-like flow will depend on the scale of the investigation and the investigation methods. Comparison between Arid- and Humid-Region Fluxes Unsaturated zones in arid regions present difficulties in analysis that are not generally found in more humid regions. Water contents can span the range from fully saturated following intense rainfall to air dry after long periods of desiccation. The resulting water potentials therefore also range from 0 to —200 MPa and lower (Gee et al., 1992). Water flux in arid regions can range from large fluxes (100-1000 mm/year) to immeasurably small fluxes (< 0.01 mm/year). The thermal regime of arid systems is more severe than in agricultural settings due to a lack of vegetation and small latent-heat fluxes. Thermally driven vapor fluxes often dominate the total water flux in the shallow subsurface, where temperature gradients are steep (Scanlon and Milly, 1994). Liquid and vapor movement under the influence of the geothermal gradient, while small, can also dominate flow at depth in arid unsaturated zones (Montazer and Wilson, 1984; Detty et al., 1993; Prudic and Striegel, 1994; Sully et al., 1994b). The depth of the water table is more critical in defining the state of water and solute flux in arid regions than in agricultural regions. Shallow groundwater often characterizes topographical low areas such as play as and salt flats. In areas of low

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

337

net infiltration and significant topographic relief, the depth to groundwater can exceed 200m. In areas of small net infiltration fluxes, the time scales over which the unsaturated zone responds to the surface boundary conditions are much longer than in more humid regions. Several studies have shown that thick unsaturated zones can be used to infer climatic changes over glacial times scales (10,000-100,000 years). The low water fluxes found in these unsaturated zones can result in excellent preservation of tracers in the infiltrating water. Solute concentrations in arid regions can range from dilute concentrations to several times that found in sea water (due to evapotranspirative concentration). Solute concentrations may vary over short distances, particularly below the root zone, and, as a result, solute gradients may affect the estimation of water flux.

Review of Current and Innovative Techniques Techniques for measuring hydraulic properties, energy status, and solute transport have developed considerably in response to the needs of the agronomic community and have now been modified or further developed for arid regions. These techniques can generally be divided into two major classes: hydrodynamic approaches, whereby the hydraulic and energy statuses are evaluated in the context of Darcy's equation and the advection-dispersion equation, and tracer approaches, in which conservative and nonconservative tracer distributions are evaluated to infer water and solute transport. Also included in the general category of hydrodynamic approaches are water-budget approaches, in which net flux and/or recharge are evaluated by measurements of the components of the water budget. To use the techniques mentioned above, subsurface samples must be obtained to assess the spatial variability of the unsaturated zone. In agronomic settings, sampling is generally straightforward, with limited depth requirements and less opportunity to disturb the samples prior to analysis. In arid regions, low water contents and greater depths needed for characterization place significantly greater restrictions on sampling methodologies. The dry nature of the material, combined with the depths required for sampling, often requires specialized drilling and sampling equipment and precludes the use of drilling fluids such as water or foam. We therefore begin with an assessment of advances in sampling methodologies, followed by a discussion of the advances in soil physics, tracers, and water-budget approaches in arid regions. Drilling Methodologies

Hollow-Stem Auger Hollow-stem angering has gained wide acceptance for drilling and sampling soils in the geotechnical and hazardous-waste industries. A large-diameter auger flight is wrapped around a hollow steel drill pipe (600-1000 mm inside diameter) through which a variety of coring tools can be lowered to obtain samples ahead of the drilling. Coring is usually accomplished by percussion of the core barrel into the

338

VADOSE ZONE HYDROLOGY

undisturbed material. In poorly consolidated soils, percussion coring can cause an increase in bulk density that should be considered when analyzing hydraulic conductivity. Casing-Advance Drilling Recently, casing-advance, underreaming drilling methods have gained wide acceptance for sampling in deep unsaturated zones. The most common of these approaches, originally developed for drilling in consolidated glacial tills, goes by the acronym ODEX. The ODEX method consists of an outer casing (typically 150--300 mm in diameter) and an inner string. The inner string conducts compressed air to the drilling bit, which subsequently carries cuttings to the surface through the annular space between the inner string and the outer casing. Both casing and inner string are advanced simultaneously, reducing any drying of the material above the bit. Coring is accomplished by removing the inner string and using either a wireline or solid percussion core barrel. Core samples typically are 7-8 cm in diameter and up to 150cm in length. The method is effective in dry and/or stony soils and has been used successfully in several vadose zone investigations (Tyler et al, 1992; REECo, 1994; Sully ct al., 1994b). Comparison of the ODEX method with hollow-stem drilling has shown that minimal drying occurs during coring, based on isotopic analysis of pore water of material sampled from both drilling methods (Tyler et al., 1996). Detty et al. (1993) and Sully ct al. (1994b) showed that laboratory-measured water potentials of cores agreed with field-measured water potentials based on thermocouple psychrometcrs (TCPs) installed after drilling, further suggesting that the introduction of drilling air may not be a significant problem, although care must be taken during drilling to reduce drilling-air losses. The ODEX system allows multiple completion options if necessary. Following completion of the core hole, both the inner string and outer casing may be removed and reused. The outer casing may be left in place and used for water-content monitoring via neutron logging (Tyler. 1988). Alternatively, the instruments can be installed and backfilled through the outer casing, which is slowly removed from the hole as instruments are emplaced. Successful installation of TCPs, heat-dissipation probes, gas-sampling ports, and pressure transducers has been conducted to depths of 200m in both alluvial sediments and fractured volcanic tuff (Detty et al., 1993; REECo, 1994). Sonic Drilling Methods Use of sonic vibration for drilling is not a new idea (Hueter and Bolt, 1954; Rockefeller, 1966), but only recently have innovations in the technology led to its practical application. In this method, a drill head equipped with a sonic vibrator imparts high-frequency, high-force vibrations to a steel drill pipe (Barrow, 1994). The vibrations cause the pipe to be pushed rapidly into the ground. The sonic method requires no mud, air, water, or other circulating fluid for penetration and can drill at almost any angle through formations or rock, clay, sand, boulders, permafrost, or glacial till. The technique yields no cuttings. It has been used success-

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

339

fully to drill wells at the Hanford site in Washington State and in Albuquerque, New Mexico, among other locations. Sonic drilling can produce nearly intact core samples for analysis. Current drawbacks to sonic drilling are cost, drilling depth, core and material displacement, and thermal effects. The sonic drill-rig and support equipment cost about $500,000. Additional replacement parts for the sonic drill head are expensive, and significant maintenance and repairs are required to keep the sonic system in peak working condition. The method performs most efficiently from 15 to 100m and drilling to greater depths requires a casing-advance system to reduce the sidewall-friction damping that limits the efficiency of the sonic drill. The sonic method produces no cuttings; thus, it displaces rather than cuts through the formation. It is not uncommon to recover more core than footage drilled in consolidated sediments. Finally the resonance of sonic drilling can create elevated temperatures in core samples of certain formations. Since sonic drilling uses no fluid as a cooling medium, the friction created in the drilling process is transferred to heat, elevating temperatures close to the drill pipe. Use of proper bit design and operator procedures helps reduce the temperatures in the core and surroundings. In spite of the current limitations, the potential of the resonant sonic drilling technique for rapidly drilling both vertical and horizontal boreholes at waste sites makes it an attractive alternative to other, more commonly used methods. In all drilling situations, care must be taken with sealing samples for shipment. Cores can be capped and then sealed with paraffin to prevent water loss during transport to the laboratory. For further protection, plastic or foil wrappers sealed by heat or adhesives are commercially available. Once the samples arc in the laboratory, humidified glove boxes can be used to minimize sample drying during handling.

Sensor Installation Techniques Installation of sensors in deep unsaturatcd zones is difficult, and sensors are prone to failure. Some innovations in sensor placement have been achieved in the past several years. The SEAMIST system was developed in 1989 by Science and Engineering Associates as a Membrane Instrumentation and Sampling Technique to simplify sensor installation (Keller, 1991). The system consists of an impermeable membrane that lines the test hole and is everted under a pressure of 10-30 kPa. The system can be used to conduct several functions, such as lining a borehole; transporting into a borehole monitoring instruments that are fastened to the membrane, such as thermocouples, absorbent pads, fiber optics, and electrodes; and carrying larger instruments (video cameras, etc.) within the impermeable membrane. The SEAMIST system can also be used to collect samples of pore fluids or gases in the unsaturated zone or to measure the gas permeability of the sediments. In regions where water potentials are greater than — lOOkPa, tensiometers have been used in the shallow ( < 1 0 m ) subsurface. Recently, Hubbel and Sisson (1996) have developed a portable tensiometer that can be installed in boreholes of any depth. The tensiometer, with or without a pressure transducer, is lowered into the hole and allowed to equilibrate with material at the bottom of the borehole. The tensiometer can also be retrieved from the borehole and tension measured at the

340

VADOSE ZONE HYDROLOGY

landsurface. The design of Hubbel and Sisson (1996) may be quite applicable for reconnaissance surveying of the vadose zone during drilling. Improvements in Hydrodynamic Measurements Methods of determining water content, water retention, hydraulic conductivity, and solute dispersion and diffusion in arid regions must be able to cover the entire range from saturated to air dry to be applicable to arid studies. One of the most critical parameters in assessing water flux in arid regions is the magnitude of the soil water potential. Water potentials found in arid regions are often orders of magnitude lower than those typically found in agricultural settings, precluding the use of tensiometers and heat-dissipation probes, which are restricted to the wetter ranges (> — 0.07MPa and > — 1.4 MPa, respectively). Only following rain events or near the water table do such techniques become operable. Filter Paper Method The filter paper equilibrium method (Campbell and Gee, 1986; Greacen et al., 1989; ASTM, 1995; Deka et al., 1995) is one technique that has proven effective and inexpensive for measuring water potential on disturbed soils, particularly in the intermediate range between tensiometers and TCPs. A recent survey and analysis of the filter paper method by Deka et al. (1995) suggests that repeatability between batches of filter paper is quite good and that the technique may be appropriate to as low as —100 MPa, provided sufficient equilibration time is allowed. The advantage of this method is sensor cost. The disadvantage is the manual labor involved. Heat-Dissipation Method Heat-dissipation sensors have been used for a number of years to measure soil water potential (Shaw and Baver, 1939; Phene et al., 1971a, 1971b; Phene and Beale, 1976; Campbell and Gee, 1986; Fredlund, 1992). In this instrument, a small amount of heat is dissipated in a porous matrix (small, unglazed ceramic cylinder), which is placed in contact with the soil. The rate of heat dissipation is a function of the water content of the ceramic. If the ceramic is in hydraulic equilibrium with the soil, then the water potential (or matric suction) of the soil can be measured by knowing the waterretention characteristic of the ceramic. Recently, Reece (1996) calibrated a number of ceramic sensors against tensiometers, pressure plates, and thermocouple psychrometers and found that thermal conductivity (heat dissipation) of the ceramic sensors was linearly related to the logarithm of matric suctions over the range from —0.01 to -1.2 MPa. The sensors were accurate to within 20% of independently measured matric suctions. The disadvantage of this method over tensiometry is the lack of sensitivity in the range from saturation to —0.01 MPa. The advantages of the method are the extended range below —0.08 MPa and the fact that the unit requires no hydraulic plumbing (no water purging, etc.). The advantages of the method over thermocouple psychrometers are the wetter operating range and the fact that the units are more robust and require less effort in calibration and main-

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

341

tenance. Cost of the units is comparable to tensiometers and thermocouple psychrometers. Hygrometer Methods Measurement of soil water potential less than —0.5 MPa in the laboratory has greatly benefited from the development of precise chilled mirror hygrometers (Gee et al., 1992). Using the commercial hygrometer (Decagon Devices, Inc., Pullman, WA), Gee et al. (1992) measured water potentials on air-dry surface soils (< —200 MPa). The hygrometer described by Gee et al. (1992) uses small (< 5g) sediment samples from cores or drill cuttings for the analysis. Gee et al. (1992) point out that the structural changes induced by sampling should have minimal impact on the measured water potential, because at low water contents the energy state of water is determined largely by surface area rather than pore geometry effects. Using water potentials obtained from similar hygrometers, Detty et al. (1993) presented hydraulic gradient data from a deep (230 m) unsaturated zone that clearly showed two distinct gradient directions. In the top 50m, hydraulic gradients were upward, indicating a gradual drying of the profile driven by transpiration, baresurface evaporation, and the geothermal gradient. Below 50m, the gradient approached unity, indicating slow gravity drainage of the profile in response to paleoclimatic factors. The magnitude of the water potential and gradient were subsequently verified by in situ measurements of water potential via thermocouple psychrometers (Detty et al., 1993; Sully et al., 1994b). The hygrometer method has been extended to indurated material (volcanic tuff); however, longer equilibration times may be needed for such measurement (Flint et al., 1992). Thermocouple Psychrometers Thermocouple psychrometers, first developed in the early 1970s, have also been used to measure water potentials in arid regions. While the designs of psychrometers have changed little, advances in electronics technology have improved the reliability of measurement in both the laboratory and field. Laboratory psychrometric methods report accuracies of ±0.01 MPa over the range of —0.1 MPa to —8 MPa. Psychrometer strings have been emplaced in boreholes from 95 to 200m deep (Hsieh et al., 1973; REECo, 1994). Fischer (1992) installed removable TCPs in a 13.7-m-deep caisson at Beatty, Nevada. The TCPs have been removed periodically to perform calibration checks. A six-wire thermocouple psychrometer, developed by Kume and Rousseau (1994) for installation in deep boreholes, has several advantages over the standard threewire thermocouple psychrometer. Separate lead wires are used to excite the sensor and to measure output voltage from the sensor. A constant current, instead of a constant voltage, is used to excite the sensor; therefore, the current supplied to the sensor is independent of the lead-wire length. Voltage output is measured directly, avoiding the uncontrolled voltage drops associated with lead wires. These sensors were installed to a maximum depth of 210m in boreholes at Yucca Mountain, Nevada.

342

VADOSE ZONE HYDROLOGY

Thermocouple psychrometers are affected by thermal gradients, and their use in the shallow subsurface must be carefully designed. In one innovative study, Caldwell and Richards (1989) documented redistribution of water from deep roots to the nearsurface soil (hydraulic lift) in Ariemesia (sagebrush). Thermocouple psychrometers were installed very near the soil surface, and thermal gradients were reduced by insulating the soil surface with thick foam. While generally inapplicable for longterm monitoring, this approach was able to document a redistribution phenomenon in dry soils that was previously unknown. Thermocouple psychrometers have also been used to document the water potential in unsaturatcd crystalline rocks (Schneebeli et al., 1995) and in simulated waste trenches in desert conditions (Andraski, 1990).

Advances in Hydraulic Conductivity Estimation To estimate water flux, both the hydraulic gradient and the hydraulic conductivity must be known. Measurement and estimation of unsaturated hydraulic conductivity has long been a goal of the soil physics community, with significant advances in theoretical estimation (e.g., Mualem, 1976; van Genuchten, 1980). The estimation methods most widely used match observations fairly well in unstructured soils at high water contents; however, few data are available for comparison at very low water contents. The introduction of a residual water content, variously defined as the water content below which the hydraulic conductivity is assumed to be zero or simply a curve-fitting parameter, may be useful in agricultural soils but is not appropriate for the very dry soils typically found in arid regions. Tn arid regions, the fluxes are often small enough that hydraulic conductivity must be defined to complete dryness rather than to some arbitrary water content. However, data sets that include conductivity measurements at very low water contents are limited. Table 13.1 shows a partial summary of the available data sets.

Centrifuge Techniques To measure unsaturated conductivity at low water contents and potentials, several new approaches have been developed in recent years. Nimmo et al. (1987) and Conca and Wright (1992) re-examined centrifuge methods for determining conductivity using ultracentrifuge techniques and flow controllers. In the design of Nimmo et al. (1987), sediment samples (up to 1000 g) are spun and flow is controlled through a low-permeability membrane at the inner radius of the sample. The sample is spun until steady state is obtained, at which time the sample is removed from the centrifuge and weighed to determine its water content. The unsaturated conductivity is determined by inversion of Darcy's law in one dimension. The experiment is repeated with various combinations of membranes until sufficient pairs of K(6) and 0 are obtained. The minimum reported conductivities obtained were approximately 10~" mis. Conca and Wright (1992) use precision-flow pumps to supply a fixed quantity of water to the inner radius of the soil sample, while measuring outflow via a strobe-lit,

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

343

Table 1 3.1 Partial Summary of Unsaturated Hydraulic Conductivity Measurements at Low Water Contents Reference

Soil Type

Water Content Range (g/g)

Measurement Method

Mehuys et al. (1975)

Rock Valley gravelly loamy sand

0.05-0.10

Outflow combined with gradient measurements

Mehuys et al. (1975)

Tubac gravelly sandy loam

0.07-0.12

Nimmo et al. (1987) Conca and Wright (1992)

Oakley sand

Outflow combined with gradient measurements Centrifuge Centrifuge

Globus and Gee (1995) Hudson et al. (1996)

Hanford sediments (sand and gravel) Palouse silt loam Berino loamy fine sand

0.063-0.116 0.02-0.30 0.05-0.30 0.03 0.29

Evaporating column/ thermal gradients Upward imbibition

calibrated, clear tube collector until steady flow is obtained. Minimum conductivities obtained were about 10"" m/s. The centrifuge method developed by Conca and Wright (1992) can also be used to measure solute-transport parameters at low water contents, as well as diffusion coefficients in gravelly soils and consolidated rocks. These capabilities, combined with its efficiency in measuring unsaturated conductivity at low water contents, show promise for laboratory analyses of cores from dry unsaturated zones. Khaleel et al. (1995) discuss comparisons of centrifuge methods with both steadystate flow experiments and predictive methods for K(ff) estimation. They report that the centrifuge methods agree reasonably well with steady-state column methods in the moderately dry range but found large discrepancies in the wet range. The steadystate flow method demonstrated better repeatability than the centrifuge method. At this time, however, the costs of the centrifuge and the time needed for analysis are still significant factors that limit its wide use. Additional research, such as that reported by Khaleel et al. (1995), is needed to verify the results by comparison with results of other methods of hydraulic conductivity estimation. Thermal Methods

A heat-pipe method for estimating water diffusivity and hydraulic conductivity of moderately dry soil has been proposed by Globus and Gee (1995). They solved equations for heat and water flow under conditions of steady-state flow in a sealed, unsaturated soil column, where a temperature gradient was imposed across the ends of the column. By measuring the water content or matric potential gradients along the column at steady state (when vapor flow from the warm end equals liquid flow from the cool end of the column), the hydraulic properties of the soil can be eval-

344

VADOSE ZONE HYDROLOGY

uated. Globus and Gee (1995) analyzed water diffusivities and hydraulic conductivities for two soils and found reasonable agreement between the heat-pipe method and an evaporating-column technique. Using 50- to 100-mm-long columns under a thermal gradient of TC/cm, they computed that the time required to achieve steady state ranged from 7 to about 20 days, with the shorter columns equilibrating fastest. The operational water potential ranged from about —0.03 MPa to —3 MPa (a range that is generally difficult to measure with other methods). Optimal water flow is induced if the initial water contents are properly selected (corresponding to potentials ranging from 0 to —1.5 MPa, depending on soil texture, surface area, etc.). The heat-pipe method produces water-content gradients that are not as steep as those produced by the hot-air method of Arya et al. (1975), which can produce both large thermal gradients and steep water-content gradients that are difficult to measure accurately. Imbibition/Drainage Methods Laboratory outflow methods have long been used to estimate unsaturated conductivity, either under a single change in applied pressure (one-step outflow) or multiple steps of applied pressure (multistep outflow). Analytic solutions to the boundary value problem have been recently replaced by inverse numerical methods (Kool et al., 1985; van Dam et al., 1994), in which hydraulic parameters are optimized to obtain best fits to measured-outflow and boundary-condition data. Improvements in the uniqueness of the solutions are obtained when water-potential measurements are made within the sample during drainage or when a priori information is available for the retention data, van Dam et al. (1994) concluded that while the multistep methods more realistically match field conditions, both one-step and multistep techniques are well suited to solution by inverse methods. The multistep approach can be more rapid than the one-step method, as equilibrium conditions are not required for solution. The smaller pressure steps used during the multistep approach may also reduce the nonuniform nature of the flow field within the sample that has been shown to occur under large pressure gradients (Hopmans et al., 1992). The inverse methods for either one-step or multistep flow experiments show significant promise in defining the unsaturated conductivity in the range of approximately —0.01 to — 1 MPa. The experimental equipment is straightforward and affordable and the numerical inversion can be rapidly accomplished by modern desktop computers. While the methods are limited by the transmissive and airentry properties of the porous plates, they can be combined with the centrifuge or thermal methods described above to obtain a more complete description of the unsaturated conductivity over the range typically encountered in arid and semiarid vadose zones. Water Content Measurements: Time Domain Reflectometry Time domain reflectometry (TDK) techniques for water-content measurement have become widely used in hydrologic studies (Topp et al., 1980). The advantages of TDR over conventional neutron logging include (1) the ability to detect near-surface

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

345

water-content changes effectively, (2) automated and remote collection of data, and (3) the absence of radiological safety concerns. However, TDR is significantly limited by installation constraints, specifically the development of air gaps around the probes, and may be difficult to use at great depths. Recently, segmented probes have been introduced that allow the measurement of soil-profile water content at discrete depths using a single probe. This probe, which employs a variation of TDR known as remote sensing diode shorting (Hook et al., 1992), has been used to monitor water-storage changes. A series of 14 segmented probes (185cm long with seven segments) has been installed along two transects across an engineered surface cover of a closed waste site at Hanford, Washington (Wing and Gee, 1994). The probes were connected with two eight-channel multiplexers to a TDR controller and data logger. Data collected to date indicate that the TDR sensors underestimate the water storage as compared with that recorded by neutron logging. This may be the result of the design of the shorting diode units, which have a sphere of influence no more than 15-20 mm in radius compared with 200-300 mm for the neutron probe. Noninvasive Monitoring Techniques Noninvasive monitoring techniques are highly desirable because installation of dedicated equipment is minimized. Equipment installation may be a problem in contaminated sites because of high cost and the possibility of providing pathways for contaminants. Electromagnetic induction (EMI) has potential for noninvasive monitoring of water content (Kachanoski et al., 1988). Cook et al. (1989) used EMI techniques in conjunction with point-measurement estimates of recharge to construct a large-scale map of recharge in southeastern Australia. The EMI data provided a much wider and more integrated measure of recharge. This technique was evaluated by Sheets and Hendrickx (1995) by conducting electromagnetic transects with the EM-31 meter (Geonics Inc., Mississauga, Canada) along an approximately 2-km section. The EM-31 meter was calibrated by measuring water content in 65 neutron-probe access tubes along the same section. A linear relationship was found between the bulk soil electrical conductivity and the total soil water content in the upper 1.5m of the soil. Ground-penetrating radar (GPR) has been used widely to detect buried objects and to define waste sites. A recent study by Du and Rummel (1994) demonstrated that GPR can be used successfully to measure water content at depth. Because of the noninvasive nature of both EMI and GPR, these techniques may become very useful in the future to monitor water-storage changes over large scales on waste-site covers. Water-Budget Methods Water budgets (which account for precipitation, runoff, water storage, and evapotranspiration) are often used in humid climates to estimate recharge. Although this approach works well when recharge is a significant portion of the total water budget (up to 50% of the precipitation), it is less useful in arid climates where recharge is generally a small fraction of the precipitation (Gee and Hillel, 1988). Lysimetry and

346

VADOSE ZONE HYDROLOGY

other methods have been widely used to estimate arid vadose zone fluxes. In the following section, we discuss the merits and limitations of micrometeorological methods and lysimetry. Micrometeorological Methods Estimates of unsaturatcd water flux may also be derived from accurate measurements of precipitation, evapotranspiration, and runoff. In semiarid and arid regions, the uncertainties in measurement of each of these components lead to very large uncertainties in net infiltration over a long time-scale (Gee and Hillcl, 1988). Given the need to quantify the role of vegetation in the long-term water balance of arid and semiarid regions, advances have been made in measurement of water-balance components, particularly evapotranspiration. Micrometeorological techniques (Bowen ratio and eddy correlation) have been used successfully to measure low (< 1 mm/day) evaporation rates across homogeneous terrains, such as playas (Malek et al., 1990; Albertson et al., 1995), and over semiarid vegetated areas (Nichols, 1994). Stem-flow measurements of transpiration have been successful in riparian zones of arid regions (Thorburn et al., 1993). Isotopic analysis of xylem waters have also been used to infer sources of water (shallow soil water vs. deeper groundwater) for several arid and semiarid vegetation species (Busch et al.,1992; Ehleringer and Dawson, 1992; Thorburn et al., 1993). These advances have led to much greater understanding of the role of vegetation in the water balance of arid and semiarid regions. However, evapotranspiration measurements are unlikely to provide sufficient resolution to calculate low rates of net infiltration. As will be discussed later, quantifying vegetation impacts and response to human activity is critical to our ability to predict the unsaturated-zone response to climate changes. Lysimetry

Lysimeters (i.e., soil-filled containers) of various types and sizes have been used to capture, store, or release incident precipitation and to document soil water balance (Allen et al., 1991). Measurements of precipitation, water storage, evapotranspiration, and drainage can all be obtained from lysimeters. While lysimeters have been widely used for purposes related to irrigation management, they arc being used with increased frequency for environmental purposes, including applications for wastesite management in arid regions. We discuss briefly several applications of lysimetry at arid waste sites. Weighing lysimeters have been useful in providing calibration data sets from which the empirical input parameters can be obtained and water-balance models improved. At the Hanford Site, Sackschewsky et al. (1995) used weight changes and drainage from tube lysimeters (0.3m diameter and 1.7m deep) to determine soil water balance for engineered surface covers. Evapotranspiration (ET) and drainage rates were measured from vegetated surfaces with and without gravel mulch and gravel admixtures. These data have been extremely useful in designing gravel admixtures into surface barriers. Payer et al. (1992) used box lysimeters (1.5-m

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

347

square by 1.7-m deep) to calibrate water-balance models for bare soils under irrigated and nonirrigated conditions. Their testing illustrates how arid-site water-balance models show great sensitivity to soil hydraulic properties and other input parameters, including estimates of winter-time ET. Several larger weighing lysimeters have also been constructed and tested recently. Young et al. (1996) have constructed a pair of cylindrical lysimeters, each 2.5m diameter by 4m deep (weighing over 501), to measure water drainage and contaminant transport below turfgrass in Tucson, Arizona. Levitt et al. (1996) have constructed two large tank lysimeters 2 m x 4 m x 2 m deep (weighing over 271) that are being used to test evapotranspiration models and water flow and drainage at a desert waste site near Mercury, Nevada. Evapotranspiration models for site-specific desert conditions currently suffer from lack of calibration; thus, lysimetry, particularly the weighing lysimeters described above, should help to provide the needed model inputs. Nonweighing lysimeters are used primarily to measure net infiltration (or drainage), the component of the water balance that is known with the least degree of certainty in arid sites (Gee and Hillel, 1988). Nonweighing lysimeters range from relatively small, drainage-type lysimeters, a few square meters in area, to large basintype lysimeters that are several hundred square meters in area. Lysimeters, placed well below the root zone, are the most useful for drainage or recharge estimates. The larger the surface area of the lysimeter, the more representative the drainage \vill be of recharge from a given site. Gee et al. (1994b) measured net infiltration and drainage from desert sites in New Mexico and Washington State using drainage-type lysimeters ranging in depth from 6 to 18m. Net infiltration or drainage at the two sites under bare-surface conditions ranged from 25% to 50% or more of the annual precipitation over test periods exceeding 8 years. No net infiltration or drainage was observed when deep-rooted vegetation was present at either site. A number of large-area basin-type lysimeters are currently being used to document drainage. One of the waste sites at Hanford is covered by a prototype surface barrier with coarse sideslopes (Gee et al., 1994a; Wing and Gee, 1994). The center 50m of the prototype barrier is covered with a mantle of 2m of sill loam overlying sand and gravel (i.e., a capillary barrier). Twelve large pan (basin-type) lysimeters, installed under the surface cover, are used to monitor drainage through the sides and top of the cover (U.S. DOE, 1994). The lysimeters ranging in size from 92 to 322 rrr, are buried al depths <4m below the surface, and can resolve water drainage to a fraction of a millimeter or less. Significant quantities (hundreds of millimeters) of water have drained from the coarse sideslopes during the first 2 years of tcsling, bul no water has drained Ihrough Ihe soil (silt loam) mantle. The site is currently being monitored so lhat a complete water balance can be obtained. At another Hanford waste site, a large basin-type lysimeter, 85m" in area, was designed (Wittreich and Wilson. 1991) and subsequently installed in the botlom of a solid-waste landfill trench in the spring of 1992. Landfill waste and soil have been placed over the lysimeter to a depth of 6m since its installation. The soil surface (coarse sand) remains unvcgelaled. Drainage was first measured in July 1996, just over 4 years after installation. In the following 4 months, about 2350 L (27 mm) of

348

VADOSE ZONE HYDROLOGY

water drained from the lysimeter. If drainage continues at this rate, recharge will exceed 82 mm/year, slightly over half of the long-term annual average precipitation (160mm/year). Soil surface modifications (e.g., revegetation) could significantly reduce the recharge at this waste site. At the Idaho National Engineering Laboratory, a series of small, pan (free-draining) lysimeters have been installed in 72 subplots under a large-cover test (Limbach et al., 1994). The pans are circular, with an area of 1.7m2 each, attached to drainage lines, and are installed at depths ranging from 1.8 to 2.7m. These depths are assumed to be below the root zone of native grass and shrub treated subplots. The lysimeters are rilled with gravel, then covered and surrounded on all sides by a silt-loam soil. This arrangement creates a capillary barrier; thus, the physics of unsaturated water flow prevents these lysimeters from functioning properly, because drainage occurs only after there has been significant divergent flow around the lysimeters. As a result, the subplot drainage cannot be determined reliably with this type of lysimeter. While lysimeters are ideally suited for measurements of drainage, they are essentially permanent fixtures and cannot be easily moved to another location. They should be as representative as possible of the field soil volume of interest. While minimally disturbed, monolithic soil blocks have been tested in lysimeters, disturbed soils are more common and certainly more realistic to test. Proper installation is an important consideration. Since water balance is often a major consideration, the system requires periodic checking to ensure that mass balance can be verified for each lysimeter system. In summary, lysimetry is an important part of arid-site water-balance studies. Lysimeters are useful in documenting drainage to estimate recharge. They are most useful if they are installed with their base below the root zone. They perform best at recharge rates above a few millimeters per year; however, large-area lysimeters (hundreds of square meters) can be constructed that are sensitive to small amounts of drainage (millimeters or less). Finally, they must be designed with flow physics in mind or the results they yield can be less than satisfactory. Advances in Numerical Modeling The complexity of flow in the shallow unsaturated zone of desert systems requires the use of numerical models to evaluate flow processes and to analyze interactions and feedback mechanisms between various controlling parameters. The models range in complexity from user-friendly, one-dimensional Richards' equation solvers, such as SWIM (Ross, 1990), to nonisothermal solvers that include both liquid and vapor transport, such as TOUGH (Pruess, 1987) and BREATH (Stothoff, 1995). User-friendliness has come from two principal areas: improvements and innovations in solver algorithms, and improvements in graphical interfaces for both data input and output visualization. Visualization software, such as that developed by Simunek et al. (1994) for the SWMS_2D simulator, greatly improves the speed of problem development and experimentation. Numerical methods used for solution of Richards1 equation are constrained by the highly nonlinear nature of the equation, and mass conservation is always a concern. Water-content-based formulations, while guaranteeing mass conservation,

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

349

are difficult to implement when soils are heterogeneous and when conditions approach saturation. Head-based formulations easily handle heterogeneity and saturated conditions, yet often produce unacceptable mass conservation. Celia et al. (1990) employed a mixed form of Richards' equation that can improve mass conservation. Time derivatives are in terms of water content, while spatial derivatives are head-based. A fully implicit time approximation guarantees improvements over strictly head-based approaches; however, oscillatory behavior was still present in finite-element formulations. Celia et al. (1990) stressed the importance of mass lumping when using finite-element formulations to reduce oscillatory behavior, particularly during infiltration into initially dry soils. Most numerical modeling studies focus on isothermal liquid flow and neglect the effect of vapor flow. However, vapor flow may be important, particularly near the soil surface in arid systems where the soils are very dry and where temperature gradients are steep. Models of nonisothermal systems for arid regions are generally based on the equations of Philip and de Vries (1957). The number of codes available to simulate nonisothermal liquid and vapor flow in response to atmospheric forcing is limited. Examples of such codes include UNSAT-H (Payer and Jones, 1990), SPLaSHWaTr (Milly and Eagleson, 1982), BREATH (Stothoff, 1995), STOMP (White et al., 1995), and AIR-TOUGH (Montazer, 1995). Application of these codes to evaluation of subsurface flow processes has been restricted because of the lack of appropriate field data. Solution of a given flow and/or transport problem requires parameterization of the hydraulic properties of the system. Such data, as discussed previously, are often lacking for very dry media. Assumptions regarding finite residual water-content models of retention and conductivity proposed by van Genuchten (1980) and Brooks and Corey (1964) do not simultaneously represent both wet and dry regions. Recent works by Milly and Eagleson (1982), Ross et al. (1991), Rossi and Nimmo (1994), and Payer and Simmons (1995) have addressed this issue by incorporating a finite value of pressure head associated with oven-dry soil. Typically, this value is established from the oven temperature during drying, the relative humidity, and the barometric pressure of the laboratory. Both Rossi and Nimmo (1994) and Payer and Simmons (1995) represent the portion of the retention curve dominated by capillary forces by either a power-law relation (Brooks and Corey, 1964) or a van Genuchten relation. In the drier regions of the retention curve, a logarithmic relationship is proposed based on the laboratory results of Campbell and Shiozawa (1995). The two functions are summed or joined in the model of Rossi and Nimmo (1994) to produce a continuous water-retention function over all ranges of water content. Payer and Simmons (1995) propose an alternative interpretation by replacing the residual water-content term with the logarithmic relationship, which also produces a continuous-retention function. Both models show significant improvement in fitting the limited observations of full-range retention. Payer and Simmons (1995) incorporate their full-range model of retention into the hydraulic conductivity model of Mualem (1976) to calculate unsaturated hydraulic conductivity. The calculated hydraulic conductivities are well above those that would be calculated using a finite residual-water content, as would be expected. Mualem's model of hydraulic conductivity is based on capillary flow and has been

350

VADOSE ZONE HYDROLOGY

shown to be applicable where such flow occurs. The logarithmic portion of the retention curve is due principally to water held as films rather than in capillaries, and it may not be appropriate to calculate hydraulic conductivities in this range based on capillary-bundle theory (Mualem, 1976). Rather, a physical model of film flow may need to be developed to capture the salient features of the conductivity behavior when water is held as films rather than capillaries. Film models for conductivity at low water contents have been proposed for soils (Toledo et al., 1990) but have not yet been extensively tested.

Tracer Development Applied tracers have been used extensively in humid and irrigated regions to study solute transport and preferential flow in field soils. In arid regions, applied tracers are often inappropriate because of the very low natural fluxes and long lime-scales involved. Instead, researchers have focused on natural tracers and tracers introduced during nuclear-weapons testing in the 1950s and 1960s. Just as in humid regions, tracers are used to better understand the mean flow behavior, as well as to quantify the nature and extent of preferential flow. Natural tracers that are continuously added to the soil surface, such as chloride and deuterium/oxygen-18, provide information on the mean flow behavior and are useful in defining temporally averaged water fluxes. With continuously added tracers, there is little opportunity to define small-scale fluctuations in the unsaturated-water flux. In direct analogy to applied field tracers, tritium and chlorine-36 from weapons testing represent a time-varying input of significant magnitude (up to three orders of magnitude over background) and can be used to define preferential flow and variance in the soil water velocity. Tracers such as chloride and tritium represent a reliable method to estimate recharge and have been used to document the potential for waste isolation at several arid sites. Caution must be exercised, however, when extrapolating recharge rates under natural surface conditions to conditions following closure of a waste site. Studies have shown that recharge rates can be drastically increased by vegetation removal or placement of rock armor on the surfaces. It is therefore critical that waste-site covers are designed to mimic, over long periods, the natural surface and subsurface conditions responsible for the observed low-water fluxes in natural systems. Such covers must also be tested over sufficiently long monitoring periods to ensure that their performance is adequate to limit the migration of water and wastes from the disposal facility. Chloride One of the simplest techniques proposed for estimating vadose zone water flux is the chloride mass balance method (U.S. Department of Agriculture, 1954; Allison and Hughes, 1978). By noting that in most environments the major source of chloride in the vadose zone pore water is from atmospheric deposition, either in precipitation or as dry fall, a simple mass balance expression of chloride may be developed to predict net water flux at any point in the profile.

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

351

The chloride mass balance method has gained wide acceptance and has been applied to a wide variety of sites to estimate flux (Scanlon, 1991; Cook et al., 1992; Phillips, 1994). It suffers from several assumptions (steady chloride deposition over the period considered, no additional chloride sources present in the system, and conservative behavior of chloride tracer) and data limitations (the chloride flux to the soil surface is both variable and difficult to measure accurately); however, it has proven to be a robust estimator, particularly for low rates of flux (Allison et al., 1994). The ratio of the net infiltration or recharge to the precipitation flux is given as

where P is the precipitation rate, Cp is the chloride concentration in precipitation and dryfall, and Cpw is the chloride concentration in pore water below the root zone. The chloride concentration in precipitation is generally augmented to account for dry deposition as well. Inferences regarding the net infiltration are also possible when water fluxes have been known to vary in time. If the time scale over which the net infiltration has changed is small compared with the time needed for water to transit the vadose zone, then regions may exist within the profile that can be considered steady (Murphy et al., 1996). The chloride profile may show regions of elevated or depressed concentration which arc advccted downward. Cook et al. (1992), in a study of chloride profiles in Senegal and Cyprus, delineated periods of enhanced recharge that were preserved within the infiltrating water and they correlated these with known pluvial periods. The chloride mass balance method can also be modified to estimate soil water age. If we assume that the chloride input has remained constant over time, the chloride age, A(z), at any depth in the soil profile, z, is taken simply as the ratio of the cumulative chloride concentration, CK (mass Cl/unit volume of sediment), from the landsurface to the depth of interest, divided by the annual chloride deposition:

where 6 is the volumetric water content. Equation (13.2) has been used by several workers (Scanlon, 1991; Stone, 1992; Phillips, S994) to estimate the age of pore water, under the assumption that the chloride ion has acted conservatively in the vadose zone. Phillips (1994) clearly showed that net infiltration in arid vadose zone profiles in the southwestern United States shifted from relatively high levels during the last glacial maximum [12,000-16,000 Y.B.P. (years before present)] to much smaller fluxes under the arid conditions of the Holocene. Tyler et al. (1996) interpreted chloride accumulations in a very deep profile and suggested that the net infiltration may have been elevated only during the penultimate glacial maximum (~ 120,000 Y.B.P.) in parts of the southern Great Basin. Chloride (and 36C1) is generally assumed to be conservative in the subsurface. However, anion exclusion effects have been documented in some soils, particularly clay-rich sediments. Anion exclusion would tend to accelerate the migration of

352

VADOSE ZONE HYDROLOGY

chloride with respect to water and lead to erroneous interpretation of water flux. At very low water contents, surface charges could also lead to ion filtration and retardation of chloride (M. Ankeny, personal communication, 1995). Further experimental work, however, is needed to quantify these effects at the low water contents typically found in arid vadose zones to determine how these processes will affect the chloride mass balance method. Other complications found when using chloride as a tracer include mineral dissolution from host rock. The chloride mass balance method appears best suited to areas of low to moderate recharge. In these areas, uncertainties in the chloride flux at the landsurface translate into tolerable absolute errors in recharge. In addition, low recharge rates also imply relatively high soil water chloride concentrations, reducing the uncertainties of analytical analysis of chloride in soil water. In soils with low water contents, it is generally required to analytically measure chloride concentration on 1:1 or 1:2 soil:water extracts. Soil water concentrations are then back-calculated from gravimetric water content analysis; both steps introduce uncertainties into the final recharge estimate. Table 13.2 shows the errors associated with selected recharge rates in a soil that assumes a uniform water content of 0.05 g/g under conditions of 160 mm/year of annual precipitation, chloride concentration in the precipitation of 0.25 mg/L, and under the conditions that the chloride is extracted from the soil in a 2:1 watersoil extract for analytical analysis. The process of extraction significantly reduces the concentration of chloride for recharge rates above 10 mm/year. Unless steps are taken to concentrate the extract prior to analysis, typical analytical uncertainties can produce large relative errors in the recharge estimate at these higher rates. Chloride concentrations in groundwater can also be used to estimate recharge on a more regional scale. In equation (13.1), the pore water concentration, Cpw, can be replaced by the ambient or basin-scale average groundwater chloride concentration. Dettenger (1989) estimated basin-scale recharge in Nevada using this approach and found very good agreement with other empirical estimates of recharge. The use of groundwater concentration reduces the reliance and uncertainty in pore water extraction estimates of chloride concentration but does not provide point-scale esti-

Table 13.2 Uncertainty in Recharge Rate Related to Measurement Error in Chloride

Recharge" (mm/year) 100 70 10 4 1 0.1

Pore Water Cflf (mg/L)

0.40 0.57 4 10 40 400

"Assumes />= 160mm/year; Cf = 0.25mg/L.

Chloride in 1:2 SoilrWater Extract (ppb)

Error of Uncertainty for Precision of ± 100 ppb chloride (%)

10 14 100 250 1000 10,000

±1000 ±700 ±100 ±40 ±10 ±1

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

353

mates of recharge. The technique may be most valuable for water resource evaluation as it can provide recharge information over large basin areas. In summary, the chloride mass balance method has proven successful in estimating water flux, net infiltration, or recharge for low flows over fairly long time-scales. At flows above a few millimeters per year, complications such as rock dissolution and analytical errors create uncertainties in recharge estimates by the chloride mass balance method. Also, as it is an integrated measure, it may not be capable of detecting short-duration fluctuations nor provide direct evidence of small-scale preferential flow, such as occasional deep infiltration along root pathways or fractures. To quantify such fluxes, tracers with short application frequency must be used. Tritium Tritium ( 3 H) from atmospheric nuclear-weapons testing has long been used in unsaturated-zone studies in arid regions (Zimmermann et al, 1967). The position of the peak concentration, the shape of the tritium profile (to account for year-to-year variations in the fallout), or the total amount of tritium that remains in the soil can be used to estimate the water flux (Allison et al., 1994). In arid regions or where the water flux is small, the effects of transit through the root zone may become important, with a resulting overestimation of net infiltration (Tyler and Walker, 1994). Net infiltration may be overestimated by orders of magnitude when tritium within the root zone is used; however, if tritium is found exclusively within the shallow root zone, this strongly implies a low water flux over the last 50 years. Because tritium exists in both the liquid and gas phases, its concentration in the unsaturated zone may reflect both liquid- and gas-phase migration. Phillips et al. (1988) found tritium distributions that were dominated by thermal vapor transport at a site in New Mexico. Smiles et al. (1995) showed that the presence of liquid-phase water should reduce the migration of tritium in the vapor phase due to equilibration between the gas and liquid phases. Recent studies (Prudic and Striegl, 1995; Striegl et al., 1996) in a waste site at Beatty, Nevada, detected tritium levels in the unsaturated zones that were much higher than would be predicted from vapor-phase transport alone, even though the aridity of the site would suggest that liquid-water flow would be limited. Prudic and Striegl (1995) suggest that inadequate and inappropriate waste-disposal practices have led to liquid migration to significant distances from the waste trenches; however, such processes as advective vapor transport by wind, and barometric or thermal effects also need to be investigated. Tritium tracing has seen significant developments in recent years in determining the dominance of piston-like or preferential flow. In arid areas or where integrated tracers, such as chloride, would suggest very low water fluxes, the presence of tritium well below the root zone suggests that some form of preferential flow is occurring. Determining the presence of preferential flow is critical in the design and evaluation of waste disposal near the landsurface. Allison and Hughes (1983) found tritiated water at a depth of 10m beneath eucalyptus vegetation in Australia, where the general aridity and chloride-tracer data suggested negligible water fluxes. They concluded that preferential flow along deep roots was responsible for tritium being much deeper than predicted by chloride. Nativ et al. (1995) investigated water flux in

354

VADOSE ZONE HYDROLOGY

fractured chalk in the Negev Desert of Israel, where the presence of groundwater contamination suggested that recharge was occurring. Tritium was detected intermittently with depth in several cores, suggesting that deep infiltration had occurred. In contrast, chloride concentrations in pore water were high near the surface, indicating that most of the precipitation was removed by evapotranspiration. The vadose zone consisted of fractured chalk, and it was deduced that preferential flow along the fractures was responsible for injecting water and tritium much deeper in the profile than would have been predicted from the chloride profile. With its low detection limits, tritium can provide a direct indication of preferential flow when found below the depth predicted by integrated tracers or soil physics measurements. Chlorine-3 6 Chlorine-36 (36C1) produced during atmospheric nuclear-weapons testing in the 1950s has been used extensively as a tracer of pore water in the unsaturatcd zone (Phillips et al., 1988; Scanlon, 1992; Fabryka-Martin et al., 1993) in much the same manner as tritium. Cook and Walker (1995) provide a review of 36C1 tracing methods and their relation to chloride and 3H dating methods. As 36C1 is present only in the liquid phase, the method provides a direct measure of liquid flux. Phillips et al. (1988) and Scanlon (1992) found 3H deeper than 36C1 in arid settings and showed that the vapor-flow component may be as high as 75% of the total flux. Deeper in the profiles, where gradients are less steep and do not vary significantly with time, the thermally driven vapor fluxes may contribute much less to the total flux. As with 3 H, the distribution of bomb-related 36C1 is strongly controlled by root-zone processes and may be an appropriate technique for determining net infiltration in excess of SOSO mm/year (Allison et al., 1994) or where preferential flow may be an important process. Liu et al. (1995) detected recent 36C1 in cuttings as deep as 440m in volcanic tuff at Yucca Mountain, Nevada, suggesting that preferential flow may be occurring through the overlying intensely fractured tuff. Naturally produced 36C1 may provide an alternative method for age dating very old (> 10,000 YBP) water. Variations in the Earth's magnetic field have been shown to cause differences in carbon-14 (' C) production in the atmosphere and in fallout of 36C1 (Phillips et al., 1991). Phillips et al. (1991) first proposed that these variations be used as a chronological dating method for pore water to provide an independent calculation of age. By matching profiles of pore water 36CI concentration with that predicted from paleomagnetic intensity, it may be possible to fingerprint soil-age dates based on their distribution in the unsaturated zone. Tyler et al. (1996), in a study of a deep (230m) vadose zone in southern Nevada, showed that pore waters dated between 20,000 and 50,000 YBP using chloride were enriched in 36C1 as predicted. These data are discussed in detail later in the chapter. Deuterium/Oxygen-18 Nonradioactive isotopes, principally deuterium ( 2 H) and oxygcn-18 (18O), have also been extensively used in studying processes in the vadose zone. Barnes and Allison

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

355

(1983) developed models of both liquid and vapor flow, based on the fractionation that occurs under evaporation, to estimate vertical water fluxes in the vadose zone. Under evaporating conditions, the profiles of 2 H and 18O can be divided into three general regimes: a vapor flux-dominated regime that begins at the landsurface, a zone of isotopic enrichment where the composition of the pore water becomes enriched in heavy isotopes selectively left behind by the evaporation process, and a lower zone of composition similar to the underlying ground water. Barnes and Allison (1983) developed simple expressions to estimate the rate of evaporation based on the depth of the vapor-transmission zone as well as the shape of the lower, liquid-dominated profile. Evaluation of net infiltration processes using stable isotopes has been conducted in many regions of the world. In general, two approaches are taken: (1) analysis of the regional groundwater and its relation to precipitation, and (2) analysis of the stable isotopic composition of pore water. The isotopic composition of water in the unsaturated zone is generally believed to be reasonably represented by the isotopic composition of the mean precipitation in an area (Gat, 1981). Groundwater in some arid regions, however, has been shown to deviate from the isotopic composition of mean precipitation, with either enrichment or depletion in heavy isotopes. Enriched compositions generally plot along evaporation lines from the local precipitation, indicating that evaporative enrichment occurs during infiltration, either from surface water prior to infiltration or by evaporative loss from the unsaturated zone. Allison et al. (1984), using data from Australia, suggested that the magnitude of enrichment from the mean precipitation could be used to infer average recharge rates in arid regions; however, this approach has not yet been verified in other regions. Depleted pore water and groundwater relative to mean precipitation has been found in arid regions and has been attributed to selective infiltration of rainfall from intense, large-volume, isotopically light rainfall events. Depleted waters can also indicate recharge of primarily winter precipitation or recharge under past, cooler climates. In a study of isotopic composition of pore water, groundwater and precipitation in southern Nevada, Tyler et al. (1996) determined that pore waters and groundwater showed no resemblance to modern precipitation and most likely were recharged during the last glacial period, a hypothesis supported by carbon-14 age dating of the groundwater. Isotopic composition of pore water in the unsaturated zone has been used to infer the dominance of evaporation over transpiration and net infiltration in arid unsaturated zones. Nativ et al. (1995) described isotopic profiles in fractured chalk that displayed the typical exponential enrichment in the upper 10-20m, suggesting the dominance of evaporation over net infiltration. At depth, however, tritium concentrations in the chalk strongly supported preferential flow of water. They concluded that the exponential shape of the stable isotope profiles was the result of dilution by preferential flow of isotopically light water deep into the unsaturated zone along fractures in the chalk. In a study of stable isotopic profiles in southern Nevada, Tyler ct al. (1996) measured evaporative enrichment to depths of 15-50m in unfractured alluvial sediments. Chlorinc-36 measurements taken simultaneously to investigate the possibility of preferential flow did not show evidence of modern water at these depths, and they concluded that the profiles were dominated by evapotranspiration.

356

VADOSE ZONE HYDROLOGY

Based on these recent studies, stable isotopic measurements of pore water in the unsaturated zone can provide insight into the dominant processes near the landsurface. They must, however, be used in concert with other tracer and soil physics measurements if preferential flow is anticipated or of concern.

Examples of Applications of New Techniques to Arid Problems In this section, we describe three recent studies of water and solute transport in arid and semiarid regions. These examples are given to show both the recent advances and the new questions and issues revealed in arid vadose zones. Figure 13.1 shows the location of the study sites. Age Dating and Analysis of Dispersion from a Thick Vadose Zone A detailed drilling and sampling program was conducted at the U.S. Department of Energy's Nevada Test Site to characterize the unsaturated zone beneath an active low-level radioactive-waste site. The site is located on alluvial sediments in Frenchman Flat, approximately 100km northwest of Las Vegas, Nevada. The site's climate is arid, with annual average precipitation of 124mm, based on a 30-year record. The depth to groundwater is approximately 240 m below the landsurface. Three deep boreholes were drilled within a 1500-m radius around the perimeter of the site (designated PW-1, PW-2, and PW-3), using the ODEX drilling method. Core samples and representative cuttings were collected throughout the unsaturated zone and analyzed for hydraulic parameters, including water content, water potential, hydraulic conductivity, water retention, and environmental tracers (Detty et al., 1993; REECo, 1994; Sully et al., 1994a, 1994b; Tyler et al., 1996) to determine the state of water flux. The boreholes were subsequently instrumented with TCPs, pressure transducers, and gas-sampling ports. The wells were also screened below the water table to allow for groundwater sampling. Detailed description of the hydraulic

Figure 13.1 Location of the three examples described in the text.

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

357

properties, water contents, and water potentials can be found in Detty et al. (1993), REECo (1994), and Sully et al. (1994a, 1994b). Chloride-concentration profiles (expressed as mg Cl/kg dry sediment) from the three boreholes are shown in figure 13.2 and display a typical bulge in the upper 1040 m of each profile. The presence of a chloride bulge was attributed to a change in water flux to significant preferential flow (Phillips, 1994). Analysis of pore water 36C1 in all three boreholes yielded no evidence of any recent bomb pulse deep in the profiles, suggesting that in these alluvial sediments preferential flow along fractures or root channels has not occurred in any appreciable quantities. Stable isotopic analysis also confirmed the lack of modern infiltration at depths below the root zone (Tyler et al., 1996). In boreholes PW-1 and PW-3, a second bulge, much more diffuse than the first, is also evident at 40 and 80m, respectively. Below 100m depth, all three profiles show very low levels of chloride, suggesting that significant water flux occurred at some time in the past. The total mass of chloride stored in the PW-1, PW-2, and PW-3 profiles is approximately four times that found in the PW-2 borehole alone. Using equation (13.2) and a realistic chloride accumulation rate, pore water at the bottom of PW-2 is found to be approximately 25,000 years old, while PW-1 and PW-3 contain pore water more than 100,000 years old (Tyler et al.. 1996). These ages are approximately commensurate with the last two major glacial maxima and pluvial periods experienced in southern Nevada (Smith, 1984) and imply that recharge was spatially variable on a rather small (1- to 2-km) scale.

Figure 13.2 Chloride concentration in cores and cuttings from boreholes PW-1, PW-2, and PW-3. Chloride concentrations from the upper 8m of ST-1, 61 m to the south, are used to augment the core record from PW-1. All concentrations are reported as mg chloride/kg dry soil. (After Tyler et al., 1996.)

358

VADOSE ZONE HYDROLOGY

The presence of secondary bulges in chloride in two of the boreholes suggests a period of downward flux that was not of sufficient magnitude or duration to reach the water table. These secondary bulges also serve as unique tracer tests in very dry soils. Assuming that each secondary bulge can be initially approximated by a Dirac function directly beneath the root zone that was subsequently advected downward, a simple analysis of the dispersion coefficient can be estimated. Figures 13.3a and 13.3b show the secondary bulges, which were fitted by a simple error-function solution to the advcction-dispersion equation. The only fitting parameter allowed was the variance in solute concentration. The fit is quite good at the leading edge of each bulge; however, the trailing edge cannot be matched, due in part to tailing and the continued accumulation of chloride from the landsurface. Using the best fit variance of concentration, the postadvcction contribution of chloride to the soil profile can be estimated by subtracting the area under the Gaussian distribution from the total stored chloride in the profile. This recent accumulation of chloride (see figures 13.3a and 13.3b) was estimated to represent 53,000 and 46,000 years of accumulation in PW-1 and PW-3, respectively. Using these ages,

Figure 1 3.3 Gaussian model fit to the secondary chloride bulge in (a) borehole PW-1; (b) borehole PW-3. (After Tyler et al., 1996.)

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

359

an "average" dispersion coefficient may be calculated from the shapes of the secondary bulges. Average, in this sense, represents a spatial average (travel distances of 40 and 80m), a temporal average (one cannot know how long it took the water to reach the depth), and a process average (both dispersion and diffusion may have been acting on the bulges for up to 50,000 years). From the ages above, the calculated dispersion coefficients from PW-1 and PW-3 are 4 x 10""" and 1 x 10 " I 0 m 2 /s, respectively. The calculated dispersion coefficients are only slightly higher than molecular diffusion rates, implying that the advective velocities were small (<10mm/ year). The ratio of dispersion coefficients is very close to the ratio of travel distances of the two bulges, suggesting that the differences arc due to differences in advective velocities rather than intrinsic dispersivity. While the calculated ages of the timing of the advective transport are closer to those found for the cessation of downward flux in PW-2, the age is still considerably older. Two explanations are possible: (1) recharge and advection of all profiles began approximately 50,000 years ago, yet for some reason continued only at PW-2, or (2) the advective-transport phase did not completely displace chloride in the upper portions of PW-1 and PW-3, leaving behind residual chloride that has biased the ages for the timing of the bulges. While both explanations are plausible, there is a suggestion of a pluvial period near 50,000 Y.B.P. in the Sierra Nevada (P.M. Phillips, personal communication, 1996); however, the pluvial period at 15,000-25,000 Y.B.P. is widely defined by palcoclimatic indicators. Incomplete flushing of salts has long been observed in irrigated lands and has been reported under changes in land use in Australia (Jolly et al., 1989). Analysis of %C1 ratios at depth in the boreholes also confirms that incomplete flushing may have occurred, based on the smearing of the peaks in concentration predicted from secular variations (Tyler et al., 1996). The secondary bulges seen in PW-1 and PW-3 probably represent advective transport that occurred near the last glacial maximum. At the same time, infiltration reached the water table at PW-2. Since the last glacial maximum, chloride has been accumulating in the unsaturated zone of all three boreholes as the region has become more arid. The differences in response to pluvial conditions between the three closely spaced boreholes are unlikely to be caused by sediment texture or climate variations. Detailed analysis of geomorphic surfaces has revealed that borehole PW-2 is along the intersection of two major alluvial fans (Snyder et al., 1994), while the other boreholes are within existing fans. At the fan intersection is a well-developed drainage channel that has probably persisted over recent geologic time. Runoff today is focused along this intersection and can clearly be seen in aerial photographs. During more pluvial periods, this topographic feature has probably concentrated runoff and increased the potential for net infiltration along its reach. No mechanisms for concentrating surface water are currently seen at the other two boreholes, suggesting that while pluvial conditions existed at the end of the last glacial period, they were not sufficient to induce widespread flux in the water table. The results of this study have shown the usefulness of environmental tracers, coupled with paleoclimatic information, in reconstructing the history of water flux in the arid southwest. Multiple tracers are needed to quantify the response. The spatial variability in water flux response also points out the importance of small-

360

VADOSE ZONE HYDROLOGY

scale surface features in defining the potential for net infiltration and the wide range of variability that can occur in arid-region vadose zones. Analysis of Vapor Flow in Arid Vadose Zones A detailed examination of liquid and vapor flow in response to atmospheric forcing in a bare soil was conducted by Scanlon and Milly (1994). The period of simulation (1 year) was much longer than the periods (hours to days) generally simulated in previous studies (Sophocleous, 1979; van de Griend et al., 1985; de Silans et al., 1989). Long-term monitoring of water potentials and temperatures in an ephemeral stream setting (Scanlon, 1994) provided initial conditions for the simulations and data to evaluate the simulation results. Hourly measurements of meteorologic parameters provided information for the upper boundary. Water retention functions for the different textures were based on the work of Milly and Eagleson (1982); they are similar to those described by Rossi and Nimmo (1994) and are more appropriate for flow in arid settings, as discussed previously. No attempt was made to calibrate the model, yet there was remarkable consistency between simulated and field-measured water potentials. Measured and simulated seasonal changes in water potentials were similar and showed high water potentials in the summer and low water potentials in the winter (figure 13.4). Seasonal fluctuations in water potential have also been recorded at Beatty (Fischer, 1992) and Yucca Mountain (Kume and Rousseau, 1994), Nevada. Good agreement was also found between computed seasonal fluctuations in temperature and field measurements. The simulations provide valuable insights into the mechanisms of water transport in the subsurface. Vertical water fluxes can be decomposed into liquid fluxes (—KdW/dz), which are driven by water-potential gradients, and diffusive-vapor fluxes, which are driven by vapor-pressure gradients that are, in turn, caused by water-potential gradients (isothermal vapor flux: -Dyv difr/dz) and temperature gradients (thermal vapor flux: —DTvdT/dz). Figure 13.5 shows the results of a 1-year simulation of fluxes. The upper 0.3-m section consisted of the active layer, in which the direction, magnitude, and mechanism of water fluxes varied in response to intermittent wetting and drying by weather events. This zone was dominated by downward liquid flux. Very close to the surface, upward isothermal vapor fluxes were significant. Below 0.3m depth, thermal vapor flux was the dominant term. Although the direction of thermal vapor flux varied seasonally with the temperature gradients, downward thermal vapor flux in the summer exceeded upward thermal vapor flux in the winter because thermal vapor diffusivity is higher in the summer, when the temperatures are higher. This downward thermal vapor flux was not balanced by upward isothermal vapor flux and upward liquid flux during the simulation time of 1 year. The simulation results are consistent with the measured distribution of bombpulse tracers in the subsurface. In arid settings, bomb-pulse tritium has been found at greater depths than bomb-pulse chlorine-36, although peak 3H fallout occurred later (1963) than that of 36C1 (1957). The deeper penetration of -''H relative to 36C1 has been attributed to enhanced downward movement of tritium in the vapor phase

Figure 1 3.4 Measured and simulated water potential for the Hueco Bolson. (After Scanlon, 1992.)

Figure 13.5 Simulated net yearly fluxes of liquid and vapor at the Hueco Bolson study site. (After Scanlon, 1992): (a) June 17, 1990; (b) January 17, 1990.

362

VADOSE ZONE HYDROLOGY

(Phillips et al., 1988; Scanlon, 1992), as suggested by the computed net downward vapor fluxes in the simulations. The major source of uncertainty in the simulations is the estimated hydraulic conductivity function. Water-retention hysteresis was also neglected in the simulations because of difficulties in simulating hysteresis. Even if an accurate model of water-retention hysteresis were available, determination of the saturation history of the sediments would be difficult. The study demonstrates, through the use of numerical modeling and environmental tracers, that the thermal vapor flux and total water flux is downward in response to seasonally varying temperature gradients in the shallow subsurface. This observation suggests that analysis of fluxes in an arid vadose zone should consider vapor flux when evaluating near-surface water fluxes. Transport models that include seasonally varying liquid and vapor fluxes will be required to provide a more detailed analysis of the mechanisms that control the subsurface distribution of these tracers.

Surface Changes and Net Infiltration in Arid Regions Lysimeter studies have been used at the Hanford Reservation in eastern Washington State since 1971 to document water movement in the thick (30-80 m) unsaturated zone. These studies have been motivated by the need to quantify the transport mechanisms responsible for existing and potential groundwater contamination from the large amount of radioactive waste disposed in shallow trenches and underground tanks at the site. Gee et al. (1992, 1994a) point out that net infiltration and recharge at the 2700km" reservation varies considerably and is primarily controlled by soil texture and vegetation species. Areas of fine-textured soil combined with deep-rooted shrubs do not significantly contribute to recharge. However, areas underlain by sands combined with shallow-rooted grasses and perennials can have net infiltration rates as high as 50% of the annual precipitation (Gee et al., 1992). While soil texture is temporally invariant, vegetation type responds rapidly to climatic and human forcing functions. Wildland fires and the surface disturbance by waste-disposal activities can lead to dramatic changes in vegetation density and species composition. In particular, the inadvertent introduction of cheatgrass (Bromus tectorum L.) in recent years to western rangeland may significantly increase net infiltration due to its shallow-rooted nature and short growing season. To test this, a scries of drainage lysimeters were constructed in 1978. Each drainage lysimctcr was 2.7m in diameter and 7.6m deep and was filled with a locally derived sandy soil. Two additional weighing lysimeters (1.5m deep) were also constructed at the site. Figure 13.6 shows the general layout of the lysimeters. Two vegetation treatments were followed in the drainage lysimeters: one lysimeter was kept free of vegetation, while the remainder were planted with a cheatgrass cover. Cheatgrass represents the predominant invading species in the region and is particularly adapted to invade an area following fire or land disturbance. After 2 years, the cheatgrass cover treatment was invaded by deeper-rooted tumbleweed. Drainage was intensely monitored from 1985 through 1989 with continual measure-

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

363

Figure 13.6 Schematic of the Buried Waste Test Facility lysimeters at the Department of Energy Hanford site, Washington State.

ment of drainage through 1991. The average annual precipitation for the site is 160mm. Drainage from the bare sand lysimeter varied with time, ranging from 40 to 111 mm/year in direct response to precipitation. Figure 13.7 shows the monitored drainage during this period, along with the precipitation occurring at the site. The bare, sand-filled lysimeter drained almost 400mm of water in 5 years, equivalent to about 50% of the annual average precipitation. Drainage is attributed to winter

364

VADOSE ZONE HYDROLOGY

Figure 1 3.7 Cumulative drainage for a 7.6-m bare-soil lysimeter at the Buried Waste Test Facility on the Hanford site.

rainfall and snowfall that infiltrates rapidly into the lysimeter's coarse sand. During the first 3 years of monitoring, the cheatgrass-covered lysimeter showed an average drainage of 62 mm/year (approximately 35% of the annual precipitation recorded at the site). The shallow-rooted cheatgrass was apparently unable to use the winter rains that infiltrated below their shallow root zone. In subsequent years, when deeper-rooted species invaded (tumbleweed), water stored deeper in the profile was removed and drainage was reduced to 0-10 mm/year. Tracer studies with chloride and Cl have been used to confirm that net infiltration is negligible (near 0 mm/year) under shrub vegetation but significant (> 5 mm/year) under grass vegetation on the coarse soils at the Hanford site (Prych, 1995). Studies at Hanford have also focused on the design of engineered barriers for waste disposal incorporating capillary barriers (Link et al., 1995). Modeling of drainage from capillary barriers (i.e., fine sediments over coarse sediments) requires empirical calibration. A series of 1.7-m-deep weighing lysimeters were filled with a capillary-barrier configuration consisting of 1.5 m of silt loam overlying about 0.2 m of sand. Drainage was measured from a lysimeter that was kept free of vegetation and irrigated with 320-480 mm/year of water for more than 5 years. Figures 13.8 and 13.9 show modeled and observed water-potential profiles and drainage for the bare lysimeter. Modeling of the water storage and drainage indicated that systematic adjustments of the model could improve the match between measured and calculated drainage. While storage changes were predicted well by some of the models tested, all attempts to simulate drainage that did not use a hysteretic model failed (Payer, 1995). Even the calibrated hysteretic model underpredicted drainage by a factor of two. Table 13.3 summarizes the various modeling strategies and their relative performance. The results of these studies indicate that vegetation, land disturbance, and hysteresis play a crucial role in determining net infiltration at the Hanford site and that the use of computer models for prediction can provide insight into the behavior of water flux.

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

365

Table 13.3 Comparison of Model Performance of Computing Lysimeter Water Storage and Drainage at the Hanford Site (RMS, root-mean-square) Storage (mm of water) Model Description UNSAT-H Standard Calibrated Heat Hysteresis HELP

RMS Error

Maximum Difference

Mean Difference

Median Difference

Cumulative Drainage3

23.6 23.6 23.4 23.7 97.6

75.8 59.3 80.2 74.8 264.4

-0.9 19.6 1.6 3.0 84.9

-6.0 16.5 -3.4 -2.0 73.1

0.0 0.0 0.0 15.3 537.0

'Measured lysimeter drainage was 30.0mm.

Conclusions Our understanding has advanced from studies of arid vadose fluxes in response to development and waste-disposal needs. In this work, we have summarized some of these recent advances; however, there is much research left to be done. Processes in arid vadose zones are complex and require sensitive laboratory and field techniques to quantify water fluxes and assess the impacts of land-use practices on groundwater quality. As more emphasis is placed on development of arid regions worldwide, it is imperative that we test our existing models with field data and reduce our uncertainties in both data collection and processes. Several key processes have been pointed out in recent research. It is clear that vegetation strongly controls water flux in arid vadose zones; however, limited data

Figure 13.8 Comparison of measured and simulated water potentials (suctions) from a lysimeter at the Hanford site. The upper dashed curve refers to simulations that did not account for hysteresis. (After Payer, 1995.)

366

VADOSE ZONE HYDROLOGY

Figure 1 3.9 Measured and simulated water potentials and cumultive drainage. Simulation results include hysteresis. (After Payer, 1995.)

are available on the water-use patterns of desert vegetation. Efforts to quantify plant/soil/water processes in arid regions must be developed in conjunction with plant biologists to provide input data for simulating both current uptake patterns and those that will occur following land-use or climatic changes. There is also a clear need for better understanding of flow dynamics at very low water contents. Current models used in agricultural or humid settings are unlikely to be applicable when film flow or vapor transport dominate. Collaborative efforts with other disciplines interested in multiphase porous media transport (chemical engineering, petroleum engineering, and groundwater hydrology) should be undertaken to develop physically correct models of liquid, vapor, and solute transport in natural porous media. The role of heterogeneity continues to be an uncertain factor in determining the direction and magnitude of water flux in arid regions. Spatial variability clearly controls not only integrated quantities, such as groundwater recharge, but also is crucial in determining the extent of preferential flow and rapid pathways for pollutants. These rapid pathways must be understood for any site proposed to isolate waste from the biosphere, but they have only begun to be documented in fractured vadose zones. As more waste-disposal facilities are built in arid regions, monitoring their performance becomes a critical safety and technological issue. There has been limited field testing of monitoring equipment and its reliability, yet waste sites continue to be proposed and licensed. Without proper monitoring by either noninvasive methods or subsurface detectors, the integrity of, and public confidence in, such facilities cannot be guaranteed. Finally, little effort to date has been made in coupled modeling of both the surface and subsurface transfer of water and energy. Such coupling is critical to subsurface processes, but, perhaps more significantly, the global climate-modeling community is becoming aware that subsurface hydrologic processes (infiltration, redistribution, surface drying, and root water uptake) play a significant role in governing the

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

367

Earth's climate. The scales of our two disciplines are still rather disparate, but as computing power increases, we will find that we are limited only by our lack of knowledge of fundamental processes of land/atmosphere exchange. This area should be one in which both fields will develop synergistically.

Acknowledgments We wish to thank Jan Hopmans and Marc Parlange for their organizational efforts for both the conference and preparation of this text. We also appreciate the efforts of Fred Phillips and two anonymous reviewers for their constructive comments and suggestions for improvement of the manuscript. Special thanks also go to Ms. Debi Noack for her invaluable assistance during preparation of the manuscript. Publication authorized by the Director, Bureau of Economic Geology, The University of Texas at Austin. Publication of this review was supported in part by the U.S. Nuclear Regulatory Commission under Fin W6503 and the Desert Research Institute. Finally, we sincerely thank Don and Jim for their many contributions to the advancement of science, education, and society.

References Albertson, J.D., M.B. Parlange, G.G. Katul, C.R. Chu, H. Strieker, and S.W. Tyler, 1995, Sensible heat flux from arid regions: a simple flux-variance method, Water Resour. Res., 31(4), 969-974. Allen, R.G., T.A. Howell, W.O. Pruitt, I.A. Walter, and M.E. Jensen (eds.), 1991, Lysimeter for evapotranspiration and environmental measurements, in Proceedings of the International Symposium on Lysimetry, American Society of Civil Engineers, New York. Allison, G.B. and M.W. Hughes, 1978, The use of environmental tritium and chloride to estimate total local recharge to an unconfined aquifer, Aust. J. Soil Res.. 16, 181-195. Allison, G.B. and M.W. Hughes, 1983, The use of natural tracers as indicators of soil-water movement in a temperate semi-arid region, /. Hydro!., 60, 157-173. Allison, G.B., C.J. Barnes, M.W. Hughes, and F.W.J. Leavey, 1984, Effect of climate and vegetation on oxygen 18 and deuterium profiles in soils, Isotope Hvdrology, 1983, IAEA, Vienna, pp. 105-124. Allison, G.B., G.W. Gee, and S.W. Tyler, 1994, Vadose-zone techniques for estimating groundwater recharge in arid and semiarid regions, Soil Sci. Soc. Am. J., 58, 6-14. Andraski. B.J.. 1990, Water movement and trench stability at a simulated arid burial site for low-level radioactive waste near Beatty, Nevada, Proceedings of the Symposium on Nuclear Waste Isolation in the Unsaturated Zone, Las Vegas, Nevada, September 1989, American Nuclear Society, La Grange Park, IL, pp. 166-173. Arya, L.M., D.A. Farrell, and G.R. Blake, 1975, A field study of soil water depletion patterns in presence of growing soybean roots; I, determination of hydraulic properties of the soil, Soil Sci. Soc. Am. Proc. 39, 424-430. ASTM, 1995, Test method for measurement of soil potential (suction) using filter paper, D 5298-94, Annual Book of ASTM Standards, American Society for Testing and Materials, Philadelphia, PA, pp. 154-159. Barnes, C.J. and G.B. Allison, 1983, The distribution of deuterium and 18O in dry soils, 1, theory, J. Hydro!.., 60, 141-156.

368

VADOSE ZONE HYDROLOGY

Barrow, J.C., 1994, The resonant sonic drilling method, an innovative technology for environmental restoration programs, Ground Water Monit. Remedial., 14(2), 153-160. Brooks, R.H. and A.T. Corey, 1964, Hydraulic properties of porous media, Hydrology Paper #3, Colorado State University, Ft. Collins, CO. Busch, D.E., N.L. Ingraham, and S.D. Smith, 1992, Water uptake in woody riparian phreatophytes of the southwestern United Slates: a stable isotope study, Ecolog. Applic., 2, 450-459. CaldwclL M.M. and J.H. Richards, 1989, Hydraulic lift and water use by plants: implications for performance, water balance and plant-plant interactions, Oecologia, 95, 565-574. Campbell, G.S. and G.W. Gee, 1986. Water potential: miscellaneous methods, in Methods of Soil Analysis, A. Klute (ed.), Agronomy No. 9(1), American Society of Agronomy, Madison, Wl. Campbell, G.S. and S. Shiozawa, 1995, Prediction of hydraulic properties of soils using particle-size distribution and bulk density data, in International Workshop of Indirect Methods for Estimating the Hydraulic Properties of Unsalurated Soils, M. Th. van Genuchten, R.J. Leij, and L.J. Lund (eds.), University of California, Riverside, pp. 317-328. Celia, M.A., E.T. Bouloutas, and R.L. Zarba, 1990, A general mass-conservation numerical solution for the unsaturated flow equation. Water Resour. Res., 26(7), 1483-1496. Conca, J.L. and J.V. Wright, 1992, Diffusion and flow in gravel, soil, and whole rock, Appl. Hydrogeo/., 1, 5-24. Cook, P.G. and G.R. Walker, 1995, An evaluation of the use of 3H and 36C1 to estimate groundwater recharge in arid and semiarid environments, in Proceedings of the International Symposium on Isotopes in Water Resources Management, Vienna, Austria, March 20-24, 1995. Cook, P.G., G.R. Walker, and l.D. Jolly, 1989, Spatial variability of groundwater recharge in a semiarid region, /. Hydro/., I l l , 195-212. Cook, P.G., W.M. Edmunds, and C.B. Gaye, 1992, Estimating paleorecharge and paleoclimate from unsaturated zone profiles, Water Resour. Res., 28, 27212731. Deka, R.N., M. Wairu, P.W. Mtakwa, C.E. Mullins, E.M. Veenendaal, and J. Townend, 1995, Use and accuracy of the filter-paper technique for measurement of soil matric potential, Environ. J. Soil Sci., 46, 233-238. de Silans, A.P., L. Bruckler, J.L. Thony, and M. Vauclin, 1989, Numerical modeling of coupled heat and water flows during drying in a stratified bare soil—comparison with field observations, J. Hydrol, 105, 109-138. Dettenger, M.D., 1989, Reconnaissance estimates of natural recharge to desert basins in Nevada, U.S.A. by using chloride balance calculations, J. Hydrol., 106, 55-78. Detty, T.E., D.P. Hammermeister, D.O. Blout, M.J. Sully, R.L. Dodge, J. Chapman, and S.W. Tyler, 1993, Water fluxes in a deep arid-region vadose zone, EOS, 74(43), 297. Du, S. and P. Rummel, 1994, Reconnaissance studies of moisture in the subsurface with GPR, Proceedings of the Fifth International Conference on Ground Penetrating Radar, Kethchener, Ontario, Canada, June 12-16. Ehleringer, J.R. and T.E. Dawson, 1992, Water uptake by plants: Perspectives for stable isotope composition, Plant Cell Environ., 15(9), 1073 1080. Fabryka-Martin, J., S. J. Wightman, W.J. Murphy, M.P. Wickham, M.W. Caffee, G.J. Nimz, J.R. Southon, and P. Shanna, 1993, Distribution of chlorine-36 in the unsaturated zone at Yucca Mt.: an indicator of fast transport paths, in FOCUS '93: Site Characterization and Model Validation, Las Vegas, Nevada, September 26-29, 1993.

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

369

Payer, M.J., 1995, Model applications and testing, in Hanford Site Long-Term Surface Barrier Development Program: Fiscal Year 1994 Highlights, K.L. Petersen, S.O. Link, and G.W. Gee (eds.), PNL-10605, Pacific Northwest Laboratory, Richland, WA. Payer, M.J. and T.L. Jones, 1990, UNSAT-H, version 2.0 unsaturated soil water and heat flow model, PNL-6779, Pacific Northwest Laboratory, Richland, WA, variably paginated. Payer, M.J. and C.S. Simmons, 1995, Modified soil water retention functions for all matric suctions, Water Resour. Res. 31(5), 1233-1238. Payer, M.J., M.L. Rockhold, and M.D. Campbell, 1992, Hydrologic modeling of protective barriers: comparison of field data and simulation results. Soil Sci. Soc. Am. Proc., 56, 690-700. Fischer, J.M., 1992, Sediment properties and water movement through shallow unsaturated alluvium at an arid site for disposal of low-level radioactive waste near Beatty, Nye County. Nevada, U.S. Geological Survey WaterResources Investigations Report 92-4032. Flint, L.E., M.S. Nash, and A.L. Flint, 1992, Rapid determination of moisture retention curves using a chilled-mirror psychrometer, EOS. Trans. Am. Geophys. Union, 73(43), 223. Fredlund, D.G., 1992, Background, theory, and research related to the use of thermal conductivity sensors for matric suction measurements, in Advances in Measurement of Soil Physical Properties, Bringing Theory into Practice, G.C. Topp (ed.), SSSA Special Publication 30, SSSA, Madison, WI, pp. 249-261. Gat, J.R., 1981, Groundwater, in Stable Isotope Hydrology, Deuterium and Oxygen18 in the Water Cycle, J.R. Gat and R. Gonfiantini (eds.), IAEA, Vienna, Austria, pp. 223-240. Gee, G.W., and D. Hillel, 1988, Groundwater recharge in arid regions: review and critique of estimation methods, J. Hydrol. Process. 2, 255-266. Gee, G.W., M.D. Campbell, G.S. Campbell, and J.H. Campbell, 1992, Rapid measurement of low soil water potentials using a water activity meter, Soil Sci. Soc. Am. J., 56, 1068-1070. Gee, G.W., P.J. Wierenga, B.J. Andraski, M.H. Young, M.J. Payer, and M.L. Rockhold, 1994a, Variations in water balance and recharge potential at three western desert sites, Soil Sci. Soc. Am. J., 58, 63-72. Gee, G.W., H.D. Freeman, W.H. Walters, Jr., M.W. Ligotke, M.D. Campbell, A.L. Ward, S.O. Link, S.K. Smith, B.G. Gilmore, and R.A. Romine, 1994b, Hanford Prototype Surface Barrier Status Report: FY 1994. PNL 10275, Pacific Northwest Laboratory, Richland, WA. Globus, A.M. and G.W. Gee, 1995, A method to estimate moisture diffusivity and hydraulic conductivity of moderately dry soil, Soil Sci. Soc. Am../., 59, 684-689. Greacen, E.L., G.R. Walker, and P.G. Cook, 1989, Procedure for the filter paper method of measuring soil water suction, CSIRO Division of Soils Report 108, Glen Osmond, Australia, pp. 1-7. Hook, W.R., N.J. Livingston, Z.J. Sun, and P.B. Hook, 1992, Remote diode shorting improves measurement of soil water by time domain reflectometry. Soil Sci. Soc. Am. J. 56, 1384-1391. Hopmans, J.W., T. Vogel, and P.D. Koblic, 1992, X-ray tomography of soil water distribution during one-step outflow experiments, Sci. Soc. Am. J., 56, 355-362. Hsieh, J.J.C., A.E. Reisenauer, and L.E. Brownell, 1973, A study of soil water potential and temperature in Hanford soils, BNWL-1712, Battelle North West Laboratory, WA. Hubbel, J.M. and J.B. Sisson, 1996, Portable tensiometer use in deep boreholes, Soil Sci. Soc. Am. J., 161(6), 376-381. Hudson, D.B., P.J. Wierenga, and R.G. Mills, 1996, Unsaturated hydraulic propertics from upward flow into soil cores. Soil Sci. Soc. Am. ./., 60, 388-396.

370

VADOSE ZONE HYDROLOGY

Hueter, T.F. and R.H. Bolt, 1954, Sonic-Techniques for the Use of Sound and Ultrasound in Engineering and Science, John Wiley & Sons, New York. Jolly, I.D., P.O. Cook, G.B. Allison, and M.W. Hughes, 1989, Simultaneous water and solute movement through the unsaturated zone, /. Hydrol., I l l , 391-396. Kachanoski, R.G., E.G. Gregorich, and I.J. Van Wesenbeeck, 1988, Estimating the spatial variations of soil water content using non-contacting electromagnetic inductive methods, Can. J. Soil Sci., 68, 715-722. Keller, C., 1991, So, what is the practical value of SEAMIST?, in Proceedings of the 5lh National Outdoor Action Conference on Ground Water Monitoring and Geophysical Methods, National Ground Water Association, pp. 59-74. Khaleel, R., J.F. Relyea, and J.L. Conca, 1995, Evaluation of van GenuchtenMualem relationships to estimate unsaturated hydraulic conductivity at low water contents, Water Resour. Res., 31(11), 2659-2668. Kool, J.B., J.C. Parker, and M.Th. van Genuchten, 1985, Determining soil hydraulic properties from one-step outflow experiments by parameter estimation: I, theory and numerical studies, Soil Sci. Soc. Am. J., 49, 1348-1354. Kume, J. and J.P. Rousseau, 1994, A borehole instrumentation program for characterization of unsaturated zone percolation, in Proceedings of the 5th Annual International High Level Radioactive Waste Management Conference, Las Vegas, NV, Vol. 1, American Nuclear Society, pp. 2076-2083. Levitt, D.G., C.F. Lohrstofer, M.J. Sully, and J.M. Gianni, 1996, An arid zone lysimeter facility for performance assessment and closure of investigations at the Nevada Test Site, Paper #38-14, Proceedings of Waste Management '96, February 26-29, Tucson, AZ, published by University of Arizona Press, Tucson, AZ -CD only. Limbach, W.E., T.D. Ratzlaff, J.E. Anderson. T.D. Reynolds, and J.W. Laundre, 1994, Design and implementation of the protective cap/biobarrier experiment at the Idaho National Engineering Laboratory, in In Situ Remediation: Scientific Basis for Current and Future Technologies, Part 1, G.W. Gee and N.R. Wing (eds.), Thirty-Third Hanford Symposium on Health and the Environment, November 7-11, 1994, Pasco, WA, Battelle Press, Columbus, OH, pp. 359-377. Link, S.O., N.R. Wing, and G.W. Gee, 1995, The development of permanent isolation barriers for buried wastes in cool deserts: Hanford, Washington, /. Arid Land Stud., 4, 215-224. Liu, B., J. Fabryka-Martin, A. Wolfsberg, B. Robinson, and P. Sharma, 1995, Significance of apparent discrepancies in water ages derived from atmospheric radionuclides at Yucca Mountain, Nevada, in Proceedings of the Conference on Water Resources at Risk, Denver, CO, 1995, W.R. Hotchkiss, J.S. Downey, E.D. Gutentag, and J.E. Moore (eds.), American Institute of Hydrology, Minneapolis, MN, NH52-NH62. Malek, E., G.E. Bingham, and G.D. McCurdy, 1990, Evapotranspiration from the margin and moist play a of a closed desert valley, /. Hydro!., 120, 15-34. Mehuys, G.R., L.H. Stolzy, J. Letey, and L.V. Weeks, 1975, Effects of stones on the hydraulic conductivity of relatively dry desert soils, Soil Sci. Soc. Am. J., 39, 37^2. Milly, P.C.D. and P.S. Eagleson, 1982, Parameterization of moisture and heat fluxes across the land surface for use in atmospheric general circulation models, Report 279, Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA. Montazer, P., 1995, AIR-TOUGH: A fully 3-d linking of atmosphere with soil using eddy diffusivity concepts and V-TOUGH, Proceedings of the 6th Annual International High Level Radioactive Waste Management Conference, Las Vegas, NV, American Nuclear Society, pp. 163-165.

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

371

Montazer, P. and W.E. Wilson, 1984, Conceptual hydrologic model of flow in the unsaturated zone, Yucca Mountain, Nevada, U.S. Geological Survey Water Resources Investigation Report 84-4345. Mualem, Y., 1976, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12(14), 593-622. Murphy, E.M., T.R. Ginn, and J.L. Phillips, 1996, Geochemical estimates of recharge in the Pasco Basin, Water Resour. Res. 32, 2853 2868. Nativ, R., E. Adar, O. Dahan, and M. Geyh, 1995, Water recharge and solute transport through the vadose zone of fractured chalk under desert conditions, Water Resour. Res. 31(2), 253-262. Nichols, W.D., 1994, Ground water discharge by phreatophyte shrubs in the Great Basin as related to depth to groundwatcr, Water Resour. Res. 30(12), 32653274. Nimmo, J.R., J. Rubin, and D.P. Hammermeister, 1987, Unsaturated flow in a centrifugal field: measuremenl of hydraulic conductivity and testing of Darcy's law, Water Resour. Res., 23, 124-134. Phene, C.J. and D.W. Beale, 1976, High-frequency irrigation for water nutrient management in humid regions, Soil Sci. Soc. Am. /., 40, 430—436. Phene, C.J., U.J. Hoffman, and S.L. Rawlins, 1971a, Measuring soil matric potential in situ by sensing heat dissipation within a porous body: I, theory and sensor construction, Soil Sci. Soc. Am. Proc., 35, 27-33. Phene, C.J., U.J. Hoffman, and S.L. Rawlins, 1971b, Measuring soil matric potential in situ by sensing heat dissipation within a porous body: II, experimental results. Soil Sci. Soc. Am. Proc., 35, 225-229. Philip, J.R. and D.A. de Vries, 1957, Moisture movement in soils under temperature gradients, Trans. Am. Geophys. Union, 38, 222-228. Phillips, P.M., 1994, Environmental tracers for water movement in desert soils of the American southwest, Soil Sci. Soc. Am. J., 58, 15-24. Phillips, P.M., J.L. Mattick, T.A. Duval, D. Elmore, and PW. Kubick, 1988, Chlorine-36 and tritium from nuclear-weapons fallout as tracer for long-term liquid and vapor movement in desert soils, Water Resour. Res., 24(10), 18771891. Phillips, P.M., P. Sharma, and P. Wigand, 1991, Deciphering variations in cosmic radiation using cosmogenic chlorine-36 in ancient rat urine, EOS, 72(44), 72. Prudic, D.E. and R.G. Striegl, 1994, Water and carbon dioxide movement through unsaturated alluvium near an arid disposal site for low-level radioactive waste, Beatty, Nevada, EOS, 75(16), 163. Prudic, D.E. and R.G. Striegl, 1995, Tritium and radioactive carbon (14C) analysis of gas collected from unsaturated sediments next to a low-level radioactive waste burial site south of Beatty, Nevada, April 1994 and July 1995, U.S. Geological Survey Open File Report 95-741. Pruess, K., 1987, TOUGH user's guide. LBL-20700, Lawrence Berkeley Laboratory, Berkeley, CA. Prych, E.A., 1995, Using chloride and chlorine-36 as soil water tracers to estimate deep percolation at selected locations on the U.S. Department of Energy Hanford Site, Washington, U.S. Geological Survey Open-File Report 94-514, Denver, CO. Reece, C.F., 1996, Evaluation of a line heat dissipation sensor for measuring soil matric potential, Soil Sci. Soc. Am. J. 60, 1022-1028. REECo (Reynolds Electrical and Engineering Company), 1994, Site characterization and monitoring data from area 5 pilot wells, Nevada Test Site, Nye County, Nevada, Contractor report prepared for the U.S. Department of Energy, Nevada Operations Office, DOE/NV/11432-74, variable pagination. Rockefeller, W.C., 1966, Bodinc resonant pile driver: characteristics and operating techniques, Report No. 501, Second Edition, Sonico, Inc.

372

VADOSE ZONE HYDROLOGY

Ross, P.J., 1990, Efficient numerical methods for infiltration using Richards' equation, Water Resour. Res. 26(2), 279 290. Ross, P.J., J. Williams, and K.L. Bristow, 1991, Equation for extending water-retention curves to dryness, Soil Sci. Soc. Am. J. 55, 923-927. Rossi. C. and J.R. Nimmo, 1994, Modeling of soil water retention from saturation to oven dryness, Water Resour. Res. 30, 701 708. Sackschewsky, M.R., C.J. Kemp, S.O. Link, and W.J. Waugh, 1995, Soil-water balance changes in engineered soil surfaces, J. Environ. Quality, 24, 352-359. Scanlon, B.R., 1991, Evaluation of moisture flux from chloride data in desert soils, J. Hydro!., 128, 137 156. Scanlon, B.R., 1992, Evaluation of liquid and vapor water flow in desert soils based on chlorine-36 and tritium tracers and nonisothermal flow simulations, Water Resour. Res., 28(1), 285-297. Scanlon, B.R., 1994, Water and heat fluxes in desert soils: 1. Field Studies, Water Resour. Res., 30, 709-719. Scanlon, B.R. and P.C.D. Milly, 1994, Water and heat fluxes in desert soils: 2. Numerical simulations, Water Resour. Res., 30(3), 721-733. Schneebeli, M., H. Flulher, T. Gimmi, H. Wydler, H.-P. Laser, and T. Baer, 1995, Measurement of water potential and water content in unsaturated crystalline rock, Water Resour. Res., 31(8), 1837-1843. Shaw, B. and L.D. Baver, 1939, Heat conductivity as an index of soil moisture, J. Am. Soc. Agron.. 31, 886-889. Sheets, K.R. and J.M.H. Hcndrickx, 1995, Noninvasive soil water content measurement using electromagnetic induction, Water Resour. Res., 31, 2401 2410. Simunek, J., T. Vogel, and M.Th. van Genuchten, 1994, The SWMS_2D code for simulating water flow and solute transport in two dimensional variably saturated media, Salinity Laboratory Research Report No. 132, U.S. Department of Agriculture. Smiles, D.E., W.R. Gardner, and R.K Schulz, 1995, Diffusion of tritium in arid disposal sites, Water Resour. Res., 31(6), 1483-1488. Smith, G.I., 1984, Paleohydrologic regimes in the southwestern Great Basin, 0 3.2 MY ago, compared with other long records of "global" climates, Quaternary Res. 22, 1-17. Snydcr, K.E., D.L. Gustafson, J.J. Miller, and S.E. Rawlinson, 1994, Geological components of site characterization and performance assessment for a radioactive waste management facility at the Nevada Test Site, Report DOEINVj 10833-20, Raytheon Services, Las Vegas, NV. Sophocleous. M., 1979, Analysis of water and heat flow in unsaturated-saturated porous media, Water Resour. Res. 15, 1195-1206. Stone, W.J., 1992, Paleohydrological implications of some deep soil water chloride profiles, Murray Basin, South Australia, /. Hydro]., 132, 201-223. Stothoff, S.A., 1995, BREATH version 1.1 coupled flow and energy transport in porous media: simulator description and user guide, NUREG/CR-6333, U.S. Regulatory Commission, Washington, DC. Striegl, R.G., D.E. Prudic, J.S. Duval, R.W. Healy, E.R. Landa, D.W. Pollock, D.C. Thorstenson, and E.P. Weeks, 1996, Factors affecting tritium and 14C distribution in the unsaturated zone near the low-level readioactive waste burial site south of Beatty, Nevada, U.S. Geological Survey Open File Report 96-110. Sully, M.J., D.E. Cawficld, D.O. Blout, L.E. Barker, B.L. Dozier, and D.P. Hammermeister, 1994a, Characterization of the spatial variability of hydraulic properties of an arid region vadose zone, EOS, 74(43), 297. Sully, M.J., T.E. Detty, D.O. Blout, and D.P. Hammermeister, 1994b, Water fluxes in a thick desert vadose zone, in Geolog. Soc. Am. Annu. Meeting, 26(6), 7, A391.

WATER AND SOLUTE TRANSPORT IN ARID VADOSE ZONES

373

Thorburn, P.J., T.J. Hatton, and G.R. Walker, 1993, Combining measurements of transpiration and stable isotopes of water to determine ground water discharge from forests, J. Hydro!. 150(2/4), 563-570. Toledo, P.O., R.A. Novy H.T. Davis, and L.E. Scriven, 1990, Hydraulic conductivity of porous media at low water content, Soil Sci. Soc. Am. Proc. 54, 673679. Topp, G.C., J.L. Davis, and A.P. Annan, 1980, Electromagnetic determination of soil water content: measurement in coaxial transmission lines, Water Resour. Res. 16(3), 574-582. Tyler, S.W., 1988, Calibration of neutron moisture meters in large diameter boreholes. Soil Sci. Soc. Am. J., 52(3), 890 893. Tyler, S.W. and G.R. Walker, 1994, Impacts of the root zone on tracer transport, Soil Sci. Soc. Am. J., 58(1), 25-31. Tyler, S.W., W.A. McKay, and T. Mihevc, 1992, Assessment of soil moisture movement in nuclear subsidence craters, J. Hydro!., 139, 159-181. Tyler, S.W., J.B. Chapman, S. Conrad, D.P. Hammermeister, D.O. Blout, J.J. Miller, M.J. Sully, and J. Ginanni, 1996, Soil water flux on the Nevada Test Site: temporal and spatial variations over the last 120,000 years, Water Resour. Res. 32(6), 1481-1499. U.S. Department of Agriculture, 1954, Diagnosis and improvement of saline and alkali soils, Agriculture Handbook #60. U.S. DOE (U.S. Department of Energy), 1994, Constructability report for the 200BP-1 prototype surface barrier, DOE/RL-94-76, U.S. Department of Energy, Richland Operations Office, Richland, WA. van Dam, J.C, J.N.M. Strieker, and P. Droogers, 1994, Inverse method to determine soil hydraulic functions from multistep outflow experiments, Soil Sci. Soc. Am. J., 58, 647-652. van de Griend, A.A., P.J. Camillo, and R.J. Gurney, 1985, Discrimination of soil physical parameters, thermal inertia, and soil moisture from diurnal surface temperature fluctuations, Water Resour. Res. 21(5), 997-1009. van Genuchten, M.Th., 1980, A closed form equation for predicting the hydraulic conductivities of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898. White, M.D., M. Ostrom, and R.J. Leahard, 1995, Modeling fluid flow and transport in variably saturated porous media with the STOMP simulator 1, nonvolatile three-phase model description. Adv. Water Resour. 18, 353-374. Wing, N.R. and G.W. Gee, 1994, Quest for the perfect cap, Civil Eng., 64(10), 38^1. Wittreich, C.D. and C.R. Wilson, 1991, Use of lysimeters to monitor a sanitary landfill, in Lysimeters for Evapotranspiration and Environmental Measurements, Proceedings of the International Symposium on Lysimetry, R.G. Allen, T.A. Howell, W.O. Pruitt, I.A. Walker, and M.E. Jensen (eds.), American Society of Civil Engineers, New York. Young, M.H., P.J. Wierenga, and C.F. Mancino, 1996, Large weighing lysimeters for water use and deep percolation studies, Soil Sci. Soc. Am. J., 161, 491-501. Zimmermann, U., D. Ehhalt, and K.O. Munnich, 1967, Soil-water movement and evapotranspiration: changes in the isotopic composition of the water, in Isotope Hydrology Proceedings Symposium, November 1966, IAEA, Vienna, pp. 14-18.

14

Water Flow in Desert Soils Near Buried Waste Repositories

A. W. WARRICK

L. PAN P. J. WIERENGA

Desert soils are frequently considered the safest choice for storing radioactive and chemical wastes (Winograd, 1974; National Research Council, 1976, 1995; Gee et al., 1992; IT Corporation, 1994). The reason is that nearly all rainwater that percolates into a desert soil is assumed to be taken up by plant roots and transpired back into the atmosphere. However, there is still recharge occurring in desert areas, although the magnitude of this recharge can vary greatly from one area to another (Rockhold et al., 1995). Therefore, proper siting of waste-disposal facilities is extremely important. This requires a good understanding of the factors that affect recharge and that minimize water flow through the waste layer. For a brief discussion of recharge in arid and semiarid regions, as well as an introduction to eight comprehensive papers on the topic, see Gee and Tyler (1994). This chapter has two major thrusts. The first part examines field measurements that have been made of the amounts of water that pass below the root zone to deeper depths in arid (and semiarid) environments. Also, some historical precipitation records are examined. The second part deals with modeling water flow in sloping, layered soils as might occur naturally or in cover designs that use capillary barriers. A simple analytical expression is presented for pressure-head distribution and diversion. This is followed by results from numerical modeling in order to test the effects of more complex boundary conditions, including steady versus nonsteady rainfall.

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

375

Soil Water and Precipitation Measurement in Desert Regions Soil Water Most rainwater that percolates into a desert soil is taken up by plant roots and transpired back into the atmosphere (Phillips, 1994). In addition, there is considerable surface evaporation. The combined processes of transpiration and evaporation, plus the lack of rainfall, cause desert soils to be dry most of the time. Furthermore, many of these soils are dry to great depths. However, not all desert soils are dry. Soils with minimal or no vegetation may contain considerably more water than soils with vegetation. Shifting sand dunes with deep, uniform sandy soils and minimal vegetation are often quite moist (Berndtsson and Chen, 1994). Similarly, soils with shallowrooted cheatgrass showed an order-of-magnitudc greater recharge to the groundwater than soils covered with deeper rooted sagebrush (Rockhold et al, 1995). Soils below ephemeral lake bottoms (playas) and streambeds can also be rather moist and allow significant recharge to the groundwater as compared with interstream settings. The number of studies dealing with long-term monitoring of water contents of desert soils is quite limited. Furthermore, most of the studies that have been conducted are of short duration (Shreve, 1934; Winkworth, 1969; Herbel and Gile, 1973; Cable, 1977). As an example, Cable (1977) measured infiltration of water into soil with an established stand of creosote bush and bur sage from June 1974 until December 1975. During this period, only three precipitation events resulted in significant accumulation of soil water down to 50cm. This water was extracted by the vegetation within 2 or 3 weeks. Wierenga et al. (1985) initiated a longer term study to determine the spatial and temporal variability of soil moisture along a 3-km transect in the Jornada Range in southern New Mexico. They measured soil moisture with a neutron probe at 30, 60, 90, 110, and 130cm below the soil surface. Moisture-content readings were taken at 30-m intervals along the transect, once a month from 1983 to 1991. The transect begins on the steep rocky slope of Summerficld Mountain ( < 8 % clay), traverses piedmont and basin slopes, and ends in an ephemeral lake (playa; > 50% clay). Away from the rocky slope and the playa, on the piedmont and basin slopes, soils generally have a loamy texture (Nash et al., 1991). Long-term rainfall at the site averages 263mm year"1 with half falling during the summer months. This study is a good example of what may be expected in a warm desert. First there is extensive spatial variability in soil moisture, which in the 9-year period varied from a mean of 0.30cm3cnT3 (±0.04cm 3 cnT 3 ) at 130cm in the playa to a 0.04 cm3 cm"3 (±0.04 cm3cirT3) at 130 cm at the upper, rocky end of the transect (figure 14.1). Soils in the playa have a relatively high clay content (> 50% clay; subangular blocky and prismatic structure). Soils at the upper end of the transect are coarser and contain more gravel (< 14% clay). As a result, the mean water contents are lower. The temporal variation in soil water content is shown in figure 14.2 for a site near the center of the transect. The vegetation at this site, in an interstream setting on an alluvial fan with a deep loamy soil, is mainly creosote bush. The data show very significant variations in soil water content at 30cm, during 6 of the 9 years shown. At

376

VADOSE ZONE HYDROLOGY

Figure 14.1 Variation in water content on an alluvial fan along a 3-km transect on the Jornada Range in southern New Mexico. Water contents are presented for depths of 30, 90, and 130cm during the week of 30 April to 6 May, 1982. Vegetation is creosote bush and annual rainfall averaged 20mm.

the 130-cm depth, however, fluctuations in water content were nearly absent, except during the wet fall and winter of 1985. Thus, during 8 of the 9 years, rainfall that infiltrated the soil was evaporated or taken up by the plant roots and evapotranspired back into the atmosphere. Only in 1 of the 9 years did rainfall penetrate down to the 130-cm depth and reached a value of 15%, an increase of 7% above the 9-year mean of 8% by volume. Although no neutron-probe readings were taken below the 130-cm depth, plant roots at this site can go down to 300cm (Wierenga et al., 1990). and therefore water percolating past the 130-cm depth is most likely taken up by plant roots.

Figure 14.2 Temporal variation in water content (1982-1991) at 30, 60, 90, 110, and 130cm below the surface of a coarse loamy soil in southern New Mexico. Vegetation is creosote bush, and longterm annual rainfall is 263 mm.

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

377

Precipitation Patterns Precipitation in desert areas can be characterized by its magnitude and by the fact that much rain falls in large storms or during relatively short wet periods. Desert precipitation is episodic in nature. As an example of precipitation patterns in the southwestern United States, we have examined rainfall records from four sites. These include the 1948-1993 record for Needles, California, the 1901-1993 record for Parker, Arizona, the 1953-1993 record for the Jornada site in New Mexico, and the 1896-1992 record for Tombstone, Arizona. The first three data sets are from Earthinfo (1994) and the Tombstone data is courtesy of David Goodrich (personal communication. Southwest Watershed Research, ARS, Tucson, AZ). For the first three sets, data was discarded for any year that had more than 15 days of missing values. Generally, the remaining years had no missing days, with very few having more than 5 missing days. The number of years used in the calculations is shown in table 14.1. For the Tombstone data, the few missing values were taken to be the modal values for those dates. The Jornada and Tombstone areas received considerably more precipitation than the other two sites (see the summary data in table 14.2). Standard deviations for the annual values for the Jornada and Tombstone were about one third of the means. For nearly a century, the measured annual rainfall at Tombstone never went below 187mm, which is about half of the average value. The Parker and Needles data are similar, with each having a standard deviation of about half the mean annual values. Of the four sites, the Parker site shows the most extreme behavior, with a range in annual precipitation from 9 to 345mm (figure 14.3). Monthly data is, as expected, even more variable, at least on a relative scale (figure 14.4). For all four sites, the standard deviation is larger than the mean

Table 14.1 Summary of Precipitation Data" Site/Time Period

n

Mean ± s

Maximum

Minimum

38 456

116 ±58 10± 17

243 120

31 0

83 996

1 24 ± 69 10±18

345 225

9 0

39 468

261 ±90 22 ±27

507

79

167

0

97 1164

357 ±95

708 293

187 0

1. Needles (California) 1948-1993 Annual Monthly 2. Parker (Arizona) 1901-1993 Annual Monthly 3. Jornada Experimental Range (New Mexico) 1953-1993 Annual Monthly 4. Tombstone (Arizona) 1896-1992 Annual Monthly "All precipitation values arc in millimeters.

30 ±38

Table 14.2 Annual Rainfall at Jornada Experimental Range 1982-1992a Year

Precipitation (mm)

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

295 249 507 327 363 271 264 252 259 412 335

"The mean rainfall for 1953-1993 is 261.2mm.

Figure 14.3 Distribution of annual precipitation for Parker, Arizona (1901-1993).

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

379

Figure 14.4 Distribution of monthly precipitation for Parker, Arizona (19011993).

value; in fact, for the two more arid sites, Needles and Parker, it is nearly twice as large. The monthly data at all sites had a considerable number of "0" values, i.e., no recorded rainfall. For example, at the Jornada site over 50 of the 468 months had no rainfall. Parker had no precipitation for about 350 out of 996 months. The suitability of arid soils for storage of waste is based on the assumption that these soils are able to store precipitation, and can subsequently recycle this water back into the atmosphere through evapotranspiration, without deep percolation losses. This same principle should be used in designing surface barriers or caps over landfills. An important parameter for the design of surface barriers for landfills and disposal sites is the amount of rainfall that needs to be stored. Table 14.1 shows that of the four sites, Tombstone has the highest monthly maximum precipitation (293 mm). A conservative estimate of the storage requirement of a surface barrier in Tombstone might be a soil that can store this amount of water. Many such soils are available, although they may not always be available where needed. An example of a soil with a high storage capacity is the Hanford Site silt-loam (Peterson et al., 1995), which has a reported maximum storage capacity of 500mm per 1.5-m-deep soil profile. Thus, a 1.5-m-thick layer of Hanford silt-loam could readily store the monthly, as well the annual, maximum precipitation for three of the four sites in

380

VADOSE ZONE HYDROLOGY

table 14.1. Many soils have a lower storage capacity than the Hanford silt-loam. However, the disadvantage of a lower storage capacity can be overcome by making the surface barrier thicker. For example, to make sure that the protective covers over proposed low-level nuclear-waste trenches in Ward Valley. California (with a rainfall similar to that of Needles, CA, 30 km to the east) can store all the rain that may fall, a cover thickness of at least 6m was selected. For a particular landfill, the optimal combination of storage capacity and soil depth are best determined by modeling water flow using soil properties and rainfall data from the site in question. Such modeling should be done for level soil conditions, and for soils with sloping interfaces. Modeling of water flow in sloping layered soils is necessary because many natural soils are layered, and have a slope. A second reason that modeling of sloping interfaces is needed is that by constructing surface barriers with a slope, water may be diverted downslope, away from the underlying waste. The next section will present models for water movement in arid soils with sloping interfaces.

Modeling Water Movement for Sloping, Layered Soils Capillary barriers generally consist of unsaturated, fine soil overlying coarser soil with a sloping contact. Their purpose is to divert water laterally, away from waste that may be placed below it. We will address only a few simplified questions, all of which are related to a sloping system shown in figure 14.5. Some generalizations will be presented based on a one-dimensional, steady-state solution of Richards' equation for a sloping system. Then, numerical results will be presented in order to investigate

Figure 14.5 Capillary barrier and deep vadose zone with sloping interface between soils 1 and 2. Surface above and water table below are at large distances.

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

381

the effects of vertical boundaries that interrupt the flow, and of transient events, such as variable rainfall patterns, as might be observed in an arid region.

Steady-State, One-Dimensional Flow Through a Sloping Interface We consider a position along a sloping profile (figure 14.5), such that the flow field will be only a function of the normal coordinate n that is measured perpendicular to the interface where it is chosen to be zero. This problem has been analyzed extensively (Zaslavsky and Sinai, 1981; Ross, 1990, 1991; Steenhuis et al., 1991; Warrick et al., 1997). The pressure profile is given as a function of n by

where /3 is the angle of the interface, q is the steady downward flow of water through the upper layer, and K2(h) is the conductivity function for the upper soil layer. The value of h at the interface is h = hi, which is consistent with q — K(ht). Note that for /J = 0, equation (14.1) is identical to the well-known steady-state solution for a nonsloping soil. As an example profile, consider a Glendale clay loam overlying a sand using the van Genuchten hydraulic functions and parameters given in table 14.3 and the conductivity functions presented in figure 14.6 (van Genuchten, 1980; Hills et al., 1989; Payer et al., 1992). Take the Darcian velocity as q — 0.1 m year"1 and a slope /3of 5 ;) . At the interface, the pressure is h\ = —0.854m, found by setting the Darcian velocity to the unsaturated hydraulic conductivity for the lower soil that is, the sand. The pressure decreases with increasing n above the interface and approaches a limiting value of h2 = —2.98m, found by setting q — 0.1 m year"1 equal to the K2(h) for the clay loam soil. The pressure values in the two soil layers can be found in figure 14.6 at the intersection of the horizontal line through K — 0.1 m year"1 (or log K = — 1) and the conductivity functions for the two soils. Clearly, clay has a more negative pressure during this steady downward flow condition while the sand is wetter. The profile of /; versus n for the above case is shown in figure 14.7A. (The analytical results are overlain by the numerical results from the next section.) The value of/) decreases as n increases in accordance with equation (14.1). The minimum h — —2.98 is shown by the dashed line. The profile looks the same as for the nonsloping case, differing only by the factor cos j). However, there is a phenomenon quite different from the nonsloping case. This is shown by plotting a streamline along z where z is the vertical distance from the interface. Without loss of generality, the streamline is chosen to be 0 at the interface (see figure 14.7B). The streamline is vertical for large z and deflects downslope as it approaches the bedding interface at z = 0. The relationship for the streamline position x is given by Warrick et al. (1997):

382

VADOSE ZONE HYDROLOGY

Table 14.3 Unsaturated Hydraulic Conductivity K and Pressure Head Function h (van Genuchten, 1980) along with Parameters used for Glendale Clay Loam and Sand

Clay loam (Hills et al., 1989):

Sand (Payer et al., 1992):

where K is for layer 2 that is n > 0. The total deflection distance, L in figure 14.7B, can be calculated by setting h = h2 in equation (14.2):

Figure 14.6 Conductivity function for Glendale clay loam (CL) (Hills et al., 1989) and sand (S) (Payer et al., 1992). Horizontal line is for 0.1 m year~' and corresponds to h = -2.98 and -0.854m for CL and S, respectively.

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES383

Figure 14.7 Profiles of (A, C) n versus h and (B, D) streamlines for clay loam overlying sand. The flow rate is q — 0.1 m year"'. The slope is 5° (A, B) or 30° for (C, D). The individual points are from the numerical model.

For the above case, with h\ = —0.854m and /?2 = —2.98m. the deflection distance is L = 0.874m. The horizontal seepage is Q = qL = 0.0874m2 year" 1 . If the flow rate is increased, then the profile can change from the above example. Consider q — 10m year"' rather than 0.1 as above. The corresponding conductivity now results in the limiting value for clay loam of h2 = —0.219 m, which is wetter than at the interface h\ — —0.415m. The result is a reversal of the h profile (figure 14.8A) with h now increasing (from -0.415 toward —0.219) above the interface. The corresponding deflection is now upslope (see figure 14.8B), albeit by only an insignificant 0.012 m. (Although the 10m year"1 is much higher than what would be expected for an average q in an arid region, it may be possible for a transient discharge during a high rainfall period.) The same effect can be obtained by keeping the lower flow rate of q = 0.1 m year"' and placing the sand above the clay.

General Expressions for the Limiting Deflected Flow Let us address two questions regarding the one-dimensional analysis and then look at the assumptions that have been made. The questions are what can we say about the maximum downslope deflection L = Lmax and about the maximum horizontal

384

VADOSE ZONE HYDROLOGY

Figure 14.8 Profile of (A) h and (B) streamlines for flow rate q = 10m year '. There is a 5° slope and clay loam overlies sand.

seepage Q = g max for any type of underlying material? At what distance above the strata interface does h approach its steady-state value? The maximum deflection L — Lmax occurs whenever hl -> 0. This is the case for a very coarse underlying material for which the unsaturated K ^ 0 until it is practically saturated. This gives, from equation (14.3),

where now we simply use K,. and K(h) for the upper layer and Kc is the capillary length given by

But K(h2) is q, and thus LmaK is more simply

For the special case of K(h) given by

Ac is equal to a and the result is the same as that of Ross (1990). For other forms including those considered by Steenhuis et al. (1991) with a finite air-entry value, equation (14.6) remains valid, but A.f will generally depend on h2 and other parameters. Note from equation (14.6) that the maximum deflection length is proportional to tan /?. For small angles, tan fi ^ p, and thus i.max is proportional to P itself. Often, Ks/q is much greater than 1 and the "—1" can be neglected in equation (14.6). Then, •Lmax = facKs/q or ?Anax = AC-^SJ- F°r this situation, and if Xc does not change, then Qmax =
WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES385

For the van Gcnuchten (1980) functions of table 14.3, r Adepends on h2, the pressure corresponding to q. However, for small values of q, K, will be approximately the limiting value for h2 -» —oo. This is illustrated in figure 14.9, which is a plot relating Lmax to q/Ks using equation (14.6). The values are plotted as a function of m = 0.2, 0.5, and 0.8 (van Genuchten's m value must fall between 0 and 1). For large
The argument on the right-hand side will be 1 for h = 0 and will become infinite as h —>• hi (i.e., Ksc\p(ah2) -» q). We arbitrarily define a normal distance n095i, corresponding to h = 0.95h2. With this definition, equation (14.8) gives

A plot of «o.95* cos ft is given in figure 14.10 for two extreme values of a; that is, a = 1 m~' and a = 10 m~'. The value a = 1 m"1 corresponds to a fine-textured soil. For high flux ratios to Ks, the n(>^ih is small, but it increases as q/Ks becomes small. For q/Ks = Q.\, the value is about 5m; for smaller fluxes, it is larger. For a coarse

Figure 14.9 Expressions for the maximum deflection downslope using the van Genuchten (1980) hydraulic functions. The marker is for log(?//Q = -2.68 and m = 0.282.

386

VADOSE ZONE HYDROLOGY

Figure 14.10 Plots of n cos /? as a function of (A) q/Ks and (B) fraction of total deflected flow. "Fine" and "Coarse" are for a = 1 and 10m"1, respectively.

material (a = 10 m ), the value of nOMh cos /B is much smaller; for \og(q/Ks) = -1, it is only a half meter or so. Another way to examine what is a significant height is to evaluate lateral flow as a function of n. With this in mind, consider the ratio of equations (14.2) and (14.3) for the Gardner function:

From the expression, we find

Since, Ks exp(or/!2) = q, the above is equivalent to

The last expression substituted into equation (14.8) gives

The x/L\ is the proportion of lateral flow, so this gives the remarkable result that the fraction of the flow occurring as a function of normal distance from the slope is independent of q/Ks. (For any ^(A)-function, we can show n cos/3 = Xc x/L\, provided \x/L\ is small and q
WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

387

Numerical Solution and Effect of Vertical Flow Barriers A numerical model for the two-dimensional (2-D), sloping system of figure 14.5 was also completed. The "/",-based" approach with a mixed form of Richards' equation was used (Pan and Wierenga, 1995, 1997; Pan et al., 1997). The discretization scheme is shown in figure 14.11. The domain is divided by a grid into control volumes, in the center of which the grid points are situated. Fully implicit schemes are used. To handle the sloping situation, the horizontal flow rate between two adjoined control volumes is evaluated as follows:

where A'+i/2./ = 0.5(Z),-_,- + Di+tj), D = K(dh/df), and f is the transformed pressure head,/ = P,'= h/(l + fth), with ft = -0.03cm"1. The (df/dx)uand (3f/dx), are the partial gradients along the x-direction in the upper and the lower triangles, respectively (figure 14.11). The boundary condition at the top was a prescribed flux while the bottom was set to a unit hydraulic gradient. To simulate an infinite length of slope, the left and right boundaries were set to <7/_i/2; = f°r all /-values, which is realized by letting

Figure 14.11 Sketch showing discretization of flow domain for 2-D model.

388

VADOSE ZONE HYDROLOGY

/ | ( =/,Y VJ and ftix+ij =fij- Here, the subscript / indicates the left-most column while the subscript NX indicates the right-most column. For all other cases of finite slopes, no flow boundaries were issued along the left and right boundaries. The results for the clay over sand is given by the individual points in figure 14.7A for the 5° slope and figure 14.7C for the 30° slope. The discretization was for Ax = 2cm and Az = 10 cm, with a total slope width of 100m and upper clay strata thickness of 9.5m. The results in figure 14.7 confirm that the 2-D model is in agreement with the pressure profiles of the 1-D solution. What is the effect of vertical flow boundaries on the flow field? The numerical model was run with the left and right boundaries blocked. This could be the case for a cover system or could also simulate an isolated waste cavity that intercepted a slope along a vertical lower face. The resulting /7-profiles as a function of n are shown for three positions along a 100-m slope in figure 14.12A. The solid line is for the center of the slope and is essentially identical to the one-dimensional analytical solution of figure 14.7A. The "dashed" curve is adjacent to the upper slope position (the —49.5 corresponds to 49.5m upslope). For that position, the /t-value is slightly less; that is, slightly drier, but only by 0.05m compared to the 1-D result of A, = —0.854m. The corresponding profile at the bottom of the slope (49.5 downslope) is wetter than the other two, again by approximately 0.05 m at the interface. The effect of the slope length on calculations can also be compared by plotting Q, the horizontal flow component. For the 2-D case, it is no longer a constant value, but will be a function of the slope position. This was done for slope lengths of 1, 10, 20, and 100 m with the results shows as figure 14.12B. The value of Q varies between 0 at the blocked ends to a maximum of 0.0874 in agreement with the 1-D solution. For the very short slope of 1 m length, the lateral flow is essential nil, and the situation is nearly equivalent to a nonsloping condition. For a slope length of 10m. Q approaches rero at either end and reaches a maximum of about 0.075 near the center. For a slope of 20m, Q = 0 at the ends, but the maximum near the center reaches the limiting values; likewise for the 100 m slope, the maximum Q exists along most of the slope. The pressure profiles are plotted over the x—z plane in figure 14.12C. These also show that 1-D approximation is very nearly correct for the entire slope. Notice a very slight "turning" of the contours, at either end, but the contours are, for practical purposes, parallel to the sloping interface.

Nonsteady Flow Simulations A nonsteady simulation was performed using, as a surface, input based on the wettest 7-day period for the Tombstone data set. For the 1896-1992 record, the wettest 7-day period was in July 1958, for which the daily, successive precipitation amounts were 64. 13, 0, 30, 15, 3, and 39 mm. For the simulation, a steady flow rate of 0.1 m year"' was established, the upper flux was then set to equal to the above 7day rainfall, after which the rate of O . l m year"1 is repeated. After the 7-days of precipitation, the flux at the upper boundary was set at q — 0.1 m year"1 (the same as the previous steady-state input).

Figure 14.12 Results from numerical model for (A) h versus z, (B) Q as a function of slope position for four slope lengths, and (C) h contours. In each case, 9.5m of Glcndalc clay loam overlies 0.5 m of sand, q is 0.1 m year"' and slope is 5".

390

VADOSE ZONE HYDROLOGY

The soil profile consisted of a 1-m slab of clay loam overlying sand, using the soil data from figure 14.1 (following Hills et al., 1989 and Payer et al, 1992). The interface at the top of the profile and the bottom of the profile were all at a slope of /? = 5°. The lower boundary condition was a unit hydraulic gradient, the upper boundary condition was the specified flux, and there was no flow at the ends O = 0 and x = 20 m). The specified q •= q~f0p is plotted in figure 14.ISA for 11 days. For days 2-8, the precipitation values are used and for the days before and after this week the g-value was 0.1 m year"1 as mentioned above. Also shown in figure 14.ISA is the flux gBc|ow for the center of the slope and 1 m below the interface. For the first day, ^Beiow 's tne steady value. The response to each rain occurs with a delayed time of 3, 2, and 1.5 days for the three peaks, respectively. The response time obviously depends on the

Figure 14.1 3 Time-dependent velocities evaluated in the center of a sloping system for a 1-week wet period followed by an inflow of O.lm year ~'. (A) Downward Darcian fluxes at the top (#Top) and bottom (Bottom); (B) the integrated horizontal flux.

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

391

previous moisture status of the profiles. Not shown here, the simulation for a case with a similar rainfall pattern but drier initial profile showed only a single response peak for q^e]ow, which occurred 7 days after the first rain. This is because of the nonlinear properties of the unsaturated flow process. For the same reason, the maximum q value of about 9m year~' occurs here at day 9, even though the corresponding rainfall event is not the maximum. The value of
Discussion

The data in figures 14.1 and 14.2 illustrate that we may expect large spatial and temporal variations of soil moisture, and consequently recharge, in desert soils. Within a relatively small geographical area, soil recharge may vary from zero to as high as 50% of annual precipitation. Areas of suspected significant recharge include washes, playas, sand dune areas with minimal vegetation, and areas with shallow-rooted vegetation. Minimal to zero recharge may be expected in deep soil profiles on slightly sloping land with significant water-holding capacities, and vegetated with deep-rooted plants. Because of the larger variations in recharge rates, proper siting of waste-disposal facilities, including landfills in desert areas, is extremely important. Placing such facilities in high recharge areas, as has been done in the past, is not prudent. The modeling efforts shown in this chapter are for relatively simple systems, but provide a framework for examining overall subsurface flow processes. The steadystate, one-dimensional model for a sloping, layered system is the easiest to use and gives some answers of interest. For reasonable steady downward flow rates, and a fine over a coarser material, flow is deflected in the downslope direction. The amount

392

VADOSE ZONE HYDROLOGY

Figure 14.14 Velocity field for sloping system after (A) 2 days and (B) 8 days of simulating the wet week in July 1995.

of the flow moving horizontal (Q) is equal to the Darcian flow rate q multiplied by the deflected distance L. The value of Q is nearly constant for q < GAKS, where Ks is the saturated conductivity. The distance above the sloping interface over which the deflection occurs is much more if the upper layer is finer than if it is coarser—on the order of a few meters for a finer textured soil compared with less than 1 m for a coarser soil (assuming the underlying material is even more coarse). A somewhat surprising result is that the distribution of the horizontal-flow component as a function of normal distance from the slope is independent of the flow rate—at least for a Gardner (1958) conductivity function. The numerical results showed that the one-dimensional analytical approximation was valid even when the sloping medium was of limited horizontal extent. The vertical pressure profile at the upslope and downslope extremes of a 100-m-long slope, for which the vertical boundaries were blocked, was nearly identical to that in the middle of the slope and for the one-dimensional solution. The horizontal flow Q for the two-dimensional solution is a function of position along the slope. However, it was again nearly the same as that for the one-dimensional solution at

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

393

more than a few meters from the blocked vertical boundaries at the upper and lower ends of the slope. The time-dependent numerical solution demonstrated that the response time for flow deep within the profile is delayed. The time delay depends on the previous moisture status in the profile. The flow process was dominated by the properties of the overlying 1 in of clay loam for a week of the heaviest precipitation on record. The horizontal flow component reversed direction to upslope during each day of heavy rain. This response is due to the flow pattern near the upper surface boundary and is a consequence of the sloping geometry. It is not because of the interface between contrasting soils. This is consistent with the results of Philip (1991), who showed that infiltration into a dry soil is nearly normal to the slope at small times. The simulations suggest that a one-dimensional, time-dependent solution would be appropriate for estimating effects of variable surface rainfall. Of course, even though the solution is one-dimensional, there is flow in two dimensions. It is just that flow parallel to the slope interface is assumed to be independent of the slope position. This assumption appears to be valid for the steady-state examples and would presumedly carry over to the nonsteady case. The one-dimensional solution is approximately the same as that with which soil physicists are familiar for onedimensional vertical flow. The gravity term for that case would be multiplied by cos £>. This leads to the pressure profiles, flow vectors, horizontal flow, or whatever is of interest other than the effects of flow interruptions along the slope. Waste-disposal facilities in arid areas should be sited where the chances of water percolating through the waste to the groundwater are minimized. But even if the siting is correct (i.e., away from washes, local depressions, areas with only shallowrooted vegetation), significant recharge can occur through the waste when covered by a thin layer of soil that has a small water-holding capacity and/or minimal vegetation. However, a good understanding of the factors that affect recharge in arid areas allows the design of waste-disposal areas such that water flow through the waste layer is minimal. For example, placement of a thick layer of loam soil with a large water-holding capacity over the waste, and revegctating the soil with deep-rooted plants, should minimize water reaching the underlying waste. It is also possible to divert water away from the waste by placing soil in sloping layers of contrasting hydraulic properties above the waste, as demonstrated here and elsewhere.

References Berndtsson, R. and H.S. Chen, 1994, Variability of soil water content along a transect in a desert area, J Arid Environ., 27, 127-139. Cable, D.R., 1977, Soil ratio changes in creosote bush and bur-sage during a dry period in Southern Arizona, J. Ariz. Acad. Sci., 12, 15-20. Earthinfo, 1994, CD2NCDC Summary of the Day, Earthinfo, Inc., Boulder CO (manual and compact disc). Payer, M.J., M.L. Rockhold, and M.D. Campbell, 1992, Hydrologic modeling of protecting barriers: comparison of field data and simulation results, Soil Sci, Soc. Am. J., 56, 690-700. Gardner, W.R., 1958, Some steady state solutions of the unsaturated flow equation with application to evaporation from a water table, Soil Sci., 85, 228-232.

394

VADOSE ZONE HYDROLOGY

Gee, G.W. and S.W. Tyler, 1994, Symposium: recharge in arid and semiarid regions, Soil Sci. Soc. Am. J., 58, 5. Gee, G.W., M.J. Payer, M.L. Rockhold, and M.D. Campbell, 1992, Variations in water balance and recharge rates at three western desert sites, Soil Sci, Soc. Am. J., 58, 63-72. Herbel C. and L.H. Gile, 1973, Field moisture regimes and morphology in some arid land soils in New Mexico. In Field Water Regimes. Soil Science Society of America, Madison, WI, pp. 119-152. Hills, R.G., I. Porro, D.B. Hudson, and P.J. Wierenga, 1989, Modeling one-dimensional flow into very dry soils. 1. Model development and evaluation, Water Resour. Res., 25, 1259-1269. IT Corporation, 1994, Use of engineered soils and other site modifications for lowlevel radioactive waste disposal. DOE/LLW-207, National Low-Level Waste Management Program, U.S. Department of Energy. Nash, M.S., P.J. Wierenga, and A. Gutjahr, 1991, Time series analysis of soil moisture and rainfall along a transect in arid rangeland, Soil Sci., 152, 189-198. National Research Council, 1976, The Shallow Land Burial of Low-Level Radioactive Contaminated Wastes, National Academy of Sciences, Washington, DC. National Research Council, 1995, Ward Valley. An Examination of Seven Issues in Earth Sciences and Ecology, National Academy of Sciences, Washington, DC. Pan, L. and P.J. Wierenga, 1995, A transformed pressure head-based approach to solve Richards equation for variably saturated soils, Water Resour. Res., 31, 925-931. Pan, L.H. and P.J. Wierenga, 1997, Improving numerical modeling of two-dimensional water flow in variably saturated, heterogenous porous media, Soil Sci. Soc. Am. J., 61, 335-346. Pan, L.H.. A.W. Warrick and P.J. Wierenga, 1997, Downward water flow through sloping layers in the vadose zone: time-dependence and the effect of slope length, J. Hydrol., 199, 36 52. Petersen, K.L., S.O. Link, and G.W. Gee, 1995, Hanford site long-term surface barrier development program: fiscal year 1994 highlights, Report PNL-10605/ UC-702, Battelle Pacific Northwest Laboratory. Philip, J.R., 1991, Hillslope infiltration: planar slopes, Water Resour. Res., 27, 109117. Phillips, F.M., 1994, Environmental tracers for water movement in desert soils of the American Southwest, Soil Sci. Soc. Am. J., 58, 15-24. Rockhold, M.L., M.J. Payer, C.T. Kincaid, and G.W. Gee, 1995, Estimation of natural groundwater recharge for the performance assessment of a low-level waste disposal facility at the Hanford Site, Report PNL-10508, Battelle Pacific Northwest Laboratory. Ross, B., 1990, The diversion capacity of capillary barriers, Water Resour. Res., 26, 2625-2629. Ross, B., 1991, Reply, Water Resour. Res., 27, 2157. Shreve, F., 1934, Rainfall runoff and soil moisture under desert conditions, Annu. Assoc. Am. Geor., 24, 131-156. Steenhuis, T.S., J.-Y. Parlange, and K.-J.,S. Kung, 1991, Comment on "The diversion capacity of capillary barriers" by Benjamin Ross, Water Resour. Res., 27, 2155-2156. Van Genuchten, M.Th., 1980, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898. Warrick, A.W., P.J. Wierenga, and L. Pan, 1997, Downward water flow through sloping layers in the vadose zone: analytical solutions for diversions, J. Hydrol., 192, 321-337.

WATER FLOW IN DESERT SOILS NEAR BURIED WASTE REPOSITORIES

395

Wierenga, P.J., J.M.H. Hendricks, M.H. Nash, J. Ludwig, and L.A. Daugherty, 1985, variability of soil and vegetation with distance along a transect in the Chihuahuan Desert, J. Arid Environ. 13, 53-63. Wierenga, P.J., D.B. Hudson, R.G. Hills, I. Porro, M.R. Kirkland, and J. Vinson, 1990, Flow and transport at the Las Graces Trench Site, NUREG/CR-5607, U.S. Nuclear Regulatory Commission. Winkworth, R.E., 1969, The soil water regime of an arid grassland (Eragrostis eriopada Benth) community in central Australia, Agric. Meteor., 7, 387-399. Winograd, I.J., 1974, Radioactive waste storage in the arid zone, Trans. Am. Geophys. Union, 55, 884-894. Zaslavsky, D. and G. Sinai, 1981, Surface hydrology: III. Causes of lateral flow, J. HydrauL, 107, 37-52.

15

Site-Specific Management of Flow and Transport in Homogeneous and Structured Soils

D. j. MULLA A. P. MALLAWATANTRI O. WENDROTH M. |OSCHKO H. ROGASIK S. KOSZINSKI

Among research publications in soil science, few have had a greater impact than those by Nielsen et al. (1973) or Biggar and Nielsen (1976). According to Science Citation Index, the former paper, entitled "Spatial variability of field-measured soilwater properties," has been cited by scientific peers over 390 times. The 1976 paper, entitled "Spatial variability of the leaching characteristics of a field soil," has been cited over 232 times. Experimental work presented in both papers represents the first-ever attempt at a large field-scale study of steady-state water and solute transport (Wagenet, 1986). Among the seminal findings of these two papers were as follows: (1) extensive spatial variability existed in soil hydraulic and solute transport properties within a relatively homogeneous field (important in the work of Pilgrim et al., 1982; Addiscott and Wagenet, 1985; Feddes et al., 1988; van dcr Molen and van Ommen, 1988); (2) soil water content, bulk density, and soil particle size exhibited normal frequency distributions, while distributions for hydraulic conductivity, hydraulic diffusivity, pore water velocity, and hydrodynamic dispersion were lognormal (work extended by van der Pol et al.. 1977; Rao et al., 1979); (3) frequency distributions were far superior to field-average parameter values (especially for lognormally distributed properties) in describing field transport behavior (demonstrated by Rao et al., 1979; Trangmar et al., 1985); (4) a simple unit hydraulic gradient method was shown to estimate saturated hydraulic conductivity accurately (results extended by Libardi et al., 1980; van Genuchten and Leij, 1992); (5) good correspondence was found between solute

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

397

velocity and pore water velocity (key assumption in Jury and Fluhler, 1992); and (6) theoretical predictions of a linear relation between hydrodynamic dispersion and pore water velocity were shown to be obeyed at the field scale (result used widely by solute transport modelers, as discussed in Nielsen et al., 1986). The seminal works by Nielsen et al. (1973) and Biggar and Nielsen (1976) produced several new directions in soil science and vadose zone hydrology research. The most interesting was a series of papers that rejected the theoretical basis and practicality of using deterministic equations, and instead introduced stochastic approaches to describe field-scale water and solute fluxes. Warrick et al. (1977) used a stochastic Monte-Carlo method to show that field-scale variability in soil water flux could be accurately estimated only if large numbers (100-1000) of samples were generated. Bresler and Dagan (1979) used data from the two seminal papers by Nielsen and Biggar to show that solute concentration variability could be modeled at the field scale using a statistical distribution for pore water velocity. In their analysis, they concluded that it was neither practical nor necessary to include solute dispersion as a model parameter for shallow soil investigations. Amoozegar-Fard et al. (1982) used a Monte-Carlo simulation to evaluate the relative importance of field-scale variability in pore water velocity, water content, and dispersion, and found that spatial variations in velocity were of far greater importance than variations in dispersion. Jury (1982) used the Nielsen et al. (1973) and Biggar and Nielsen (1976) frequency distributions as the basis for proposing a lognormal travel time density function in a transfer function model for solute transport at the field scale. The paper by Biggar and Nielsen (1976) stimulated the transition in solute transport research from an emphasis on the laboratory scale to the field scale. Their results also spurred the beginning of a decade-long debate over the importance of uniform displacement flow versus preferential flow (Kissel et al., 1974; Quisenberry and Phillips, 1976; Starr et al., 1978). The description of soil heterogeneities that contribute to preferential flow is now a key issue in field-scale solute transport research. Two case studies influenced by the research of Nielsen and Biggar are presented in the remainder of this chapter. The first describes a field-scale study in which sitespecific estimates are made of pesticide leaching loss risks. This study emulates the Biggar and Nielsen (1976) paper by characterizing solute transport using an anionic tracer, and fitting measured solute concentrations to the convective-dispersive equation (CDE) to obtain spatial patterns in pore water velocity and dispersion. The second case describes a field-scale study in which spatial variability of soil hydraulic properties and infiltration rates are characterized. This study extends the Nielsen et al. (1973) paper by evaluating the feasibility of predicting measured soil hydraulic properties from soil structure classifications obtained using x-ray computed tomography (CT).

First Case Study: Effects of Spatial Variability on Risk Assessment of Metribuzin Leaching At the field scale, there is growing interest in using precision farming (Larson and Robert, 1991) to control runoff (Khakural et al., 1994) and leaching (Mulla and

398

VADOSE ZONE HYDROLOGY

Annandale, 1990; Mallawatantri and Mulla, 1996) of agrichemicals applied to farms. Precision fanning allows chemical inputs to be varied by rate and form according to site-specific needs and conditions (Sawyer. 1994). The key to implementation of precision farming recommendations is an accurate map that shows spatial patterns in the factors used as a basis for management decisions (Mulla, 1993). When the objective is reductions in leaching losses of pesticides, an accurate map that shows spatial patterns in predicted leaching losses is needed (Mulla et al., 1996). Estimation of dispersion and its spatial variability at the field scale is difficult and time-consuming (Biggar and Nielsen, 1976). Yet, solute dispersion in heterogeneous media is recognized as one of the most important factors that influences the contamination of water resources by chemicals moving through soil (Sposito et al., 1986). In an attempt to simultaneously account for dispersion effects and reduce the difficulty of accounting for its spatial variability, some authors have estimated leaching loss risks using field-average values for dispersion (League et al., 1989; Kleveno et al., 1992). Even simpler approaches for estimating risks of leaching are based upon predicting movement of the solute center of mass (Nofziger and Hornsby, 1987; League, 1991). By considering only the movement of the center of mass of a chemical, the effects of dispersion are neglected. Dispersion controls the concentration and timing of the initial arrival of the solute at the water table. When the toxicity of a given chemical is high or the concentration of the initial arrival is high enough to pose a contamination hazard, accurate estimation of solute dispersion may be critical. Management of environmental degradation by non-point-source agrochemical residues requires an accurate understanding of the uncertainties associated with using different approaches for risk assessment. Understanding is needed of the effects of spatial variability in solute dispersion, pore water velocity, and other parameters that influence the accuracy of leaching risk assessments (Amoozegar-Fard et al., 1982). In particular, it is important to understand the effect of ignoring dispersion or using field-average estimates for dispersion in risk assessments.

Objectives Our objectives in this study were: 1. To evaluate spatial variability in pore water velocity and solute dispersion in a large vegetated, irrigated field; 2. To compare the results of risk assessments for agrochemical leaching using various combinations and spatial averaging techniques for transport parameters in the CDE model.

Materials and Methods Study Site and Data Collection Data on bromide leaching were collected from 40 experimental plots established in a 57-ha commercial potato field near George, Washington. Soil types at the site

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

399

include Quincy loamy fine sand (mixed, mesmic, Xeric Torripsamment) and Timmerman coarse sandy loam (sandy, mixed, mesic, Xerollic Camborthid). Four north-south transects (parallel to potato rows) approximately 800m long and 60m apart were marked, and in each transect ten 13-m2 plots (3.1 x 4.3m) were established. Two manual (funnel and a bottle) rain gauges and a neutron access tube were installed in each plot. Thirty-three days after planting Russet Burbank (Solarium tuberosum) potatoes, a pulse of 21.25 g Br~ m~ 2 was sprayed using a bromide solution of 50.0 gL~'. In addition to plot measurements of irrigation and soil moisture, measurements were taken of solar radiation, wind speed, and relative humidity at a weather station on the edge of the field. Field capacity water contents were estimated from particle size data measured in each plot (Campbell, 1985). Soil organic carbon contents measured in the same field by Mulla and Annandale (1990) were used to estimate pesticide sorption coefficients for each plot. Soil samples to a 70-cm depth from furrow locations in each plot were obtained 15 days after spraying bromide. Soil samples in the depth ranges of 0-10, 10-25, 2540, 40-55, and 55-70cm were composited in each plot. Bromide concentration in airdry soil was determined in the laboratory using a bromide ion-specific electrode (Abdalla and Lear, 1975). Resident concentrations of bromide in soil depths were calculated using the bulk density and soil moisture content at sampling depths measured at the time of soil sampling. Parameter Estimates for the CDE Model

The CXTFIT program (Parker and van Genuchten, 1984) was used to estimate the pore water velocity (u) and dispersion coefficient (D) in each of the 40 plots sprayed with bromide. Bromide resident concentrations at different depths were fitted to the linear equilibrium adsorption model. The retardation factor (R) for bromide sorption in soil was assumed to be unity. Background bromide concentrations in the soil were less than O.SmgL" 1 , and were assumed to be zero. Several scenarios were investigated to illustrate the effects of using field-averaged solute transport parameters in risk assessments. The effect of using varying levels of information about dispersion and pore water velocity on the accuracy of risk assessment was examined. Pore water velocities and dispersion coefficients estimated using CXTFIT for each plot were used to calculate field-scale average values. The pesticide metribuzin was selected as the model chemical, since it is heavily used in commercial potato production. The fate of metribuzin during a 75-day period was predicted using the behavior assessment model (BAM) of Jury et al. (1983). The critical depth for leaching risks to groundwater was assumed to be 2 m, which is the depth of the deepest rooted crop grown at the site. A leached factor (LF) was defined as:

where / is the time (75 days), T\/2 is the half-life of metribuzin (37 days), z is the critical depth (2 m), C0 is the initial concentration, and CT is the total concentration of metribuzin in gas, solid, and solution phases at any given depth from the BAM

400

VADOSE ZONE HYDROLOGY

(Jury et al., 1983). The BAM assumes linear equilibrium adsorption, and Henry's law partitioning between vapor and liquid phases. Dispersion coefficients and pore water velocities estimated using CXTFIT from measured bromide concentrations were used in the analytical solution for BAM to calculate total metribuzin concentration. Values for the organic carbon partition coefficient (Koc), Henry's constant (KH) and half-life for metribuzin (T{/2) were obtained from Jury el al. (1987; see also table 15.1). The first term in equation (15.1) represents the fraction of metribuzin present at a given time following first-order degradation. The second term represents the fraction of metribuzin residing in the zone between the surface and the critical depth of 2 m. Hence, LF represents the relative mass of metribuzin leached below the critical depth. Log /./•'-values were used as an indicator of potential leaching risks for metribuzin according to criteria in table 15.2. To understand the effects of velocity and dispersion, LF-values for each field plot were calculated using the following five different scenarios: 1. 2. 3. 4. 5.

Field-average pore water velocity and zero dispersion, Plot-scale pore water velocity and zero dispersion, Field-average pore water velocity and field-average dispersion, Plot-scale pore water velocity and field-average dispersion, Plot-scale pore water velocity and plot-scale dispersion.

For each of the scenarios, one simulation was run for each of the 40 experimental plots. In each simulation, measured values from each plot were used for organic carbon content and field-capacity water content (table 15.3). The only difference between simulations was in the selection of values for pore water velocity (v) and dispersion (D). Field-averaged values for v and D were estimated from frequency distributions of v and D (table 15.3) obtained from the CXTFIT analysis of measured bromide

Table 15.1 Soil, Pesticide, and Environmental Parameters Used in the Behavior Assessment Model (Jury et al., 1983) to Estimate Metribuzin Concentrations and the LF-lndcx Parameter Bulk density Time for leaching Critical depth of leaching Relative humidity Temperature Boundary layer thickness Depth of incorporation K*. Half-life Henry's law constant Diffusion in water

Value 1.60gem"3 75 days 200 cm 0.5 298 K 0.475cm 1 cm 24m 3 kg-' 37 days 0.0000001 0.43 cm2 day"1

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

401

Table 15.2 Mctribuzin Leaching Risks Based on the LF-Index -Log (LF)

Risk Category

<0 0-1 1 2 2 3 >3

Very high High Moderate Low None

concentration data in all 40 plots. For each simulation, equation (15.1) was then used to estimate the leached fraction of metribuzin.

Results and Discussion Estimation of CDE Parameters There was excellent agreement between measured and predicted (using the linear equilibrium model) concentrations of bromide in soil at different depths in 40 plots on the first sampling (figure 15.1). These results confirm Biggar and Nielsen's (1976) findings that the CDE model can be used to adequately describe field-scale solute leaching behavior. Considerable spatial variability existed within the field for pore water velocity and dispersion. The coefficient of variation (CV) for pore water velocity was 36%, while the CV for the dispersion coefficient was 83% (table 15.3). The observed CV for velocity in the 57-ha field is much less than the CV of 58% observed by Jury (1982) within a 0.58-ha area, or the CV of 165% observed by Biggar and Nielsen (1976) within a 150-ha field. In contrast to the study by Biggar and Nielsen (1976), no significant linear relationship was observed between v and D. This may have been due to nonuniform and transient water flow caused by noncontinuous irrigation, plant root uptake, and redistribution. Effect of Dispersion and Velocity on Risk Assessment Based on the Behavior Assessment Model and the five risk categories in table 15.2, the 57-ha field was divided into zones with differing risks of metribuzin leaching Table 15.3 Estimated Transport Parameters and Soil Characteristics Used as Input for the Behavior Assessment Model (Jury et al., 1983) Property Pore water velocity (cm/day) Dispersion coefficient (cm /day) Field capacity water (cm 3 /cm 3 ) Organic carbon fraction

Average

SD

Min.

Max.

1.83 6.18 0.13 0.006

0.66 5.14 0.02 0.001

0.90

3.34 27.97 0.17 0.008

1.73

0.09 0.004

402

VADOSE ZONE HYDROLOGY

Figure 15.1 Relationship between measured versus convective-dispersive fitted bromide concentrations.

(table 15.4) for each of five input parameter scenarios. Our best estimate of leaching risks is represented by scenario 5, in which information was utilized on the spatial variability in both velocity and dispersion. In this scenario, about 0.5 ha is at high risk for leaching losses, 2.0 ha is at moderate risk, and 9.3 ha is at low risk. There are also 42.5 ha without any risk of metribuzin leaching losses. In contrast, when dispersion was ignored (scenarios 1 and 2), there was no risk of leaching losses in any part of the field. Therefore, by ignoring dispersion we tend to seriously underestimate leaching risks at the field scale. Using values for field-average dispersion with average velocity (scenario 3) or with spatially variable velocity (scenario 4) produced results that were nearly identical. In particular, the area in the low-risk category increased to about 39 ha using average velocity versus 34 ha using variable velocity. Both of these values are significantly larger than the best estimate of only 9 ha in the low-risk category. While assuming average values for dispersion overestimates the area having low risks, it

Table 15.4 Effect of Varying Pore Water Velocity (v) and Dispersion Coefficient (D) on Risk Assessments for Metribuzin Leaching Below 200cm. Scenario

Risk Category

No

Low

Moderate

High

Aeral Coverage (ha) 1 . Average v and zero D 2. Variable v and zero D 3. Average v and Average D 4. Variable v and Average D 5. Variable v and Variable D

57.0 57.0 18.1 22.8 45.2

0 0 38.9 34.0

9.3

0 0 0 0.2 2.0

0 0 0 0 0.5

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

403

also resulted in underestimating the areas having moderate and high risk. Identifying small areas with high risks may be difficult if average values for dispersion are assumed. These results show the importance of spatial variability in dispersion for estimating risks of pesticide leaching. The northeast portion of the field generally had the highest leaching loss risks (figure 15.2). This region has a sandy soil texture, which is somewhat more susceptible to leaching losses than other portions of the field. Also, measurements of sprinkler irrigation application depth showed larger applied depths in the northeast portion of the field, probably because the prevailing direction of wind was from the southwest to northeast. Thus, the region with highest leaching loss risks generally corresponds to the region that has coarser soil texture and larger depths of applied water. For management decisions, it may be possible to estimate leaching loss risks from easily measured properties, such as soil texture and irrigation depth (Mulla and Annandale, 1990), rather than properties that are difficult to measure, such as solute velocity and dispersion.

Conclusions: First Case Study Bromide transport in irrigated sandy soils was consistent with linear equilibrium convective-dispersive transport theory. Estimated values for pore water velocity and the dispersion coefficient from the latter theory exhibit significant spatial variability. Risk assessments for leaching were more sensitive to proper estimation of dispersion than estimation of pore water velocity. Using plot-scale values for both dispersion and pore water velocity showed that risks for metribuzin leaching at the 57-ha study site were high for 0.5 ha of the field, moderate for 2.0 ha, low for 9.3 ha, and nil for 45.2 ha. Risk of metribuzin con-

Figure 1 5.2 Spatial distributions of leaching loss risks using spatially variable velocity and dispersion inputs to the LF-model.

404

VADOSE ZONE HYDROLOGY

lamination was severely underestimated (all 57 ha with no risk) when dispersion was ignored. Overestimation of risks was seen when field-average dispersion was used with average or plot-scale pore water velocity. High leaching risk areas in the field (0.5 ha) were not identified using either zero or average values for dispersion. It is important to account for spatial variations in dispersion when estimating the leaching risk of agrichemicals. Neglecting dispersion in risk assessments caused significant overcstimation of the area with no leaching risk. Using average values for dispersion caused significant Overestimation of areas with low leaching risks and failed to identify small areas with high leaching risks. These findings suggest that management of leaching risk must focus on strategies that minimize leaching from the most vulnerable regions, rather than the field-average behavior.

Second Case Study: Spatial Variability in Soil Hydraulic Properties and Soil Morphology Soil hydraulic properties affect water infiltration and runoff, water storage, leaching of solutes, and evaporation within agricultural field soils. Soil management can often be improved with an accurate understanding of the field-scale spatial variation in the latter soil processes. Soil water transport and storage properties are highly influenced by the state of the soil structure and soil texture (Brewer and Slceman, 1960; Ehlers et al., 1995). The importance of classifying soils according to their structure for predicting water and chemical transport has been frequently expressed (Quisenberry et al., 1993). Soil structural elements may be considered as regionalized variables. Their arrangement determines site-specific storage and transport functions. The spatial pattern of structural types at the field scale may control large-scale vadose zone hydrology. However, evidence for the latter aspect of soil structural variability on a field scale is rare, possibly because rapid methods to assess soil structure using large numbers of samples are scarce (Moran et al., 1989). The water-retention curve (soil hydraulic pressure head h as a function of soil water content 9) and the hydraulic conductivity function (hydraulic conductivity K as a function of h) are controlled by various pore domains that range between soil structure and texture. The drier portions of the water-retention curve and hydraulic conductivity function are controlled by pedogenic macroporcs and smaller pores that are, in turn, strongly influenced by soil texture rather than by soil structure. Many rapid, precise methods for measuring soil hydraulic functional properties are currently available (Eching and Hopmans, 1993; Tamari et al., 1993; Wendroth et al., 1993a; Eching ct al., 1994), even for the wet range where soil structure dominates hydraulic properties (Perroux and White, 1988; Booltink et al., 1991). X-ray computed tomography, a relatively new approach, provides improved opportunities to nondestructively investigate soil macropore space (Joschko et al., 1991, 1994; Anderson and Hopmans, 1994; Hcijs ct al., 1995). A combination of the above methods may contribute to the causal analysis of observed functional patterns in hydrologic processes of variably saturated soil. And,

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

405

if this combination of methods is applied to field-scale studies, the spatial covariance structure (Shouse et al., 1995) and spatial coincidences between soil and morphological features (Greminger et al., 1985; Buchter et al., 1991) may be used to describe site-specific variations of pore and functional features that would suggest better management alternatives. The aims of this study were (1) to determine the spatial variance structure of soil hydraulic properties, (2) to assess the spatial pattern of soil structure type and pores, (3) to identify zones of higher drainage potential via numerical simulation, and (4) to identify coincidence between functional [0(h), K(h), drainage potential] and morphological soil parameters as a basis for sustainable site-specific field management decisions. Materials and Methods Study Site The field site is located in the area of Boelkendorf, 60km northeast of Berlin, Germany. The soil types along this catena, typical for the northeast German morainal landscape, were Lithic Udorthent (FAO: calcareous regosol), Rhodoxeralf (calcic luviso), Humudalf (humic luvisol), and Paleustalf (humic planosol), from the top to the bottom of the catena. In general, soil texture in the Ap horizon was a sandy loam. The site, which is under agricultural management, was cropped to rape seed (Brassica napus) at the time of sampling, and is characterized by relatively large populations of earthworms (162m~ 2 ).

Sampling In spring 1993, at 50 locations along a transect, a soil core was sampled every 1.8m in the Ap horizon (4-22 cm depth) in plexiglass cylinders (height 18cm, i.d. 19cm). Within 10cm of each soil-core sampling location, a sample was taken for soil textural analysis and field surface water content Of.

Experimental Two days after sampling, soil cores were scanned in a hospital with a Siemens Somatom Plus CT scanner (Siemens AG, Hafenstrasse 60, 38112 Braunschweig, Germany) at 120kV, 330 mAs, zoom 2.4, with a slice thickness of 1mm at 1-cm intervals. The size of a picture element (pixel) was 0.4mm x 0.4mm. The scan slices were fixed on radiographic film and subsequently transferred via a video camera into an image analysis system. For pore analysis of each scan slice, a threshold density of 18 units out of a 128value density scale was used. The following pore classes (PC) were distinguished according to pore area in scan slices: 0.002 < (PC 1) < 0.004cm2, 0.002 < (PC 2) < 0.070cm2, and 0.02 < (PC 3) < 1.00 cm2. The latter pore class could have been produced by earthworms. Five soil cores from location nos. 9, 31, 34, 40, and 49 were

406

VADOSE ZONE HYDROLOGY

consecutively scanned with a slice thickness of 1 mm. The CT data were saved on magnetic tape and processes according to Joschko et al. (1991). A segmentation threshold of 10 units out of a 256-value density scale was used. Macropores > 1 mm were subsequently visualized in three dimensions. Soil cores stored at 4°C after scanning were randomly chosen for hydraulic conductivity measurement. For determination of K in the range close to soil water saturation (h = —10, —5, and —1 cm, respectively), a lab version of a disc infiltrometer device was used for supplying water to the top of the soil core with a constant, predetermined pressure head. The soil core was placed on a porous plate that provided the same negative pressure head at the bottom of the core as that at the top of the core. When the water infiltration rate became constant, it was used to calculate the value of K according to the Darcy equation. After the infiltration experiment was completed, a soil core sample was taken in a stainless steel cylinder (height 6cm, i.d. 8 cm) from the center of the larger plexiglass-encased soil core. This smaller soil core was subsequently used in an evaporation experiment to obtain the water-retention curve and the hydraulic conductivity function in the range between —30cm and —450cm of pressure head (Wendroth et al., 1993a). Theory

Spatial distribution and spatial structure of soil water content and hydraulic conductivity at predetermined pressure heads were analyzed using semivariograms (Isaaks and Srivastava, 1989). The spatial process of hydraulic conductivity at a given pressure head was described with a state-space model, a special autoregressive technique. In the statespace analysis, the process or development of a variable through time or space is considered in a way that the state of one variable or a set of p-variables at location i is linked by some kind of function or model to the state at location / — 1 plus an error term. In our case, the state vector Z, is linked to Z,_! in a first-order autoregressive model. The state equation is then

where $ is a p*p matrix of state coefficients that indicate the measure of spatial regression and &>,- is the uncorrelated zero mean model error. In the state-space methodology, the observation of a system's state is not taken to be true but the state vector or the state variable is embedded in an observation equation given by

where 7, is the observed vector, related via an observation matrix Mf to the true state vector Zt plus an uncorrelated mean zero observation error vh which is due to uncertainties in the measurement itself, the calibration, and the reproducibility. In the state-space methodology, the propagation of the system is estimated or predicted. Unlike in ordinary autoregressive approaches, the prediction is then updated based on the state of available observations and on both error components cot and v,. In most cases, these error components are not known well and can be estimated together with the ^-matrix. This simultaneous solution was obtained in

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

407

our case with the so-called Kalman filter technique (Kalman, 1960). Initial estimates of the ^-matrix, the spectral density—that is, the variance of a)t—and the measurement variance are given and optimized iteratively. For further details, see Shumway (1988), Katul et al. (1993), Parlange et al. (1993), Wendroth et al. (1993b), and Nielsen et al. (1994). In our case, the spatial process of K(h)f was described in a first-order state-space model. That way, the spatial coherence of K(K), clay content, and Of was determined. For modeling soil water transport and estimating potential drainage losses, Richards' equation was integrated using a one-dimensional finite difference scheme developed by J.W. Hopmans (personal communication) and described by Wendroth et al. (1993a). As model input, water-retention curves were parameterized according to van Genuchten (1980) and polynomials were fitted to measured A^(/z)-relations. The initial pressure-head distribution was taken as that for hydraulic equilibrium above a water table at the 1-m soil depth. The rate of applied water was 30mm day"1. These conditions are considered typical of those prevailing during spring time at the experimental site. The amount of water simulated to be moving downward through the 30-cm soil depth was considered to be the drainage flux potential.

Results and Discussion So/7 Structure

The structure of each soil core was classified according to the main structure elements on the scan slices. Three structure types were visually distinguished, covering a range between 1 and 3 with increasing number of structure elements. Structure type 1 is characterized by biogenic macropores embedded in a dense soil matrix, type 2 by pedogenic macropores in a dense soil matrix with fractures, and type 3 is characterized by a heterogeneous soil structure severely influenced by biotic activity—namely, soils that have a large number of animal burrows, casts, and root channels (figure 15.3). This morphological classification led to an approximately equal number of soil cores in the three classes. Type 1 was found in the calcareous regosol at the top and bottom of the catena (figure 15.4). Fractures in scan slices (type 2) were dominant in soil cores from the humic luvisol. Their appearance seemed to coincide with soils that have clay contents >0.15gg~' (figure 15.4). Although type 3 was distributed across the entire transect, it occurred primarily between positions 29 and 40 (figure 15.4). Three out of the four highest /T(//)-values at h — — 1 cm were linked to structure type 3, manifesting a structure produced by biotic activity. The average number of pores in the three size classes (PC 1, PC 2, and PC 3, respectively) determined from 15 CT-scan slices within each core showed high variability across the catena. A spatial range of autocorrelation was not clearly manifested. In a similar investigation, Koszinski et al. (1998) were not able to detect a spatial range of influence for micromorphometrically determined pore numbers.

Figure 15.3 Soil structure types 1, 2, and 3 respectively, present across the catena.

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

409

Figure 15.4 Spatial distribution of clay, and sand content, and of the structure type across the catena. Soil Hydraulic Properties Soil water content values (fy) across the transect are presented for predetermined pressure heads of h = —10, —30, —100, and —300cm, and for the conditions during soil sampling (figure 15.5a). In figure 15.5b, values of K(h) are shown for h — —\, —5, —10, —100, and —300cm. With decreasing h, 6 and K show increasingly more systematic patterns, reflecting the spatial pattern in soil clay content. The semivariograms show an increasing range of spatial correlation for 0(h) with decreasing h (not shown). Hydrauli conductivity K(h) = —1 cm varies randomly; that is, y(l) is a pure nugget effect, whereas the range is approximately 9m for h — —5 and h = -10cm and further increases with decreasing /) (figure 15.6). Hence, a unique range of spatial dependence for soil hydraulic properties does not exist owing to the fact that the variance structure depends upon the value of h. Hydraulic conductivity was modeled as a first-order autoregressive process. For predetermined pressure-head conditions (—50 and —300cm, respectively), K at location i is a function of K, clay content, and Of at location ; — 1 (figures 15.7a and b). In order to evaluate the estimation quality for locations assumed to be unobserved, every other A'-observation was left out in the parameter estimation. Afterwards, estimated values could be compared with measured values. For both /i-conditions, the accuracy of estimation using state-space analysis was promising. Notice the extreme oscillation of estimated K(—300cm) confidence intervals at the first five locations (figure 15.7b). The magnitude of the oscillation may be due to the higher impact of clay,_i and 6tl_\ compared with K(—50cm). Another reason for the oscillation is that the processes of K(—300cm), clay and 9f seem to follow a slightly different relationship at the first five locations than for the following 45 locations; that is, K(—300cm) stays relatively constant from locations 1 through 5 with both clay and Oj- increasing, whereas .^(-300 cm) proceeds inversely related to clay and 9f from locations 6 through 50. Although K-0-h functions are known to be related to clay content for a wide range of differently textured soil types, it can be difficult to estimate the spatial

410

VADOSE ZONE HYDROLOGY

Figure 15.5 Spatial distribution of (a) soil water Of and (b) hydraulic conductivity K at predetermined pressure heads h across the catena. The symbol Of denotes the surface field water content at the time of sampling. process of K(h)t for a particular field site by ordinary regression or pedotransfer functions based on clay content. The advantage of using a first-order state-space approach for modeling the spatial process of K(h)t is that the impact of several other variables beside clay and Of on K(h)t can be integrated by introducing the model uncertainty and by basing the estimation on neighboring observations. Under soil water conditions where hydraulic conductivity is mainly influenced by soil structure (at h = — 1 cm) and where a spatial range of K could not be identified, the distribution of K cannot be described using an autoregressive model. This result is probably due to the random nature of spatial variation in soil structure rather than measurement uncertainty of K close to soil water saturation. To illustrate the relationship between the number of pores in size class 1 (0.002 < PC 1 < 0.004cm2) and K(— 1cm), the number of pores within PC 1 for each scan slice in each core was aggregated for each core by averaging results from three groups

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

411

Figure 15.6 Semivariograms for hydraulic conductivity at various pressure heads h.

of five scan slices. The lowest of these three average values (nPm[n) represents the smallest cross-sectional area in PC 1, and controls the upper limit of water flux through pores of that size. Hydraulic conductivity values at h = — 1 cm and nPm^n are plotted versus distance along the transect in figure 15.8. Although log[A"(—1 cm)] and nPmm are hardly correlated (r = 0.2), the increase or decrease in log[A^(—1 cm)] and nPm-m from one position to the next coincides in 34 out of 49 cases as indicated by the +-symbols in figure 15.8. For several positions, noncoincidence between log[A"(—1 cm)] and nPm\n can be ascribed to earthworms that were still alive and were found when soil columns were taken apart after the experiments. They may have changed the soil structural state between CT-scanning and Admeasurement.

Drainage Potential In order to estimate drainage loss vulnerability across the catena, a scenario with a rainfall event of 30mm day"1 was simulated. The simulated amount of water that

412

VADOSE ZONE HYDROLOGY

Figure 15.7 State-space model of hydraulic conductivity K at (a) —50 and (b) —300cm of pressure head.

had percolated below the 30-cm soil depth—that is, the drainage loss DL—was taken as an indicator of the potential for drainage. Except for some large fluctuations (figure 15.9), DL coincides with soil clay content and surface water content during sampling and shows a similar spatial structure. Hence, DL could be autorcgrcssivcly described together with both of these parameters in a state-space model (figure 15.9). Moreover, when the transect was divided into three drainage loss categories, structure types 1 to 3 (figure 15.3) coincided with low, medium, and high potential, respectively, in 25 out of 50 cases. Conclusions: Second Case Study It is important to ascertain which soil parameters can be the foundation for decisions about sustainable and site-specific management of soil hydrological processes. Three

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

41 3

Figure 15.8 Hydraulic conductivity K at h = — 1 cm and limiting number of pores in scan slices, «-Pmjn.

types of soil structure were evaluated using x-ray computed tomography: namely, a type characterized by biogenic macropores in a dense soil matrix, a type characterized by biogenic macropores in a fractured soil matrix, and a heterogeneous soil structure influenced by extensive biological activity. Soil structure types 1 and 2 were largely controlled by spatial patterns in clay content, while structure type 3 was randomly distributed. Spatial patterns in unsaturated soil hydraulic conductivity at pressure heads (h) between —10 and —350cm and infiltration flux could be accurately described using state-space models based upon clay and field water content distributions. Spatial patterns in hydraulic conductivity close to soil water saturation

Figure 15.9 State-space model of cumulative downward water drainage (DL) across the 30-cm soil depth.

414

VADOSE ZONE HYDROLOGY

(h — —1cm) were uncorrelated with soil texture or water content, but coincided closely with patterns in the pore size class of 0.002-0.004 cm2. Although some subjectivity is included in structure type determination, this approach for combined morphological and functional property characterization is promising. State-space models for soil texture and soil surface water content in spring were useful for characterizing the spatial structure of important soil hydrologic functional properties and drainage potential. Morphological analyses of soil structure and pore features that vary rather randomly across a field are linked to physical properties, especially close to soil water saturation.

Summary Papers published by Nielsen et al. (1973) and Biggar and Nielsen (1976) demonstrated the importance of spatial variability in soil hydraulic properties and solute leaching characteristics at the field scale. The two case studies presented in this chapter confirm the importance of field-scale spatial variability in solute leaching risks and soil hydrologic processes. The two case studies extend the results of research by Nielsen and Biggar by demonstrating new approaches for characterizing spatial patterns in solute leaching risks or soil water drainage. These patterns can be the basis for precision farming or site-specific strategies designed to optimize fieldscale management of water and solutes by minimizing environmental degradation while sustaining crop production.

Acknowledgments O. W., M. J., H. R., and S. K. thank Dr. J. Reiger and Ms. Zimmernann, University Hospital Rudolf-Virchow, Berlin, for scanning the soil columns, D. Beutler, I. Onasch, K. Seidel, and N. Wypler for excellent technical assistance, and K. Kotzke for the three-dimensional reconstruction of pore systems. The technical support of Siemens AG regarding CT application is appreciated. O.W., M. J., H. R., and S. K. gratefully acknowledge the helpful comments of D. R. Nielsen on this manuscript.

References Abdalla, N.A. and B. Lear, 1991, Determination of inorganic bromide in soils and plant residues with a bromide selective ion electrode, Commun. Soil Sci. Plant Anal., 6, 489-494. Addiscott, T. M. and RJ. Wagenet, 1985; Concepts of solute leaching in soils: a review of modelling approaches, J. Soil Sci., 36, 411-424. Amoozegar-Fard, A., D.R. Nielsen, and A.W. Warrick, 1982, Soil solute concentration distributions for spatially varying pore water velocity and apparent diffusion coefficient, Soil Sci. Soc. Am. J., 46, 3-9. Anderson, S.H. and J.W. Hopmans, 1994, Tomography of Soil-Water-Root Processes, SSSA Special Publication No. 36, Madison, WI. Biggar, J.W. and D.R. Nielsen, 1976, Spatial variability of the leaching characteristics of a field soil, Water Resour. Res. 12, 78-94.

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

415

Booltink, H.W.G., J. Bouma, and D. Gimenez, 1991, Suction crust infiltrometer for measuring hydraulic conductivity of unsaturated soil near saturation, Soil Sci. Soc. Am. /., 55, 566-568. Bresler, E. and G. Dagan, 1979, Solute dispersion in unsaturated heterogeneous soil at field scale: II. Applications. Soil Sci. Soc. Am. J., 43, 467^72. Brewer, R. and J.R. Sleeman, 1960, Soil structure and fabric: their definition and description, /. Soil Sci., 11, 172-185. Buchter, B., P.O. Aina, A.S. Azari, and D.R. Nielsen, 1991, Soil spatial variability along transects, Soil Technol., 4, 297-314. Campbell, G.S, 1985, Soil Physics with Basic Transport Models for Soil-Plant Systems, Developments in Soil Science, 14, Elsevier, New York. Eching, S.O. and J.W. Hopmans, 1993, Optimization of hydraulic functions from transient outflow and soil-water pressure data, Soil Sci. Soc. Am. J., 57, 11671175. Eching, S.O., J.W. Hopmans, and O. Wendroth, 1994, Unsaturated hydraulic conductivity from transient multistep outflow and soil water pressure data, Soil Sci. Soc. Am. J., 57, 1167-1175. Ehlers, W., O. Wendroth, and F. de Mol, 1995, Characterizing pore organization by soil physical parameters, in K.H. Hartge and B.A. Stewart, Soil Structure—Its Development and Function, Advances in Soil Science, Lewis, New York, pp. 257-275. Feddes, R.A., P. Kabat, P.J.T. van Bakel, J.J.B. Bronswijk, and J. Halbertsma, 1988, Modelling soil water dynamics in the unsaturated zone—state of the art, /. Hydrol. 100, 69-111. Greminger, P.J., K. Sud, and D.R. Nielsen, 1985, Spatial variability of field-measured soil-water characteristics, Soil Sci. Soc. Am. J., 49, 1075-1082. Heijs, A.W.J., J. de Lange, J.F. Th. Schoute, and J. Bouma, 1995, Computed tomography for non-destructive analysis of flow patterns in macroporous clay soils, Geoderma, 64, 183-196. Isaaks, E.H. and R.M. Srivastava, 1989, Applied Geostatistics, Oxford University Press, New York. Joschko, M., O. Graff, P.C. Miiller, K. Kotzke, P. Lindner, D.P. Pretschner, and O. Larink, 1991, A non-destructive method for the morphological assessment of earthworm burrow systems in three dimensions by X-ray computed tomography, Biol. Pert. Soils, 11, 88-92. Joschko, M., O. Wendroth, H. Rogasik, and K. Kotzke, 1994, Earthworm activity and functional and morphological characteristics of soil structure, Proceedings of the 15th Conference oflSSS, Vol. 4a, pp. 144-162. Jury, W.A., 1982, Simulation of solute transport using a transfer function model, Water Resour. Res., 18, 363-368. Jury, W.A. and H. Fluhler, 1992, Transport of chemicals through soil: mechanisms, models, and field applications, Adv. Agron., 47, 141-201. Jury, W.A., W.F. Spencer, and W.J. Farmer, 1983, Behavior assessment model for trace organics in soil: I. Model description, J Environ. Qual. 12, 558-564. Jury, W.A., D.D. Focht, and W.J. Farmer, 1987, Evaluation of pesticide groundwater pollution potential from standard indices of soil-chemical adsorption and biodegradation. /. Environ. Qual. 16, 422^28. Kalman, R.E., 1960, A new approach to linear filtering and prediction problems, Trans. ASME J. Basic Eng., 8, 35-45. Katul, G.G., O. Wendroth, M.B. Parlange, C.E. Puente, and D.R. Nielsen, 1993, Estimation of in-situ hydraulic conductivity function from nonlinear filtering theory, Water Resour. Res., 29, 1063-1070. Khakural, B.R., P.C. Robert, and W.C. Koskinen, 1994, Runoff and leaching of alachlor under conventional and soil-specific management, Soil Use Mgmt., 10, 158-164.

416

VADOSE ZONE HYDROLOGY

Kissel, D.E., J.T. Ritchie, and E. Burnett, 1974, Nitrate and chloride leaching in a swelling clay soil, /. Environ. Qual., 3, 401-404. Kleveno, J.J. K. League, and R.E. Green, 1992, Evaluation of a pesticide mobility index: impact of recharge variation and soil profile heterogeneity, J. Cont. Hydrol., 11, 83-99. Koszinski, S., O. Wendroth, J.L. Lehfeldt, 1998, Field scale heterogeneity of soil structural properties in a moraine landscape of north-east Germany, Int. Agrophys, 9, in press. Larson, W.E. and P.C. Robert, 1991, Farming by soil, in Soil Management for Sustainability, edited by R. Lai and F.J Pierce, Soil and Water Conservation Society, Ankeny, IA, pp. 103-112. Libardi, P.L., K. Reichardt, D.R. Nielsen, J.W. Biggar, 1980, Simple field methods for estimating soil hydraulic conductivity, Soil Sci. Soc. Am. J., 44, 3-7. League, K, 1991, The impact of land use on estimates of pesticide leaching potential: assessments and uncertainties, J. Cont. Hydrol., 8, 157-175. League, K.M., R.E. Green, C.C.K. Liu, and T.C. Liang, 1989, Simulation of organic chemical movement in Hawaii soils with PRZM: I. Preliminary results for ethylene dibromide, Pacific Sci., 43, 67-91. Mallawatantri, A.P. and D.J. Mulla, 1996, Uncertainties in leaching risk assessments due to field averaged transfer function parameters, Soil Sci. Soc. Am. J., 60, 722-726. Moran, C.J., A.B. McBratney, and A.J. Koppi, 1989, A rapid method for analysis of soil macropore structure. I. Specimen preparation and digital binary image production, Soil Sci. Soc. Am. J., 53, 921-928. Mulla, D.J., 1993, Mapping and managing spatial patterns in soil fertility and crop yield, in Proceedings of Soil Specific Crop Management, edited by P. Robert, W. Larson, and R. Rust, American Society of Agronomy, Madison, WI, pp. 15-26. Mulla, D.J. and J.G. Annandale, 1990, Assessment of field scale leaching patterns for management of nitrogen fertilizer application, in Field-Scale Water and Solute Flux in Soils, edited by K. Roth, H. Fluhler, W.A. Jury, and J.C Parker, Monte Verita, Birkhauser-Verlag, Basel, Switzerland, pp. 55-63. Mulla, D.J., C.A. Perillo, and C.A. Cogger, 1996, A site-specific farm-scale GIS approach for reducing groundwater contamination by pesticides, /. Environ. Qual. 25, 419-425. Nielsen, D.R., J.W. Biggar, and K.T. Erh, 1973, Spatial variability of field-measured soil-water properties, Hilgardia, 42, 215-259. Nielsen, D.R., M.Th. van Genuchten, and J.W. Biggar, 1986, Water flow and solute transport processes in the unsaturated zone, Water Resour. Res., 22, 89S-108S. Nielsen, D.R., G.G. Katul, O. Wendroth, M.V. Folegatti, and M.B. Parlange, 1994, State-space approaches to estimate soil physical properties from field measurements. Proceedings of the 15th Conference of ISSS, Vol. 2a, pp. 61-85. Nofziger, D.L. and A.G. Hornsby, 1987, Chemical Movement in Layered Soils: User's Manual, Circular No. 780, University of Florida, Gainesville, FL. Parker, J.C. and M.Th. van Genuchten, 1984, Determining Transport Parameters from Laboratory and Field Tracer Experiments, Bulletin 84-3, Virginia Agricultural Experimental Station, Blacksburg, VA. Parlange, M.B., G.G. Katul, M.V. Folegatti, and D.R. Nielsen, 1993, Evaporation and the field scale diffusivity function, Water Resour. Res., 29, 1279-1286 Perroux, K.M. and I. White, 1988, Designs for disc permeameters. Soil Sci. Soc. Am. J., 52, 1205-1215. Pilgrim, D.H., I. Cordery, and B.C. Baron, 1982, Effects of catchment size on runoff relationships, J. Hydrol., 58, 205-221. Quisenberry, V.L. and R.E. Phillips, 1976, Percolation of surface-applied water in the field, So/7 Sci. Soc. Am. J., 40, 484-489.

SITE-SPECIFIC FLOW/TRANSPORT MANAGEMENT IN SOILS

41 7

Quisenberry, V.L., B.R. Smith, R.E. Phillips, H.D. Scott, and S. Nortcliff, 1993, A soil classification system for describing water and chemical transport, Soil Sci., 156, 306-315. Rao, P.V., P.S.C. Rao, J.M. Davidson, and L.C. Hammond, 1979, Use of goodnessof-fit tests for characterizing the spatial variability of soil properties. Soil Sci. Soc. Am. J., 43, 274-278. Sawyer, J.E., 1994, Concepts of variable rate technology with considerations for fertilizer application, J. Prod. Agric., 7, 195-201. Shouse, P.J., W.B. Russel, D.S. Burden, H.M. Sclim, J.B. Sisson, and M.Th. van Genuchten, 1995, Spatial variability of soil water retention functions in a silt loam soil, Soil Sci. 159, 1-12. Shumway, R.H., 1988, Applied Statistical Time Series Analysis, Prentice Hall, Englewood Cliffs, NJ. Sposito, G., W.A. Jury, and V.K. Gupta, 1986, Fundamental problems in the stochastic convection-dispersion model of solute transport in aquifers and field soils, Water Resour. Res. 22, 77-88. Star, J.L., H.C. DeRoo, C.R. Frink, and J.Y Parlange, 1978, Leaching characteristics of a layered field soil, So/7 Sci. Soc. Am. J., 42, 386-391. Tamari, S., L. Bruckler, J. Halbertsma, and J. Chadoeuf, 1993, A simple method for determining soil hydraulic properties in the laboratory, Soil Sci. Soc. Am. J., 57. 642-651. Trangmar, B.B., R.S. Yost, and G. Uehara, 1985, Application of geostatistics to spatial studies of soil properties. Adv. Agron., 38, 45-94. van der Molen, W.H. and H.C. van Ommcn, 1988. Transport of solutes in soils and aquifers, /. Hydro!., 100, 433^51. van der Pol, R.M.P., P.J. Wierenga, and D.R. Nielsen, 1977, Solute movement in a field soil, Soc. Sci. Soc. Am. J., 41, 10-13. van Genuchten, M.Th., 1980, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soi7 Sci. Soc. Am. J., 36, 380-383. van Genuchlen, M.Th. and F.J. Leij, 1992, On estimating the hydraulic properties of unsaturated soils, in Proceedings of the International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, edited by M.Th. van Genuchten, F.J Leij, and L.J. Lund, University of California Riverside, Riverside, CA, pp. 1-14. Wagenet, R.J., 1986, Principles of modeling pesticide movement, in Evaluation of Pesticides in Ground Water, edited by W.Y. Garner, R.C. Honeycutt, and H.N. Nigg, American Chemical Society. Washington, DC, pp. 330-341. Warrick, A.W., G.J. Mullen, and D.R. Nielsen, 1977, Predictions of the soil water flux based upon field measured soil-water properties, Soil Sci. Soc. Am. ./., 41, 14-19. Wendroth, O., W. Ehlers, J.W. Hopmans. H. Kage, J. Halbertsma, and J.H.M. Wosten. 1993a, Reevaluation of the evaporation method for determining hydraulic functions in unsaturated soils, Soil Sci. Soc. Am. J., 57, 1436-1443. Wendroth, O., G.G. Katul, M.B. Parlange, C.E. Pucnte, and D.R. Nielsen, 1993b, A nonlinear filtering approach for determining hydraulic conductivity functions in field soils, So/7 Sci., 156, 293-301.

16

Customizing Soil-Water Expertise for Different Users

R. J. WAGENET I. BOUMA

Our lives depend upon and determine the fluxes of water and chemicals in the environment. Atmospheric, aquatic, and terrestrial systems are all characterized by transfer processes that make our lives possible. Some of these processes deliver the air, water, and nutrients that we need to produce food and fiber. Other transfer processes relocate our wastes as environmental contaminants that must be properly managed. As society grows in absolute numbers, so, too, must our concern for maintaining the balance between the wise use of our natural resources in a sustainable manner on the one hand, and the misuse of these resources through shortsightedness and mismanagement on the other hand. Utilization of our resources must be accompanied by protection of them, and knowledge of the role that transfer processes play in this balancing act is important. Management for the long term means that wise decisions in the short term are based on two key issues. First, there is a crucial need to further understand how natural processes, particularly transfer processes, operate. Without this knowledge base, we are unable to formulate logical and lasting solutions to environmental problems. While soil scientists have always focused on tabulating land characteristics in the form of soil surveys, there now is the need to translate these static characterizations into dynamic land qualities, such as soil transfer processes. As important, but less appreciated, is the fact that scientists are becoming increasingly accountable to our clients, the public, for approaches to solve problems that are important to society. This is particularly true for those scientists knowledgeable in transfer processes, for the obvious reasons of public focus on environmental management and pollution prevention. The decisions regarding the impact of our science will be debated, enacted, and enforced outside the scientific community. As we now realize, this means we must consider solutions to environmental problems that are endorsed not only by the scientific community, but also by the public citizenry and regulatory bodies. Many soil and water scientists are experts on transfer processes in the unsaturated zone of the soil. This zone is crucial to most environmental transfer processes; it is

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

419

essentially the "zone of action" for many of the processes that mediate fluxes of water and chemicals. Dynamic transfer processes- such as water infiltration, evaporation, and redistribution; chemical transport and transformation; root growth and extraction of water and nutrients; microbial growth and degradative processes; the evolution of some gases and the absorption of others; the transfer, retention, and release of heat—are expressed most strongly in this region. This complex region can also be recognized as the "zone of opportunity," in which we have the opportunity to wisely manage the application of fertilizers, pesticides, water, and other amendments, including waste materials. We can manipulate the soil conditions through tillage, organic matter incorporation, and irrigation scheduling. We can also sample relatively conveniently and economically in this zone, which allows data collection for multiple purposes, including the study of transfer processes. Some professionals have expertise in the soil-water-plant-chemical system. They all have a vested interest in ensuring that the natural or managed transfer processes in the unsaturated zone work to the betterment, rather than the detriment, of soil and water resources. Bouma (1993) distinguished between users and specialists and showed that each played a characteristic role in a number of different case studies. In this chapter, the key individuals are the farmer, the farm advisor, the conservationist, the policy maker, and the soil and water scientist. As we consider the unique interests of each of these individuals, we need to recognize that the objectives and concerns of each are different, that the spatial scale at which each operates is different, and that the use of models that describe water flow and solute transport are different. In the end, we hope to make the case that modeling of transfer processes is an activity that is constructive, and perhaps even essential, to meet the objectives of this diverse group of individuals.

Objectives by Profession It is to be expected that the farmer, farm advisor, conservationist, policy maker, and soil and water scientist will have different objectives when they consider a unit parcel of soil. Since a specific case makes the discussion more clear, we take the example of a herbicide applied to a corn crop on a farmer's field. The farmer uses the harvested corn to partially support the feeding of his dairy herd, and also uses his land as a disposal site for the manure, in the process gaining the added benefit of nutrient recycling. The field is located within a landscape that has multiple uses and multiple soil types. Additionally, farms of about equal size are located nearby. It is a generally rural setting, with the farmers dependent on shallow well water for their domestic and agricultural use. The objectives of each professional might be stated as follows: Farmer—To maximize the economic return from inputs and to achieve a sustainable production system. Farm advisor—To identify where and at what rates fertilizer, herbicide, and manure should be applied to achieve the farmer's objectives with minimum impact on the environment.

420

VADOSE ZONE HYDROLOGY

Conservationist—To preserve and protect the natural characteristics of the landscape, including the flora and fauna, that may be affected by multipleuse, including farming. Policy maker—To establish logical limitations to the use of farm chemicals and disposal of manures from farming based on soil and chemical properties, depth to ground water, erosion potential, and use of local water supplies. Soil-water scientist—To identify key additional information needed on transfer processes, and to develop methodologies to incorporate that information to best manage the system at all scales from local to larger. The use of models as tools to address these issues has a precedent in each case. While the community of soil and water scientists has spent much time with the Richards equation and the convection-dispersion equation (CDE), and developed alternative formulations for heterogeneous soils, these are not the representations of dynamic soil transfer processes most often used by many professionals. The crucial concern is the use of the model formulation suited to supply the best information to each professional for use in meeting their objective. In some cases, there will be the need for extension or revision of existing models. At each scale, the appropriate method for considering transfer processes must be established to identify the correct model. This, in turn, derives from the issue of the spatial scale at which each professional operates.

Spatial-Scale Considerations A number of recent papers have dealt with spatial scale and the use of leaching models (Hoosbeek and Bryant, 1993; Bouma and Hoosbeek, 1995; Wagenet and Hutson, 1995). These propose a hierarchy of modeling approaches (figure 16.1) that proceed from very small spatial scales (molecular interactions, aggregate structures) to larger scales (soil profiles, pedons, fields and landscapes). In these papers, modeling approaches were related to the spatial scale of interest. Further, a physical scale (and methodology) for sample collection was identified that was presumed to be consistent with the process representation in the models identified for each scale. For the present case, the scale of the farmer's field (usually at a map scale of about 1:5000), the conservationist's multiple fields (at a map scale of 1:20,000), and the policy makers' landscape (as a collection of fields in a gcomorphologically similar area, at a scale of 1:200,000) seem consistent with these concepts. The soil and water scientist has a responsibility to advance the state of the management through increased understanding of the transfer processes across all these scales. Perhaps more important, the soil and water scientist must discover linkages between scales that allow transfer of knowledge from one scale to another. This rarely has been accomplished in an orderly manner that enhances modeling of transfer processes, but is recognized as an important next step. Such a step was proposed by Bouma and Hoosbeek (1996) as represented in figure 16.2. The relationships indicate that the models and the users are related in a

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

421

Figure 16.1 Hierarchy of modeling approaches (Hoosbeek and Bryant, 1993).

logical manner based upon their knowledge base. The farmer and farm advisor have a knowledge base somewhere between positions 1 and 2, which leads them to use models that are generally relatively qualitative, but with some degree of physical, chemical, or biological mechanism included. The conservationist and policy maker need to employ tools derived from individuals whose knowledge base places them between positions 3 and 4, and even between 4 and 5, depending upon their specific education and the problem being addressed. The models that should be employed become more quantitative and mechanistic as the degree of scientific input increases. The soil and water scientist should occupy position 5, and be able to contribute to problem solving across the entire plane represented in figure 16.2.

422

VADOSE ZONE HYDROLOGY

Figure 16.2 The five knowledge levels with respect to the land quality moisture availability applied to the / + 1 plane of the model classification framework (Bouma and Hoosbeek, 1996).

Modeling at Each Scale Farm Scale—The Farmer The farmer usually has such intimate knowledge of his land and its behavior that a physical model is not required, unless he wants to change his management practices. Certainly, he is able to identify by experience those land areas of excess wetness, shallow soil profile, and reduced fertility that can be designated as "problems." Under normal practice, the farmer then follows his own experience to manage the

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

423

system in whatever way he has evolved. This mostly mental model is experiential, and is good as long as the farmer stays within his experience. It is not process driven, it is observation driven. This means he can manage well to achieve the goals he can see, such as a visibly healthy corn crop with a certain estimated yield. However, his experience-based model can take him only as far as his limited observations allow. This may be to the point of measuring crop yield or soil sampling for residual nitrogen and pesticide content, usually at the end of a growing season. This may have been acceptable to the farmer in the past, and it meets the objectives stated above. However, it does not recognize that the farmer is living on borrowed time if he does not expand his tools to predict the impact of his farming activity on off-farm areas. Farmers are now beginning to recognize, often with help of the farm advisor, that transfer processes in soil and water are the determinants of most off-farm impact. Transfer processes also continue to be important in the fertility of their own soils. The common experience-based model does not help the farmer much to estimate processes he cannot see, which are land qualities such as chemical leaching, organic matter turnover, rates and lowered or raised water tables. Therefore, when his farm management practices are questioned, such as in the consequences of herbicide use in an existing farming system, or the use of a new herbicide, or the adoption of new farming techniques and their possible effects on water quality, the experience-based model is less useful.

Quantitative Assessment at the Farm Scale— The Farm Advisor As quantitative assessment becomes more important, a more predictive, objective model is often useful. A farm advisor has the opportunity to guide the farmer from measurement of soil characteristics to the estimation of dynamic changes in these characteristics. In the past, written documentation has served as a guide to better farm practice. The farm advisor now has the responsibility to help the farmer deal with the dynamics of the system, both to conserve fertilizer and herbicide costs, and to minimize off-site effects. This is the opportunity for the farm advisor to achieve his objective in an innovative way, through the use of a model. It is usually perceived that simple models are better, but this does not necessarily solve the farmer's problem. For example, a simple attenuation factor (AF; Rao et al., 1985) may be proposed as AF = f (soil characteristics, pesticide properties, and rainfall or irrigation) (16.1) calculated through additive numerical values derived from tabular data of the presumed important factors. For example, the mobility of a particular herbicide might be rated 1, 2, or 3 based on a laboratory-derived value of a linear sorption isotherm measured for different soil with different organic matter content and different soil water relations. This approach may be a nice educational tool for the farmer, but it does not involve sufficiently resolved descriptions of dynamic soil transfer processes to provide the predictive capability needed for site-specific estimation of fluxes.

424

VADOSE ZONE HYDROLOGY

A simple leaching model, based on fundamental principles of water and chemical fluxes in cropped situations (Nofziger and Hornsby, 1986) can perhaps be useful as a first step. The farmer's objective of evaluating current management practices or testing new scenarios can be accomplished within limits using such a tool. The major limitation to this approach is that the relative lack of detailed information on soil hydraulic properties and solute movement in his field prevents a truly quantitative assessment. The CMLS model (Nofziger and Hornsby, 1986) assumes the following representations of transfer processes: Depth of wetting front (dK), Penetration depth (dp) of noninteracting pesticide, Penetration depth of interacting pesticide,

where / is depth of added water, T-t is initial soil water content, Tfc is field-capacity water content, p is soil bulk density, and Kd is pesticide-soil sorption coefficient (assuming linear, equilibrium partitioning). This is a functional model (Addiscott and Wagenet, 1985) of pesticide leaching that simplifies basic mechanisms of transport processes to the degree that less input data is needed to use the model. Basic information from the soil survey database and local climate records arc usually considered sufficient for scenario comparisons of pesticide leaching options. If the additional information on organic matter turnover was available as well, then models such as those of Burns (1980) and Addiscott (1991) would be useful in identification of nitrogen management options. It should be noted that such simplified approaches are the best current tools at the farmer's disposal for estimating water and chemical fluxes at this scale. Substantial research effort has been invested at this level to build comprehensive, mechanistic models (Addiscott and Wagenet. 1985) that describe transfer processes, hopefully more accurately than with simplified models. These models initially are often based on the Richards equation and the CDE (Nielsen et al., 1986), and all need reliable soil hydraulic data (NLEAP, Shaffer et al., 1991; LEACHM, Hutson and Wagenet, 1992; GLEAMS, Knisel et al., 1989). Sometimes, the mechanistic models are simplified to functional representations of transfer processes (Addiscott, 1977; Nicholls et al., 1982; Hutson and Wagenet, 1993), yet such models still are often criticized as being too data-intensive and computational-intensive for practical, farm-scale usage. This is perhaps true for the farmer, but the farm advisor should have within his grasp, within the next few years, more comprehensive, pragmatic models of dynamic soil behavior available for use on a routine basis. With the continuing development of pedotransfcr functions (Bouma and van Lanen, 1987; Vereecken ct al., 1992; Tietje and Tapkenhinrichs, 1993) to estimate soil hydraulic properties from the standard soil survey database, the development of regionally accurate nitrogen turnover rates for both crop residue and manures, and the widening availability of lowcost computing power, these shortcomings should gradually disappear.

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

425

While it is unlikely that an individual farmer will make use of such a tool, it is the responsibility of the farm advisor, in meeting his/her objective, to adopt dynamic assessment tools, not only for soil processes, but also for crop, economic, and farm management. The use of such a tool for the soil system, in concert with soil sampling, will provide not only the information normally provided to the farmer on the status of his soil, but also will help the farmer minimize off-site effects caused by transfer processes, but which cannot be estimated with an experience-based model limited to on-farm production issues (figure 16.1). Landscape Scale—The Conservationist The conservationist works at a larger spatial scale than an individual farm, usually 1:20,000 or larger, and therefore must be knowledgeable on a broad range of farming issues, as well as soil science. This professional must extrapolate farm-scale expertise across space to estimate processes at the landscape level. At this level, the system becomes too complex for a comprehensive mechanistic model. Issues of spatial variation in soil properties and the focus on two- or three-dimensional problems become more important. The processes of runoff and erosion, as well as leaching, are now presumed to occur within or across volume increments of soil, instead of the one dimension often used in leaching models at the farm scale. Biological populations and the protection of riparian zones are not easily modeled. Even if we consider only soil and water transfer processes at this larger spatial scale, we face a daunting increase in the need for data, often unavailable, to comprehensively predict the results of soil and water transfer processes. Despite these constraints to accurate modeling of soil and water transfer processes at this scale, some attempts have been made. Currently, these approaches are still being researched, and have taken three forms. First, there are complex two- and three-dimensional models that attempt to describe the landscape as an integrated system. An example of this approach is the MIKE SHE model (Danish Hydraulic Institute, 1993), a comprehensive, deterministic, spatially distributed, and physically based system for the simulation of all major hydrological processes of the terrestrial portion of the hydrological cycle. This model is applicable to a wide range of water resources problems related to surface and groundwater quality, such as point and non-point-source contamination, soil erosion, and irrigation. This model is used primarily by scientists and consulting engineers to address landscapes and even larger scales of concern. The complexity of the model and the demand for significant system characterization have limited the use of this model to cases where sufficient finances arc available to parameterize and reliably execute the model. A similar, though somewhat less mechanistic, modeling approach is found in the combination of digital terrain models with Geographic Information Systems (see below) to estimate both surface and subsurface hydrology. Both of these approaches have academic as well as applied merit, but require substantial time and resources for further development. The second approach is the use of the one-dimensional, CDE-type leaching models in an ad hoc stochastic manner. That is, multiple model executions are accomplished, each one of which draws model parameter input from a presumed parameter

426

VADOSE ZONE HYDROLOGY

frequency distribution (Carsel et al., 1988). The expectation is that the actual variability in water and solute fluxes in the system will be at least bracketed by the calculated values. This is a reasonable assumption when the results of this modeling exercise are expressed in terms of the means and variances of the frequency distributions of the calculated values. The few comparisons of this modeling with field data demonstrate that, given the measured spatial variability of the system, reasonable agreement is obtained between calculated and measured values. Yet, this result is not very satisfying to those who recognize that we are generally using principles derived for a much smaller spatial scale to describe a scale where driving forces for the transfer processes may be quite different. The third method is a simplified modeling approach, usually more functional than mechanistic, to estimate the results of transfer processes. We recognize our inability to fully characterize the system at this scale, and once again employ an attenuation factor to estimate pesticide leaching potential (League et al., 1990). Or, from watershed studies, we use the unit hydrograph as a tool to infer watershed-scale transfer processes. In both cases, less data are required than with mechanistic modeling, the exercise can be accomplished relatively quickly, and only the verification of degree of accuracy is presently missing from the literature. Of course, this shortcoming exists with the use of SHE and the ad hoc stochastic approach as well. Yet, given the well-established nature of soil variability, and the difficult issue of identifying correct driving forces at each scale, the use of this third category of simplified models may provide a representation of landscape-scale water and chemical fluxes as accurate as more elaborate mathematical approaches. Ideally, the conservationist is an individual who possesses excellent training and experience in transfer processes at the field scale. Yet, this individual, like the farmer and the farm advisor, will probably not personally use even a simple computer model until the models are packaged into a much more usable form. These models currently lack the preprocessing subroutines, useful interfaces, and incorporation into decision support systems (DSS) that are necessary before they can be routinely useful to anyone beyond the academic community (Larson and Robert, 1991). More realistically, the conservationists can only achieve their professional objectives in the short run through presentation of the modeling results in a manner useful to nonmodelers. This might take the form of a nearly site-specific key or nomogram that progressively leads to resolution of guiding the protection of natural resources, including soil and water resources. Or the technology of Geographic Information Systems, discussed further below, can be used as either a visual presentation or management tool. Further, there is the opportunity to use mechanistic models that have been calibrated and validated to generate sets of synthetic data (as opposed to measured data), which, in turn, could be expressed in simple summary terms, such as regression equations. An example would be to calculate possible crop yields for a large series of years with different weather conditions, and then to use that synthetic data to develop a regression between rainfall, solar radiation, and yield suitable for that area. In all of the above cases, the uncertainty of the simulation guidance could (and should) be included in such contexts as soil variability and its impact on water and solute fluxes for different climates or application patterns, or for different soils. Such

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

427

applications of the modeling exercise are available for a limited number of cases. An example is found in the work of Finke (1993), who used interpolation techniques to express results of simulations of potato production and nitrogen leaching for point data in an agricultural field. By using disjunctive kriging, he obtained stochastic expressions in terms of probability of exceedance of a defined leaching limit.

Integrating Scales—The Policy Maker

The policy maker is responsible at all scales for the impacts of human activities upon society. Policy makers decide issues such as land-use planning and policy, pesticideuse guidelines, and establishment of exposure guidelines through risk assessment. From these decisions come zoning limitations, water-quality standards, and pesticide-use restrictions. At the 1:200,000 scale, the policy maker is envisioned as a county supervisor or planner who has limited training in transfer processes, but has the responsibility of using scientific information to form policy. Providing input to the policy maker is a crucial responsibility, from the farmer to the scientist (whom we have not yet discussed). At each scale, there are models of dynamic transfer processes, the results of which would be useful as policy decisions are made. Yet the policy maker is not interested in the details of the model or the modeling process so long as it is an accurate and objective analysis of the system. Yet, the consequences of soil transfer processes are very site-specific and usually variable with time. Given the great fluctuations in soil and water transfer processes operative in nature, there is need for a tool that can express the results of the modeling exercise in a convincing and straightforward form. A Geographic Information System (GIS) provides such an opportunity. This computer-assisted tool, used for purposes far beyond the subject of this discussion, allows spatial referencing of many of the characteristics, whether natural of anthropogenic, that are important in describing soil transfer processes. It organizes, stores, retrieves, integrates, and displays digital data that can be used for environmental assessment. The GIS can accommodate data at different spatial scales, and provides the opportunity to assess, through map overlays, the integrated effects of soil transfer processes on land use and management, delivery of pollutants to surface water and groundwater, and agricultural production potential. These dynamic problems are logically considered to be the next step in the use of the models outlined above. While there is much enthusiasm for this idea, the policy maker needs to be aware of the limitations of the models, the sources of data at each scale that can be used as model input or to confirm or deny model predictions, and the sometimes misleading nature of the attractive color graphics of the GIS display. How should current models be used with GIS to provide an accurate assessment of the consequences of important soil transfer processes? According to Bleecker et al. (1995), after a study of the potential for pesticide leaching using regional-scale databases, and a simplified leaching model developed for use with data available at that scale (Hutson and Wagenet, 1993), leaching indices should be mapped at scales no finer than 1:250,000 when using regional-scale databases ... uncertainty associated with spatial and temporal

428

VADOSE ZONE HYDROLOGY

variability, model type, and environmental database quality limit interpretations of regional model simulations (p. 495). In fact, it appears, after all their effort, that a much easier way to develop the map was through the inverse correlation of pesticide leaching potential and soil organic carbon content. This information was available in the Soil Survey report, and required no modeling of dynamic transfer processes. Given the large variability in the data when aggregated to that scale, and the large uncertainty in model output as a result, a similar map could be produced by either method and both would be very coarse, but comparable, estimates. This issue has also been raised in another context through the combined "qualitative/quantitative" approach of van Lanen et al. (1992). The bottom line is that providing an assessment of a dynamic soil transfer process at the regional scale may be more misleading than illuminating, and policy decisions generally should not be made at this spatial scaie by use of leaching models. There have been more successful applications of GIS and simulation modeling of transfer processes at smaller spatial scales (larger map scales), where more accuracy is available in the databases related to soil characteristics. It is at these scales, perhaps the farm to county level, where these tools are most useful with respect to management of dynamic transfer processes. The policy maker can be assisted at these scales through the production of map products that indicate the impacts of certain management schemes at a scale where they are subject to nearly site-specific regulatory efforts. As shown by (1) the programs of local soil and water conservation districts, (2) the focus on on-farm planning, and (3) point-source pollution-prevention programs, there is much to be gained from very local implementation of flexible policy that derives from relevant scientific products. The policy maker would therefore be wise to focus on dynamic soil transfer processes at the most local scale possible. The use of GIS improves the opportunity to use simulation models of water and chemical fluxes, particularly at the local scale for which these models were initially developed. Basic information from the soil survey database and local climate records are usually sufficient for scenario comparisons of pesticide leaching options. Of course, additional data, such as organic matter turnover rates, would increase the usefulness of the modeling exercise. Responsibility at All Scales—The Soil and Water Scientist Since the tools used by the farm advisor, the conservationist, and the policy maker all derive from an understanding of dynamic soil transfer processes, there is a role for the soil and water scientist at each of those scales. It is also clear that there is a role for models of these processes at each of these scales and for each user, including the farmer. Yet, not everyone needs to become a modeler to reap the benefits of the modeling exercise. For example, the soil and water scientist could provide databases that result from many simulations, perhaps by soil scries at the field scale. As several fields are considered, the soil series becomes a component of soil associations at the regional and global scale. In both cases, the soil series "simulation" database could be "tapped into" for information on the particular soil series, as produced by the

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

429

model exercise. At larger scales, it can be said that a soil series occurs as part of the complex unit, but the identification of the exact spatial coordinates is not possible. With a database of relevant simulations of soil processes expressed by soil series, there may be the opportunity to better area-weight soil processes at the landscape level for routine planning and management decisions (Bouma, 1994). The responsibilitiexS of the soil and water scientist are threefold in accomplishing his/her objective: (1) to be a participant in defining the aspects of the problem that can be resolved through better understanding and management of soil transfer processes, (2) to develop and communicate methodologies for the resolution of these problems, and (3) to continue the search for more precision, accuracy, and efficiency in those methodologies. In terms of scientific progress, further understanding of the system and the processes underpins the scientist's goal. Many issues remain unclear, among them the quantitative treatment of heterogeneity and macropores, wcttability, soil crusting,and the effects of strong layering on root growth, water flow, and chemical leaching. The escalating wealth of scientific literature is evidence of the strong commitment of the scientist. It is clear that with every new technique introduced into practice, whether it is fractal analysis, time domain reflectometry, satellite or aircraft remote sensing, space-state analysis, or faster computers, there are more opportunities to better explore dynamic soil transfer processes. It is very satisfying to the soil and water scientist to use quantitative skills in his/her ever-increasing analysis of the same problems. But, the scientist must avoid "mathematistry" (Box, 1976), which Klemes (1986) summarizes as using mathematics to redefine a problem rather than to solve it.

The Challenge for the Soil and Water Scientist The scientific community dealing with soil and water must be more responsive to the needs of society. We need to look more outward, to the professionals described here. To date, a significant amount of, and perhaps too much, time has been spent looking inward to our peer group for recognition. If we accept that fact that the professionals discussed above are dealing with complex, transient, and variable natural systems on a daily basis, then the scientific community must provide tools to resolve the problems. The provision of properly derived and tested simulation models of soil transfer processes is one example of scientific contribution to problem resolution. But, the contribution cannot stop at this point. The scientist needs to be continually involved in the use of the models by each professional. At the first step, this ensures proper use of the models. However, just as importantly, the scientist must understand the weaknesses of the models that appear during their use, and be ready to conduct the relevant research to better understand the transfer processes that will lead to model improvement. A prime example of this process is the spatial variability studies of the late 1960s and early 1970s (Nielsen et al., 1973) that demonstrated, to the consternation of more than a few, that the Richards equation and CDE models confirmed under laboratory soil column studies were not directly transferable to description of

430

VADOSE ZONE HYDROLOGY

water and solute fluxes at the field scale. The quest to describe field variability was thereby born, and the modeling of field-scale fluxes further developed. One consequence of such studies and the many that have followed is the emphasis on developing stochastic models to describe dynamic, spatially and temporally variable soil transfer processes. There is no debate on the conceptual validity of this approach. It certainly better describes the statistical reality of the uncertainty of parameters and processes in soil-water systems. Since most field soils are now realized to be heterogeneous assemblages of pores, particles, and aggregates, rather than the homogeneous soils imagined in the early days of application of the Richards equation and CDE, the stochastic approach is even more useful given the opportunity to directly incorporate the variability of nonequilibrium processes (macropores, kinetic sorption) in the formulation. The science of soil-water systems is advancing, and that is all for the better. Yet, again, the public perception is that the scientist is engaged in mathematistry until usable products are produced that solve their problems. Colleagues in computer science, remote sensing, and geographical analysis are now producing products that make people's lives better. It is incumbent upon the soil-water scientist to similarly advance the understanding, modeling, and management of soil transfer processes. Collaboration with a variety of related disciplines is surely needed in this effort.

References Addiscott, T.M., 1977, A simple computer model for leaching in structured soils. /. Soil Sci. 28, 554-563. Addiscott, T.M., 1991, Relating the nitrogen fertilizer needs of winter wheat crops to th soil's mineral nitrogen. Influence of the downward movement of nitrate during winter and spring. /. Agric. Sci. 117(2), 241-249. Addiscott, T.M. and R.J. Wagenet, 1985, Concepts of solute leaching in soils: a review of approaches. /. Soil Sci. 36, 411^24. Bleecker, M., S.D. DeGloria, J.L. Hutson, R.B. Bryant, and R.J. Wagenet, 1995, Mapping atrazine leaching potential with integrated environmental databases and simulation models. J. Soil Water Conserv. 50(4), 388-394. Bouma, J., 1993, Soil behavior under field conditions: differences in perception and their effects on research. Geoderma 60, 1-15. Bouma, J., 1994, Sustainable land use as a future focus for pedology. Soil Sci. Soc. Am. J. 58, 645-646. Bouma, J. and M.R. Hoosbeek, 1996, The contribution and importance of soil scientists in interdisciplinary studies dealing with land, in R.J. Wagenet and J. Bouma (eds.), The Role of Soil Science in Interdisciplinary Research. SSSA Special Publication No. 45, ASA/CSSA/SSSA. SSSA, Madison, WI. Bouma, J. and H.A.J. van Lanen, 1987, Transfer functions and threshold values: from soil characteristics to land qualities, in K.J. Beek, P.A. Burrough, and D.E. McCormack (eds.), Quantified Land Evaluation Procedures, International Institute of Aerospace Survey and Earth Sciences (ITC) Publication 6. Enschede, The Netherlands, pp. 106-110. Box, G.E.P., 1976, Science and statistics. J. Am. Stat. Assoc. 71(356), 791-799. Burns, I.G., 1980, A simple model for predicting the effects of leaching of fertilizer nitrate during the growing season on the nitrogen fertilizer need of crops. /. Soil Sci. 31, 175-185.

CUSTOMIZING SOIL-WATER EXPERTISE FOR DIFFERENT USERS

431

Carsel, R.F., R.L. Jones, J.L. Hansen, R.L. Lamb, and M.P. Anderson, 1988, A simulation procedure for groundwater quality assessments of pesticides. /. Contam. Hydrol. 2(2), 125-138. Danish Hydraulic Institute, 1993, MIKE SHE WM— Release 5.1, Water Movement Module. DHI, Horsholm, Denmark. Finke, P.A., 1993, Field-scale variability of soil structure and its impact on crop growth and nitrate leaching in the analysis of fertilizing scenarios. Geoderma 60, 89-108. Hoosbeek, M.R. and R.B. Bryant, 1993, Towards the quantitative modeling of pedogenesis. A review. Geoderma 55, 183-210. Hutson, J.L. and R.J. Wagenet, 1992, LEACHM, Leaching Estimation and CHemistry Model, Version 3.0, Department of SCAS Research Report No. 923. Cornell University, Ithaca, NY. Hutson, J.L. and R.J. Wagenet, 1993, A pragmatic field-scale approach for modeling pesticides. J. Environ. Qual. 22, 494-499. Klemes, V., 1986, Dilettantism in hydrology: transition or destiny? Water Resour. Res. 22(9), 177S-188S. Knisel, W.G., R.A. Leonard, and P.M. Davis, 1989, GLEAMS User Manual. Southeast Watershed Research Laboratory, USDA-ARS, Tifton, GA. Larson, W.E. and P.C. Robert, 1991, Farming by soil, in R. Lai and F.J. Pierce (eds.) Soil Management for Sustainability. Soil and Water Conservation Society, Ankeny, IA, pp. 103-112. League, K., R.E. Green, T.W. Giambelluca, T.C. Liang, and R.S. Yost, 1990, Impact of uncertainty in soil, climatic, and chemical information in a pesticide leaching assessment. J. Contam. Hydrol., 5, 171-194. Nicholls, P.H., A. Walker, and R.J. Baker, 1982, Measurements and simulation of the movement and degradation of atrazine and metribuzin in a fallow soil. Pestic. Sci. 13, 484-494. Nielsen, D.R., J.W. Biggar, and K.T. Erh, 1973, Spatial variability of field-measured soil-water properties. Hilgardia 42, 215-260. Nielsen, D.R., M.Th, van Genuchten, and J.W. Biggar, 1986, Water flow and solute transport processes in the unsaturated zone. Water Resour. Res. 22, 89S-108S. Nofziger, D.L. and A.G. Hornsby, 1986, A microcomputer based management tool for chemical movement in soil. Appl. Agric. Res. 1, 50-56. Rao, P.S.C., A.G. Hornsby, and R.E. Jessup, 1985, Indices for ranking the potential for pesticide contamination of groundwater, in Proceedings of the 44th Annual Meeting of the Soil and Crop Society of Florida, Vol. 44, 1-8. Shaffer, M.J., A.D. Halvorson, and F.J. Pierce, 1991, Nitrate leaching and economic analysis package (NLEAP): model description and application, in R.F. Follett, D.R. Keeney, and R.M. Cruse (eds.), Managing Nitrogen for Groundwater Quality and Farm Profitability. Soil Science Society of America, Madison, WI. Tietje, O. and M. Tapkenhinrichs, 1993, Evaluation of pedotransfer functions. Soil Sci. Soc., Am. J. 57, 1088-1095. van Lanen, H.A.J., M.J.D. Hack ten Broeke, J. Bouma, and W.J.M. de Groot, 1992, A mixed qualitative/quantitative physical land evaluation methodology. Geoderma 55, 31-54. Vereecken, H., J. Diels, J. Van Orshoven, J. Feyen, and J. Bouma, 1992, Functional evaluation of pedotransfer functions for the estimation of soil hydraulic properties. Soil Sci. Soc. Am. J. 56, 1371-1378. Wagenet, R.J. and J.L. Hutson, 1995, Consequences of scale-dependency on application of chemical leaching models: a review of approaches, in A.I. El-Kadi (ed.), Groundwater Models for Resources Analysis and Management, CRC Press/ Lewis, Boca Raton, FL, pp. 169-184.

17

Present Directions and Future Research in Vadose Zone Hydrology

WILLIAM A. JURY

The last decade has been an active one for research in vadose zone hydrology (VZH). There are a host of new experimental devices, lots of new theories, and a bright new generation of scientists eager to unlock the mysteries of the discipline. It would be tempting to say that we are well on our way to conquering the most difficult problems that face experimentalists and modelers in the VZH field. However, as is so often the case in science, new problems are discovered in the process of solving other ones. I have been given the task of providing an overview of the current directions in our field, and of pointing out unsolved problems and future research directions for the discipline. Execution of such a task is well beyond my abilities or vision, so what you will get is a compendium of my personal preferences and bias. I chose several methods carry out my charge. First, I examined the poster abstracts to get an idea of the content and breadth of the offerings for the symposium "Vadose Zone Hydrology—Cutting Across Disciplines." Next, I examined 1 year's worth of articles in the S-l section of the Soil Science Society of America Journal and in Water Resources Research at a 10-year interval to get an idea of the changes in people's interests in research over that time span. Finally, I polled my own research group and asked some colleagues what the really tough problems were in the discipline of VZH.

Current Research One way to find out what is going on in the world of VZH is to examine the poster abstracts from the above-named conference. Table 17.1 presents an organizational summary of the 78 posters by subject matter.1 It is clear that the most active areas are property measurement, monitoring, and characterizing large-scale systems, which 'l could have chosen other ways of grouping them. There are, for example, 9 papers on instrumentation, 12 reports of field studies, and so on.

PRESENT DIRECTIONS AND FUTURE RESEARCH

433

Table 17.1 Summary of the Posters at the Conference by Subject Matter Subject Hydraulic property measurement Flow experiments and monitoring Regional scale and spatial variability Unstable or preferentialflow Basic research investigations Water flow modeling Chemical transport modeling Chemical transport monitoring Hydraulic property modeling Soil-air interface Non-aqueous-phase liquids

Number of Posters 14 10 10 10

8 7 6 5 3 3 2

reflects both the influx of new monitoring devices and also increased attention paid to details of scale-dependence, interpolation, disturbance during monitoring, and other issues that have become research areas in their own right. Regional-scale investigations are much more prevalent now than a decade ago, and Geographic Information Systems (GIS) seems destined to become a standard tool for analysis and representation of information (Corwin and Wagenet, 1995). There is a also a healthy representation in areas of basic research, spanning topics such as hysteresis, swelling phenomena, and surface tension. Basic research has been neglected over much of the last decade as funding organizations shifted their priorities toward society's more pressing short-term problems. It is encouraging to see us return to a better balance of fundamental and applied science. A systematic review of the contents of the poster presentations is beyond the scope of this chapter. My impression is that the level of originality in the profession is rising in recent years, and that some very difficult problems are being addressed that were taboo for years. I am less excited about advances in theory than in experiments and instrumentation, and I feel that we have stagnated somewhat in our descriptions of transport processes. I feel strongly that this is due mainly to the absence of foundational experiments that examine specific hypotheses, and that transport theory must await the arrival of new information before the next advance is made. It is worth noting that computers have fundamentally changed the way we conduct research and analyze data. Overall, they have had a positive impact, allowing us to do things like multidimensional flow and transport, coupled flow, and MonteCarlo simulations that were unthinkable a few years ago. The Internet and GIS have brought formidable analytical tools and huge databases to our desktops for the investigation of large-scale systems, while molecular dynamics calculations have allowed us to visualize phenomena too small to see or work with directly. Computers also have great potential as a teaching tool, although we have not yet developed a systematic approach to using them in this capacity.

434

VADOSE ZONE HYDROLOGY

The downside is, of course, that computers offer the illusion of perfection while often concealing egregious faults in logic or conception. They make us lazy by doing much of the work instantly, providing outputs on high-quality graphics, and sparing us the kind of tedious work that used to serve an oversight function at the same time. We are in the era of computer codes and software products whose functions, and even operating assumptions, are a mystery to the majority of people who use them. Worst of all, models can gain acceptance merely because of their convenience and not their validity. We would be well advised as a discipline to police our software domain better than we have. Otherwise, we will all bear implicit responsibility for the dissemination of false information to students, scientists in other disciplines, and the public and private sector. I will conclude this section with my list of the 10 biggest changes in VZH over the last decade, in terms of impact and acceptance. The list, again, reflects my own limitations and bias, and is merely intended to show the dynamic nature of our discipline across a 10-year time span. 1. Time domain reflectometry (TDK) measurement of water content: The neutron probe is no longer the standard for water-content measurement near the soil surface. The convenience, safety, and automating capacity of TDK have made it a much handier tool for monitoring. Neutron probes still have their place in the deep subsurface, where TDR is difficult to install (Gee et al., 1994), and in saline soils where the TDR signal is strongly attenuated (Dalton and van Genuchten, 1986). 2. New infiltrometers: With the Guelph (Reynolds and Elrick, 1986) and tension infiltrometers (Jarvis et al., 1987), we have a completely new set of minimum-disturbance instrumentation to replace the ring infiltrometer. The new devices are also more amenable to mathematical analysis, so that various hydraulic properties can be estimated from the infiltrometer readings (Russo and Bresler, 1980). Also, when used in concert, these two instruments can isolate the macropore influence on infiltration rate and saturated hydraulic conductivity. 3. Geostatistics: Geostatistics has an international newsletter and a variety of software packages. Spatial correlation is routinely reported now, and kriging has become part of our vocabulary. The theoretical foundations of geostatistics are shaky (Philip and Watson, 1985), but can be violated rather seriously without affecting interpolation accuracy. Spatial correlation length and covariance estimates are another matter (Ruso and Jury, 1987). 4. Fractal geometry: After years of stagnation struggling with simplistic structures such as twisted capillary tubes, we have a new and versatile geometric foundation for representing porous media. Self-similarity, even if it describes only a small range of pore sizes, offers huge advantages over the competition. 5. Standard forms for hydraulic and retention functions: With widespread use of a few standard forms like the van Genuchten relations (van Genuchten, 1980), we have begun to develop relations among the parameters and prototype functions for characteristic soil types. This is the first step in developing a world library of transport properties for soils.

PRESENT DIRECTIONS AND FUTURE RESEARCH

435

6. Noninvasive monitoring devices: Electromagnetic (EM) induction, electrical resistivity, ground-penetrating radar, lidar, etc., show us a fuzzy picture of a large area without disturbing its contents. This opens up a host of new applications in survey, remediation, and research (Hendrick, 1994). 7. Numerical experiments: Impossible a decade ago, numerical experiments at large and small scales use raw computing power to show details that real experiments cannot. This has been a boon to stochastic modeling for checking various transport theories (Ababou et al., 1989), and has made Monte-Carlo simulation a viable alternative to closed-form calculation (Unlu et al., 1990). Molecular dynamics calculations of water interactions in solution and at solid surfaces show promise for revealing attributes that have remained hidden from experimentalists in the past. However, we must have a rigorous foundation for all models used in calculations, or we merely verify our own preconceptions and learn nothing new. 8. Stochastic flow and transport modeling: This was underway 15 years ago, but was largely untested and was the province of a few specialists. Now, it is a mainstream topic in groundwater research. The latest research has developed methods for predicting the variance, as well as the mean value of parameters like pressure-head and solute concentration (Graham and McLaughlin, 1989), and for extending results over length-scales (Rubin and Gomez-Hernandez, 1990). Stochastic flow and transport modeling is entering the realm of unsaturated flow and transport, but faces formidable obstacles not present in the groundwater domain (Jury and Kabala, 1993). 9. Rate process descriptions: Sophisticated new multiprocess formulations have emerged and been tested for solute sorption, NAPL dissolution, etc. Researchers have also addressed the measurement problem and have coupled the rate process descriptions with transport models (Brusseau et al., 1989). The implications for the new research on standard characterizations like the adsorption/desorption isotherm are just being explored (Streck et al., 1995). 10. NAPLs: Nonaqueous-phase liquid experimentation and modeling have become very dynamic fields, after a few decades of relative inactivity. New computer codes capable of handling the complex multiphase equations have been developed, and three-phase pressure-saturation relationships have been measured (Parker, 1989). This is an undeveloped area that will mature as new information arrives and theories are tested.

A Status Report Where are we now? We have a lot of research going on worldwide, and many difficult problems to solve. My impression is that we are about to embark on another "golden age" when changes occur rapidly and great advances are made. I have been asked to handicap the race for new knowledge, and pass along my choices for both the most fruitful and fruitless pursuits. To aid my analysis I examined 1 year's worth of hydrologic science articles from the S-l section of the Soil Science Society of America Journal and from Water Resources Research 10 years ago, and currently, to see what changes had occurred in subject matter (tables 17.2 and 17.3).

Table 1 7.2 Summary of Soil Science Society of America Journal S-l Articles by Subject Matter: 1984 and 1994 Subject Matter Water flow —lab Waterflow—field Water flow —theory Chemical transport—lab Chemical transport— field Chemical transport— theory Scaling and statistics Heat flow Gas flow Static properties Hydraulic properties New instruments Preferential flow Sediment transport Total

Number in 1984-85

Number in 1994-95

0.0 0.5 9.5 2.5 1.5 2.0 6.0 3.0 1.0 8.0 5.0 3.0 0.0 0.0

1.0 0.0 1.5 2.5 3.5 10.5 5.0 4.0 0.0 2.0 4.0 12.0 2.0 3.0

42.0

51.0

Table 1 7.3 Summary of Water Resources Research Articles by Subject Matter: 1984

and 1995 Subject Matter Regional hydrology Precipitation Surface water hydrology Snow and ice Evapotranspiration Water flow —lab Water flow — field Water flow —theory Chemical transport— lab Chemical transport— field Chemical transport—theory Scaling and statistics Heat flow Gas flow Static properties Hydraulic properties New instruments Preferential flow Sediment transport Multiphase flow Flow in fractures Total

Number in 1984

Number in 1995

11.0 7.0 22.0 3.0 4.0 1.0 2.0 27.0 3.0 0.0 23.0 3.0 2.0 2.0 1.0 2.0 0.0 1.0 9.0 3.0 6.0

20.0 8.0 25.0 3.0 3.0 0.0 0.5 38.0 4.0 13.5 43.0 14.0 3.0 7.0 3.0 3.0 5.0 4.0 15.0 16.0 8.0

132.0

236.0

PRESENT DIRECTIONS AND FUTURE RESEARCH

437

The Areas of Greatest Benefit My top choice is instrumentation. Ten years ago, we were taking soil cores and sucking solution out of the ground and very little else. Today, we have high-tech tools for detailed inspection at all scales. Eventually, although not at the moment, these tools will reveal a picture that will inspire theory to new heights. Another area I have been impressed with is NAPL experimentation, both in terms of characterizing multiphase pressure-saturation relations, but also in dissolution, and to a lesser extent, volatilization. These are difficult experiments, and the people in this area have done some excellent work. Finally, I am optimistic that the new generation of analytical tools (e.g., fractals, percolation theory) for characterizing the geometry of a porous medium will yield major improvements in media scaling, modeling of hydraulic properties, and so on. These representations are much more versatile than the early scaling theories, such as geometric similitude, whose assumptions were not well met in field soil.

The Areas of Debatable Benefit The active areas are not necessarily the ones that are bearing the most fruit. My personal view is that we are going down a few dead-end trails that will eventually have to be abandoned and retraced. I am treading on thin ice here, and will only expound on a few subjects that I feel familiar with.

Stochastic Continuum Modeling of the Vadose Zone Stochastic continuum modeling has enjoyed some success in groundwater, where its predictions have been tested in a few heavily monitored aquifers. It has been developed in several forms for the vadose zone, but not actually tested. There are several reasons why I do not think it will enjoy the same success in unsaturated soil as in groundwater. 1. Second-order stationarity along the direction of flow (downward) is very unlikely in the vadose zone, where soil layering is the rule rather than the exception. 2. Transverse dispersion must be estimated, as it controls the extent of mixing between stream tubes of different velocity. No one knows how to do this. 3. Perturbation or cumulant expansion of the nonlinear flow equation is not as straightforward as of the linear transport equation. In fact, an equation for the mean or ensemble average water content or potential may not even exist. 4. The key parameters are all functions in the unsaturated zone, and the spatial correlation structure of these functions must be known at all water contents or potential of interest in the modeling exercise. This presents a formidable, if not insurmountable, experimental problem.

438

VADOSE ZONE HYDROLOGY Multiphase Flow Modeling

Frankly, I do not believe that the equations are complete. They predict smooth infiltration patterns, but all of the data are dominated by instabilities. Such instabilities are often triggered by microscale heterogeneities that are not present in the models. These are enormously complicated models that cannot be validated, or even compared with simpler approaches. Caveat emptor. Advective-Dispersive Transport Modeling Two things become apparent to a reader of the VZH literature: (1) virtually everyone uses the advection-dispersion (sometimes called convection-dispersion) equation to represent transport of dissolved solutes through soil; (2) almost invariably, the assumptions (e.g., residence time > > mixing time) of this infinite-time model are stretched or violated outright where the equation is used. This misuse seems to be a failure of our educational system more than anything else, although I frequently hear the comment that the user knows the equation is wrong, but nothing else is available.

A Look to the Future The most difficult role I have been asked to play is that of a seer. It is instructive to begin with a look at what needs to be done, regardless of whether anyone knows how to do it. I offer these items as a challenge to all of us, and readily admit that I do not myself know how to meet it. A List of Critical Areas 1. Measurement of preferential flow: Preferential flow is generally detected in one of two ways. Either we record it at the outlet of a transport volume, such as a tile drain, or we trace its path with dye and autopsy the soil after the fact. In the first case, we can determine the velocity but not the pathway; and in the second case, we know where it went but not how long it took. Attempts to study preferential flow in the laboratory under controlled conditions have thus-far raised serious and justifiable fears about interference from column walls and boundary effects. Consequently, we must rely primarily on field observation to provide information about this elusive process. 2. Scaling of rate processes: Essentially all of our detection devices volumeaverage the process under observation. Virtually all that we know about such basic processes as microbial degradation, NAPL dissolution, solute sorption, etc., is in the form of this volume-averaged information. We may never see the pure process at work at the local scale, and its attributes at progressively larger scales may be obscure. How can we develop models that integrate over spatially variable domains or time when rate processes are present? 3. Lab-to-field transformations: It is never going to be feasible to conduct all of our experimental work in the field. Yet, the field is the domain of

PRESENT DIRECTIONS AND FUTURE RESEARCH

4.

5.

6.

7.

8.

439

application of the vast majority of our applied research. Too little attention has been paid in the past to the problem of adapting lab measurements to the field. For example, how does one extrapolate from the kinetics of a batch sorption experiment conducted under continuous agitation to the kinetics of sorption under laminar flow in natural soil? We need more experiments comparing lab and field studies conducted on the same material. Measuring "mobile" water: Solute velocity is variable when total water content is not. We simply have to find a way of delineating experimentally the portion of the wetted pore space that is active in solute transport. Although mobile and immobile water are an idealization of a continuum of water flow regions of differing velocity, the concept is useful and often represents an essential improvement over piston-flow characterizations of completely mobile water. However, except by simultaneous parameter fitting of particular simulation models (a dubious procedure when process description is uncertain), we have no way to divide water into zones of different mobility. Improved scaling theories: We know that a real field does not obey geometric similitude2 (Warrick et al., 1977), but we have scarcely scratched the surface to explore other ways of scaling a heterogeneous porous medium. Whether by group theory, fractals, percolation theory, or some new conceptualization, we must continue to look for ways of avoiding having to measure every soil property at every point of interest. A comprehensive scaling theory may also allow us to address problems such as rate processes at different scales. Preferential-flow modeling: Preferential flow is no longer a pathological phenomenon found only in Tennessee soil columns; it is manifest in virtually every field where it has been investigated (Flury et al., 1994). It might be due to instabilities, geometry, or simply lateral flow and channeling, and it depends strongly on water content and even boundary conditions of the experiments where it is observed. At the present time, we do not even know what soil characteristics to look for other than gaping cracks and crevices (Jury and Roth, 1990). We need a way of estimating a priori how important the preferential flow phenomenon is in a given location. Fundamentals of soil physics: We need a more robust basic component of research in our discipline. The rather applied nature of research funding over the last 10-15 years has made it difficult to attack some of the foundational problems that lie at the core of our science. For example, we still cannot predict the temperature-dependence of the matric potential. Water flow theory: The Richards equation provides the foundational basis of all water flow theory. Its assumptions and relevance have never been questioned, regardless of the scale of the problem. Yet, I cannot recall a single field test of this equation. Aside from difficulties with volume-averaging over discrete structures like preferential flow channels, there remain more fundamental questions about, for example, ty(8) equilibrium during

2 In geometric similitude, each region is a magnified version of a standard region and can be characterized completely by a length-scaling factor.

440

VADOSE ZONE HYDROLOGY

rapid flow (Davidson et al., 1966), which deserve attention and have not received it to date. 9. Quantification of structure in porous media: We need a way of representing the structural patterns in a manner that can be coupled into models of scaling, rate processes, etc. This next stage of advance may have to await new information from the experimentalists and their three-dimensional probes (e.g., NMR, tomography). 10. Interdisciplinary research: The toughest problems out there need teams of scientists whose expertise transcends any one discipline. Hydrologists can profitably collaborate with biologists, engineers, chemists, economists, and so on, on a wide variety of problems running the gamut from virus transport and fate to molecular dynamic simulations of chemical reactions with surfaces. Together, we can travel much farther than we will ever reach in isolation.

Concluding Remarks The search for new knowledge is never-ending. As scientists, we can only walk a small distance on this quest during our lifetimes, and hopefully leave behind something useful and inspiring to guide those who follow. Don Nielsen and Jim Biggar have left us many such gifts as they moved through the many difficult problems they tackled during their brilliant careers. Some of the major accomplishments of the discipline I have mentioned in this chapter are largely theirs, and others belong to people they trained. For those of you just starting your careers, and for all of you eager to attack the tough problems perplexing us all, I cannot offer two better role models.

References Ababou, R., D. McLaughlin, L.W. Gelhar, and A. Tomson, 1989. Numerical simulation of 3-dimensional saturated flow in randomly heterogeneous porous media. Transp. Porous Media 4: 549-565. Brusseau, M.L., R.E. Jessup, and P.S.C. Rao, 1989. Modeling the transport of solutes influenced by multiprocess nonequilibrium. Water Resour. Res. 25: 1971-1988. Corwin, D. and R.J. Wagenet, 1995. Applications of GIS to the modeling of nonpoint source pollutants in the vadose zone. Proceedings of the 1995 Bouyoucos Conference May 1-3, 1995, Riverside, CA. USDA-ARS and US Salinity Laboratory, Riverside, CA. Dalton, F.N. and M.Th. van Genuchten, 1986. The time-domain reflectometry method for measuring soil water content and salinity. Geoderma 38: 237-250. Davidson, J.M., D.R. Nielsen, and J.W. Biggar, 1966. The dependence of soil water uptake and release upon the applied pressure increment. Soil Sci. Soc. Am. Proc. 30: 298-304. Flury, M., H. Fluhler, W.A. Jury, and J. Leuenberger, 1994. Susceptibility of soils to preferential flow: a field study. Water Resour. Res. 30: 1945-1954. Gee, G.W., P.J. Wierenga, B.J. Andraski, M.H. Young, M.J. Payer, and M.L. Rockhold, 1994. Variations in water balance and recharge potential at three western desert sites. Soil Sci. Soc. Am. J. 58: 63-72.

PRESENT DIRECTIONS AND FUTURE RESEARCH

441

Graham, W. and D. McLaughlin, 1989. Stochastic analysis of nonstationary subsurface solute transport; 1, unconditional moments. Water Resour. Res. 25: 215232. Hendrickx, J., 1994. Future directions and opportunities in field instrumentation. Agronomy Abstracts, p. 252. American Society of Agronomy, Madison, WI. Jarvis, N.J., P.B. Leeds-Harrison, and J.M. Dosser, 1987. The use of tension infiltrometers to assess routes and rates of infiltration in a clay soil. J. Soil Sci. 38: 633-640. Jury, W.A. and Z.J. Kabala, 1993. Stochastic modeling of flow and transport in unsaturated field soil. pp. 48-71, in A. Mermoud (ed.), Porous or Fractured Unsaturated Media: Transports and Behaviour. Proceedings of International Workshop at Ascona, Switzerland, October 5-9, 1992. Jury, W.A. and K. Roth, 1990. Evaluating the role of preferential flow on solute transport through unsaturated field soils. Think Tank Workshop Report, pp. 23-30, In K. Roth et al. (eds.) Field Scale Water and Solute Flux in Soils. Birkhauser, Basel, Switzerland. Parker, J.C., 1989. Multiphase flow and transport in porous media. Rev. Geophys. 27: 311-328. Philip, G.M. and D.F. Watson, 1985. Some limitations in the geostatistical evaluation of ore deposits. Int. J. Mining Eng. 3: 155-159. Reynolds, W.D. and D.E. Elrick, 1986. A method for simultaneous in situ measurement in the vadose zone of field saturated hydraulic conductivity, sorptivity and the conductivity-pressure head relationship. Ground Water Mon. Rev. 6: 84-95. Rubin, Y. and J. Gomez-Hernandez, 1990. A stochastic approach to the problem of upscaling of conductivity in disordered media; theory and unconditional numerical simulations. Water Resour. Res. 26: 691-701. Russo, D. and E. Bresler, 1980. Field determinations of soil hydraulic properties for statistical analyses. Soil Sci. Soc. Am. J. 44: 697-702. Russo, D. and W.A. Jury, 1987. A theoretical study of the estimation of the correlation scale in spatially variable fields. II. Nonstationary fields. Water Resour. Res. 23: 1269-1280. Streck, T., N. Poletika, W. Jury, and W. Farmer, 1995. Description of simazine transport with rate-limited, two-step linear and nonlinear adsorption. Water Resour. Res. 31: 811-822. Unlu, K., D.R. Nielsen, and J.W. Biggar, 1990. Stochastic analysis of unsaturated flow; one-dimensional Monte-Carlo simulations and comparisons with spectral perturbation analysis and field observations. Water Resour. Res. 26: 2207-2218. van Genuchten, M.Th., 1980. A closed form solution for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: 892-898. Warrick, A.W., G.J. Mullen, and D.R. Nielsen, 1977. Scaling field-measured soil hydraulic properties using a similar media concept. Water Resour. Res. 12: 355362.

This page intentionally left blank

Index

active regions, 26, 28-37 ADE equation, 168 adsorbed islands, 4 adsorption isotherm, 159, 160 Advanced Microwave Scanning Radiometer (AMSR), 324 advection, 168 advection-aridity model, 263 advection-dispersion equation (ADE), 87, 90, 132, 156, 157, 163, 181, 182 advective/dispersive flux, 138 advective-dispersive transport, 169, 438 advective transport, 359 advective velocities, 359 age dating, 356-60 agrichemicals, case study, 397^404 AIRSAR, 323, 328 AIR-TOUGH, 349 alternating direction implicit (ADI), 184 angular momentum equation, 63 aqueous-phase mole fraction, 219 aquifer heterogeneity, 144 arid regions, 334-73 examples of applications of new techniques, 356-64 hydrodynamic measurements, 340-5 net infiltration, 362-4 numerical modeling, 348-50 review of current and innovative techniques, 337-56 solute concentrations, 337 surface changes, 362-4 tracer development, 350-6 vapor flow analysis, 360-2 waste-disposal facilities, 393 water-budget methods, 345-8

water flux, 366-7 atmospheric boundary layer (ABL), 263-5, 275 atmospheric surface layer (ASL), 263-5, 269, 273 averaging procedure, 61-3 averaging theorem, 11-13 bacterial colonies diffusion-limited growth, 196 physiological and metabolic properties, 197-8 on solid porous media, 198 substrate-unrestricted zone in, 205, 207 balance equations, 63, 73, 214, 215 balance laws, 63 behavior assessment model (BAM), 399-400 Berca-Aerolith-10 system, 47 biodegradation, 166, 238 equations, 166 kinetics, 243-5 and mass transfer, 242-9 and transport, 246 of VOCs, 240-2 biomass change, specific rates, 198-9 block successive overrelaxalion (BSSOR), 184 Boltzmann similarity variable, 108 bomb-pulse tracers, 360 Bond number (Bo), 15 Borden, Ontario, site, 139 aquifer material, 217 natural-gradient field experiment, 144 boundary conditions, 44

444

INDEX

boundary value problems, 9, 14, 19, 20, 23 Boussinesq approximation, 269 Bowen ratio, 273-4 Bowen ratio/energy budget (BREB), 265, 273^ BREATH, 348, 349 Brinkman corrections, 13, 14 bromide, 144 Brunauer-Emmett-Teller (BET) equation, 239 buried waste repositories, 374-95 Cape Cod site, 139 capillary barriers, 380 capillary equilibrium, 27, 37 capillary forces, 82 capillary interfaces, 82 capillary networks, 9 capillary pressure, 26-7, 30-2, 37, 44, 61, 71-7 capillary pressure-saturation curves, 33, 42 capillary region, 30, 31 carbon tetrachloride, 144 casing-advance drilling, 338 CDE model, parameter estimates, 399-401 centrifuge techniques, 342-3 CGSTAB, 184, 185 chain rule, 68, 73 charge-coupled device (CCD) camera, 283, 290 chloride concentration in groundwater, 352 profiles, 357-60 chloride mass balance method, 350-1, 353 chlorine-36, 299, 351, 354, 359, 360 closure problems, 15-20, 23, 32, 36, 39, 43, 45 closure variables, 17 CMLS model, 424 Co , transport of, 135 coefficient of variation (CV), 401 cometabolism, 240-1 complex behavior, 34 composite media, 174 Compton scattering, 282 computational network models, 75

computed tomography (CT), 279, 284-8 concentration distributions, 173 conductivity function for pores of varying moisture content, 121 cone penetrometer technology, 296 conservation equations, 63, 64, 66, 73 conservationist objectives, 420 landscape scale, 425-7 constitutive functions, 59, 67 constitutive laws, 62 constitutive theory, 61, 67-8 contaminant aging, 133-4 contaminant transformations, 194 contaminant transport in porous media, 130-54 continuity equations, 11-12, 27, 44 contributing depth, microwave wavelength, 320 convection, VOC vapors, 236-7 convection-dispersion equation (CDE), 397, 420, 424 Cornell High Energy Synchrotron Source (CHESS), 285 coupled equations, 15 coupled-processes models, 145 coupling permeability tensors, 9 coupling tensors, 24 coupling terms. 9 cross-borehole techniques, 304-5 cubic lattice, 76 cumulant expansion technique, 89 CXTFIT, 399, 400 Darcy scale, 6, 8, 11, 31 closure problem, 15-20 equations, 19, 24 Darcy's equation, 157 Darcy's law, 58, 94, 95, 102-3, 157, 158, 179 DDT, 139 decision support systems (DSS), 426 degradation, 165-6 depth profiles, 298 desert regions precipitation, 377-80 soil water content, 375-6 desert soils, water flow in, 374-95 deuterium/oxygen-18, 354-6 dielectric constant, 319-20

INDEX

diffusion into concave cylindrical colony, 203-4 gas phase, 237-8 into hemispherical colony, 203-4 liquid phase, 238-9 of VOCs, 237-9 diffusion equations, 200, 201-2 diffusion-limited growth of bacterial colonies, 196 diffusion-limited regions, 219 diffusion-linked microbial metabolism, 194-209 dimensionless dissipation of temperature variance, 270 dimensionless dissipation rate for water vapor variance, 272 Dirac delta-function, 109 disc infiltrometer method, 100 disparate length-scales, 30 dispersion, 168 dispersion analysis, 356-60 dispersion coefficient, 132, 359, 402 dispersion tensor, 90 modeling, 91^4 dispersive transport, 132 dissolution mass transfer, 221 diurnal patterns, 325-8 dominant permeability tensors, 8 double integration, 109 drag tensors, 24 drainage potential, 411-12 drilling methods, 337-^0, 356 dual-porosity media, 174 dual-porosity model, 171-3 dynamic-convective sublayer (DCSL), 269, 270 dynamic effects, 27, 32, 33, 43, 47 dynamic parameter, 32 dynamic sublayer (DSL), 269, 270 dynamic theory, 44-5 echo-planar imaging (EPI), 289 electrical resistance tomography, 304-5 electrical resistivity technique, 301-2 electromagnetic induction (EMI), 300-1, 345 electromagnetic radiation, 281, 304 ensemble-mean concentration modeling, 87-91 entropy equations, 65

445

entropy inequality, 62, 64-7, 70-2 with common line properties neglected, 65-6 with interface properties neglected, 65 EPICS, 248 equilibrium adsorption equations, 160 equilibrium condition, 74 equilibrium molar concentrations, 216 equilibrium pressure, 74 equilibrium sorption isotherms, 161 equivalent first-order exchange models, 171 ERS-1, 324 ESTAR, 323, 328 Eulerian approach, 181 Eulerian-Lagrangian approach, 182 Eulerian velocity covariance tensor, 93 Eulerian velocity field, 91, 94 evaporation, 260-78 field-scale measurements, 262 evaporative flux, 271 farm advisor modeling objectives, 423-5 objectives, 419 farm scale modeling objectives, 422-5 quantitative assessment, 423-5 farmer modeling objectives, 422-3 objectives, 419 fast-spin echo (FSE), 289 fiber-optic sensors, 289 Fickian approximation, 214 Fickian transient diffusion, 245 Pick's equation, 265 Pick's law, 237-8 prediction errors, 214 field scale, 101-2 reactive contaminant transport, 138-9 water movement, 107-23 filter paper equilibrium method, 340 filtering, 3, 14, 19-20 fine-grid to coarse-grid method, 37 fingered flow in homogeneous sandy soils, 116-18 first-order mass transfer coefficient, 172 first-order models, 171 first-order rate equations, 172

446

INDEX

first-order solute mass transfer coefficient, 171 flow management in homogeneous and structured soils, 396-417 fluid-fluid interfaces, 60, 61, 75, 79, 82, 283 fluid-phase pressures, 71 fluid phases, momentum equations, 74 fluid saturation, 61 fluid-solid interfacial areas, 78 flux-dissipation methods, 268-9 flux limiters, 182 Fourier power spectra approach, 272 Fourier transform, 91-3, 95 fractal geometry, 434 fracture-matrix interface, 169, 172, 174 hydraulic conductivity, 178 fracture network, 174 fracture pore system, 177, 179 fracture system, 173 free convective sublayer (FCSL), 269, 270 free energy, 68-72 Fresnel inversion model, 325 Fresnel reflection equations, 318 Freundlich isotherm, 219 Gardner function, 386 Gardner soil, 111 Gardner's equation, 110 gas-liquid interface, 217 sorption, 218 gas-phase velocity, 213 Gauss-Seidel method, 184 Geographic Information System (GIS), 124, 427-8, 433 geometry-based transport models, 168-71 geostatistics, 434 Gibbs equation, 217 Glendale clay loam and sand, 382 GMRES, 184 governing equations, 62, 63, 156-8 gradient-recalled echo (GRE), 289 gravimetric soil moisture samples, 261 gravitational effects, 21, 27, 38 ground-penetrating radar (GPR), 302-3, 345 groundwater chloride concentrations, 352

sampling, 356 solute transport, 139 Haines' jumps, 82 heat-dissipation sensors, 340 heat-pipe method, 343 heat-pulse probe, 296 Helmholtz free energy, 62-4, 68, 70, 72 Henry's law, 217, 225, 245 heterogeneous porous media, 8, 25, 34, 87 inactive fluid, 29 spatially periodic model, 33 stratified, two-region model, 38 transport equation formulation for two-phase flow, 3 52 two-phase flow, 45 two-region model (TRM), 35, 37, 39 heterogeneous system, thermodynamics, 59-60 hollow-stem augering, 337-8 homogeneous porous media, 7-8 transport equation formulation for two-phase flow, 3-52 homogeneous sandy soils, fingered flow in, 116-18 homogeneous soils, flow management and transport, 396-417 homogeneous three-phase system, 10 horizontal deflection, 386 humid-region fluxes, 336-7 hydraulic conductivity, 99, 174, 177, 413 estimation methods, 342 spatially variable, 137-8 variability, 145 hydraulic conductivity functions, 157, 172, 179 hydraulic functions, 177, 434 hydraulic gradient, 58 hydraulic parameters, 173 hydrodynamic measurements for arid regions, 340-5 hydrostatic equilibrium, 77 hydrostatic pressure gradients, 71-2 hygrometer methods, 341 imbibition/drainage outflow methods, 344 immobile water, 439 inactive regions, 26, 29-37

INDEX

incomplete lower-upper (ILU) factorization, 184 inequality equation, 73 inertial dissipation scaling, 270-2 inertia! subrange scaling, 269 infiltration, 335 equations, 102 ponded surface condition, 111-12 surface pressure constant (negative or zero), 107 11 infiltration-overland flow, 101 infiltrometers, 434 integrating scales, policy maker, 427-8 integro-differential equations, 45 interdisciplinary research, 440 interface equations, 72 4 interface properties, 64, 73 interfacial areas, 74, 77, 78, 82 in models of two-phase flow, 58-85 interfacial tension, 73 internal boundary layer, 265-8 internal vapor blanket, 275 interphase mass exchange, 212 intrinsic average, 11 irrigation flow, 101 isotope hydrology, 298-300 isotopic composition of pore water, 355 Jacobi method, 184 JERS-1, 324 lab-to-field transformations, 438-9 laboratory experiments, 45-50 Lagrangian-Eulerian approach, 181 Lagrangian methods, 181, 182 Lagrangian solute plume dynamics, 87 Lagrangian velocity covariancc tensor, 91,93

Lambert-Beer's law, 282, 283 landscape scale, conservationist objectives, 425-7 Laplace transforms, 183 large-area multitemporal mapping, 328-30 large eddy simulation (LES), 268 large-scale dynamic pseudofunctions, 37 large-scale flow properties, 37 large-scale mass balance, 124 large-scale models of water movement, 123-4

447

large-scale permeability, 37, 43 large-scale pressure gradients. 37 large-scale problem, 33 large-scale properties, 35 large-scale relative permeabilities. 34 large-scale saturations, 36, 37 versus time, 49-50 large-scale single-phase permeability, 36 large-scale theory, 40 large-scale values, 37 large-scale volume fraction of water, 46 latent heat flux, 270-2 lattice element, 76 leaching metribuzin, case study, 397-404 models, 420, 424, 425 length-scale, 3, 4, 6, 7, 9, 12, 13, 28, 30 LF-index, 400-1 lidar system, 266 light nonaqueous-phasc liquids (LNAPL), 303 limiting deflected flow, 383-6 linear dependence, 19 linear equilibrium solute transport, 158-9 liquid-solid distribution coefficients, 217 liquid vapor partition coefficients, 248 local problem, 15, 33 local saturations, 38 local scale, 100-1 water movement, 107-23 local theory, 40 local values, 37 locally heterogeneous porous media, 136-7 lysimetry, 297-8, 346-8, 362^ macrodispersion, 137-8 macroscale equations, 61, 62 magnetic resonance imaging (MRI), 279-80 Manning's equation, 179 mass attenuation coefficient, 282 mass balance equations, 208. 214 mass transfer, 144, 145 and biodegradation, 242-9 mass transfer coefficients, 171, 220-2, 226 matrix equation solvers, 183-5 matrix pore system, 173, 174

448

INDEX

maximum downslope deflection, 383-5 maximum horizontal seepage, 383-5 mechanistic models, 424 meniscus, 77 metabolic rate equations, 208 metabolic reactions, 199-200, 208 metribuzin leaching, case study, 397^04 Michaclis-Menten constant, 196 Michaelis-Menten kinetics, 196, 200, 208 Michaelis-Menten relationship, 200 micrometeorological methods, 346 micromodels, 289-90 micropores, 4 microscale capillary pressure, 76 microscale equations, 61 microscale information, 14 microscale surface tension, 76 microscopic technologies, 289-90 microwave observations of soil hydrology, 317-33 microwave remote sensing, 318-22 active methods, 321-2 aircraft-based platforms, 323 current and near-future sensor systems, 322-5 ground-based platforms, 322-3 large-area multitemporal mapping, 328-30 passive methods, 320-1 recent research, 325-30 satellite-based sensors, 323-5 truck-based systems, 323 microwave wavelength, contributing depth, 320 MIKE SHE model, 425 MISER, 225 mobile water, 439 molar balance, 215 momentum equations, 12, 21, 27, 44, 66-7, 71, 74 Monin-Obukhov formulations, 273 Monin-Obukhov similarity theory, 261 Monte-Carlo simulation, 435 multicomponent flow, mathematical modeling, 225-7 multicomponent transport, 166-8, 212 modeling, 167 problems, 167 multidimensional flow, 157 multifactor nonideal transport. 144

multifactor transport models, 145 multilayer resistance formulations, 263 multiphase compositional modeling, 182 multiphase flow, 63, 65, 212 mathematical modeling, 225-7 modeling, 438 thermodynamic theory, 60 multiregion model, 28 NAPL-aqueous mass transfer, 216, 221 NAPL-gas interfacial areas, 220 NAPL-gas mass transfer, 216, 227 NAPL-vapor interphase mass transfer, 213, 215, 220 NAPLs, 165, 210, 212, 215, 237, 435 dissolution rate, 216 entrapped, 219-25 experimental observations, 219-25 residual saturations, 220 Navier-Stokes equations, 102 negligible coupling, 22-3 net infiltration, 335-6, 337, 351 in arid regions, 362-4 processes, 355 network models, 61, 75 neutron probe access tubes, 261 Newton-Raphson method, 179-80, 183 nitrogen/Brunauer-Emmett-Teller (BET) method, 216 nodular system, 47-9 nonadvective flux, 214 nonaqueous-phase liquids see NAPLs nonequilibrium adsorption equations, 162 nonequilibrium transport, 161 nonideal contaminant transport analysis, 139-45 factors responsible for, 132-8 mathematical modeling, 139^5 nonideal transport definition, 131 multifactor, 144 noninvasive monitoring techniques, 345, 435 nonlinear adsorption-desorption, 159-61 nonlinear sorption, 132-3 nonlocal problem, 13 nonlocal theory, 44 nonsteady flow simulations, 388—91

INDEX

TV-scale problem, 7 nuclear magnetic resonance (NMR), 281, 288-9, 303^ nuclear magnetic resonance imaging (NMRI), 288 numerical experiments, 435 numerical modeling for arid sites, 348-50 numerical simulation, 75-80 numerical solution Richards' equation, 179-81 transport equations, 181-3 two-dimensional (2-D) sloping system, 387-8 nutrient transformations, 194 Obukhov length, 267 ODEX drilling method, 338, 356 Ogallala aquifer, 139 one-dimensional diffusion, 201, 205, 207 one-dimensional Galerkin finite element simulator, 225 one-dimensional multicomponent advective-dispersive chemical transport, 167 one-dimensional transport equation, 245 one-point Bowen ratio method, 273^ one-site sorption models, 161-2 organic compounds, preferential flow of, 139 organic liquid contaminants, 210-34 organic liquid saturation, 210 ORTHOFEM, 185 ORTHOMIN, 184, 185 Owen's Lake, 272 Owen's Valley, 272, 274 packed-bed catalytic reactor, 4 pair production, 282 Palo Alto Baylands, 139 partial differential equations, 167 passive microwave remote sensing, 261, 262 PCE, 223 Penman-Brutsaert formulation, 261 Penman-Monteith resistance-type models, 263 permeability, determination, 20-3 permeability tensors, 8, 17-20, 22, 23 pesticide leaching, case study, 397-404

449

pesticide transport in vadose zone, 138 Petrov-Galerkin methods, 182 phase equations, 72^ with expanded dependence of free energy on independent variables, 70-2 with simple dependence of free energy on independent variables, 68-70 photoelectric absorption, 282 photoluminescent volumetric imaging (PVI), 290 physical transport, 245-6 Picard iteration method, 179-80, 183 piston-like flow, 336 point values, 13 policy maker integrating scales, 427-8 objectives, 420 ponded surface condition, 111-12 pore fluid distribution, 212 pore groups, water exchange between, 121 pore-scale models for unsaturated conductivities, 102^ pore water age, 351 isotopic composition, 355 velocity, 402 porous catalyst, 4 porous media, 4 contaminant transport, 130-54 hierarchical, 6 nonideal contaminant transport of reactive solutes, 130-54 quantification of structure, 440 solute transport in, 131-2 (see also heterogeneous porous media; homogeneous porous media; stratified porous media) position vectors, 14 preasymptotic regime, 91 precipitation in desert areas, 377-80 preconditioned conjugate gradient (PCG) method, 184 preferential flow, 173, 336 measurement, 438 modeling, 122, 439 of organic compounds, 139 process, 179 simulations, 177

450

INDEX

preferential flow (cont.) in structured clay soils, 118-23 pressure deviations, 21, 31 pressure gradients, 31, 42 pressure head, 175, 178, 382 pressure-like variables, 20, 21 pressure profiles, 388 Priroda, 324 probability density function, 88, 89 process-dependent properties, 27 process time, 49 product formation, specific rates, 199 pseudofunction theories, 4 pushbroom microwave radiometer (PBMR), 323 quasi-static closure problems, 35 quasi-static flow, 33, 35, 40 quasi-static theory, 41, 43-5, 47, 48 RADARSAT, 324 radiography, 281-3 Raoult's law, 216 rate-limited desorption, 219 rate-limited sorption, 144, 145 rate-limited sorption/desorption, 133-4 rate process descriptions, 435 scaling, 438 Rayleigh scattering, 282 reactive contaminant transport, field scale, 138-9 reactive solutes, nonideal contaminant transport in porous media, 130-54 recharge, definition, 336 recharge rates, 352 reciprocity relation, 23-4 relative humidity (RH), 216 relative permeability curves, 36 repression, 241 residual flux, 335 retention functions, 434 Richards' equation, 102, 107, 108, 112, 122, 156, 168, 170, 172, 179, 348, 420, 424, 439 numerical solution, 179-81 risk assessment effect of dispersion and velocity, 401-3

effect of spatial variability, 397^104 root water uptake, 158 sand properties, 48 sandstone properties, 48 saturation, 62, 74, 77 saturation gradient, 27, 80 scalar diffusion, 90 scale effect, 87, 137 scaling theories, 439 SCS curve number method, 124 SEAMIST system, 296, 339 second law of thermodynamics, 59 sedimentary basin, 4, 5 seismic reflection and refraction methods, 302 semiarid zones, 334-73 sensible heat flux, 270-2 sensor installation techniques, 339 Sherwood number, 221 simulation statistics, 78 single-phase flow, 28, 58 single-species solute transport, 156-64 SIR-C/X-SAR, 324 slope length, 388 sloping interfaces, steady-state one-dimensional flow through, 381-3 sloping layered soils, water movement modeling for, 380-91 soil aridity function, 262 soil dielectric properties, 318 soil electrical conductivity, 296 soil hydraulic properties determination, 100-6 spatial variability, 404-14 and water movement, 99-129 soil hydrology microwave observations of, 317-33 processes, 99 soil-liquid partition coefficients, 248 soil moisture characteristic relationships, hysteresis, 104-6 soil moisture content, 216 soil morphology, spatial variability, 404-14 soil physics, 439 soil-plant system, 158 soil-root interface, 158

INDEX

soil solution extraction in vadose zone, 294-5 soil surface boundary condition, 173 soil vapor extraction (SVE), 210-11, 216 modeling framework, 211-19 soil-water age, 351 soil-water conductivity function, 107 soil-water content in desert regions, 375-6 temporal variation, 376 soil-water expertise, 418-31 objectives by profession, 419-20 soil-water-plant-chemical system, 419 soil-water potential measurement, 293-4, 341 soil-water pressure, 99 soil-water retention curves, 99, 179 soil-water retention function, 157 soil-water scientist challenge for, 429-30 objectives, 420 responsibility at all scales, 428 solid-aqueous mass transfer coefficient, 227 solid-phase Lagrangian strain tensor, 68 solid-phase sorption, 218 solute concentration, 176 in arid regions, 337 solute mass. 176 solute retardation factor, 157 solute transfer rates, 176 solute transport in groundwater systems, 139 in porous media, 131-2 sonic drilling methods, 338-9 sorption, 245 variability, 145 of VOCs, 239-40 sorption/desorption, rate-limited, 133-4 sorptivity. exact and approximate values, 109 spatial covariance tensor, 95 spatial decompositions, 13 spatial-scale considerations, 420-30 spatial variability effects on risk assessment, 397-404 hydraulic conductivity, 137-8 in soil hydraulic properties and soil morphology, case study, 404-14

451

sorption, 134-5 spatially heterogeneous porous geologic formation, 90 specific humidity, 266 SPLaSHWaTr, 349 SSM/I satellite sensors, 324 statistical physics, 88 steady-state one-dimensional flow through sloping interfaces, 381-3 Stefan-Maxwell equations, 238 stochastic continuum modeling, 437 stochastic flow, 435 Stokes' equations, 8, 10, 13, 19 Stokes' flow problem, 18 stratified porous media, 7 two-phase flow perpendicular to, 47, 48 unit cell, 35 stratified unit cells, 34 stress tensors, 68-9, 74 strongly implicit procedures (SIP), 184 structured clay soils, preferential flow in, 118-23 structured media transport, 168 structured porous media, 136-7 structured soils, flow management and transport, 396-417 styrenc volatilization, model simulation, 226, 228 substrate concentration, 200-1 consumption, 200 1 diffusion, 201 profile, 202-3 unrestricted zone in bacterial colonies, 205, 207 uptake, specific rates, 199 subsurface porous media, 87 solute transport, 86-98 successive line overrelaxation, 184 successive overrelaxation (SOR), 184 superficial average, 11, 12 superposition principle, 112-15 surface changes in arid regions, 362-4 surface pressure, constant (negative or zero), 107-11 surface resistance approaches, 263 surface tension, 20 surface viscosity, 11

452

INDEX

SWIM, 348 symmetric spatial covariance tensor, 90 symmetry, 23-4 synthetic-aperture radar (SAR), 322, 324 Taylor series, 31, 33 Taylor's hypothesis, 271 tension infiltrometer (TI), 295 tensor coefficients, 23 tetrachloroethene, 144 thermal estimation methods, 343^ thermocouple psychrometers (TCPs), 338, 341-2 thermodynamic relations, 63 thermodynamic theory for multiphase flow, 60 thermodynamics, heterogeneous system, 59-60 third-order structure function, 272 third-order structure function equation, 269 three-dimensional pore-water velocity distribution, 287 three-dimensional sonic anemometer, 272 three-phase system, 11 homogeneous, 10 time-dependent numerical solution, 393 time domain reflectometry (TDR), 261, 291-3, 305, 344-5, 434 toluene, 236, 238 biodegradation, 241-2 concentration change with time and distance, 248-54 physical transport, 245-6 total variation diminishing (TVD) schemes, 182 TOUGH, 348 toxicity, 241 tracer development for arid regions, 350-6 tracer experiments, 139 tracer plume movement, 90 transfer processes, 424 transformations, lab-to-field, 438-9 transient flow, 173 transient styrene dissolution experiment, 224-5 transient variably saturated flow, 167

transient volatilization, 224 transport and biodegradation, 246 in homogeneous and structured soils, 396-417 transport equations, 156-8, 266 formulation for two-phase flow in homogeneous and heterogeneous porous media, 3-57 mathematical modeling, 225-7 numerical solution, 181-3 transport models, 155-93, 435 geometry-based, 168-71 multifactor, 145 trichloroethene, 144 trichloroethylene (TCE), 236, 238, 240 biodegradation, 241-2 concentration change with time and distance, 248-54 physical transport, 245-6 tritium, 353-4, 360 turbulent kinetic energy (TKE), 269-70 two-chamber diffusion cell shown, 246 two-dimensional steady groundwater flow, 90 two-phase flow, 28 in heterogeneous porous media, 45 interfacial areas in models of, 58—85 perpendicular to stratified system, 47, 48 in porous media, 63 quasi-static case, 25—37 transport equation formulation for homogeneous and heterogeneous porous media, 3-57 two-region chemical nonequilibrium transport, 162-3 two-region model (TRM), 34, 163 heterogeneous porous media, 35, 37-9 two-region physical nonequilibrium transport, 163^ UNSAT-H, 349 unsaturated hydraulic conductivity, 382 vadose zone, 86 bacteria, 197 characterization, 279-316 diffusion-linked microbial metabolism, 194-209

INDEX

vadose zone (con?.) flow, recent advances, 155-93 pesticide transport in, 138 solute transport through, 138 vadose zone emerging measurement techniques, 279-316 computed tomography (CT), 284-8 cross-borehole techniques, 304-5 electrical resistivity technique, 301-2 electromagnetic induction technique, 300-1 field/landscape scale, 297-305 ground-penetrating radar (GPR), 302-3 in situ, 295 isotope hydrology, 298-300 lysimetry, 297-8, 346-8, 362-4 micromodels, 289-90 microscale, 281-97 noninvasive geophysical techniques, 300-4 noninvasive, nondestructive, 281 nuclear magnetic resonance (NMR), 281, 288-9, 303^ radiographic, 281-3 seismic reflection and refraction methods, 302 soil-water potential measurements, 293^ time domain rcflectometry (TDR), 261, 291-3, 305, 344-5, 434 vadose zone hydrology (VZH) changes over past decade, 434 current research, 432-5 future directions, 438 soil solution hydrology, 294—5 status report, 435-8 summary of posters by subject matter, 433 Vadose Zone Hydrology (VZH) Conference, 279 van Genuchten relations, 434 vapor blanket, 266 vapor flow analysis in arid zones, 360-2 vapor-phase transport, 164-5 variably saturated dual-porosity model, 177 variably saturated flow, 1 7 1 9 velocity covariance tensor modeling, 94-6

453

velocity-like variables, 20, 21 vertical flow barriers, 387-8 vertical flow boundaries, 388 vinyl chloride, 144 viscous cross-flow, 47 viscous drag tensors, 8, 9, 17 VOCs, 210-11 background on fate processes, 236-42 biodegradation of, 240-2 coupling vapor transport and transformation, 235-59 distribution and mobility, 216 mass transfer, 218 migration, 212 retention, 217 sorption, 216 transport, 212 vapor transport and fate, 235-6 volatile organic chemicals see VOCs volatilization, 164-5, 221 mass transfer correlation, 221, 222 transient, 224 volume-averaged momentum equations, 16 volume-averaged transport equations, 14,22 volumetric soil moisture, 319-20 volumetric water content, 99, 175, 178 vorticity, 94 waste disposal, 365-6 facilities in arid areas, 393 water-budget methods for arid sites, 345-8 water content measurements, 344—5 water exchange between pore groups, 121 water-flooding experiments, 45 water flow, 156-64 in arid regions, 366 in desert soils, 374-95 theory, 439 water-gas interface, 289, 290 water movement field scale, 107-23 large scale, 123^ local scale, 107-23 modeling for sloping layered soils, 380-91 and soil hydraulic properties, 99-129

454

INDEX

water movement (cont.) in unsaturated soils, 104 water oil flow, 46 water penetration velocity as function of moisture content, 122 water potentials, measured and simulated, 361, 365 water retention, 174 curves, 104, 404 functions, 172 water transfer rates, 175, 177, 178 WATSOLV, 184 wetting fluid/nonwetting fluid interfacial area, 79

wetting fluid/solid interfacial area versus elevation, 80 wetting phase, 61 films, 82 saturation versus elevation, 79 x-ray computed microtomography (CMT), 284, 285, 286 x-ray imaging, 285 x-ray tomographic microscopy (XTM), 285 Young-Laplace equation, 75, 82, 83