El Nino and the Earth's Climate: from Decades to Ice Ages

El Niño and the Earth’s climate : from decades to Ice Ages. Julien Emile-Geay Verlag Dr Müller 2008 Acknowledgemen...

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El Niño and the Earth’s climate : from decades to Ice Ages.

Julien Emile-Geay

Verlag Dr Müller

2008

Acknowledgements There are many people who generously contributed their time, ideas and encouragement to this work, and to whom I would like to extend my heartfelt thanks. First of all my advisor Mark Cane, for his support, patience, wisdom, thoughtful guidance, his love of science and his love for talking, sometimes, about everything else but science. If it were not for his invitation, I would not have come to the United States for my PhD - I would have stayed in Paris and my life would have taken a very, very diﬀerent turn. Richard Seager, for being always available for sassy, ironic, and sometimes scientiﬁc comments, for his precious and inoxidizable enthusiasm, for his diligence at reading and editing my non-native prose, for his patience at correcting my mistakes and for (exceptionally) wearing pink socks with a pink hawaiian shirt. Peter deMenocal, for his support, breadth of knowledge and encouragement throughout my thesis. Ming-Fang Ting, for a patient appraisal of all my mistakes, and for her relentless kindness in answering my questions, which taught me the 2 or 3 things I know about atmospheric Rossby waves. Steve Zebiak , for being such an inspiring model to follow and for his willingness to share ZC black magic. Ed Cook, for being as much at ease with singular-spectrum analysis as with the history of Bhutan. Edwyn Schneider and Adam Sobel, for constructive reviews of the thesis manuscript. Gerald Haug, Bette Otto-Bliesner, Chris Hewitt, for kindly providing access to their data. C.Gao, E. Hendy, R.Stothers, M.Mann, R. Bay, J.Cole-Dai, T. Johnson, T. de Putter, W. Qian, J.Li, M.Evans, R.Villalba, A. Schilla, N. Dunbar, M. Lachniet, Andrew Wittenberg, for some inspiring advice. Everyone in the Lamont Climate Group for making it such a friendly environment to work in. In particular : Bruno Tremblay, for having found put me on the track of the one bug that bugged me most, for uncountable rides home, for his enthusiasm for science, his open mind, his joy and friendship. Alexey Kaplan, for his patience,

availability, interest and wit. Naomi Naik, for being such a tech wizard and always tweaking the knobs in the right direction. Gustavo Correa for his incredible patience, kindness and availability ; for educating me somewhat about the strange language of computers ; and giving me unique training in this universal language called Brazilian music. Larry Rosen for the IT, the Bush-bashing, the 800-pound gorilla, and above all for naming my hard drive ”Gonzo” after the death of Hunter S. Thompson. Jennie Velez for all the computer tricks, Ingrid bits, Matlab scripts and freebie candy. Virginia DiBlasi Morris, for ﬁxing all the troubles. Yochanan Kushnir, Nili Harnik for educating me ever-so-slightly about our atmosphere. Doug Martinson for his profound insight on timeseries analysis and his inexhaustible sense of humor. Jason Smerdon, for his good will with Mathematica and his great enthusiasm. Irina Gorodetskaya, my oﬃce-mate, for putting up with my desktop sound system for close to 2 years. I am somewhat disappointed that after all that time, she never understood the essential distinction between Deep House and Minimal Techno, but thankfully we got along on Brad Mehldau, Keith Jarrett and brazilian tunes. More thanks go to : Alexander van Geen, for starting it all. My parents for all their support, though they were dreadfully close to asking the “When are you done with that thesis ?” question one time too many. Marc Spiegelman, for his great teachings and most important of all his good mood at all times. Edward Spiegel, for a very inspiring look at non-linear dynamics, and the memorable story of Voltaire’s sneering at Maupertuis, en français dans le texte. Alex Hall, Dan Schrag, for encouraging me to persevere in this ﬁeld. The Boris Bakhmeteﬀ Fellowship for supporting me over the 2004-2005 academic year. Martin Visbeck, for teaching me that a number without error bars is utterly worthless. Natalie Boelman, Felix Waldhauser, Chris Zappa, David Ho, Heather Griﬃth, Meredith Kelly, Trevor Williams, for making my life more enjoyable at Lamont in yoga and in traﬃc. Fellow students Celine Herweijer, Peter Almasi, Richard Katz, Allegra LeGrande, Sharon Stammerjohn, Jessie Cherry, for sharing my pains and smiles. Colin Stark, for his long-lasting scientiﬁc friendship, for being the only man who understood Mulholland Drive apart from David Lynch, and for an evening crunching numbers in Mathematica while I was cooking. Gary Snyder sensei, Ken Polotan sensei and all of Columbia Kokikai Aikido for helping me keep One Point in all circumstances (or trying to, at least). Stephanie, Dafna, Matthew and Fernando, for all the lunchtime escapes. Kashi, for reminding me of what I had come for.

Ori Heﬀetz and Dror Weitz, for convincing me by example that one’s scientiﬁc activity is only as great as one’s enjoyment of existence. Ross, Mike, Andrew for being my New York family and for religiously adhering to the Sunday night Simpsons gospel. Lara Eastburn, for diligent and generous review of this manuscript, which added a much-needed literary touch. Vincent Aurora, for a bit of the same. Amy Whitehouse, for her fantastic pictures of rock stars and scientists alike. Michael and Genevieve, my Atlanta family, for Elements of Style and healthy portions of Taste. Vanita, for sharing my life.

This thesis is dedicated to my family, who owns nothing but knowledge.

I would like to dedicate it especially to my grandfather, Maurice Geay, who made my New York adventure possible and died shortly after it had begun.

Foreword This book is the outcome of my PhD work at Columbia University, under the supervision of Prof. Mark A. Cane, Dr Richard Seager, and Prof. Peter B. deMenocal. It was originally published as my dissertation, albeit in a much more unpleasant form that seemed to the liking of the Columbia Library. When Verlag Dr Müller offered to publish it in a bona fide book form, I felt both honored and overwhelmed. Honored that it would be deemed readable by more than an academic thesis committee and overwhelmed by the amount of work required to make it (hopefully) a worthy read for a broader audience. This was a year ago. In the meantime, some adventures on the blogosphere have taught me that our field is currently under intense scrutiny for some alleged failures of the peer-review process. It therefore seemed important that the largest fraction of this book must pass through the rigorous review process of top journals of the American Geophysical Union and the American Meteorological society, which was only recently achieved. Hence, the first three chapters are essentially reprints of said articles, differing only in a few updated figures. The fourth chapter has only been reviewed by my thesis committee, and is admittedly less polished. It is given here as it was submitted in November 2006 and is the topic of ongoing research. Since the requirements of the production process meant that all figures herein would be printed in black and white, a PDF of this book is available in full colors at http://jeg.ocean3d.org/texts/JEG_book.pdf. The attentive reader will soon notice that the formal “We” is used throughout this work. Far from being a statement of royalty, it should be taken as a tribute to the collective nature of the scientific process that eventually resulted in those pages - as well as a certain Old World side of me that even New York, cultural capital of the New World, could never quite subdue. As I put the last touches on this book, I am amazed at how much I would like to change it. Perfectionism, however, is often the enemy of deadlines, and I must resolve to put down the pen at this point. This feeling of incompleteness is a testimony to the dynamic nature of science – never set in stone, growing and evolving as organically as a living creature. Thus, this work should merely be taken as a snapshot of our current (and fragmentary) knowledge of a few special topics in paleoclimatology, centered around the infamous El Niño. I have no doubt (and in fact actively hope) that new data will come to challenge some of these ideas in the near future. For the time being, I hope you find it an enjoyable and instructive read nonetheless. Julien Emile-Geay, Atlanta, GA. July 25th 2008.

Table of Contents Introduction: Of low-frequency tropical climate variability Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 9

1 Pacific Decadal Variability 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Linear Equatorial Wave Theory at Decadal Frequencies . . . . . . 1.2.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 The Free Mode . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 The Forced Solution: Green’s Function . . . . . . . . . . . 1.2.4 Total Solution . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Low vs Mid-Latitudes . . . . . . . . . . . . . . . . . . . . 1.3.2 Modes Do Not Matter . . . . . . . . . . . . . . . . . . . 1.3.3 Response to Idealized Wind Patterns . . . . . . . . . . . . 1.4 Comparison with Previous Work . . . . . . . . . . . . . . . . . . 1.4.1 Comparison with Liu [2003] . . . . . . . . . . . . . . . 1.4.2 Comparison with Cessi and Louazel [2001] . . . . . . . . 1.4.3 Equivalence with the PGPV Solution. Scaling Arguments 1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

17 17 21 21 22 26 28 30 30 31 31 35 36 36 36 38 41

2 El Niño and Volcanoes 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 2.2 Explosive Volcanism and ENSO Regimes . . . . . . 2.2.1 Volcanic Forcing over the Past Millennium 2.2.2 Experimental Setup . . . . . . . . . . . . . 2.2.3 Results . . . . . . . . . . . . . . . . . . . . 2.2.4 A Phase Diagram for ENSO regimes . . . . 2.3 A Remarkable Case: the 1258 Eruption . . . . . . . 2.3.1 Forcing . . . . . . . . . . . . . . . . . . . . 2.3.2 Results . . . . . . . . . . . . . . . . . . . . 2.3.3 Comparison to the Proxy Record . . . . . . 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . .

45 45 47 47 48 49 51 56 56 56 59 61

xi

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

3 El Niño and the Sun 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Climate Forcing over the Holocene . . . . . . . . . . . . . . . . . . 3.2.1 Orbital Forcing . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Solar Irradiance Forcing . . . . . . . . . . . . . . . . . . . . 3.3 Experimental Setting . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Representation of Weather Noise . . . . . . . . . . . . . . . 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Solar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Orbital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Orbital & Solar . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Global implications . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Solar-induced ENSO and North America . . . . . . . . . . 3.5.2 Solar-induced ENSO and the North Atlantic . . . . . . . . 3.5.3 Solar-induced ENSO and the Monsoons . . . . . . . . . . . 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Limitations of the Model Arrangement . . . . . . . . . . . 3.6.3 Forcing Uncertainties . . . . . . . . . . . . . . . . . . . . . 3.6.4 Theoretical Implications of a Solar-Induced ENSO-like Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 73 75 76 76 79 79 79 80 80 83 83 86 86 88 89 91 91 91 92

4 El Niño in the Icehouse 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Climate of the Last Glacial Maximum . . . . . . . . . . . . . 4.2.1 The CCSM3 Simulations . . . . . . . . . . . . . . . . . . 4.2.2 The HadCM3 simulations . . . . . . . . . . . . . . . . . 4.2.3 Intercomparison of Simulated LGM Climates . . . . . . . 4.3 Characterizing Ice Age Teleconnections . . . . . . . . . . . . . . . 4.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Results: Glacial Teleconnections Patterns . . . . . . . . . 4.4 Modeling Ice Age Teleconnections . . . . . . . . . . . . . . . . . 4.4.1 A Nonlinear Model of Stationary Waves (NLIN) . . . . . 4.4.2 A Linear, Steady-State Model of Stationary Waves (ELM) . 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

. . . . . . . . . . . . .

92 93 94 101 101 103 104 104 105 108 108 113 119 120 127 135 137

Conclusion 143 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 A Pacific Decadal Variability: Boundary-Layer Correction

151

B El Niño and the North Atlantic

153

xiii

List of Figures 1.1

1.2

1.3

1.4

1.5

The Cold tongue index and its spectral properties (a) Cold Tongue index (CTI) and its 7-year lowpass filtered version. (b) Spectral estimate of the CTI using multi-taper method (MTM) and the robust noise estimation procedure of Mann and Lees [1996]. The black curve identifies harmonic components together with noise and broadband signals, while the “reshaped” spectrum only includes the latter two. Numbers above the curves correspond to the period of oscillation, in years. (c) Significance test of harmonic components, based upon an F -test [Mann and Lees, 1996]. A peak is deemed signicant if its F value is above the critical threshold imposed by a particular confidence level (95% or 99% here). . . . . . . . . . . . . . . . . . . . .

19

Eigenstructure of the free mode hM , for Ÿω = ≠0.029 to facilitate comparison with the gravest planetary basin mode of Yang and Liu [2003] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

Amplitude and phase of the functions E and Z , which characterize the response via hE . Along the functions are their asymptotic expansions for large and small ◊, denoted by the subscripts ∞ and 0, respectively. See text for details. . . . . . . . . . . . . . . . . . . . .

29

Eﬀect of the latitudinal position of the wind forcing. a1) Varying extent of wind forcing in the F = 1 case ; a2) Thermocline response ; b1) Varying location in the F = 1 case ; b2) Thermocline response c1) Varying location in the F = sin(ﬁ yyN ) case ; c2) Thermocline response. The numbers above the spectra on the right-hand side correspond to the period of oscillation (years). . . . . . . . . . . . . . .

33

y2

Response of the INC model to F = e≠µ 2 for varying values of the width parameter µ. The values of hE plotted here are the average over the last year of a 200-year integration of the shallow-water solver INC [Israeli et al., 2000], with a constant forcing applied. The model was run in a symmetric basin with yN = 60◦ N and Rayleigh friction r = 50 year≠1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

35

1.6

2.1 2.2

2.3 2.4

2.5

Reproducing Fig 5 of LIU03. The right-hand panels present the forc2 ing (a) F (y) = e≠µy /2 , b) F (y) = 1, c) F (y) = cos(ﬁ yyN ), and d) F (y) = sin(ﬁ yyN ), respectively. The left-hand panels present the corresponding thermocline response |hE („)| . . . . . . . . . . . . . . .

37

Response of the Zebiak-Cane model to volcanic forcing during the past millennium. Forcing and 200-member ensemble average. . . .

49

ENSO regimes as a function of the intensity of volcanic cooling . The abscissa is the intensity of volcanic forcing in a given year (k) and the ordinate is the fraction of the ensemble members that went into an El Niño event during the following year (k + 1). Colored dots correspond to remarkable eruptions of the past millennium . . . . .

52

ENSO regimes as a function of the intensity of volcanic forcing. Same as Fig 2.2 but with a forcing weakened by 30%. . . . . . . . .

54

ENSO regimes as a function of the intensity of volcanic forcing (2). As in Fig(2.2), except that the ordinate is the ensemble mean of the maximum of monthly NINO3 values reached by the model during the calendar year following the eruption. This gives insight into the impact of the forcing on the amplitude of events, as opposed to their frequency of occurrence. . . . . . . . . . . . . . . . . . . . . . . . .

55

Intra-ensemble distribution of the monthly NINO3 index in the period Jan 1259 - Dec 1259 (light gray curve), compared to the reference distribution computed over the rest of the millennium (black curve). We used a kernel density estimation with a Gaussian kernel and a width of 0.15◦ C. . . . . . . . . . . . . . . . . . . . . . . . . .

57

2.6

Multiproxy view of the 1258 eruption: (a) Volcanic forcing (black curve) in Wm≠2 and 200-member ensemble mean response of NINO3 in the Zebiak-Cane, after applying a 20-year low-pass filter (light blue curve). (b) year-to-year change in PDSI over the american West [Cook and Krusic , 2004] (c) Standardized tree-ring width at El Asiento, Chile [Luckman and Villalba, 2001] (d) Titanium percentage in core 1002 from the Cariaco basin [Haug et al., 2001] (standard deviation units). 60

2.7

A flood proxy from Peru: record of fine-grained lithics since 800 A.D. from Rein et al. [2004]. The thick red curve is lowpass filtered, and the shaded area corresponds to the Medieval Climate Anomaly. Note the sharp transition around 1260 A.D. . . . . . . . . . . . . . . . . xvi

62

3.1

EOF analysis of the top-of-the-atmosphere insolation over the Holocene. The leftmost column shows the EOF pattern as a function of calendar month (Jan =1, Feb =2, etc..), the center column shows the PC timeseries, and the rightmost column its spectral density, computed with the multitaper method [Thomson, 1982]. Numbers above the graph refer to the period in kyr. To obtain the contribution of a mode to the total insolation at any given time, each EOF pattern must be weighted by the value of the corresponding PC. . . . . . . . . . . . 74

3.2

Spectral analysis of the 14 C production rate record. a) 14 C timeseries from Bond et al. [2001], converted to Wm≠2 for the intermediate scaling (a Maunder Minimum solar dimming of 0.2%◊S◦ , see text for details). b) Multi-taper spectra and 99% confidence level for rejecting the null hypothesis that the series is pure ”red noise” (AR(1) process). This follows the methodology of Mann and Lees [1996]. . . . . . . .

78

Model response to solar forcing (∆F = 0.2%So , experiment Sol0.2 ). a) Solar forcing (grey) and response (TW ≠ TE ) (black). b) Wavelet spectral density (arbitrary units, with maxima in black, minima in white). The thick black line is the cone-of-influence, the region under which boundary eﬀects can no longer be ignored [Torrence and Compo, 1998] . The Morlet wavelet was used here) c) Global Wavelet Spectrum and 95% confidence level (see text for details). d) Probability of a large El Niño event over a 200 year window. . . . . . . . . .

82

3.4

Same as Fig 3.3 but for orbital forcing (experiment Orb ). . . . . .

84

3.5

Same as Fig 3.3 but with orbital and solar forcing (∆F = 0.5%So , experiment Orb_Sol_0.5). . . . . . . . . . . . . . . . . . . . . . .

85

Linear prediction of ENSO variability from solar parameters. a) Lowpass-filtered zonal SST diﬀerence (EW), and predictor variables: PC1 and PC2 from Fig 3.1 and Fo from Fig 3.2, with ∆F = 0.5%So b) Comparison between predicand and predicted variable. See text for details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

ENSO influence over the North Atlantic. On the left are regression patterns of wind vectors from the specified product, smoothed by a 3-month running average, on the NINO3 index, normalized to unit variance. Hence, units of regression coeﬃcients are given per standard deviation of the index. On the right are corresponding correlation patterns, shown for the meridional component only. (a) GFDL H1 surface wind-stress regression, (b) GFDL H1 meridional wind-stress correlation. (c) POGA-ML surface wind-stress regression (d) POGAML meridional wind-stress correlation (e) Analysis of ICOADS data, surface wind regression (f ) Analysis of ICOADS data, meridional wind correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

3.3

3.6

3.7

xvii

4.1

Intercomparison of GCM Climatologies: Surface Air Temperature. (a) Present climate, taken from the NCEP/NCAR Reanalyses [Kalnay, 1996] ; (b) HadCM3 CTL ; (c) CCSM3 CTL ; (d) [b -a] ; (e) HadCM3 LGM (f ) CCSM3 LGM . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Intercomparison of GCM Climatologies: Upper Tropospheric Zonal Wind. (a) Present climate, taken from the NCEP/NCAR Reanalyses [Kalnay, 1996] ; (b) HadCM3 CTL ; (c) CCSM3CTL ; (d) [b -a] ; (e) HadCM3 LGM (f ) CCSM3 LGM. (The color scales and contour intervals are the same within a row). . . . . . . . . . . . . . . . . . 4.3 SVD Analysis of Present Day Teleconnections from the tropical Oceans. Mode 1 a) SST pattern (left singular vector) ; b) Geopotential height field (Z250) (right singular vector) c) Expansion coefficients (normalized) . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 SVD Analysis of Present Day Teleconnections from the Tropical Oceans. Mode 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 SVD Analysis of CCSM3 (CTL) Teleconnections from the Tropical Oceans. Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 SVD Analysis of the CCSM3 (LGM) Teleconnections from the Tropical Oceans. Mode 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 SVD Analysis of the HadCM3 (CTL) Teleconnections from the Tropical Oceans. Mode 1 . . . . . . . . . . . . . . . . . . . . . . . 4.8 SVD Analysis of the HadCM3 (LGM) Teleconnections from the Tropical Oceans. Mode 1 . . . . . . . . . . . . . . . . . . . . . . . 4.9 Validation of the Non-Linear Model (NLIN) a) El Niño composite of diabatic Heating field in the NCEP Reanalyses, 1949-1999 ; b) Model streamfunction response to such heating at 250 mb, in 106 m2 s≠1 c) El Niño composite of 250mb streamfunction in the NCEP Reanalyses, 1949-1999 (blue contours are negative, red contours are positive values). Units are in 105 m2 s≠1 . . . . . . . . . . . 4.10 Response to El Niño and Idealized Heating in NLIN: NCEP Basic State: a) Realistic El Niño heating cut outside the tropical Pacific ; b) Streamfunction response (to be compared to Fig 4.9b) ; c) Gaussian heating centered at [190◦ E,0◦ N] ; d) Streamfunction response. . . . 4.11 Response to El Niño Heating in NLIN: CCSM3 Basic State: a) Precipitation-derived heating in CTL b) geopotential height response for the pre-industrial case c) Same for LGM d) geopotential height response for the LGM . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Response to El Niño Heating in NLIN: HadCM3 Basic State: a) Precipitation-derived heating in CTL b) geopotential height response for the pre-industrial case c) Same for LGM d) geopotential height response for the LGM . . . . . . . . . . . . . . . . . . . . . . . . . xviii

106

107

111 112 114 115 117 118

122

124

125

126

4.13 EOF Analysis of Pseudo-Green’s Function Forcing in ELM: CCSM3 CTL basic state. a) First EOF b) corresponding PC, indicated the favored location for forcing exciting such a mode c) Second EOF d) corresponding PC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.14 EOF Analysis of Pseudo-Green’s Function Forcing in ELM: as in Fig 4.13, but with the CCSM3 LGM basic state. . . . . . . . . . . . 4.15 Diﬀerence in El Niño Heating in CCSM3: LGM minus CTL . . . 4.16 EOF Analysis of Pseudo-Green’s Function Forcing in ELM: as in as in Fig 4.13, but for the HadCM3 CTL basic state. . . . . . . . . . . 4.17 EOF Analysis of Pseudo-Green’s Function Forcing in ELM: as in as in Fig 4.16, but for the HadCM3 LGM basic state. . . . . . . . . .

xix

129 130 131 132 133

List of Tables 2.1

2.2

Count of warm ENSO events in the year following a volcanic eruption. Comparison to Table 1 of Adams et al. [2003], with chosen keydate lists over the period 1649-1979. IVI = Ice-Core Volcanic Index [Zielinski, 2000; Robock and Free, 1995]. VEI=Volcanic Explosivity u Index [Simkin and Siebert , 1994]. ‘ Crowley’= chronology adjusted to the forcing used for our numerical experiments. M/L =“medium to large” eruptions. Listed are the number of eruptions in each list, the number of eruptions followed by a El Niño event within a year, and the ratio of the two previous numbers. See text for details. . . . Probability of an El Niño event after the 1258 eruption. Shown here is the fraction of ensemble members that produced an El Niño event in a 12-month window following the eruption. We applied the 3 following criteria for El Niño occurrence: {NINO34 Ø 0.5} for 6 consecutive months, {NINO34 Ø 1} (“strong El Niño”) and {NINO34 Ø 2} (“very strong El Niño”) over identical intervals. . . .

51

58

3.1

Summary of the numerical experiments used in this study. . . . . .

4.1

Variance analysis of Northern Hemisphere winter geopotential height. The total variance is the integral of 250 millibar geopotential height ss Õ 2 variance over the Northern Hemisphere NH ÈZ250 ÍdA, in 106 m2 . Then shown, for each mode, are the squared covariance fraction (SCF), in percent of the total covariance between SST and Z250 , and the fraction of the total variance in the field explained by the projection onto a given mode (FOV) . Only modes 1 through 4 are shown for brevity. (See text for details.) . . . . . . . . . . . . . . . . . . . . . . . . . . 116 EOF analysis of the sliding tropical forcing experiments in ELM. Numbers shown here are the fraction of variance explained by each mode for geopotential height at the ‡ = 0.257 level (close to 250 mb). Only modes 1 to 4 are shown for brevity. See text for details. . 134

4.2

xxi

80

Introduction: Of Low-Frequency Tropical Climate Variability “I am far too much in doubt about the present, far too perturbed about the future, to be otherwise than profoundly reverential about the past.” Augustine Birrell

Why climate? The fate of so many human societies has been so contingent upon atmospheric and oceanic conditions that it has become diﬃcult to overstate climate’s importance in shaping History as we know it. Indeed, it is widely recognized that the relative climate stability of the Holocene (roughly, the past 10,000 years of the Earth’s history) has been the necessary condition for the growth of human populations, their sedentarization, the domestication of crops and large mammals, the development of large-scale food production and technology, and their spreading among diﬀerent parts of the globe along similar biomes, chiefly defined by their climate [Diamond , 1999]. The backdrop for what we term Civilization, its origins, evolution and expansion across continents and overseas, seems to have been largely conditioned by climate. Yet, within the seemingly quiescent Holocene, intense droughts catalyzed the demise of highly organized human societies (Akkadian Empire, Tiwanaku and Classic Mayan civilizations), often in a matter of a few years [deMenocal , 2001; Haug et al., 2003]. It is the Trade winds and their northeasterly direction that pushed Columbus to the Caribbean to find “Indians”. The people of Japan partly owe the idiosyncrasy of their culture and language to a Mongol invasion reduced to nothingness by a tropical cyclone in 1281, thereafter named typhoon, or “divine wind” [Emanuel , 2005]. Closer to us, former commerce secretary William Daley estimates that “at least $1 trillion of [the U.S.] economy is weather-sensitive”* . Still, it would be excessive to claim that weather and climate are the sole determinants of human history and economics – to quote Gordon Manley, “the fall of Rome should not be attributed to a joggle of the * http://www.research.ibm.com/weather/DT.html

1

2

Introduction

barometer”. Nonetheless, it is now clear that they have had a pervasive influence on human aﬀairs, at times a critical one [Davis, 2001]. This growing awareness, and the necessity to better understand the dynamics of the Earth’s climate, have underpinned a tremendous research eﬀort in the past 50 years. Prominent in such a development has been the increasing recognition that anthropogenic emissions of greenhouse gases (carbon dioxide and methane, chiefly), have been warming the global mean temperature by about 0.8◦ C since 1860 (http:// data.giss.nasa.gov/gistemp/2005/), a sizable change only expected to worsen as emissions grow [Houghton, 2001], and to which many human and biological systems will have trouble adapting [McCarthy, 2001]. It then becomes critical to understand how the climate of our planet functions and how it could change under external forcing. Why low frequencies? Just as history informs us about the nature of human beings and dynamics of the complex social entities they form, so do past climates inform us about the dynamics of Earth’s climate system. By teaching us about the vastness of its parameter space, they provide a crucial testbed for the numerical models used to forecast its future evolution. As Edward Gibbon put it, “we know of no way of judging the future but by the past”. One of the past’s most salient messages, coming from all manner of geological and instrumental sources, is the demonstration that climate displays most of its variability on the longest timescales – the lowest frequencies – as epitomized by the Ice Ages of the Quaternary. Vexingly enough, we still don’t know precisely why the latter occurred. Other sources of low-frequency variability remain at the forefront of modern climate research and forecasting. What do we mean by low-frequency? Here we face a problem of definition, as the lowest resolvable frequency a dataset may oﬀer is inversely proportional to its length. In the 1970s, the term “low-frequency” described oceanic phenomena with a time-scale longer than a few seasons, and atmospheric scales longer than a few days. In the three subsequent decades, an ever-expanding stream of data has been gathered, showing almost ubiquitously that a climate record exhibits significant (if not dominant) variability on the longest timescale it resolves. As timeseries grew longer, spectra went redder. In our case, the lowest frequency we shall consider is determined by the availability of reliable data allowing a quantitative assessment of climate variability. This criterion is undoubtedly subjective, and here we have chosen to restrict our focus to timescales of 10 to 105 years: decades to Ice Ages. Why the Tropics? The Tropics are the Earth’s recipient of net annual mean radiation, and it is within cumulus towers of the deep Tropics that most of the energy that drives the atmospheric heat engine is transferred from the surface in the form of latent heat release [Peixoto and Oort , 1992]. Moreover, they cover about 50% of the surface of the Earth. Any theory of global climate change must therefore address changes in the Tropics in some way. El Niño and the Earth’s climate: from decades to Ice Ages.

Of low-frequency tropical climate variability

3

In addition, they are currently the stage of vigorous climate phenomena (chiefly, monsoons and the El Niño-Southern Oscillation, or ENSO) and there is ample evidence that these can organize atmospheric flow across the globe [e.g. Horel and Wallace, 1981; Ropelewski and Halpert , 1987; Trenberth et al., 1998]. Finally, low-frequency variability has been abundantly documented over the tropical oceans and continents ; from Pacific Decadal Variability [Trenberth and Hurrell , 1994; Zhang et al., 1997; Mantua et al., 1997; Guilderson and Schrag , 1998], to centennial changes in the tropical Pacific [Quinn, 1992; Hendy et al., 2002; Cobb et al., 2003] and Atlantic [Haug et al., 2003], to millennial cycles in the Asian monsoon [Neﬀ et al., 2001; Fleitmann et al., 2003; Gupta et al., 2003; Wang et al., 2005] and glacial/interglacial changes in ENSO frequency and amplitude [Moy et al., 2002; Tudhope et al., 2001]. At present, there is little or at best incomplete physical understanding of the causes of this variability. The long-standing paradigm of paleoclimatology holds that variations in the amount of sunlight received at the surface, amplified by a number of feedbacks, give rise to important variations in global climate. The scientific debate bears on exactly which parts of the system matter for the amplification of changes seeded by natural forcing (orbital, volcanic or solar), or whether some subparts of the system (the carbon cycle or the ENSO system, for instance) can produce self-sustained variability without invoking external forcing. This is true of timescales ranging from a few decades to the entire Quaternary era. Historically, the vast majority of ice age theories has shown a one-sided view of global heat balance, focused almost exclusively on high latitudes, with a belief that ice-albedo feedbacks were the cornerstone of glacial-interglacial cycles. Foremost amongst them, Milankovitch’s theory contends that it is the amount of summer insolation received at 65◦ N over continents that determines whether or not the winter snows survive the summer season [Milankovitch, 1941], thereby determining the growth or decay of large continental ice sheets. Though there are problems with this view [e.g. Paillard , 2001; Cane et al., 2006], orbital variations in insolation are still considered to be the “pacemaker of Ice Ages” [Hays et al., 1976], despite discrepancies between the spectrum of the climate response (stacked ” 18 O , showing a dominant peak around periods of 100 kyr) and that of the forcing, which is dominated by precession (with a period close to 23 kyr). This diﬀerence implies a strongly non-linear response of the climate system to insolation forcing. What is the dominant source of this non-linearity? By far the most widely accepted explanation is that of Broecker et al. [1985] that the North Atlantic thermohaline circulation (THC) may switch rapidly between two quasi-stable modes of operation (“on” or “oﬀ”), an argument later refined for glacial-interglacial transitions by Broecker and Denton [1989]. In the current climate, this meridional overturning circulation (MOC) contributes significantly to the poleward ocean heat transport in the Atlantic [Gordon, 1986; Ganachaud and Wunsch, 2000], and there is ample indication that its intensity varies in concert with climate over the last few glacial cycles: reduced or suppressed during Greenland cold episodes, and near current levels during warm periods [Boyle and Keigwin, 1987; Adkins et al., 1997; McManus et al., 2004]. There are, however, numerous problems with a THC-centric view of climate change.

4

Introduction

Clement and Cane [1999] point out a number of observations that the paradigm fails to explain when it comes to glacial cycles. In particular, state-of-the art climate models fail to produce a temperature response to THC shutdowns that is of the magnitude and extent implied by the geologic record. While absence of proof is not proof of absence, these shutdowns imply buoyancy perturbations of epic proportions, which raises suspicion as to their realism (see Clement and Peterson [2006]; Seager and Battisti [2007] for a review). Wunsch [2002] pointed out that the acronym THC is now often invoked as a “deus ex machina”, which has come to symbolize the cause of lowfrequency climate change on decadal [Sutton and Hodson, 2005] to millenial timescales [Alley et al., 1999], as well as extremely abrupt climate change [Clark et al., 2002] like the Younger Dryas cooling [Broecker , 1997], without always establishing how changes in the Atlantic MOC come about. As it is now clear that the ocean is a not a heat engine, but a mechanically-driven system [Munk and Wunsch, 1998; Gnanadesikan, 1999; Wunsch and Ferrari, 2004], there is every reason to believe that the most potent driver of THC changes is the global wind field [Wunsch, 2002], which is known to be significantly aﬀected by tropical SSTs. This is not so say that the THC is irrelevant to low-frequency variability. Still, these elements provided a strong incentive to explore alternate mechanisms of climate change actively involving the tropics. The pioneering work of Amy Clement and collaborators [Clement and Cane, 1999; Cane and Clement , 1999; Clement et al., 1999, 2000] aimed at providing a physically-based alternative. They established the ENSO system as the potential source of global, low-frequency climate variability – precisely via its non-linear behavior. In many ways, this book can be seen as a continuation of their pioneering work, by investigating a subset of mechanisms whereby low-frequency variability is produced within the tropical Pacific and exported to the rest of the globe. Where are we in 2008? Some of these original ideas have survived, others have not. The proposition that ENSO would be repressed during mid-Holocene due to an increased precessional insolation contrast [Clement et al., 2000] has been qualitatively supported by various proxy records [Tudhope et al., 2001; Moy et al., 2002; Koutavas et al., 2006]. The idea that the tropical Pacific can account for some of the changes in proxy records all over the world is rapidly gaining currency On the other hand, the suggestion that the glacial world would be more La Niña-like [Cane, 1998; Cane and Clement , 1999] has not been confirmed by observation, as preliminary assessments of the zonal SST gradients from sediment cores hinted to a more El Niño-like state at the LGM [Koutavas et al., 2002; Stott et al., 2002] (though some recent evidence calls for a near-neutral change from present conditions [Mix , 2006; Lea et al., 2006]). Furthermore, Seager and Battisti [2007] suggest that the cold periods recorded in Greenland ice cores (“stadials”) correspond to an El Niño-like state, and conversely for interstadials, La Niña-like. This is partly borne out of a better theoretical understanding of ENSO teleconnections developed in the past few years [Seager et al., 2003, 2005a], and a much improved documentation of its behavior over the past millennium [Cobb et al., 2003; Mann et al., 2005], all of which have provided a strong motivation to El Niño and the Earth’s climate: from decades to Ice Ages.

Of low-frequency tropical climate variability

5

look at the intriguing changes of the Medieval Climate Anomaly (known to some as the Medieval Warm Period) and the Little Ice Age. Coupled model simulations of glacial climates have also tremendously improved, allowing for a perusal at how ENSO changed under glacial boundary conditions. Closer to us, much work has been done on the causes of the decadal modulation of ENSO, with the emerging consensus that it is unlikely to originate outside the tropics [Hazeleger et al., 2001; Schneider et al., 2002; Karspeck and Cane, 2002; Karspeck et al., 2004; Seager et al., 2004] Therefore, the objective of the present work is to further explore the origins and the consequences of low-frequency tropical climate variability, on timescales of decades to Ice Ages. This scope is ambitious indeed, and we shall not fool the reader into thinking that all scientific questions on the topic shall be answered in the following pages – only a few mechanisms could be researched in detail. The very disparity of these timescales and our limited ability to model or analyze them made it necessary to reduce these broad scientific questions to a set of manageable problems. As the tool is enslaved to the problem it aims at investigating, assumptions and simplifications had to be made, often tied to the physical timescale of interest. In this spirit, the following four chapters reflect the four spectral bands under investigation: 1. Chapter 1 , 101 ≠ 102 years: Pacific Decadal Variability 2. Chapter 2 , 102 ≠ 103 years: Volcanoes and ENSO over the past Millennium 3. Chapter 3 , 103 ≠104 years: Millennial-scale, solar-induced variability of ENSO over the Holocene 4. Chapter 4, 104 ≠ 105 years: Ice Age changes in ENSO teleconnections In Chapter 1 we revisit recent theories of decadal variability [Liu, 2003; Cessi and Louazel , 2001] that use a shallow-water formalism of the tropical Pacific and argue that tropical Pacific decadal variability (PDV) can be accounted for by basin modes with eigenperiods of 10 to 20 years, amplifying a mid-latitude wind forcing with an essentially white spectrum. We question this idea using a diﬀerent formalism of linear equatorial wave theory. We obtain a general solution that allows us to explore more realistic wind forcings, and we find that the equatorial thermocline is inherently more sensitive to local than to remote wind forcing (Planetary Rossby modes only weakly alter the spectral characteristics of the response). This leads us to rule out basin modes as the cause for the “memory” of the system, and we discuss alternative mechanisms that can more plausibly account for it. Next we look at how the ENSO system behaved in the past millennia. Though we previously described internal mechanisms of variability, they seem insuﬃcient to explain the tropical Pacific SST varability observed over the past millennium, as reconstructed from coral biogeochemistry [Cobb et al., 2003]. If variability was indeed not endogenous, then it is only natural to look for an external origin: namely, the radiative forcing due to solar and volcanic activity. This work directly follows that of Mann et al. [2005], who found that the SST anomalies of the Little Ice Age (≥ 1650 ≠ 1850) and

6

Introduction

Medieval Climate Anomaly (MCA, ≥ 1000≠1300) could be partially explained by the dynamic response of the ENSO system to solar and volcanic (thermodynamic) forcing, notwithstanding the system’s tremendous internal variability. The answer lies in the fact that the solar irradiance is thought to have varied on centennial timescales and that these changes coincided with periods of diﬀerent volcanic activities. For instance, during the Little Ice Age, a dimmer Sun and more active volcanoes conspired to produce a colder global climate, but the tropical Pacific responded by a more El Niño-like state, a consequence of the “thermostat mechanism” [Clement et al., 1996]. The latter governed the model’s response to any change in imposed radiation. It should be noted that the current generation of coupled general circulation models [Vecchi et al., 2006, and Vecchi et al., in prep.] tends to exhibit the opposite reaction to a uniform change in radiation (i.e. increased radiation goes with a more El Niño-like state), a potential caveat which shall be discussed later. In Chapter 2 we carry out a detailed analysis of the response of ENSO to volcanic forcing over the past millennium. The work of Mann et al. [2005] had raised important questions, since it was the first to advance a dynamical explanation for the idea that volcanic eruptions may cause El Niño events [Handler , 1984]. We reassess this controversial claim, building on their work, by using estimates of volcanic forcing over the past millennium [Crowley, 2000] and a climate model of intermediate complexity [Zebiak and Cane, 1987] of similar design to theirs. We draw a diagram of El Niño likelihood as a function of the intensity of volcanic forcing, which shows that in the context of this model, only eruptions larger than that of Mt Pinatubo (1991) can shift the likelihood and amplitude of an El Niño event above the level of the model’s internal variability. Since the past 150 years have not seen any significantly larger eruption, this finding reconciles, on one hand, the demonstration by Adams et al. [2003] of a relationship between explosive volcanism and El Niño, and on the other hand, the ability to predict El Niño events of the last 148 years without knowledge of volcanic forcing [Chen et al., 2004]. The study is also partly motivated by the increasing amount of evidence that hydroclimates on continents adjacent to the Pacific are largely governed by tropical SST anomalies in modern times [Schubert et al., 2004; Seager et al., 2005b] for much of the past two millennia [Cook et al., 2004; Herweijer et al., 2006, 2007]. We therefore make use of such teleconnections to seek El Niño’s footprint in extratropical paleoclimatic records and suggest that the 1258 eruption briefly interrupted a solar-induced megadrought in the American west, via its influence on ENSO. In Chapter 3 we take a step back and refocus on the last 10,000 years, the Holocene. The motivation for this work came from the intriguing correlation, uncovered by the late Gerard Bond, that over the Holocene episodes of lower solar irradiance were accompanied by sizable surges of iceberg discharge into the North Atlantic, with a recurrence time of roughly 1500 years [Bond et al., 2001]. As often, the explanation involved the THC in some way, which enticed us to test the possibility that the record of ice rafted debris (IRD) of Bond et al. [2001] could instead be driven by the Sun via ENSO and its teleconnections. We use the same ENSO model as before, forced by El Niño and the Earth’s climate: from decades to Ice Ages.

Of low-frequency tropical climate variability

7

irradiance changes from cosmogenic isotopes and a range of radiometric scalings that bracket the current uncertainties of the reconstruction. It will be shown that for a moderate to strong scaling, the model responds with comparable sensitivity to orbital and solar forcing, despite the order of magnitude that separates them. As a result, our model ENSO produces persistent tropical SST anomalies that vary in concert with fluctuations detected by cosmogenic isotopes, of the order of magnitude required to trigger noticeable extratropical impacts. In the spirit of Chapter 2, we delve into the paleoclimate record to test the validity of this mechanism, which we find supported by available data. We also establish a link between tropical Pacific SSTs and North Atlantic winds, which shows that ENSO has the capacity to orchestrate the surface ocean circulation there, with the sign suggested by the IRD record. We thus propose that ENSO acted as a mediator of the solar influence on climate. An important caveat of Chapters 2 and 3 is that they assume stationary ENSO teleconnections. However, there is no reason to believe that teleconnections patterns are immutable. On the contrary, the odds are that as the mean climate state changes, so do teleconnections. The assumption of stationarity is not thought to be a major impediment at times when the atmospheric circulation was quite close to the present time’s, but this does not hold for glacial times when large swaths of northern hemisphere continents were covered by ice sheets 3 to 4 km thick. There is ample modeling evidence that this drastic orographic diﬀerence, along with the more moderate changes in tropical SSTs (typically 2 or 3◦ C), must have fundamentally reorganized the structure of the Jet Streams, the stationary and low-frequency Rossby waves, and therefore the transient eddies that interact with them along the “storm tracks” – so that teleconnection patterns must have been profoundly altered [Cook and Held , 1988; Yin and Battisti, 2001]. This we tackle in Chapter 4, by analyzing simulations of the Last Glacial Maximum (LGM, ≥21,000 ago) using two state-of-the-art climate models. The hope was that the models would concur to show sizable changes in teleconnections, with at least some common features that would give credence to their physical basis. It will be shown that the changes are sizable indeed, but that the two models show little consistency. This failure, however, provides us with an opportunity to examine the causes of discrepancies between coupled general circulation models (GCMs), which we do by using simplified models. Both are based on the primitive equations of atmospheric motion. One is a fully non-linear time-marching model [Ting and Yu, 1998] ; the other a linear, stationary wave model that is essentially the linearized version of the former [Ting and Held , 1990]. Use of these models, which ignore transient eddy feedbacks, allows for an exploration of the extent to which one can account for observed teleconnections only on the basis of planetary wave propagation. Experiments confirm the established fact that present-day ENSO teleconnections can largely be understood by stationary wave dynamics (see Held et al. [2002] and references therein). A similar attempt proves unsuccessful for LGM teleconnections, and herein we investigate why. The approach taken here is a minimalist one: how might we account for observed climate fluctuations on decadal to millennial timescales with as few physical processes

8

Introduction

as necessary ? ENSO dynamics will be found able to explain a great number of them, but many puzzles remain, and a more holistic view of the system will be presented in the discussion’s closing.

El Niño and the Earth’s climate: from decades to Ice Ages.

BIBLIOGRAPHY

9

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12

Introduction

Herweijer, C., R. Seager, E. Cook, and J. Emile-Geay (2007), North American droughts of the last millennium from a gridded network of tree-ring data, J. Climate, 20, 1353–1376. Horel, J., and J. Wallace (1981), Planetary-scale atmospheric phenomena associated with the Southern Oscillation, Mon. Weather Rev., 109, 814–829. Houghton, E., J. T. et al. (Ed.) (2001), Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, UK ; New York. Karspeck, A., R. Seager, and M. A. Cane (2004), Predictability of tropical Pacific decadal variability in an intermediate model, J. Climate, 18, 2842–2850. Karspeck, A. R., and M. A. Cane (2002), Tropical pacific 1976-77 climate shift in a linear, wind-driven model, J. Phys. Oceanogr., 32(8), 2350–2360. Koutavas, A., J. Lynch-Stieglitz, J. Marchitto, Thomas M., and J. P. Sachs (2002), El Niño-Like Pattern in Ice Age Tropical Pacific Sea Surface Temperature, Science, 297 (5579), 226–230, doi:10.1126/science.1072376. Koutavas, A., P. deMenocal, G. C. Olive, and J. Lynch-Stieglitz (2006), MidHolocene El Niño-Southern Oscillation (ENSO) attenuation revealed by individual foraminifera in eastern tropical Pacific sediments, Geology, 34 (12), 993–996. Lea, D., D. K. Pak, C. L. Belanger, H. J. Spero, M. A. Hall, and N. J. Shackleton (2006), Paleoclimate history of galapagos surface waters over the last 135,000 years, Quatern. Sci. Rev., 25(11-12), 1152–1167. Liu, Z. (2003), Tropical ocean decadal variability and resonance of planetary wave basin modes, J. Climate, 16 (18), 1539–1550. Mann, M. E., M. A. Cane, S. E. Zebiak, and A. Clement (2005), Volcanic and solar forcing of the tropical Pacific over the past 1000 years, J. Climate, 18(3), 447–456. Mantua, N., S. Hare, Y. Zhang, J. Wallace, and R. Francis (1997), A Pacific interdecadal climate Southern Oscillation with impacts on salmon production, Bull. Am. Meteor. Soc., 78, 1069–1079. McCarthy, E., J.J. et al. (Ed.) (2001), Climate Change 2001: Impacts, Adaptation, and Vulnerability., 142 pp., Cambridge University Press, Cambridge, UK ; New York, doi:ISBN0521807689. McManus, J. F., R. Francois, J.-M. Gherardi, L. D. Keigwin, and S. Brown-Leger (2004), Collapse and rapid resumption of Atlantic meridional circulation linked to deglacial climate changes, Nature, 428, 834–837, doi:10.1038/nature02494. El Niño and the Earth’s climate: from decades to Ice Ages.

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Milankovitch, M. (1941), Canon of insolation and the Ice Age problem, 484 pp., U.S. Department of Commerce, Israel program for Scientific Translations. Mix, A. C. (2006), Running hot and cold in the eastern equatorial pacific, Quatern. Sci. Rev., 25 (11-12), 1147–1149. Moy, C., G. Seltzer, D. Rodbell, and D. Anderson (2002), Variability of El Niño/Southern Oscillation activity at millennial timescales during the Holocene epoch, Nature, 420 (6912), 162–165. Munk, W., and C. Wunsch (1998), Abyssal recipes II : Energetics of tidal and wind mixing, Deep-Sea Res., 45, 1977–2010. Neﬀ, U., S. Burns, A. Mangini, M. Mudelsee, D. Fleitmann, and A. Matter (2001), Strong coherence between solar variability and the monsoon in Oman between 9 and 6 kyr ago, Nature, 411(6835), 290–293. Paillard, D. (2001), Glacial cycles: Toward a new paradigm, Rev. Geophys., 39, 325–346, doi:10.1029/2000RG000091. Peixoto, J. P., and A. H. Oort (1992), Physics of climate, New York: American Institute of Physics (AIP), 1992. Quinn, W. H. (1992), Large - scale ENSO event, the El Niño and other important regional features, in Registro del fenómeno El Niño y de eventos ENSO en América del Sur, vol. 22, edited by L. Macharé, José; Ortlieb, pp. 13–22, Institut Fran cais d’Etudes Andines, Lima. Ropelewski, C., and M. Halpert (1987), Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation, Mon. Weather Rev., 115, 1606–1626. Schneider, N., A. J. Miller, and D. W. Pierce (2002), Anatomy of North Pacific Decadal Variability., J. Climate, 15, 586–605. Schubert, S. D., M. J. Suarez, P. J. Pegion, R. D. Koster, and J. T. Bacmeister (2004), On the Cause of the 1930s Dust Bowl, Science, 303(5665), 1855–1859, doi:10. 1126/science.1095048. Seager, R., and D. Battisti (2007), Challenges to our understanding of the general circulation: abrupt climate change, in The global circulation of the atmosphere: Phenomena, Theory, Challenges, edited by T. Schneider and A. H. Sobel, pp. 331–371, Princeton University Press. Seager, R., N. Harnik, Y. Kushnir, W. Robinson, and J. Miller (2003), Mechanisms of hemispherically symmetric climate variability, J. Climate, 16 (18), 2960–2978.

14

Introduction

Seager, R., A. R. Karspeck, M. A. Cane, Y. Kushnir, A. Giannini, A. Kaplan, B. Kerman, and J. Velez (2004), Predicting pacific decadal variability, in Earth Climate: The ocean-atmosphere interaction, Geophys. monogr., vol. 147, edited by C. Wang, S.-P. Xie, and J. A. Carton, pp. 105–120, Amer. Geophys. Union, Washington, D. C. Seager, R., N. Harnik, W. A. Robinson, Y. Kushnir, M. Ting, H. Huang, and J. Velez (2005a), Mechanisms of ENSO-forcing of hemispherically symmetric precipitation variability, Quart. J. Royal Meteor. Soc., 131, 1501–1527, doi:10.1256/qj.04.n. Seager, R., Y. Kushnir, C. Herweijer, N. Naik, and J. Velez (2005b), Modeling of tropical forcing of persistent droughts and pluvials over western North America : 1856-2000, J. Climate, 18(19), 4068–4091. Stott, L., C. Poulsen, S. Lund, and R. Thunell (2002), Super ENSO and Global Climate Oscillations at Millennial Time Scales, Science, 297 (5579), 222–226, doi: 10.1126/science.1071627. Sutton, R. T., and D. L. R. Hodson (2005), Atlantic Ocean Forcing of North American and European Summer Climate, Science, 309 (5731), 115–118, doi: 10.1126/science.1109496. Ting, M., and I. M. Held (1990), The stationary wave response to a tropical SST anomaly in an idealized GCM, J. Atmos. Sci., 47, 254–2566. Ting, M., and L. Yu (1998), Steady response to tropical heating in wavy linear and nonlinear baroclinic models, J. Atmos. Sc., 55, 3565–3582. Trenberth, K., and J. Hurrell (1994), Decadal atmosphere-ocean variations in the Pacific, Clim. Dyn., 9, 303–319. Trenberth, K. E., G. W. Branstator, D. Karoly, A. Kumar, N.-C. Lau, and C. Ropelewski (1998), Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures, J. Geophys. Res., 103, 14,291–14,324, doi:10.1029/97JC01444. Tudhope, A. W., et al. (2001), Variability in the El Niño-Southern Oscillation through a Glacial-Interglacial Cycle, Science, 291, 1511–1516. Vecchi, G. A., B. J. Soden, A. T. Wittenberg, I. M. Held, A. Leetmaa, and M. J. Harrison (2006), Weakening of tropical Pacific atmospheric circulation due to anthropogenic forcing, Nature, 441, 73–76, doi:10.1038/nature04744. Wang, Y., et al. (2005), The Holocene Asian Monsoon: Links to Solar Changes and North Atlantic Climate, Science, 308(5723), 854–857, doi:10.1126/science. 1106296. Wunsch, C. (2002), OCEANOGRAPHY: What Is the Thermohaline Circulation?, Science, 298(5596), 1179–1181, doi:10.1126/science.1079329. El Niño and the Earth’s climate: from decades to Ice Ages.

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15

Wunsch, C., and R. Ferrari (2004), Vertical Mixing, Energy, and the General Circulation of the Oceans, Annual Review of Fluid Mechanics, 36, 281–314. Yin, J. H., and D. S. Battisti (2001), The Importance of Tropical Sea Surface Temperature Patterns in Simulations of Last Glacial Maximum Climate., J. Climate, 14, 565–581. Zebiak, S. E., and M. A. Cane (1987), A model El Niño-Southern Oscillation, Mon. Weather Rev., 115 (10), 2262–2278. Zhang, Y., J. Wallace, and D. Battisti (1997), ENSO-like interdecadal variability: 1900-93, J. Climate, 10, 1004–1020.

17

Chapter 1 Pacific Decadal Variability in the View of Linear Equatorial Wave Theory * “The book of nature is written in the language of mathematics.” Galileo Galilei

1.1

Introduction

The existence of decadal-scale variability in the Pacific Ocean is now well documented, and aﬀects the climate and fisheries of the neighboring regions to a significant extent [e.g. Trenberth and Hurrell , 1994; Zhang et al., 1997; Mantua et al., 1997]. This Pacific Decadal Variability (PDV) is in the North Pacific usually described by the Pacific Decadal Oscillation (PDO) index [Mantua and Hare, 2002], which is quite energetic in the interdecadal spectral range. There have been suggestions [e.g. Newman et al., 2003] that the PDV derives much of its characteristics from the decadal properties of El Niño-Southern Oscillation (ENSO), notwithstanding feedbacks with subtropical and midlatitudes winds, which may have a significant role in amplifying decadal variability over the whole basin [Sarachik and Vimont , 2003]. Hence, rather than asking ”why is there a PDV?”, it is worthwhile to ask the more fundamental question of why there are decadal SST variations in the Tropical Pacific. To describe such variations, one can look at the Cold Tongue Index (CTI) [Deser and Wallace , 1990], computed here from the historical SST analysis of Kaplan et al. [1998]. The index and its spectrum are shown in Fig(1.1). The spectrum was estimated via the multi-taper method [Thomson, 1982; Ghil et al., 2002] and the robust noise estimation procedure of Mann and Lees [1996]. At the 95% level, one can see a number * Published

in Journal of Physical Oceanography with co-author Mark Cane. Reprinted with permission from the American Meteorological Society.

18

Chapter 1. Pacific Decadal Variability

of significant broadband peaks between periods of 2 to 7 years, as well as narrowband peaks in the quasi-biennial and quasi-quadrennial range [Jiang et al., 1995], all of which compose ENSO. One also finds some peaks in the decadal to multi-decadal range, none of which seem to rise above the red noise background used for significance testing, perhaps due to the shortness of the record. Thus, for our purpose, the salient feature tropical Pacific SST variability is the overall warm color of its spectrum at low-frequencies. An intriguing mechanism for this variability has recently been proposed in the work of Cessi and collaborators (Cessi and Louazel [2001], hereafter CL01, Cessi and Primeau [2001]; Cessi and Paparella [2001]) and that of Liu [2003] (hereafter L03) in the framework of the linear shallow water equations. These authors made an attempt to explain decadal variability as a “reddening” of weather fluctuations by dynamical ocean processes, planetary basin modes in this case. They argue that in a meridionally bounded basin, such modes with decadal timescales can be preferentially excited by the appropriate wind forcing in midlatitudes, resulting in a large local response and a somewhat weaker – but still sizable – equatorial response. The wind need not be highly organized; the usual “white noise” variations in midlatitudes might be all that is needed. Moreover, this scenario does open the possibility of tropical anomalies forcing teleconnections to higher latitudes that excite favorable winds, reinforcing the decadal mode of variation [Cessi and Paparella, 2001]. Cessi and collaborators work with the linear planetary geostrophic equations, while Liu, following Jin [2001], uses a truncated series of equatorial waves. L03 shows that the two approaches yield the same results. However, the latter are highly dependent on a few functional forms chosen to exemplify the forcing, which prevents rigorous comparison between the influence of low- and high-latitude forcing. We therefore approach the problem in a diﬀerent way, one which relies heavily on results obtained by Cane and Moore [1981] and Cane and Sarachik [1981] (herafter CM81 and CS81) to derive the Green’s function of the problem in a closed basin. We obtain answers that are mathematically equivalent to those of CL01 and L03, but our approach leads us to an interpretation at odds with theirs. Most importantly, we find that high latitude winds have no advantage in forcing tropical ocean motions. On the contrary, they are typically less eﬀective than low latitude winds. Since it is all too easy for the reader to get lost in the mathematical details, it may be worthwhile to give a brief informal account of the approach we will take. We wish to find the ocean’s response to a periodic wind forcing. As in CS81 we write the solution as a sum of a forced part and a free part. Both are made up of forced or free long equatorial Kelvin waves and long Rossby waves, the only modes that exist in the interior of the basin at low frequencies. These modes suﬃce to satisfy the boundary condition of vanishing zonal velocity at the east, but cannot satisfy the same boundary condition at the west. That requires the short Rossby waves that make up the western boundary currents. It is known [Cane and Sarachik, 1977] that the appropriate boundary condition for the long, low-frequency waves alone is that the meridional integral of the zonal velocity vanish along the boundary. This means that El Niño and the Earth’s climate: from decades to Ice Ages.

1.1. Introduction

19

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Figure 1.1: The Cold tongue index and its spectral properties (a) Cold Tongue index (CTI) and its 7-year lowpass filtered version. (b) Spectral estimate of the CTI using multi-taper method (MTM) and the robust noise estimation procedure of Mann and Lees [1996]. The black curve identifies harmonic components together with noise and broadband signals, while the “reshaped” spectrum only includes the latter two. Numbers above the curves correspond to the period of oscillation, in years. (c) Significance test of harmonic components, based upon an F -test [Mann and Lees, 1996]. A peak is deemed signicant if its F value is above the critical threshold imposed by a particular confidence level (95% or 99% here).

20

Chapter 1. Pacific Decadal Variability

the mass propagated into the western boundary by long Rossby waves forced by the wind is all returned to the interior in free equatorial Kelvin waves; this condition determines the Kelvin wave amplitude at the west. The role of the short Rossby waves (the western boundary currents) is to close the fluid circuits. The free Kelvin waves, generated at the western boundary, and the Kelvin wave forced in the interior propagate eastward to be reflected in a series of Rossby waves, whose amplitudes are determined by the boundary condition at the east. These Rossby waves propagate across to the west and generate new Kelvin waves. And so on. A Kelvin wave plus its reflected Rossby waves is the free part of our solution. There is some amplitude A for this free part which allows the forced plus free Rossby wave mass flux incident on the western boundary to just balance the outgoing Kelvin wave mass flux. It turns out (Section 1.2.1) that A is the correct measure of oﬀ equatorial wind eﬀects on the equatorial thermocline, being equal to the thermocline depth at the eastern boundary (hE ). Clearly, the greater the amplitude of the wind forced mass flux at the western boundary, the greater hE will be. So the right forcing can increase the movement of the equatorial thermocline. There is a second mechanism, which depends on the free mode. If the free mode were self-consistent, so that the Kelvin wave generated at the west reflects into Rossby waves that are exactly what is needed to generate that Kelvin wave in the first place, then it would be a self-sustained basin mode, a complete solution of the unforced equations in the basin: a resonant mode. If the free mode is close to this condition, then it adds little net mass flux at the west and it will take a large amplitude of hE to complete the forced solution. Hence the emphasis on basin modes in the work cited above. However, even in the absence of any friction, it is known that there are no true very-low-frequency basin modes; there are no eigenfunctions satisfying the shallow water equations and the boundary conditions whose eigenfrequencies are real [Moore, 1968]. The only solutions have complex eigenfrequencies, meaning that the associated quasi basin modes are damped [Cessi and Louazel , 2001]. Thus, to determine what sort of midlatitude winds might excite a large equatorial response means we have to investigate two questions. What latitudinal distribution of winds is especially eﬃcient at forcing a large net mass flux at the western boundary? What frequencies and basin dimensions bring the free mode close to resonance? It should be noted that, since any free mode must satisfy the eastern boundary condition, the free mode we describe here, a Kelvin wave at frequency ω together with its eastern boundary reflected Rossby waves, is the only possible form for a low-frequency basin mode. Its form is the same as that found numerically by CL01 and L03. Here we add a closed form description, which takes advantage of the analytical results of CM81. In the next section, we present the mathematical formalism we use to address this problem. In particular, we modify the CM81 mode to fit in a meridionally bounded basin and we calculate hE when the forcing is a delta function in latitude (a Green’s function). This allows a systematic investigation of the eﬀect of forcing latitude, which we do in Section 3. We compare those results with previous work in section 4, and El Niño and the Earth’s climate: from decades to Ice Ages.

1.2. Linear Equatorial Wave Theory at Decadal Frequencies

21

oﬀer an explanation for the diﬀerences we find. We conclude with a discussion section.

1.2 1.2.1

Linear Equatorial Wave Theory at Decadal Frequencies The Problem

Consider an ocean basin defined by {0 Æ x Æ XE ; yS Æ y Æ yN }. We start from the classical reduced-gravity model, with the non-dissipative rotating shallow water equations, in the low-frequency, long-wave approximation (e.g. Moore [1968]; Cane and Sarachik [1976]). In non-dimensional form: ut ≠ yv + hx = τx yu + hy = τy ht + ux + vy = 0

(1.1a) (1.1b) (1.1c)

with boundary conditions [Cane and Sarachik, 1977]: ⁄

yN

yS

u(XE , y, t) = 0 ∀y ∈ [yS ; yN ]

(1.2a)

u(x = 0)dy = 0

(1.2b)

As a consequence of the low-frequency, long-wave approximation, the vt term is absent and the boundary condition (1.2b) has to include the indirect eﬀect of the short Rossby waves, as discussed above. As in CS81, we consider periodic wind perturbations (tantamount to solving in the frequency domain), and we further idealize them as strictly zonal and independent of longitude: τ = (F (y)eiωt , 0). This functional form facilitates comparison with CS81, L03 and CL01. The solution to this system is a sum of forced Rossby and Kelvin waves, together with their reflections, which are free waves. As is often done (e.g. CS81) we write the solution as the sum of a forced solution uF of (1.1) and a free solution uM (i.e. one satisfying (1.1) with the right-hand side set to zero): u = (u, v, h)T = uF + AuM

(1.3)

where A(t) is a function of time only, determined by the boundary conditions. Both the forced and free parts satisfy the boundary condition (1.2a) at the east. We normalize uM = (uM , vM , hM )T so that hM (x = XE , y) = 1. In the absence of meridional wind stress, the meridional momentum balance reduces to geostrophy and the boundary condition u(XE , y) = 0 implies that h(XE , y) = hE (t), a function of time only.

22

Chapter 1. Pacific Decadal Variability

It turns out that A = hE , which is entirely determined by the condition (1.2)b that the net mass flux be zero at the west. After substituting (1.3) into (1.2)b, a few manipulations lead to: IF hE = ≠ ; IM

where IM ≡

⁄

yN

yS

uM (x = 0)dy and IF ≡

⁄

yN

yS

uF (x = 0)dy.

(1.4)

hE is also the physical variable of greatest interest since the eastern equatorial SST is

so tightly coupled to the local thermocline depth (e.g. Zelle et al. [2004] and references therein). As noted above, if the wind forcing is far from the equator then all variations in h along the equator are determined solely by hE . The rest of the analysis will thus focus on this variable. As is apparent from (1.4), any mode rendering IM small will generate a large response in thermocline depth, regardless of the magnitude of the forcing. If IM = 0 then uM is a true basin mode, as in CM81, and we therefore begin by seeking the free solutions to the system (F = 0).

1.2.2

The Free Mode

The general form for this mode is the sum of a Kelvin wave and all its Rossby reflections. To take advantage of prior work, we split the solution between a part corresponding to a meridionally infinite basin u∞ M and a boundary layer correction uB . The first term u∞ can readily be written in the closed form obtained by CM81: M

u∞ M









u∞ ≠i tan(2„›) M 1 tan 2„› 2  ∞  1/2 =  vM  = eiωt  exp iy 2 iωy sec2 (2„›) [cos(2„›)] 2 h∞ 1 M

wherein: ›=

x ≠ XE , XE

ωXE c

„=

(1.5)

(1.6)

› goes from ≠1 in the west to 0 in the east and „, which is 2ﬁ times the ratio of the

Kelvin-wave crossing-time to the period of the oscillation, is the relevant frequency parameter for analysis of the response (CS81). For a meridionally infinite basin, IM =

⁄

∞

u∞ M (x ≠∞

1/2

= 0)dy = i tan(2„)[cos(2„)] √

⁄

∞

e≠iy

≠∞

2 tan 2„ 2

dy =

Ò

2ﬁi sin 2„ (1.7)

For very low frequencies („ π 1), IM ≈ 2 iﬁ„ . A true basin mode must satisfy the boundary condition at the east; hence in an infinite basin all low-frequency basin modes have the form (1.5). A basin mode must also satisfy the western boundary condition, IM = 0. This will hold if „ is a multiple of ﬁ/2, a result first obtained by CM81. The longest eigenperiod is 4XE , the time for a Kelvin wave to cross the basin plus the time for the gravest Rossby wave to return El Niño and the Earth’s climate: from decades to Ice Ages.

1.2. Linear Equatorial Wave Theory at Decadal Frequencies

23

(about 8 months for typical parameters). Thus all true basin modes are high frequency compared to decadal (or even interannual) timescales. Any low-frequency modes must correspond to complex eigenfrequencies and so will be damped. The form of the phase function in (1.5) means that phase variations increase with latitude and with proximity to the western boundary. Hence the most rapid variations are found in the northwestern and southwestern corners of the basin. If the modes are damped, then these areas will also have larger amplitudes. These characteristics may be seen in the basin modes shown by CL01 and L03 (their Fig(2) and (2b), respectively). In a bounded basin, (1.5) is still a free solution satisfying the boundary condition at the eastern boundary, but it fails to satisfy the boundary conditions at (yS , yN ). The complete solution requires the addition of boundary layers to make the meridional velocity vanish at those latitudes. All we need is the mass flux they deliver to the western boundary, and this does not require complete knowledge of the structure within the boundary layer. (The boundary-layer structure is discussed, for example, by CL01) Consider the situation at, say, the northern boundary y = yN . We add a boundary layer structure uB to u∞ M to satisfy the boundary condition at y = yN that 0 = vM = ∞ B vM +v . At low frequencies the narrow meridional scale of the boundary layer reduces the continuity equation to uBx + vyB ≈ 0. Integrating this continuity equation from the east where uB = 0 and noting that the boundary layer variables vanish far from the boundary, ⁄

⁄

yN

uB (x = 0)dy =

≠∞

C

XE

0

vB

DyN

≠∞

which, using (1.5), is ⁄

yN

uB (x = 0)dy = ≠iyN

≠∞

⁄

0

sec2 (2s)eiy

dx = ≠

2 tan 2s 2

≠„

⁄

XE

∞ vM (y = yN )dx;

(1.8)

È ≠1 Ë 2 tan 2„ 1 ≠ e≠iyN 2 . yN

(1.9)

0

ds =

Similarly, at the southern boundary: ⁄

∞

yS

uB (x = 0)dy =

È 1 Ë 2 tan 2„ 1 ≠ e≠iyS 2 yS

(1.10)

We also have (cf. (1.7)): ⁄

yN

yS

defining ‡ = ⁄

yN

yS

u∞ M (x

u∞ M (x

tan 2„ 2

1/2

= 0)dy = i tan(2„)[cos(2„)]

⁄

yN

yS

e≠iy

2 tan 2„ 2

≈ „ and ◊ = ‡y 2 , we may write 1/2

= 0)dy = 2(i‡)

1/2

[cos(2„)]

⁄

√ i◊N

√ i◊S

≠s2

e

1/2

ds ≈ 2(i‡)

(1.11)

dy;

⁄

√ i◊N

√ i◊S

2

e≠s ds

(1.12) Here the subscripts N and S refer to the northern or southern boundary, respectively. Henceforth we will use the last expression since the relative error is „2 +

24

Chapter 1. Pacific Decadal Variability

O(„4 )which is . 1% for the very low-frequency motions („ π 1) of interest here. (For a 20-year period and a basin the size of the Pacific, „ ≈ 0.06.)

Now rewriting (1.12) with the help of the error function 2 ⁄ x ≠s2 √ erf(x) = e ds ﬁ 0

(1.13)

[e.g. Abramowitz and Stegun, 1965], and combining this with Eqs (1.9) and (1.10), the total mass flux can be written: IM („, yN , yS ) =

È √ Ë 2 i‡ Z(‡yN ) ≠ sgn(yS )Z(‡yS2 )

(1.14)

√ √ 1 ≠ e≠i◊ ﬁ erf( i◊) ≠ √ i◊

(1.15)

where we have introduced the function Z : Z(◊) =

If IM = 0 then the free mode is a basin mode. This holds if ‡ = 0, but the only very low-frequency solution is the steady solution „ = 0. Otherwise, let yS = 0 so that 2 IM = 0 reduces to Z(‡yN ) = 0, which is the same as Eq(2.9) in L03. This is easily shown by integrating (1.15) by parts: Z(◊) = ≠

⁄

0

√ i◊

1 ≠s2 1 ≠ e≠i◊ d(e ) ≠ √ s i◊

=

⁄

√ i◊

0

2

1 ≠ e≠s ds s2

(1.16)

The solutions may be found numerically, as in CL01 and L03. The resulting eigenstructure, displayed in Fig 1.2 is almost identical to that found by CL01 (their Fig 2), and Yang and Liu [2003] (their Fig 3). The peculiar physics of equatorial wave propagation on a — -plane further means that these modes can be described by a single parameter ◊ = „y 2 . It is worth dwelling on its physical interpretation, since it appears repeatedly throughout this chapter. Recalling that the non-dimensional Rossby phase speed at latitude y is c(y) = y ≠2 , ◊ can be interpreted as the ratio of the basin crossing time at latitude y to the period of interest (up to a factor of 2ﬁ ); thus, for small ◊ the wave has had the time to go around the Kelvin-Rossby wave pathway before the signal has changed too much, and all latitudes equatorward of y are in phase ; for large ◊ there are important phase diﬀerences, leading to interfences. We can obtain relatively simple asymptotic expressions for Z in these two interesting limits: • For ◊ π 1:

Z ≥ Z0 ≡

which has amplitude: |Z0 | ≥

4 √ 3 i 1 i◊ 1 ≠ ◊ ≠ ◊2 6 30 Û

3

◊ 7 2 1≠ ◊ 2 360

4

(1.17)

(1.18)

El Niño and the Earth’s climate: from decades to Ice Ages.

1.2. Linear Equatorial Wave Theory at Decadal Frequencies

0 -0.2 -0.4

25

Eigenfunction of the free mode at !=-0.029 -0.6 -0.8

12 -0.8

10

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

8

y

0.8

6

4

2

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

Figure 1.2: Eigenstructure of the free mode hM , for Ÿω = ≠0.029 to facilitate comparison with the gravest planetary basin mode of Yang and Liu [2003]

26

Chapter 1. Pacific Decadal Variability and phase: ϕ(Z0 ) ≥

ﬁ ◊ ≠ 4 6

(1.19)

• For ◊ ∫ 1† : Z ≥ Z∞

A

√ 1 sin ◊ ≠ cos ◊ ≡ ﬁ≠√ 1+ 2◊ 2◊

B

A

i sin ◊ + cos ◊ ≠√ 1+ 2◊ 2◊

which has amplitude: |Z∞ | ≥

√ 1 1 ﬁ≠√ + √ 2◊ 4 ﬁ◊

B

(1.20)

(1.21)

and phase: 1 1 ϕ(Z∞ ) ≥ ≠ √ ≠ 2ﬁ◊ 3(2ﬁ◊)3/2

(1.22)

Taking (1.20) to the limit ◊ → ∞ by having yN = ≠yS = ∞ we find that for „ π 1 , IM ≥ 2(i„ﬁ)1/2 , in agreement with Eq (1.7) and the work of CS81, who considered such an unbounded basin. The function Z is plotted in Fig. 1.3, along with its asymptotic approximations. We see that the asymptotic approximations are quite good. Note that Z is non-zero unless ◊ = 0. It has a number of local minima (cf. Eq (1.20)) but all are quite shallow so the value of Z at these minima is not very diﬀerent from that at neighboring points. There are no true basin modes; zeroes of Z require that ◊ be complex (with ⁄(◊) > 0), which means that the associated eigenmodes will be damped.

1.2.3

The Forced Solution: Green’s Function

We seek the response to a delta function in latitude: a Green’s function. We take F (y) = ”(y ≠y∗ )/XE so that the integral of F over the basin is unity. Kuklinski [1984] solved the related problem of a delta function at a point, F (y) = ”(y ≠ y∗ )”(x ≠ x∗ ), while Jin and Neelin [1993] solved the problem F (x, y) = ”(x≠x∗ ). We will first solve the problem for a meridionally infinite basin, and then argue that the same solution applies in the bounded basins of interest here. The solution for a general F (y) may be written, following CS81 [their Eq(12), together with (14) and (21)], ≠ς 2

q

n (2n≠1)!! the following asymptotic expansion: erf(ς) ≥ 1 + e√ﬁ n (≠1) 2n ς 2n+1 , with (2n ≠ 1)!! = 1 · 3 · 5 · · · (2n ≠ 1). The leading oscillatory terms cancel each other.

† use

El Niño and the Earth’s climate: from decades to Ice Ages.

1.2. Linear Equatorial Wave Theory at Decadal Frequencies I

27 J

∞ 1 2 1 2 ÿ eiωt uF = dK K(y) 1 ≠ e≠i„› + rn Rn (y) 1 ≠ ei(2n+1)„› i„ n=0

(1.23)

where K(y) and Rn (y) are the meridional structures associated with the Kelvin mode and the nth Rossby mode, respectively. (See CS81 for details.) The coeﬃcients dK and {rn , n ∈ N} are the projections of the forcing onto the Kelvin and Rossby modes. For the Green’s function F (y) = ”(y ≠ y∗ )/XE , they are: dK = K u (y∗ ) 4n(n + 1) u rn = Rn (y∗ ) 2n + 1

(1.24a) (1.24b)

where K u , Rnu denote the u components of the Kelvin wave and the nth Rossby wave, respectively. We need only the western boundary mass flux: ⁄



1 2 eiωt  u i„ eiωt IF = uF (x = 0)dy = ﬁ 1/4 K (y ∗) 1 ≠ e i„  ≠∞ ∞



1 ≠ e≠i(2n+1)„  ≠2 –n Rnu (y∗ ) (1.25)  2n + 1 n=0 ∞ ÿ

where –n is the sequence defined as:  0

–n =  1/4 ≠1 s ∞ (2ﬁ ) ≠∞ yψn (y)dy

n even , n odd.

(1.26)

( ψn is the nth Hermite function, as defined, for example, in Abramowitz and Stegun [1965]). Eq (1.25) can be rewritten as: IF = ﬁ

1/4

I

∞ ÿ i⁄„ Õ Õ u i„Õ d„ K (y∗ )e + 2 –n Rnu (y∗ )e≠i(2n+1)„ „ 0 n=0

J

(1.27)

Once again, the term in brackets is the sum of a free Kelvin mode and its Rossby reflections, this time evaluated at the forcing latitude y∗ . Again, we use the result of Cane and Moore [1981] to rewrite it as in (1.5): IF =

Õ i⁄„ Õ 2 tan 2„ d„ tan(2„Õ )[cos(2„Õ )]1/2 e≠iy∗ 2 „ 0

(1.28)

Remarkably, the mass flux due to the forced mode simply writes as the integral of the free mode zonal flux over [0, „]. This integral has no obvious analytical simplification, but in the limit of small „ becomes: 2i ⁄ „ Õ ≠i„Õ y∗2 Õ IF = „e d„ . „ 0

(1.29)

28

Chapter 1. Pacific Decadal Variability

An integration by part leads to: C

D

2 ≠2 i 1 2 2 IF = 2 e≠iy∗ „ + 2 1 ≠ e≠iy∗ „ y∗ y∗ „

(1.30)

We now define the function E : C

1 ≠ e≠i◊ e≠i◊ E(◊) = + ◊2 i◊

so that IF can be written:

D

(1.31)

IF = ≠2i„E(„y∗2 )

(1.32)

Before we examine E more closely, we wish to justify applying this solution in a bounded basin. We argue heuristically that the solutions do not spread poleward enough to be aware of the boundaries; that is, they do not generate any motions at the boundary that require boundary layer corrections. If the forcing latitude is far from the equator (y∗ ∫ 1) then the motions are going to be geostrophic, the linear planetary geostrophic equations hold, and the wave operator y 2 ht ≠ hx allows only propagation along latitude lines so the signal cannot spread poleward. On the other hand, if the forcing is in low latitudes, then it has a very small projection onto the high n modes, i.e. the ones that do not die oﬀ exponentially at middle latitudes. The result that the forced motions will not be significant far poleward of the forcing can also be argued from results on ray paths of equatorial waves [Kuklinski, 1984; Schopf et al., 1981]. Only in the case of a forcing reaching the boundary of the basin does the solution require a boundary layer correction ; it is presented in Appendix A. Finally, our results agree with the closed basin solutions of L03 and CL01, as we will show in the next section. We plot the function E in Fig(1.3) and note some of its properties: 2

• for ◊ π 1, E0 ≥ ≠ 12 + i 3◊ + ◊8 , so |E0 | ≥ ϕ is the phase.

1 2

1

1≠

◊2 36

2

, ϕ(E0 ) ≥ ﬁ ≠ 2◊/3, wherein

• for ◊ ∫ 1, |E∞ | ≥ 1/◊, ϕ(E∞ ) ≥ 3ﬁ/2 ≠ ◊. • |E| decreases strongly with ◊. Thus, for a given frequency, low-latitude winds are more eﬃcient at generating thermocline motion than high latitude winds.

1.2.4

Total Solution

In the case of a symmetric basin (yS = ≠yN ) and a delta-function forcing, we can use expressions (1.14) and (1.32) for the free and forced mass fluxes to rewrite (1.4) into the following form, which is the Green’s function of the eastern boundary height: h∗E („, y∗ ) =

Ò

i„

E(„y∗2 ) 2 Z(„yN )

(1.33)

El Niño and the Earth’s climate: from decades to Ice Ages.

1.2. Linear Equatorial Wave Theory at Decadal Frequencies

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Figure 1.3: Amplitude and phase of the functions E and Z , which characterize the response via hE . Along the functions are their asymptotic expansions for large and small ◊, denoted by the subscripts ∞ and 0, respectively. See text for details.

30

Chapter 1. Pacific Decadal Variability

which depends solely on the frequency, basin size and latitude of the forcing, y∗ . Thus for an arbitrary wind profile F (y), the total solution is simply F weighted by the integral kernel h∗E :

hE („) =

⁄

yN

yS

F (y∗ )h∗E („, y∗ )dy∗

√ 2 i„ ⁄ yN = F (y∗ )E(„y∗2 )dy∗ 2 Z(„yN ) 0

(1.34)

This expression is new, and allows a systematic evaluation of the equatorial thermocline response to arbitrary wind forcings. It is to be compared with the response functions given by equation (2.8) in L03 or equation (23) in CL01 (the latter two being identical except for notation). The denominator is identical in all expressions for „ π 1, so the diﬀerence resides in the numerator: as is traditional in QG theory, L03 and CL01 express the wind-forcing as an Ekman pumping term (≠∂y (F /y) in our notation), while we use no such transformation. Their choice makes direct computations challenging if F is non-zero at the equator, while ours circumvents this limitation. Were our results to be recast in a similar form, we would obtain an expression nearly identical to theirs, diﬀering only by an extra term multiplying the Ekman pumping within the integrand. Consequently, we obtain very similar results in cases where F ≥ y at the equator, but not otherwise (section 1.4). This is therefore a more general solution.

1.3 1.3.1

Results Low vs Mid-Latitudes

The first result of interest, and the one that motivated this chapter, is the sharp decrease of E with latitude for a given frequency, as seen in Fig(1.3) (recall that ◊ ≥ y 2 ). |E(◊)| falls to half its value from ◊ = 0 at approximately ◊ = 5. For a 20-year period in the Pacific this corresponds to a latitude of about 43◦ . This means that the equatorial thermocline is best excited locally, in the tropics; subtropical or mid-latitude wind forcing is less eﬀective. As has been known for a long time, the longer the period the broader the range of latitudes that influence the equator. In agreement with earlier work, we find that the latitudinal extent increases like the square root of the period. While it is true then that the lower the frequency the greater the impact of midlatitude winds, tropical winds always have the advantage. An alternative explanation of the relative ineﬀectiveness of mid-latitude winds can be derived from midlatitude quasi-geostrophic (QG) theory: Consider a 1.5 layer — -plane ocean. Suppose there is a midlatitude pycnocline displacement h which is zero outside of some latitude band (y≠ , y+ ). The equatorial response (i.e. the Kelvin wave amplitude) is set by the magnitude of the total mass flux U impinging on the western boundary. Using geostrophy, El Niño and the Earth’s climate: from decades to Ice Ages.

1.3. Results

U≈

31 ⁄

y+ g

y≠

C

Dy+

g hy dy = ≠ h f f

y≠

⁄

⁄ y+ h h ≠ g— 2 dy = ≠ g— 2 dy f f y≠ y≠ y+

(1.35)

which is small – the quasi in quasi-geostrophic. Therefore the higher the latitude of the forcing, the lesser the impact at the western boundary and therefore the equator. For a fixed width (y+ ≠ y≠ ) we again have the result that the impact decreases like the square of the latitude. This result comes out of an inviscid theory, and would be even more relevant in the presence of damping; since the Rossby-wave crossing time increases quadratically with latitude, midlatitude forcing is also more severely damped by the time it reaches the eastern boundary.

1.3.2

Modes Do Not Matter

We have seen that the free mode amplitude depends on the mass flux at the western boundary that the wind forcing excites. The larger this mass flux, the larger the free mode amplitude. If an oﬀ-equatorial forcing excites a direct response that by itself satisfies the free mode condition that the net mass flux at the western boundary be zero, then it will have no impact on the equator. Of course, there are no true free modes since all the eigensolutions with frequency greater than zero are damped. This is true even in the infinite basin case where the free mode is an artifact of the low-frequency, long wave approximation (cf. CM81). Moreover, as shown in CM81, even the “true” modes of the approximate equations all have periods shorter than interannual. In a closed basin, there are pseudo-modes with complex frequencies, as emphasized by CL01 and L03. Such modes would be important if they meant that IM was especially close to zero for corresponding real frequencies. However, they introduce only small amplitude oscillations in Z(„yN 2 ), hence in hE (cf Fig1.3). We also point out that a combination of basin size and frequency that minimizes IM and so increases hE does so equally for forcings at all latitudes. It does not favor midlatitudes.

1.3.3

Response to Idealized Wind Patterns

It is instructive to look at simple wind patterns, the response to which may be obtained analytically via (1.34), for simple enough functional forms. A useful identity is: ∀ ◊ > 0, ∀ ‹ ∈ C∗ ,

⁄

0

◊

1√ 2 e≠‹ϑ 1 √ dϑ = √ erf ‹◊ ‹ﬁ ϑ

(1.36)

through which the various integrals can be computed. In all the following, a white spectrum for the forcing is implicitly assumed, as in CL01 and L03. This should not be thought of as a naïve simplification of reality, since it is known that the spectrum of midlatitude surface winds is far from flat, with significant power in the ENSO band. Instead, the idea is to see whether this low-frequency variability can arise via the amplification of stochastic wind forcing by ocean dynamics alone. Since synoptic weather

32

Chapter 1. Pacific Decadal Variability

systems are known to occur spontaneously with approximately Gaussian statistics, this is meant to provide a null hypothesis for the redness of the CTI spectrum. Response to F = 1 Let us consider the simplest forcing:  1

F = 0

for y ∈ [≠L, L] otherwise.

(1.37)

The analytical response to such forcing is: 2 hE = 3

√ √ √ i◊L E(◊L ) + ﬁ erf( i◊L ) Z(◊N )

(1.38)

where ◊N = „yN 2 and ◊L = „L2 . This case provides a useful cross-check because the zero-frequency is easy to compute without recourse to our theory: if such a steady forcing were to cover the whole basin, then the slope of the equatorial thermocline depth would be unity, by virtue of the Sverdrup balance; there would be a node in the center of the basin, and hE = 1/2. Using the previous expansions for E and Z in the limit of small ◊, and the results from Appendix A, one can verify that the response to a steady forcing („ = 0) is indeed hE = 1/2 for this solution. In Fig 1.4(a1 and a2) we show the spectrum of the response to a varying latitudinal extent of this forcing, with yLN = 13 , 23 , 1, respectively. For L = yN , the forcing is nonzero at the northern wall, so that the boundary layer correction needs to be applied, as outlined in Appendix A. It is interesting to note that a spectral peak does arise for periods between 10 and 20 years range, but only in the case of tropical forcing. The more poleward the forcing, the weaker the peak and the lower its central frequency, so that basin-wide forcing alone does not, in fact, produce a peak anymore. The subtropical case produces a peak in the 50-100 year range. As the extent of the forcing increases, it eventually comes close enough to the northern boundary that the boundary layer correction has to be applied. It is a peculiarity of this Heaviside forcing, with a sharp jump introducing an infinite wind-stress curl at the edge, that the interior and boundary layer contributions are of similar magnitude when L = yN , and tend to cancel each other (see Appendix A). This explains the decrease between the zerofrequency response to L = 2y3N (black solid line) and L = yN (black dashed line) on panel a2). However, the comparison between latitude bands is not very meaningful in this case where the area under the forcing keeps increasing with its extent. Instead, one can divide the domain in three equal chunks‡ , called for convenience “tropics ”, “subtropics ”, and “midlatitudes ”. This is done in b1) and b2), where it can be seen that the shift of the peak towards low frequencies is indeed a consequence of the location ‡ Recall

that the convergence of meridians is neglected in the — -plane approximation. El Niño and the Earth’s climate: from decades to Ice Ages.

1.3. Results

33

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Figure 1.4: Eﬀect of the latitudinal position of the wind forcing. a1) Varying extent of wind forcing in the F = 1 case ; a2) Thermocline response ; b1) Varying location in the F = 1 case ; b2) Thermocline response c1) Varying location in the F = sin(ﬁ yyN ) case ; c2) Thermocline response. The numbers above the spectra on the right-hand side correspond to the period of oscillation (years).

34

Chapter 1. Pacific Decadal Variability

of the forcing, not its extent (the more poleward it is, the lower the frequency). In this case, the midlatitude spectrum shows a peak around 50-100 year periods, like the subtropical case, only weaker in magnitude. One can verify that this result is not an artifact of the chosen functional form, by applying another one – say, a sinewave – similarly cut into latitude bands (panels c1) and c2): the amplitude of the thermocline response increases in proportion to the strength of the forcing over a given region, but the location of the peaks is the same as in the F = 1 case. In fact, in this case, the midlatitude forcing fails to produce a peak. As remarked above, a caveat of such forcings is that they possess a discontinuous first derivative, which introduce an infinite wind-stress curl and are therefore unphysical. For the purposes of comparison with earlier work and numerical testing, it is instructive to look at a smooth forcing. y2

Response to F (y) = e≠µ 2

In this case as in the L = yN case seen above, the forcing is non-zero at the northern wall, requiring the boundary layer correction. However, for µ large enough, this correction is evanescent. The solution is: i1/2 hE = Z(◊N )

where p =

2„ µ

C√

A

ﬁ 1/2 y2 p + K(µ, „, yN ) exp ≠µ N 2 2

(1.39)

as in CS81, and:

2p≠1/2 K(µ, „, yN ) = 3

A

1 ≠ e≠i◊N i◊N

B

√ ◊N ≠ E(◊N ) 3 i ≠ √ 2 ◊N

Since K e≠µ

BD

y2 N 2

A

1 ≠ e≠i◊N 1≠ i◊N

B

(1.40)

→ 0 as yN → ∞, the solution reduces to: hE =

p1/2 iﬁ/4 e 2

(1.41)

which is identical to Eq(31) in CS81. For a bounded basin (yN < ∞) and „ π 1, the lowest order response simplifies to: lim hE =

„→0

A

2ﬁ 2 µyN

B1 2

(1.42)

Note that according to Eq(1.42), hE is equal to the integral of F (y) divided by yN and thus is independent of the scale of the forcing with the total amplitude held fixed. Remarkably, it is independent of „. We find therefore an O(1) zero-frequency response, which contrasts with CS81, but is a consequence of their considering an El Niño and the Earth’s climate: from decades to Ice Ages.

1.4. Comparison with Previous Work

35

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Figure 1.5: Response of the INC model to F = e≠µ 2 for varying values of the width parameter µ. The values of hE plotted here are the average over the last year of a 200-year integration of the shallow-water solver INC [Israeli et al., 2000], with a constant forcing applied. The model was run in a symmetric basin with yN = 60◦ N and Rayleigh friction r = 50 year≠1 .

unbounded basin, where mass within any finite region need not be conserved. We checked this behavior in a numerical model using the INC scheme [Israeli et al., 2000]. In Fig 1.5 we plot the equilibrium response of this model. The µ≠1/2 scaling law from is found to hold over a broad parametric range.

1.4

Comparison with Previous Work

Since our results are in stark contrast with the claims of CL01 and L03, we dedicate this section to understanding the origin of the diﬀerence.

36

Chapter 1. Pacific Decadal Variability

1.4.1

Comparison with Liu [2003]

It is instructive to see to which extent our solution resembles that of L03. In Fig(1.6) we reproduce the results from his figure 5, using the methods of this chapter. For this computation we used his ideal wind forcings and the Green’s function obtained from (1.28), complemented by the boundary layer correction (see Appendix A) when needed. Except for a few minor diﬀerences in amplitude, the two pictures are in good agreement, especially for case d (F (y) = sin(ﬁ yyN )). When they are not, (case c, F (y) = cos(ﬁ yyN )), it is likely to be related to the fact that L03’s HE and HP solutions diverge from each other, presumably due to a singularity in the forcing used at the equator (one that corresponds to an infinite Ekman pumping, as illustrated by the dashed lines in the right-hand side of his figure a, b and c). When the latter Ekman pumping is non-singular, his HP and our solution are in close agreement. For well-behaved cases, we agree with L03’s conclusion that equatorial wave theory and planetary geostrophy give identical results at very low frequencies. As we shall see in the section 1.5, it is our interpretation that diﬀers.

1.4.2

Comparison with Cessi and Louazel [2001]

This comparison is complicated by the fact that the wind patterns prescribed as a forcing of the PGPV equation (their Eq(19)) are specified in terms of the function gÂ ≡ (F /y)y (in our notation). As this involves a diﬀerential, an integration constant is needed to fully determine F . Furthermore, one can show that all of the wind patterns used in their study imply that F scales at least as y 2 , as one approaches the equator. Any lesser-order polynomial would render the solution singular. These wind patterns have far greater amplitude in high latitudes so this part of the wind forcing naturally dominates. However, if a more realistic wind pattern were chosen, one characterized by a comparable amplitude in midlatitudes and the equator, then the PGPV solution would not show enhanced sensitivity to extratropical winds, since it behaves similarly to the equatorial wave solution at low frequencies, as explained by Liu [2003]. The reason for this similarity deserves a formal explanation.

1.4.3

Equivalence with the PGPV Solution. Scaling Arguments

Why does the PGPV equation seem to capture the thermocline motion of the equatorial wave solution at very low frequencies? A formal way to see this is to show that it is a special case of the low-frequency, long-wave approximation. Recall that the latter is obtained by using the following scaling [Cane and Sarachik, 1976]: ∂ ≥ O(‘), ∂t

∂ ≥ O(‘), ∂x

∂ ≥ O(1); ∂y

u, h ≥ O(1),

v ≥ O(‘)

(1.43)

El Niño and the Earth’s climate: from decades to Ice Ages.

1.4. Comparison with Previous Work

37

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()*(

!"< $! #

!"% !

! !

!"!# !"$ !"$# 749JI905:-F+4+E9H94-!

!"%

Figure 1.6: Reproducing Fig 5 of LIU03. The right-hand panels present the forcing (a) F (y) = 2 e≠µy /2 , b) F (y) = 1, c) F (y) = cos(ﬁ yyN ), and d) F (y) = sin(ﬁ yyN ), respectively. The lefthand panels present the corresponding thermocline response |hE („)|

38

Chapter 1. Pacific Decadal Variability

wherein ‘ is a small parameter. This scaling makes vt appear as order ‘2 , and must therefore be dropped to lowest order. At very low-frequencies (∂t ≥ O(‘2 )), consistency requires adding the constraint ∂y ≥ O(‘) and so, for y & O(1), (1.1c) implies that u ≥ ‘h. Hence ut must also be dropped to lowest order, yielding the planetary geostrophic equations: ≠ yv = ≠hx + F (y, t) yu = ≠hy ht + ux + vy = 0

(1.44a) (1.44b) (1.44c)

The immense advantage of this system is that a vorticity equation can be formed for h, which is readily integrable. It is surprising that this equation should be valid near the equator (y π 1), however, since the Rossby wave speed there goes to infinity. L03 showed that the planetary geostrophic solution accounts implicitly for the mass transport achieved by the equatorial Kelvin wave, and retains the essential Sverdrup balance in the vicinity if the equator. The reason for the consistency between verylow-frequency linear equatorial wave theory and planetary geostrophy is that, in both theories, the equatorial thermocline depth must proceed from the balance hx = F . Direct integration from the eastern boundary yields: h = hE + (x ≠ XE ) F

(1.45)

where it can seen that hE is simply the constant of integration of the problem, which is determined by the boundary conditions. As we show in Section 2.2, the two theories have the same boundary conditions for low-frequencies, hence their similar behavior.

1.5

Discussion

We have investigated the sensitivity of the equatorial thermocline depth to wind forcing at various latitudes. Following previous work, we used a — plane, non-dissipative shallow-water system and showed that its solution can be approximated by a closedform expression in the limit of low frequencies. Throughout this derivation we have made extensive use of the results of CS81 and CM81, but our solution now applies to a bounded basin, not an infinite one – via a boundary layer correction. This implicitly introduces friction in the model – albeit concentrated at the domain edges. The resulting modes are thus no longer limited to those identified by CM81, whose lowest frequency is on the order of 8 months. Indeed, the solution reproduces the salient aspects of those obtained by CL01 and L03, but also holds at shorter period (seasonal to interannual), though in this work we only make use of the very-low-frequency approximation. Since the fundamental variable describing the response is ◊ = „y 2 , this means that the latitudinal range aﬀected by the waves is proportional to the square-root of El Niño and the Earth’s climate: from decades to Ice Ages.

1.5. Discussion

39

their period: the longer the period, the broader the meridional extent of the wave, and the easier it becomes to force hE from higher latitudes. However, contrary to the suggestion of CL01 and L03, we find pseudo-modes unable to redden the response to a midlatitude wind forcing with a white spectrum, nor do they introduce noticeable spectral peaks. Further, we computed the Green’s function of the problem, which exhibited a rapid decrease with latitude. This suggested that the equatorial thermocline response inherently favors local forcing, and that tropical winds dominate the response on interannual to decadal timescales. Midlatitude winds are hard pressed to produce any sizable equatorial response, unless one looks at very low frequencies, low enough for ◊ to be small at those latitudes. In dimensional units, this corresponds to periods of 50 to 100 years. In such a case, Rossby waves have the time to cross the basin at the poleward boundaries within a period of oscillation and we do find that subtropical and midlatitude winds are thus able to generate power in the centennial band. So in our model at least, it seems that tropical winds are the preferred way of generating tropical ocean decadal variability, but modes could play a role at lower frequencies. May this conclusion carry over to the Pacific ocean as a whole? While seemingly simplistic, reduced-gravity models have proven a surprisingly valuable interpretive tool in tropical oceanography. Their applicability to midlatitude oceans is less clear. We argue that shallow-water basin modes are unlikely to be operating in nature, for three reasons. First, as one appeals to the spatial structure of eigenmodes to generate a response, the exact geometry of the basin becomes crucial to their reinforcement: the straight coastlines used in this model are known to be a singular case of quasi-geostrophic dynamics [Primeau, 2002] characteristic of midlatitude oceans. For realistic Pacific coastlines, his study found that basin modes are still present in the reduced-gravity context, but with a Q factor of order one: in other words, they are far from resonance and hence oﬀer no outstanding advantage in forcing tropical motion. Second, since the Rossby wave crossing time increases quadratically with latitude, the presence of any small amount of friction (or other diabatic processes) will tend to damp such modes much more eﬃciently than it would damp a dynamically forced response confined to the equatorial waveguide. Lastly, LaCasce and Pedlosky [2004] have shown in a 2layer quasi-gesotrophic context that Rossby waves are vulnerable to destruction by baroclinic instability. As the growth rate of this instability increases approximately quadratically with latitude [Eady, 1949], there exists a critical latitude beyond which Rossby waves “succumb to baroclinic instability” and transfer most of their energy to the barotropic eddy field [LaCasce and Pedlosky, 2004] before propagating too far from the eastern boundary, letting the authors conclude that “Rossby basin modes, if they exist, would be limited to tropical domains ”. Therefore, this simple model suggests that the most direct origin for decadal thermocline varability is decadal wind variability occurring in the tropics themselves [see also Karspeck and Cane, 2002]. Where, in turn, does such variability arise? We argue that midlatitude oceans need not be invoked to explain its origin. It has been shown

40

Chapter 1. Pacific Decadal Variability

that the Bjerknes feedback central to ENSO physics also operates on decadal and interdecadal timescales in the Zebiak-Cane model [Zebiak and Cane, 1987; Clement and Cane , 1999; Seager et al., 2004] as well as in a coupled GCM [Vimont et al., 2003]. Thus coupled ocean-atmosphere dynamics internal to the Tropical Pacific can produce significant power at decadal frequencies, with simulated variability resembling that observed [Karspeck et al., 2004], including the 1976/77 “climate shift”. In turn, oceanatmosphere feedbacks involving the eastern subtropical Pacific may explain some attributes of the PDV [Wang et al., 2003a,b]. It is also plausible that some elements of subtropical stochastic variability participate in this, as in the seasonal footprinting mechanism of Vimont et al. [2001] and the Pacific Meridional Mode of [Chiang and Vimont , 2004]. Work reported here advances these ideas only indirectly, by ruling out resonant ocean basin modes as a viable null hypothesis for the origin of Pacific Decadal Variability.

El Niño and the Earth’s climate: from decades to Ice Ages.

BIBLIOGRAPHY

41

Bibliography Abramowitz, M., and I. A. Stegun (1965), Handbook of Mathematical Functions, National Bureau of Standards, Applied Math # 55, Dover Publications. Cane, M. A., and D. W. Moore (1981), A note on low-frequency equatorial basin modes, J. Phys. Oceanogr., 11(11), 1578–1584. Cane, M. A., and E. S. Sarachik (1976), Forced baroclinic ocean motions .1. linear equatorial unbounded case, J. Mar. Res., 34 (4), 629–665. Cane, M. A., and E. S. Sarachik (1977), Forced baroclinic ocean motions .2. linear equatorial bounded case, J. Mar. Res., 35 (2), 395–432. Cane, M. A., and E. S. Sarachik (1981), The response of a linear baroclinic equatorial ocean to periodic forcing, J. Mar. Res., 39 (4), 651–693. Cessi, P., and S. Louazel (2001), Decadal oceanic response to stochastic wind forcing, J. Phys. Oceanogr., 31, 3020–3029. Cessi, P., and F. Paparella (2001), Excitation of basin modes by ocean-atmosphere coupling, Geophys. Res. Lett., 28, 2437–2441. Cessi, P., and F. Primeau (2001), Dissipative selection of low-frequency modes in a reduced-gravity basin, J. Phys. Oceanogr., 31, 127–137. Chiang, J. C. H., and D. J. Vimont (2004), Analogous Pacific and Atlantic Meridional Modes of Tropical Atmosphere Ocean Variability, J. Climate, 17, 4143–4158. Clement, A., and M. A. Cane (1999), A role for the tropical pacific coupled oceanatmosphere system on Milankovitch and millenial timescales. part i: A modeling study of tropical pacific variability, in Mechanisms of Millennial-Scale Global Climate Change, edited by P. Clark and R. Webb, p. 363, 29 Am. Geophys. Union. Deser, C., and J. M. Wallace (1990), Large-Scale Atmospheric Circulation Features of Warm and Cold Episodes in the Tropical Pacific., Journal of Climate, 3, 1254–1281. Eady, E. T. (1949), Long waves and cyclone waves, Tellus, 1, 33–52. Ghil, M., et al. (2002), Advanced spectral methods for climatic time series, Rev. Geophys., 40 (1), 1003–1052. Israeli, M., N. H. Naik, and M. A. Cane (2000), An unconditionally stable scheme for the shallow water equations, Mon. Weather Rev., 128(3), 810–823. Jiang, N., J. D. Neelin, and M. Ghil (1995), Quasi-quadrennial and quasi-biennial variability in the equatorial Pacific, Clim. Dyn., 12, 101–112.

42

Chapter 1. Pacific Decadal Variability

Jin, F.-F. (2001), Low-frequency modes of tropical ocean dynamics, J. Climate, 14 (18), 3874–3881. Jin, F. F., and J. D. Neelin (1993), Modes of interannual tropical ocean-atmosphere interaction - a unified view. part i : Numerical results, J. Atmos. Sci., 50, 3477–3503. Kaplan, A., M. A. Cane, Y. Kushnir, A. C. Clement, M. B. Blumenthal, and B. Rajagopalan (1998), Analyses of global sea surface temperature 1856-1991, J. Geophys. Res. Oceans, 103(C9), 18,567–18,589. Karspeck, A., R. Seager, and M. A. Cane (2004), Predictability of tropical Pacific decadal variability in an intermediate model, J. Climate, 18, 2842–2850. Karspeck, A. R., and M. A. Cane (2002), Tropical pacific 1976-77 climate shift in a linear, wind-driven model, J. Phys. Oceanogr., 32(8), 2350–2360. Kuklinski (1984), The eﬀect of wind measurement errors on linear simulations of equatorial circulations, Master’s thesis, Massachusetts Institute of Technology. LaCasce, J. H., and J. Pedlosky (2004), The instability of Rossby basin modes and the oceanic eddy field, J. Phys. Oceanogr., 34, 2027–2041. Liu, Z. (2003), Tropical ocean decadal variability and resonance of planetary wave basin modes, J. Climate, 16 (18), 1539–1550. Mann, M., and J. Lees (1996), Robust estimation of background noise and signal detection in climatic time series, Clim. Change, 33, 409–445. Mantua, N., and S. Hare (2002), The Pacific Decadal Oscillation, J. Oceanogr., 58, 35 – 44. Mantua, N., S. Hare, Y. Zhang, J. Wallace, and R. Francis (1997), A Pacific interdecadal climate Southern Oscillation with impacts on salmon production, Bull. Am. Meteor. Soc., 78, 1069–1079. Moore, D. W. (1968), Planetary-gravity waves in an equatorial ocean, Ph.D. thesis, Harvard University, Cambridge, MA. Newman, M., G. P. Compo, and M. A. Alexander (2003), ENSO-Forced Variability of the Pacific Decadal Oscillation, J. Climate, 16, 3853–3857. Primeau, F. (2002), Long Rossby Wave Basin-Crossing Time and the Resonance of Low-Frequency Basin Modes, J. Phys. Oceanogr, pp. 2652–2665. Sarachik, E., and D. Vimont (2003), Decadal variability in the pacific, in Chaos in Geophysical Flows, edited by G. B. et al., pp. 12–167, OTTO. El Niño and the Earth’s climate: from decades to Ice Ages.

BIBLIOGRAPHY

43

Schopf, P., D. L. T. Anderson, and R. Smith (1981), Beta-dispersion of low-frequency Rossby waves, Dyn. Atm. and Oc., 5(3), 187–214. Seager, R., A. R. Karspeck, M. A. Cane, Y. Kushnir, A. Giannini, A. Kaplan, B. Kerman, and J. Velez (2004), Predicting pacific decadal variability, in Earth Climate: The ocean-atmosphere interaction, Geophys. monogr., vol. 147, edited by C. Wang, S.-P. Xie, and J. A. Carton, pp. 105–120, Amer. Geophys. Union, Washington, D. C. Thomson, D. J. (1982), Spectrum estimation and harmonic analysis, Proc. IEEE, 70(9), 1055–1096. Trenberth, K., and J. Hurrell (1994), Decadal atmosphere-ocean variations in the Pacific, Clim. Dyn., 9, 303–319. Vimont, D. J., D. S. Battisti, and A. C. Hirst (2001), Footprinting: A seasonal connection between the tropics and mid-latitudes, Geophys. Res. Lett., 28(20), 3923–3926. Vimont, D. J., D. S. Battisti, and A. C. Hirst (2003), The Seasonal Footprinting Mechanism in the CSIRO General Circulation Models, J. Climate, 16, 2653–2667. Wang, X., F.-F. Jin, and Y. Wang (2003a), A Tropical Ocean Recharge Mechanism for Climate Variability. Part I: Equatorial Heat Content Changes Induced by the Oﬀ-Equatorial Wind., J. Clim., 16, 3585–3598. Wang, X., F.-F. Jin, and Y. Wang (2003b), A Tropical Ocean Recharge Mechanism for Climate Variability. Part II: A Unified Theory for Decadal and ENSO Modes., J. Clim., 16, 3599–3616. Yang, H., and Z. Liu (2003), Basin Modes in a Tropical–Extratropical Basin, J. Phys. Oceanogr., 33, 2751–2763. Zebiak, S. E., and M. A. Cane (1987), A model El Niño-Southern Oscillation, Mon. Weather Rev., 115 (10), 2262–2278. Zelle, H., G. Appeldoorn, G. Burgers, and G. van Oldenborgh (2004), The relationship between sea surface temperature and thermocline depth in the eastern equatorial pacific, J. Phys. Oceanogr., 34, 643–655. Zhang, Y., J. Wallace, and D. Battisti (1997), ENSO-like interdecadal variability: 1900-93, J. Climate, 10, 1004–1020.

45

Chapter 2 Volcanoes and ENSO over the Past Millennium* “I had a dream, which was not all a dream. The bright sun was extinguish’d, and the stars Did wander darkling in the eternal space, Rayless, and pathless, and the icy earth Swung blind and blackening in the moonless air.” Lord Byron, Darkness (1816)

2.1

Introduction

One of the very largest volcanic eruptions in the entire Holocene occurred ca 1258 A.D. [Stothers, 2000]. Although both its timing and location are controversial [Oppenheimer , 2003], tephra and sulfate aerosols are found ubiquitously in climate archives within a year of the event. Its impact on top-of-atmosphere incoming solar radiation was estimated by Crowley [2000] as a dimming of approximately ≠11.5 Wm≠2 , about 6 times the estimated anthropogenic climate forcing since 1750, the median of which is close to 1.85 Wm≠2 [Hansen et al., 2005]. By some measures, it was the largest eruption of the past millennium. Thus, Crowley [2000] indicates that its ice core sulfate concentration reached eight times that of Krakatau (1883) and two times that of Tambora (1815), which accounted for the ’year without a summer’ [Stommel and Stommel , 1979; Stothers, 1984]. Given such prominence, it is surprising that its precise location has not yet been pinpointed, though its presence in ice cores of both poles points to a tropical origin: El Chichón (Mexico) and Quilotoa (Ecuador) are * Published

as Emile-Geay, J., R. Seager, M.A. Cane, E.R. Cook and G. Haug., Volcanoes and ENSO over the past millennium, Journal of Climate, 21, 3134–3148, DOI:10.1175/2007JCLI1884.1. Reprinted with permission from the American Meteorological Society

46

Chapter 2. El Niño and Volcanoes

the preferred candidates (Palais et al. [1992] ; R.Bay, personal communication, 2006). Such a radiative perturbation must have had sizable climate impacts worldwide. Indeed, Stothers [2000] lists an impressive body of historical evidence for the eruption having occurred early in 1258 (probably January) and having caused massive rainfall anomalies, with adverse eﬀects on agriculture, spreading famine and pestilence across Europe. Some of these consequences are consistent with what we know of the atmospheric response to recent tropical eruptions [Robock, 2000], but it is diﬃcult to characterize for two main reasons: 1. The shape of the volcanic veil is highly dependent on the atmospheric velocity field at the time of the injection, which determines the dispersion of the sulfate aerosols and their eﬀect on optical thickness worldwide: the atmospheric response is a function of its initial state, a fundamentally non-linear problem. 2. The direct (radiative) and indirect (dynamical) eﬀects of the eruption are often confounded by other sources of natural variability – in particular the nearsimultaneous occurrence of El Niño events [Robock, 2000]. The last point is a sensitive issue. A temporal correlation between both phenomena was recognized early on, and a possible volcanic determinism of the El Niño-Southern Oscillation (ENSO) was even proposed [Handler , 1984], albeit on the basis of the relatively short instrumental record. However, doubt was soon cast on this explanation once ENSO began to be understood and was shown to be predictable without invoking volcanic forcing [Cane et al., 1986]. Further, Handler’s statistical analysis was shown not to withstand a careful scrutiny [Nicholls, 1990; Self et al., 1997]. The idea that this correlation was no accident was recently revived by Adams et al. [2003], who applied superposed epochal analysis to a proxy-based reconstruction of the NINO3 index [Mann et al., 2000], and showed that the likelihood of an El Niño event following an eruption in the subsequent cold season was roughly double that based on chance alone. Since ENSO is known to drive and organize atmospheric flow across the globe [e.g. Horel and Wallace, 1981; Ropelewski and Halpert , 1987; Trenberth et al., 1998], it is of considerable importance to determine how it responds to natural climate forcing, as this is a necessary step to project its evolution under rising amounts of greenhouse gases [Cane, 2005]. The proposition that explosive volcanism could be influencing ENSO behavior therefore merits serious attention. In support of the Adams et al. [2003] analysis, a dynamical explanation was recently proposed, invoking the so-called “thermostat” response of the tropical Pacific to uniform exogenous forcing [Mann et al., 2005; Clement et al., 1996]. The composites of Adams et al. [2003] are dominated by large eruptions, and the ENSO model used in their study tended to consistently produce El Niño events thereafter, though it also generated its own in the absence of volcanic forcing. However, several outstanding questions remain unanswered: since Mann et al. [2005] looked mainly at ensemble means, little is known about how individual eruptions influence the statistics of the ENSO system. Their result also seems to contradict that of Chen et al. [2004] who El Niño and the Earth’s climate: from decades to Ice Ages.

2.2. Explosive Volcanism and ENSO Regimes

47

showed that all major El Niño events since 1856 could be forecast up to 2 years ahead with the sole knowledge of initial sea-surface temperatures† . In the present work, we wish to further explore the quantitative relationship between explosive volcanism and ENSO. Of particular interest is the derivation of a relationship between sulfate aerosol forcing and the likelihood of an El Niño in a given year. We construct such a diagram of ENSO regimes as a function of volcanic forcing, which shows that only eruptions larger than about the size of Mt Pinatubo (1991) significantly “load the dice”, raising the likelihood of an El Niño event above the model’s level of internal variability. In particular, the model predicts a 75% probability for the occurrence of an El Niño in the year following the tremendous eruption of 1258. We then exploit the diversity of the proxy record and find multiple lines of evidence suggesting that a moderate-to-strong El Niño did happen in 1258/59. Consistent with the model’s prediction, we find that even a major eruption does not seem to bolster the intensity of the event out of the usual range, though it significantly raises the likelihood of its occurrence. The chapter is structured as follows: we start by describing and analyzing numerical experiments covering the past millennium, before focusing on the 1258 eruption in the model and the paleoclimate record (section 3). Discussion follows in section 4.

2.2 2.2.1

Explosive Volcanism and ENSO Regimes Volcanic Forcing over the Past Millennium

Volcanic forcing is the best constrained of natural forcings over the past millennium [e.g. Crowley, 2000; Jones and Mann, 2004], and can be estimated from the amount of sulfate aerosols present in ice core records [Hammer , 1980; Hammer et al., 1980; Robock and Free , 1995; Cole-Dai et al., 2000] with tropical volcanoes identified by events having a bipolar signature [Langway et al., 1988, 1995]. The radiative impact at the top of the atmosphere ∆F can be estimated via the following formula [Pinto et al., 1989; Hyde and Crowley, 2000]: ∆F = (∆F )K

3

M MK

42/3

(2.1)

wherein M is the sulfate aerosol loading, MK that of the Krakatau (1883) eruption, estimated at about 50 Mt [Self and Rampino, 1981; Stothers, 1996], corresponding to a solar dimming of (∆F )K = ≠3.7 Wm≠2 [Sato et al., 1993]. Crowley [2000] estimated M from two continuous ice core sulfate measurements to produce a record of global explosive volcanism, subsequently restricted to tropical eruptions by only selecting those eruptions simultaneously present in records from † This

result is supported by Luo et al. [2007], who used a fully-coupled general circulation model over the period 1982-2004

48

Chapter 2. El Niño and Volcanoes

both poles [Adams et al., 2003], before applying Eq(2.1). A major caveat of this reconstruction is the absence of a formal error estimate in the forcing. In some cases, enough ice cores sulfate measurements are available throughout tropical and polar regions to allow for a meaningul error bar to be assessed [Gao et al., 2006]. Error propagation analysis can then provide uncertainty in the radiative forcing itself, assuming Eq(2.1) is free of errors. This is done in Section 2.3.1, for instance, where we estimate a 30% uncertainty. It is beyond the scope of this chapter to extend this methodology to every eruption of the past 1000 years. Two choices help us address this limitation: firstly, we generate a second forcing timeseries, scaled down by 30%, as input for a companion set of model experiments. Secondly, we only draw quantitative conclusions from the one eruption for which we have a forcing error estimate (1258 A.D.), eﬀectively treating the others as a random sequence.

2.2.2

Experimental Setup

We use the model of Zebiak and Cane [1987], which has linear shallow-water dynamics for the global atmosphere [Zebiak, 1982] and the Tropical Pacific ocean [Cane and Patton, 1984], coupled by non-linear thermodynamics, and displays self-sustained ENSO variability. The ocean model domain is restricted to [124◦ E-80◦ W; 29◦ S29◦ N], which means that only tropical processes are considered. The model is linearized around a constant climatology [Rasmussen and Carpenter , 1982]. We employ the same configuration as Clement et al. [1999] and Emile-Geay et al. [2007], in the model version written by Takashi Kagimoto at the International Research Institute for Climate Prediction. Radiative forcing anomalies are included as a source term of the (prognostic) equation for sea surface temperature (SST). Conversion is made from the top-of-the-atmosphere pertubation to a surface flux by multiplying by (1 ≠ 0.62 C + 0.0019–) where C is the cloud fraction and – is the noon solar altitude [Reed , 1977]. Consistent with the absence of radiative scheme in the model, we hold the cloud fraction constant, 50%. As in Mann et al. [2005], the solar forcing estimates are multiplied by a factor of ﬁ/2, since the model represents only the Tropics. Since Crowley [2000]’s record of volcanic forcing is a yearly one, all eruptions were arbitrarily assumed to occur in January of each year, and stay constant for 12 months. Modestly diﬀerent results would ensue with an exponential decay and varying eruption dates. The veil’s spatial extent is uniform throughout the model domain, for simplicity. We also include the slowly-varying solar irradiance component derived from cosmogenic isotopes [Bard et al., 2000], as in Mann et al. [2005]. To ensure meaningful results, we produced 200 independent realizations of the model’s response to radiative forcing, using random initial conditions. For the first 4 months of each experiment, the model was subjected to a steady wind forcing over the Western Pacific area [ 165◦ E-195◦ E, 5◦ S-5◦ N], whose amplitude was drawn from a normal distribution. Accordingly, the initial SST distribution between ensemble members was close to normally distributed (not shown). Model runs are then let free El Niño and the Earth’s climate: from decades to Ice Ages.

2.2. Explosive Volcanism and ENSO Regimes

49

G4H!I,BB1-2J.;/151-2J456.782,7-2CDCE$217B1:K;1!:1,7251BI47B12=7L!""@

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Figure 2.1: Response of the Zebiak-Cane model to volcanic forcing during the past millennium. Forcing and 200-member ensemble average.

to evolve under the sole influence of the radiative forcing described above.

2.2.3

Results

In Fig 2.1 we show the 200-member ensemble mean response of the NINO3 index, in order to isolate the eﬀect of boundary conditions over the model’s strong internal variability. As in Mann et al. [2005] (their Fig 3a), the notable result is the occurrence of El Niño events in the year following major tropical eruptions, such as, for instance, Tambora (1815), Krakatau (1883), and 1258. In other words, a strong volcanic cooling is seen to produce a warming in the eastern equatorial Pacific within a year, with noticeable eﬀects up to 24 months after the eruption. The reason for this counterintuitive result lies in the “thermostat” mechanism [Clement et al., 1996]: the strong upwelling, sharp thermocline and surface divergence in the eastern equatorial Pacific make the SST harder to change by radiative forcing alone. In contrast, the deeper thermocline and small divergence in the Western Pacific Warm Pool make it more

50

Chapter 2. El Niño and Volcanoes

sensitive to alterations of the surface energy balance. Given a uniform reduction in incoming surface radiation, the SST will therefore cool faster in the West, initially reducing the zonal SST gradient. This provokes a slackening of the trade winds, which promotes a further reduction of the SST gradient, via the Bjerknes [1969] feedback: the upshot of those air-sea interactions is that a uniform solar dimming results in more El Niño-like conditions. Conversely, a uniform radiative increase produces La Niña-like conditions. In individual simulations, an El Niño event may or may not occur, but a higher ensemble-mean NINO3 means that warm events are favored. In other words, it is the likely behavior of the system, though some eruptions – especially weaker ones – may not follow the rule. Overall, this procedure gives insight into the general tendency of the system but should not be taken as a perfect predictor of events: they could have happened by pure chance, without volcanic interference. How does this compare to the results of Adams et al. [2003]? Selecting five of their eruption lists (their Table 1) corresponding to the longest period they analyze (16591979), we applied their criterion of El Niño occurrence to our results (NINO3 > 0.3◦ C for the October to March average following the eruption). The eruption lists are based on the Ice-Core Volcanic Index (IVI, Zielinski [2000]; Robock and Free [1995]) or Volcanic Explosivity Index (VEI, Simkin and Siebert [1994]). Because the latter may not be conservative enough, it was amended by Adams et al. [2003] to exclude consecutive years (their VEI∗ ). Since both chronologies used diﬀerent data and criteria to describe explosive volcanism, they diﬀered from each other and from that of Crowley [2000]. Also, since the same eruption may be reported with a time lags of 1 or 2 years between chronologies, we adjusted the eruptions lists to those actually present in the forcing of the experu iment. Such cases are denoted by ‘ Crowley’, and can diﬀer substantially from the original lists. The results are shown in Table 2.1, which displays the number of eruptions, the number of them immediately followed by an El Niño event, both in our analysis (center columns) and theirs (rightmost columns). The agreement is quite remarkable for the largest eruptions and deteriorates for weaker ones, as expected from theoretical grounds. Further, restricting the list of large eruptions to those present in our forcing tends to raise the fraction of simulated events that go into an El Niño immediately after an eruption, and, perhaps coincidentally, yields numbers surprisingly close to those of Adams et al. [2003]. There is an important diﬀerence, however: since our model tends to produce El Niño-events more often than suggested by the Mann et al. [2000] reconstruction (a 32% vs 25% likelihood, i.e. one warm event every 3 years as opposed to one in 4), the marginal increase in ENSO likelihood, albeit sizable, is correspondingly lesser in our case. Note that the model’s ENSO frequency is very close to that quoted by Trenberth [1997] over the twentieth century (a 31% likelihood in any given year), though there is suggestion that the latter it is anomalously high in the context of the past five centuries [Gergis and Fowler , 2006]. Although this is a useful diagnostic of the system’s behavior around key dates, it gives little information about the quantitative influence of volcanic forcing on ENSO El Niño and the Earth’s climate: from decades to Ice Ages.

2.2. Explosive Volcanism and ENSO Regimes

51

Table 2.1: Count of warm ENSO events in the year following a volcanic eruption. Comparison to Table 1 of Adams et al. [2003], with chosen key-date lists over the period 1649-1979. IVI = Ice-Core Volcanic Index [Zielinski,u2000; Robock and Free, 1995]. VEI=Volcanic Explosivity Index [Simkin and Siebert , 1994]. ‘ Crowley’= chronology adjusted to the forcing used for our numerical experiments. M/L =“medium to large” eruptions. Listed are the number of eruptions in each list, the number of eruptions followed by a El Niño event within a year, and the ratio of the two previous numbers. See text for details. # Eruptions

# Warm events

Fraction

(this study) IVI M/L IVI M/L VEI M/L VEI M/L

u

Crowley

u

VEI∗ M/L VEI∗ M/L

Crowley

u

Crowley

IVI Largest 1649-1979 IVI Largest

u

Crowley

VEI Largest 1649-1979 VEI Largest

u

Crowley

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(Adams et al. 2003)

40% 50% 35% 45% 35% 42% 42% 56% 38% 50%

9 15 11 6 6 -

36 % 48% 55% 50% 46% -

statistics. The question we now ask is: how large an eruption is needed to significantly alter the likelihood of an El Niño event in any given year?

2.2.4

A Phase Diagram for ENSO regimes

We consider a 200-member ensemble of simulations of the past millennium, as described before. Since these experiments idealize volcanic forcing as starting in January and persisting for a year, and since El Niño typically grows in April/June and peaks at the end of the calendar year, we look at the following quantity: for each year between 1000 and 1998 A.D. when the forcing was negative, consider the time window going from January to December of the following year. Our criterion for a given simulation to exhibit an El Niño is that NINO34 exceed 0.5 degrees for at least 6 consecutive months during the time window, consistent with the definition of NOAA’s Climate Prediction Center. We then plot, for each year, the fraction of ensemble members that went into an El Niño versus the corresponding volcanic forcing. The result is shown in Fig 2.2 . One can distinguish 3 regimes: for a volcanic dimming weaker than about 1 Wm≠2 , the model is essentially unperturbed, and remains in a regime of free oscillations, where the likelihood of an El Niño event in any given year never exceeds 0.43. The likelihood is, on average, clustered around 0.29, close to the observed 0.31 [Trenberth, 1997], which means than a warm event is to be expected

52

Chapter 2. El Niño and Volcanoes

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El Niño and the Earth’s climate: from decades to Ice Ages.

2.2. Explosive Volcanism and ENSO Regimes

53

every 3.5 years or so. (Note that this diagram does not contain information about years of zero or positive radiative forcing, which would slightly increase the spacing between events). For a dimming greater than 4 Wm≠2 , however, all plotted points are above the limit value of 0.43, which is therefore a forced regime, to which all major eruptions of the millennium pertain. Between 0.8 and 4 Wm≠2 , the model ENSO likelihood is sometimes above, sometimes below the threshold: a transition regime. Interestingly, both Pinatubo (≠3.73 Wm≠2 ) and Krakatau (≠3.70 Wm≠2 ) find themselves at the boundary between the transition and forced regimes. Since the uncertainties on the forcing are probably very large (on the order of 30% at least), and since the model lacks an explicit representation of radiative processes, the exact value of these transition points is not to be taken literally. As an illustration, we ran the model with a volcanic forcing weaker by 30%, leaving solar forcing untouched. The same phase diagram is presented in Fig 2.3, where it can be seen that the boundary between transition and forced regimes is now shifted to ≠3.3 Wm≠2 . This diﬀerence stems largely from the paucity of large (|F | > 2 Wm≠2 ) tropical eruptions in the icecore based chronology of Crowley [2000], and the fact that in these 200 realizations of the experiment, the unforced probability of a warm event never reached above 40% (versus 42% in the previous case). Nonetheless, the qualitative behavior is identical, and the quantitative result quite close. Do strong volcanic eruptions also produce noticeably stronger El Niño events? One way of seeing this is to consider the maximum value of NINO3 in the same time window as before, presented in Fig 2.4. To limit intra-ensemble fluctuations, we limit ourselves to the ensemble average of this statistic for each year (1000 data points). It is clear that the average maximum size of ENSO events does increase sharply with volcanic forcing in the transition and forced regimes. However, the model physics constrain the index between about ≠2.5 and 3.5 ◦ C (vs ≠1.8 to 3.8◦ C in the Kaplan SST dataset‡ ), and even the strongest eruption (1258) does not alter this absolute (intra-ensemble) maximum reached by the index. So while very strong eruptions make an event significantly more likely, its amplitude will not fall outside the model’s range of internal variability. Hence, a simple way of understanding the eﬀect of volcanic forcing is that for suﬃciently high values, it adds to the likelihood of a warm event, which is normally nonzero because of the model’s self-sustained oscillatory behavior. Explosive volcanism does not trigger El Niño events per se, but rather “loads the dice” in favor of El Niño, also favoring higher amplitudes. Following eruptions associated with a cooling larger than 1 Wm≠2 , ENSO likelihood increases by about 50% on average. The most spectacular example of such behavior coincides with the largest eruption of the past millennium (1258 A.D.), upon which we shall now focus. ‡ http://iridl.ldeo.columbia.edu/SOURCES/.Indices/.nino/.EXTENDED/.NINO3/

54

Chapter 2. El Niño and Volcanoes

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El Niño and the Earth’s climate: from decades to Ice Ages.

2.2. Explosive Volcanism and ENSO Regimes

55

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Figure 2.4: ENSO regimes as a function of the intensity of volcanic forcing (2). As in Fig(2.2), except that the ordinate is the ensemble mean of the maximum of monthly NINO3 values reached by the model during the calendar year following the eruption. This gives insight into the impact of the forcing on the amplitude of events, as opposed to their frequency of occurrence.

56

Chapter 2. El Niño and Volcanoes

2.3 2.3.1

A Remarkable Case: the 1258 Eruption Forcing

The year 1258 (1259 in some chronologies) features an outstanding volcanic anomaly [Langway et al., 1988; Palais et al., 1992] that has been found: • In 9 Northern Hemisphere ice core timeseries from 7 cores (NGT-B20, GISP2, A77, A84, Renland, NorthGRIP1, and Crete), 3 of which had sulfate signals used to estimate the stratospheric aerosol loading. (C.Gao, personal communication, 2006). All are from Greenland except A77 and A84, sampled from the nearby Agassiz Ice Cap on Ellesmere Island, Canada. • In 6 Southern Hemisphere (Antartica) ice cores (SP2001c1, Plateau Remote, TalosDome, G15, B32, PS1), 5 of which have sulfate records. (C.Gao, personal communication, 2006) • in Lake Malawi sediments [34.5◦ E, 1◦ S], as a thick ash layer of age within dating uncertainties (±100 years) of 1258 A.D. (Thomas C. Johnson, personal communication). This strongly suggests that the eruption occurred in the Tropics, though data from tropical ice cores would be extremely valuable to establish this fact. The mass sulfate injection is estimated to lie between 190 and 270 Mt [Budner and Cole-Dai, 2003; Cole-Dai and Mosley-Thompson, 1999]. The radiative impact at the top of the atmosphere can be estimated via (2.1). The sulfate stratospheric loadings given above translate to perturbations of ≠8.9 to ≠11.4 Wm≠2 , all extremely large, but with an error bar of about 30%. Results are qualitatively similar for all estimates within this range. Because the eruption of interest was only recorded in both poles in 1259, this is the date where it is included in the model, but shifting the spike to 1258 only shifts the response a year earlier. Similar lags might be present for other eruptions.

2.3.2

Results

It is clear from Fig 2.1 that the 1258 eruption stands out in the context of the millennium, both in the forcing and the response, which is a 1.5◦ C warming in the ensemble mean NINO3. This result is virtually identical to that of Mann et al. [2005] (their Fig 1a), despite slight coding diﬀerences. It is instructive to look at the distribution of NINO34 values, for the full 1258 forcing and its more conservative estimate, reduced by 30%. In Fig 2.5 we present such distributions obtained by a kernel density estimation amongst the 200 ensemble members. While the model usually displays a unimodal distribution centered around ≠0.4◦ C and skewed towards positive events (as does nature), the year 1259 stands out in both cases as a bimodal anomaly whose dominant peak is centered around ≥ 1.5◦ C. El Niño and the Earth’s climate: from decades to Ice Ages.

2.3. A Remarkable Case: the 1258 Eruption

57

NINO34 distribution and the 1258 eruption $%(

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58

Chapter 2. El Niño and Volcanoes

Which fraction of ensemble members produced an El Niño event that year, and of which amplitude? We apply the Climate Prediction Center criterion of ENSO occurrence once more (NINO34 > 0.5◦ C for at least 6 months), also considering the thresholds of 1◦ C and 2◦ C. The results are shown in Table 2.2 (left column). Within the 200-member ensemble, and over that particular period, the model saw the development of a warm event in 75% of cases. This figure is almost 2.5 times larger than that based on chance alone (32%). The ratio further increases for stronger NINO34 anomalies: their likelihood is bolstered by a factor of ≥ 3 for strong El Niños, and almost 6 for a very strong El Niños. This brings the results of Section 2.22.2.4 into a new light, and illustrates how strong eruptions tend to raise both the likelihood and the intensity of El Niño events in the model. Would these numbers change significantly in the presence of a weaker forcing? Considering again the case where volcanic forcing was reduced by 30%, we find lower, but still significant increases of 2.1, 2.8 and 4.6, respectively, for the same likelihood ratios. Table 2.2: Probability of an El Niño event after the 1258 eruption. Shown here is the fraction of ensemble members that produced an El Niño event in a 12-month window following the eruption. We applied the 3 following criteria for El Niño occurrence: {NINO34 Ø 0.5} for 6 consecutive months, {NINO34 Ø 1} (“strong El Niño”) and {NINO34 Ø 2} (“very strong El Niño”) over identical intervals.

Threshold 0.5◦ C 1◦ C 2◦ C 0.5◦ C 1◦ C 2◦ C Case Full forcing 30% reduced Year 1259 75% 71% 47% 68% 64% 37% Millennium 32% 24% 8% 32% 23% 8% Thus, in the vast majority of cases, the model tended to produce a moderate-tostrong El Niño in response to the 1258/1259 volcanic dimming of solar irradiation. This needs to be put in the longer context of medieval climate, which was also aﬀected by variations in solar irradiance [Jones and Mann, 2004]. When reconstructions thereof were added to the volcanic forcing, as in Mann et al. [2005], we found that the early part of the millennium (1000-1300 A.D.), a period of anomalously high irradiance (possibly related to the so-called Medieval Climate Anomaly), the model’s Eastern equatorial Pacific was anomalously cold by a few tenths of a degree. The persistence of such La Niña-like conditions is consistent with evidence of epic megadroughts that struck the American West at the time [Cook et al., 2004], as well as modeling results [Schubert et al., 2004; Herweijer et al., 2006] and other proxy evidence for medieval hydroclimate worldwide [Graham, 2004; Herweijer et al., 2007; Seager et al., 2007; Graham et al., 2007]. We thus propose that the 1258 eruption produced a moderate-to-strong El Niño in the midst of prevailing La Niña-like conditions and now ask whether the paleoclimate record is consistent with such a proposition. El Niño and the Earth’s climate: from decades to Ice Ages.

2.3. A Remarkable Case: the 1258 Eruption

2.3.3

59

Comparison to the Proxy Record

Since the year 1258 pre-dates any reliable instrumental or documentary evidence of an El Niño event, we must turn to more indirect geological sources: climate proxies. Though each of them is fraught by a number a of limitations, Mann and collaborators [Mann et al., 1998; Mann, 2002] demonstrated than their combination can exploit the complementary strengths of these proxies to skillfully reconstruct climate events of the past. Such a multiproxy approach has recently been applied to devise a chronology of ENSO events back to 1525 AD [Gergis and Fowler , 2005; Gergis, 2006], in the spirit of earlier reconstructions by Quinn [1992] and Whetton and Rutherfurd [1994]. Unfortunately, no such reconstruction extends back to 1258 A.D., and we must therefore turn to a semi-quantitative analysis. The coast of the Americas is dotted with ENSOsensitive sites [e.g. Ropelewski and Halpert , 1987; Graham, 2004; Trenberth et al., 1998] which can be used to monitor ENSO conditions via proxy records. In Fig 2.6 we confront the model results [panel (a)] with proxy evidence from a variety of high-resolution climate records from such regions: 1. The North American Drought Atlas [Cook and Krusic , 2004], which uses a 2000-year long tree-ring chronology to estimate the Palmer Drought Severity Index (PDSI, [Palmer , 1965]) over the American West ([25◦ N-47.5◦ N; 122◦ W100◦ W]). PDSI can be viewed as a proxy for soil moisture with built-in persistence. Tree-ring records from this region have been shown to be extremely sensitive to droughts, which were tied to tropical Pacific SST patterns [Cole et al., 2002; Seager et al., 2005; Herweijer et al., 2007]: specifically, a negative value of PDSI is indicative of drought conditions of the American West, and by inference of La Niña-like conditions. The decade beginning in 1250 was exceedingly dry, with some of the driest years on record (1253, 1254) over the region. Year 1258 itself reaches an extremely negative value for the PDSI, which then undergoes its biggest upward jump of the millennium (+4.52 units), bringing the drought conditions back to almost normal for 1259. This jump is presented on Fig 2.6b, which features the year-to-year change in the index. Based on the aforementioned relationship between tropical Pacific SSTs and droughts in the American West, its most likely cause is a strong or very strong El Niño. 2. A record of tree-ring width from El Asiento, Chile, which is the most ENSOsensitive tree-based record of the past 1000 years over South America [Luckman and Villalba, 2001] (Fig 2.6c). The standardized width is a proxy for fractional expected growth, which is dominated by water supply. Typically, wetter years yield thicker rings, and those tend to occur more frequently during El Niño events. While the 1258/59 jump (+0.48 units) is not the largest in the record in absolute terms (the return to near-normal conditions after the severe drought of 1304, not shown, is of +0.89 units), it is also consistent with a moderate-tostrong El Niño. 3. Titanium content (%) in the Cariaco basin sediments core at ODP Site 1002 (

60

Chapter 2. El Niño and Volcanoes

Figure 2.6: Multiproxy view of the 1258 eruption: (a) Volcanic forcing (black curve) in Wm≠2 and 200-member ensemble mean response of NINO3 in the Zebiak-Cane, after applying a 20-year low-pass filter (light blue curve). (b) year-to-year change in PDSI over the american West [Cook and Krusic , 2004] (c) Standardized tree-ring width at El Asiento, Chile [Luckman and Villalba, 2001] (d) Titanium percentage in core 1002 from the Cariaco basin [Haug et al., 2001] (standard deviation units).

El Niño and the Earth’s climate: from decades to Ice Ages.

2.4. Discussion

61

10◦ N, 65◦ W) as in [Haug et al., 2001]. This record (Fig 2.6d) is best interpreted as a proxy for rainfall over northern South America, which El Niño tends to reduce by pushing the Atlantic ITCZ further north [Enfield and Mayer , 1997], thereby decreasing the riverine flux of titanium into the core. Hence, an El Niño event should manifest itself as a dip in Ti concentration. For this study, the core was analyzed at 50 µm resolution over the 13th century, providing unprecedented detail on ITCZ dynamics during this time window. Despite the uncertainties of the age model published in Haug et al. [2001], which are of several years to decades, notable Ti minima are observed synchronously with upward jumps in PDSI ca 1220, 1259, 1289 and 1299, consistent with the occurrence of El Niños at those times. While none of these records singlehandedly establishes the occurrence of an El Niño event in 1258/1259, their conjunction is strongly suggestive thereof. Furthermore, we show in Fig 2.7 the number of fine-grain lithics in a sediment core taken oﬀ the Peruvian coast, taken as a proxy for ENSO-induced rainfall [Rein et al., 2004]. A spike is indeed present around 1258 (within dating uncertainties), shortly before the end of the period of low ENSO activity that prevailed from about 800-1250 A.D. This is broadly consistent with the Medieval Climate Anomaly. We conclude that there was indeed an El Niño event in 1258/59, though perhaps not exceptional in amplitude.

2.4

Discussion

Thus, the evidence supports the notion that the Americas did record signals consistent with a moderate-to-strong El Niño in 1258/1259, which came on the heels of a major, prolonged La Niña-like anomaly of the Medieval Climate Anomaly [Rein et al., 2004]. This can be explained by the “thermostat” response of the Tropical Pacific to the massive volcanic sulfate aerosol loading reconstructed for that time, in the midst of a period of strong solar irradiance, which has been found to significantly organize the model ENSO activity on centennial-to-millennial timescales [Emile-Geay et al., 2007]. Regardless of solar forcing, we find that the model ENSO is only noticeably influenced by volcanic eruptions with a radiative forcing greater, in absolute value, than ≥ 3.3 to 4 Wm≠2 (roughly the magnitude of the Krakatau or Pinatubo eruptions). However, our quantitative conclusions must be tempered by the incompleteness of the model physics and uncertainties in both the forcing and dataset considered for validation. Uncertainties in the forcing, though largely unreported, are sizable: on the order of 30%, as seen in section 2.2, perhaps more for certain eruptions. We highly welcome research eﬀorts aiming at better documenting, and reducing, this uncertainty. The simplicity of the model is what allowed us to study the coupled system over the entire length of the millennium, yet it creates caveats that are inherent to its for-

62

Chapter 2. El Niño and Volcanoes

FINE GRAIN LITHICS CONCENTRATION IN SEDIMENTS OFF THE COAST OF PERU AS A PROXY OF CONTINENTAL RUN-OFF AFTER FLOOD (EL NINO) EVENTS 0.98

FINE GRAIN LITHICS

0.97 0.96 0.95 0.94 0.93 0.92 0.91 800

1000

1200

1400

1600

1800

YEAR

Figure 2.7: A flood proxy from Peru: record of fine-grained lithics since 800 A.D. from Rein et al. [2004]. The thick red curve is lowpass filtered, and the shaded area corresponds to the Medieval Climate Anomaly. Note the sharp transition around 1260 A.D.

El Niño and the Earth’s climate: from decades to Ice Ages.

2.4. Discussion

63

mulation [Clement et al., 1999]. While the chain of physical reasoning linking volcanic and solar forcing to equatorial SSTs (the “thermostat” mechanism) is certainly correct as far as it goes, the climate system is complex and processes not considered in this argument, such as cloud feedbacks and thermocline ventilation, might be important. The model has a very idealized representation of tropospheric radiative processes and no representation of stratospheric processes at all. While it has had some success in explaining some observations of radiatively forced climate change [Cane et al., 1997; Clement et al., 1999; Mann et al., 2005; Emile-Geay et al., 2007], a more comprehensive atmosphere model would be desirable. Targeted experiments in a coupled general circulation model (CGCM) featuring a realistic ENSO cycle and idealized volcanic forcing for 1258 would shed light on this issue. However, it is not clear that the current generation of CGCMs is up to the task, with a simulated ENSO generally exhibiting an excessive 2-year phase-locking, too little skewness in the NINO3 statistics, and numerous biases in the tropical climatology [Latif et al., 2001]. The consequence is that there is still no agreement in the ENSO response to greenhouse forcing in CGCMs for ENSO [Collins, 2005], which does not bode well for a similar test with volcanic forcing. Nonetheless, substantial progress has recently been achieved in simulating ENSO over various timescales [Cane et al., 2006; Guilyardi, 2006]. Some CGCMs do exhibit a thermostat-like behavior [e.g. Schneider and Zhu, 1998], proving that it is not merely an artifact of the simplicity of the Cane-Zebiak model. Recently, Stenchikov et al. [2007] conducted experiments with the state-of-the-art CGCM of the Geophysical Fluid Dynamics Laboratory (GFDL CM 2.1, Delworth and Coauthors [2006]) forced by radiative eﬀects of volcanic aerosols calculated using observed aerosol parameters for the Mt Pinatubo eruption, as well as 3 and 5 times such impact. They found that the thermostat mechanism is at work in their model, leading to an El Niño-like response to a Pinatubo-type eruption, though such eﬀect is fairly weak. Thus, while it is encouraging to see a convergence between the qualitative behavior the Cane-Zebiak model and fully coupled CGCMs, there are still quantitative discrepancies that hamper the establishment of a precise threshold in the ENSO response to volcanic forcing. Other problems stem from the proxy records themselves: since they are imperfect by nature, only the convergence of independent indicators can give confidence in a result. A more direct measure of tropical Pacific SSTs would be desirable, but is unavailable at this time. One could also turn to more remote ENSO proxies, but it then becomes diﬃcult to disentangle the direct, local eﬀects of the volcanic veil and the more indirect ENSO teleconnections [Santer et al., 2001]. There is no obvious way to separate these, since the geographical distribution of the sulfate stratospheric cloud is unknown, and the El Niño episodes need not have been exceptional in amplitude. Also, one cannot rule out that the influence of the assumed radiative perturbation on land surface temperature may have been large, and overwhelmed a more distal ENSO signal. More fundamentally, and regardless of the accuracy of the records, the problem becomes one of detection and attribution of causes: even if it turns that an El Niño

64

Chapter 2. El Niño and Volcanoes

did happen during the year following a given eruption, is it sensible to claim that it was triggered by volcanic forcing alone? Of course, there could have been an El Niño anyhow (a one in three chance, roughly). The main contribution of this work is to have drawn a quantitative phase diagram (section 2.2.4), which outlined by how much volcanic forcing can “load the dice” of ENSO likelihood in any given year. In our case it made it 75% likely in 1259/1260, and overall, about 80% more likely for an El Niño event to occur after a large eruption than based on chance alone (32%). However, as the prediction made in this diagram is probabilistic in essence, a definitive test of its veracity can only come from a long record of ENSO occurrences. So far, the work of Adams et al. [2003] supports a correlation between explosive tropical volcanism and ENSO, but the test will become more stringent as the number of high-resolution proxy records becomes more widely available throughout the millennium and beyond, and allow a full chronology of ENSO events over the past 1000 years to be developed. One might see an apparent paradox in our results. If volcanoes can cause El Niños, it would seem that ENSO could not be predicted unless one could predict volcanic eruptions. Yet all current prediction schemes, many of which have demonstrated considerable skill [e.g. Goddard et al., 2001], use only climate information, only including the eﬀects of volcanic forcing insofar as they aﬀect the initial conditions in sea-surface temperatures. However, in common with Adams et al. [2003] and Mann et al. [2005], we have shown that only outsized volcanic eruptions are highly likely to generate an El Niño; more modest eruptions create only a slight bias toward warm events (see Fig 2.2). Hence there is no inconsistency between the existence of a robust statistical relationship between large volcanic eruptions on ENSO, and the work of Chen et al. [2004] who showed that all major El Niño events since 1856 could be forecast up to 2 years ahead with the sole knowledge of initial SSTs. Both results are consistent with the proposition that the “forced regime” only begins for eruptions larger than Pinatubo and Krakatau, which are absent from the hindcast period (1856-2004).

El Niño and the Earth’s climate: from decades to Ice Ages.

BIBLIOGRAPHY

65

Bibliography Adams, J., M. Mann, and C. Ammann (2003), Proxy evidence for an El Niño-like response to volcanic forcing, Nature, 426, 274–278, doi:10.1038/nature02101. Bard, E., G. Raisbeck, F. Yiou, and J. Jouzel (2000), Solar irradiance during the last 1200 years based on cosmogenic nuclides, Tellus, 52B, 985–992. Bjerknes, J. (1969), Atmospheric teleconnections from the equatorial Pacific, Mon. Weather Rev., 97 (3), 163. Budner, D., and J. Cole-Dai (2003), The number and magnitude of large explosive volcanic eruptions between 904 and 1865 A.D.: Quantitative evidence from a new South Pole ice core, in Volcanism and the Earth’s Atmosphere, Geophys. Monogr. Ser., vol. 139, edited by A. Robock and C. Oppenheimer, pp. 165–175, Amer. Geophys. Union, Washington, D. C. Cane, M. A. (2005), The evolution of El Niño, past and future, Earth Planet. Sci. Lett., 230, 227–240, doi:10.1016/j.epsl.2004.12.003. Cane, M. A., and R. J. Patton (1984), A numerical-model for low-frequency equatorial dynamics, J. Phys. Oceanogr., 14 (12), 1853–1863. Cane, M. A., S. E. Zebiak, and S. C. Dolan (1986), Experimental Forecasts of El Niño , Nature, 321(6073), 827–832. Cane, M. A., A. C. Clement, A. Kaplan, Y. Kushnir, D. Pozdnyakov, R. Seager, S. E. Zebiak, and R. Murtugudde (1997), Twentieth-century sea surface temperature trends, Science, 275 (5302), 957–960. Cane, M. A., et al. (2006), Progress in paleoclimate modeling, J. Climate, 19, 5031–5057. Chen, D., M. A. Cane, A. Kaplan, S. E. Zebiak, and D. J. Huang (2004), Predictability of El Niño over the past 148 years, Nature, 428(6984), 733–736. Clement, A. C., R. Seager, M. A. Cane, and S. E. Zebiak (1996), An ocean dynamical thermostat, J. Climate, 9 (9), 2190–2196. Clement, A. C., R. Seager, and M. A. Cane (1999), Orbital controls on the El Niño/Southern Oscillation and the tropical climate, Paleoceanography, 14 (4), 441–456. Cole, J. E., J. T. Overpeck, and E. R. Cook (2002), Multiyear La Niña events and persistent drought in the contiguous United States, Geophys. Res. Lett., 29, 25–1.

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Cole-Dai, J., and E. Mosley-Thompson (1999), The Pinatubo eruption in South Pole snow and its potential value to ice-core paleovolcanic records, Ann. Glaciol., 29, 99–105. Cole-Dai, J., E. Mosley-Thompson, S. P. Wight, and L. G. Thompson (2000), A 4100year record of explosive volcanism from an East Antarctica ice core, J. Geophys. Res., 105, 24,431–24,442, doi:10.1029/2000JD900254. Collins, M. (2005), El Niño- or La Niña-like climate change?, Clim. Dyn., 24, 89, doi:DOI10.1007/s00382-004-0478-x. Cook, E., and P. Krusic (2004), North American Summer PDSI reconstructions, in IGBP PAGES/World Data Center for Paleoclimatology, Data Contribution Series # 2004-045.NOAA/NGDC, Paleoclimatology Program, Boulder CO, USA. Cook, E., C. Woodhouse, C. Eakin, D. Meko, and D. Stahle (2004), Long-term aridity changes in the western United States, Science, 306(5698), 1015–1018. Crowley, T. J. (2000), Causes of Climate Change Over the Past 1000 Years, Science, 289 (5477), 270–277. Delworth, T., and Coauthors (2006), GFDL’s CM2 global coupled climate modelsPart 1: Formulation and simulation characteristics, J. Climate, 19, 643–674. Emile-Geay, J., M. Cane, R. Seager, A. Kaplan, and P. Almasi (2007), El Niño as a mediator of the solar influence on climate, Paleoceanography, 22(3), A3210+, doi: 10.1029/2006PA001304. Enfield, D. B., and D. A. Mayer (1997), Tropical Atlantic sea surface temperature variability and its relation to El Niño-Southern Oscillation, J. Geophys. Res., 102, 929–946, doi:10.1029/96JC03296. Gao, C., et al. (2006), The 1452 or 1453 A.D. Kuwae eruption signal derived from multiple ice core records: Greatest volcanic sulfate event of the past 700 years, J. Geophys. Res. Atmos., 111(D10), 12,107–+, doi:10.1029/2005JD006710. Gergis, J. (2006), Reconstructing El Niño - Southern Oscillation (ENSO); evidence from tree-ring, coral, ice core and documentary palaeoarchives, A.D. 1525-2002, Ph.D. thesis, School of Biological, Earth and Environmental Sciences, University of New South Wales, Australia. Gergis, J., and A. Fowler (2005), Classification of synchronous oceanic and atmospheric El Niño - Southern Oscillation (ENSO) events for palaeoclimate reconstruction, Int. J. Climatol., 25, 1541–1565. El Niño and the Earth’s climate: from decades to Ice Ages.

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Palais, J. M., M. S. Germani, and G. A. Zielinski (1992), Inter-hemispheric transport of volcanic ash from a 1259 A.D. volcanic eruption to the Greenland and Antarctic ice sheets, Geophys. Res. Lett., 19, 801–804. Palmer, W. C. (1965), Meteorological drought, Research Paper 45, 58 pp., U.S. Dept. of Commerce. Pinto, J. P., O. B. Toon, and R. P. Turco (1989), Self-limiting physical and chemical eﬀects in volcanic eruption clouds, J. Geophys. Res., 94, 11,165–11,174. Quinn, W. H. (1992), Large - scale ENSO event, the El Niño and other important regional features, in Registro del fenómeno El Niño y de eventos ENSO en América del Sur, vol. 22, edited by L. Macharé, José; Ortlieb, pp. 13–22, Institut Fran cais d’Etudes Andines, Lima. Rasmussen, E., and T. Carpenter (1982), Variations in tropical sea-surface temperature and surface winds associated with the Southern Oscillation/ El Niño, Mon. Weather Rev., 110, 354–384. Reed, R. (1977), On estimating insolation over the ocean, J. Phys. Oceanogr., 7, 482–485. Rein, B., A. Lückge, and F. Sirocko (2004), A major Holocene ENSO anomaly during the Medieval period, Geophys. Res. Lett., 31(L17211), doi:10.1029/2004GL020161. Robock, A. (2000), Volcanic eruptions and climate, Rev. Geophys., 38, 191–220, doi: 10.1029/1998RG000054. Robock, A., and M. P. Free (1995), Ice cores as an index of global volcanism from 1850 to the present, J. Geophys. Res., 100, 11,549–11,568, doi:10.1029/95JD00825. Ropelewski, C., and M. Halpert (1987), Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation, Mon. Weather Rev., 115, 1606–1626. Santer, B., et al. (2001), Accounting for the eﬀects of volcanoes and ENSO in comparisons of modeled and observed temperature trends, J. Geophys. Res. - Atmos, 106 (22), 28,033–28,059. Sato, M., J. Hansen, M. McCormick, and J. Pollack (1993), Stratospheric aerosol optical depths, 1850-1990, J. Geophys. Res. Atm., 98(D12), 22,987–22,994. Schneider, E. K., and Z. Zhu (1998), Sensitivity of the Simulated Annual Cycle of Sea Surface Temperature in the Equatorial Pacific to Sunlight Penetration., J. Climate, 11, 1932–1950.

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Schubert, S. D., M. J. Suarez, P. J. Pegion, R. D. Koster, and J. T. Bacmeister (2004), On the Cause of the 1930s Dust Bowl, Science, 303(5665), 1855–1859, doi:10. 1126/science.1095048. Seager, R., Y. Kushnir, C. Herweijer, N. Naik, and J. Velez (2005), Modeling of tropical forcing of persistent droughts and pluvials over western North America : 18562000, J. Climate, 18(19), 4068–4091. Seager, R., N. Graham, C. Herweijer, A. Gordon, Y. Kushnir, and E. Cook (2007), Blueprints for medieval hydroclimate, Quat. Sci. Rev., doi:10.1016/j.quascirev. 2007.04.020. Self, S., and M. R. Rampino (1981), The 1883 eruption of Krakatau, Nature, 294, 699–704, doi:10.1038/294699a0. Self, S., M. R. Rampino, J. Zhao, and M. G. Katz (1997), Volcanic aerosol perturbations and strong El Niño events: No general correlation, Geophys. Res. Lett., 24, 1247–1250, doi:10.1029/97GL01127. Simkin, T., and L. Siebert (1994), Volcanoes of the World, Second edition, Smithsonian Institution, 349 pp., Geoscience Press, Tucson, Arizona. Stenchikov, G., T. Delworth, and A. Wittenberg (2007), Volcanic climate impacts and ENSO interactions, Eos Trans. AGU, 88(23), Abstract A43D–09. Stommel, H., and E. Stommel (1979), The Year without a Summer, Scientific American, 240 (6). Stothers, R. (1984), The great Tambora eruption in 1815 and its aftermath, Science, 224 (4654), 1191–1198. Stothers, R. (2000), Climatic and demographic consequences of the massive volcanic eruption of 1258, Clim. Change, 45 (2), 361 – 374, doi:DOI:10.1023/A: 1005523330643. Stothers, R. B. (1996), Major optical depth perturbations to the stratosphere from volcanic eruptions: Pyrheliometric period, 1881-1960, J. Geophys. Res., 101, 3901–3920, doi:10.1029/95JD03237. Trenberth, K. E. (1997), The Definition of El Niño., Bull. Amer. Met. Soc., 78(12), 2771–2777. Trenberth, K. E., G. W. Branstator, D. Karoly, A. Kumar, N.-C. Lau, and C. Ropelewski (1998), Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures, J. Geophys. Res., 103, 14,291–14,324, doi:10.1029/97JC01444. El Niño and the Earth’s climate: from decades to Ice Ages.

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Whetton, P., and I. Rutherfurd (1994), Historical enso teleconnections in the eastern hemisphere, Clim. Change, 28, 221–253. Zebiak, S. E. (1982), A simple atmospheric model of relevance for El Niño, J. Atmos. Sc., 39, 2017–2027. Zebiak, S. E., and M. A. Cane (1987), A model El Niño-Southern Oscillation, Mon. Weather Rev., 115 (10), 2262–2278. Zielinski, G. A. (2000), Use of paleo-records in determining variability within the volcanism-climate system, Quat. Sci. Rev., 19, 417–438.

73

Chapter 3 El Niño as a Mediator of the Solar Influence on Climate* “My mistress’s eyes are nothing like the Sun.” William Shakespeare, Sonnets

3.1

Introduction

The concept of a solar influence on the Earth’s climate is hardly new. Sunspots were a favored explanation for monsoon failures as early as 1875 [see Davis, 2001, ch 7] and the link between the Maunder Minimum and the Little Ice Age was made a century later [Eddy, 1977; Rind , 2002; Bard and Frank, 2006]. Since solar radiation is the primary source of energy driving atmospheric and oceanic flow, and since its intensity is thought to vary on long timescales [e.g. Fröhlich and Lean, 2004], it is often invoked to explain natural climate change on decadal [van Loon and Labitzke, 1988] to multicentennial timescales [e.g. Jones and Mann, 2004]. The puzzling fact is that even generous reconstructions of past total irradiance changes do not yield changes bigger than 0.5% of the current solar irradiance (about 6.8 out of 1366 Wm≠2 ) since the Maunder Minimum. The challenge is to understand how these subtle radiative fluctuations could emerge as a significant driving force of the Earth’s climate, a system showing a considerable degree of internal variability. In a seminal paper, Bond et al. [2001] demonstrated an intriguing correlation between proxies of solar activity and the quantity of ice-rafted debris recorded at their coring site of the northeastern North Atlantic (Denmark Strait and Feni Drift). They concluded to a ”persistent solar influence on North Atlantic climate during the * Published as: Emile-Geay, J., M. A. Cane, R. Seager, A. Kaplan, and P. Almasi (2007), El

Niño as a mediator of the solar influence on climate, Paleoceanography, 22, PA3210, doi:10.1029/2006PA001304

74

Chapter 3. El Niño and the Sun

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Figure 3.1: EOF analysis of the top-of-the-atmosphere insolation over the Holocene. The leftmost column shows the EOF pattern as a function of calendar month (Jan =1, Feb =2, etc..), the center column shows the PC timeseries, and the rightmost column its spectral density, computed with the multitaper method [Thomson, 1982]. Numbers above the graph refer to the period in kyr. To obtain the contribution of a mode to the total insolation at any given time, each EOF pattern must be weighted by the value of the corresponding PC.

El Niño and the Earth’s climate: from decades to Ice Ages.

3.2. Climate Forcing over the Holocene

75

Holocene”. Prompted by Bond’s work, a number of investigators have attempted to understand this link. So far, the main dynamical pathway from the Sun to the surface has invoked the stratosphere and its eﬀect on planetary wave propagation [e.g. Geller and Alpert , 1980; Haigh, 1996]. Fluctuations in the ultra-violet (UV) spectral band have been shown to alter stratospheric ozone photochemistry, and therefore latitudinal temperature gradients in the lower stratosphere. This translates into changes in the index of refraction of upward-propagating planetary waves, which forces a redistribution of momentum fluxes in the upper troposphere, eventually leading to surface climate change, mainly over northern hemisphere continents [Shindell et al., 1999]. A more recent account describes a mechanism with a very diﬀerent premise, but with similar route through the stratosphere: Shindell et al. [2001] propose that, with increased irradiance, tropical and subtropical sea surface temperatures (SSTs) increase, leading to a warmer tropical and subtropical upper troposphere via moist convection. This results in an increased latitudinal temperature gradient near the tropopause, again refracting upward-propagating tropospheric planetary waves equatorward. The associated angular momentum transport produces changes in surface temperature and pressure corresponding to a high AO/NAO index. However, Bond et al. [2001] show that this can only partially explain their record. In this chapter we explore a new pathway of solar influence on climate, one centered around the El Niño-Southern Oscillation(ENSO) (that is to say, of purely tropical origin), and irrespective of the spectral signature of solar changes. Following Mann et al. [2005] and Clement et al. [1999], we employ a simplified model of the tropical Pacific atmosphere-ocean system [Zebiak and Cane, 1987] and diagnose its reaction to solar and orbital forcing over the past 10,000 years, in a variety of experiments. We show that even in the face of realistic amounts of weather noise, low-frequency solar irradiance fluctuations induce notable changes in the east-west temperature gradient, and in ENSO activity. The changes, albeit subtle, are of suﬃcient magnitude to produce sizable hydroclimatic impacts around the Pacific [Seager et al., 2005b]. We show that this response can also generate substantial impacts worldwide, in particular over the North Atlantic, and submit this mechanism as an explanation for the key paleoclimate records documenting the Sun-climate relationship over the Holocene.

3.2

Climate Forcing over the Holocene

Given our model’s formulation in terms of anomalies (see section 3), the climate forcings of interest are departures from the current radiative budget. Firstly, one has to consider fluctuations in solar forcing arising from the changes in the Earth’s orbit (”orbital forcing”), as in Clement et al. [1999]. Secondly, changes in the actual solar irradiance need to be accounted for (”solar forcing”). Thirdly, one should include the eﬀect of volcanic aerosol loading in the lower stratosphere, which has been suggested to account for some important SST anomalies in the tropical Pacific over the past millennium [Mann et al., 2005]. Unfortunately, such a dataset is currently unavail-

76

Chapter 3. El Niño and the Sun

able over the entire Holocene. The present study will therefore ignore this eﬀect, with the recognition that a thorough analysis must include tropical volcanic forcing when such data becomes available.

3.2.1

Orbital Forcing

The orbital forcing is well known, and can be readily and accurately computed [Berger , 1978]. In order to separate the eﬀect of various orbital motions, we carry out an empirical orthogonal function (EOF) decomposition of insolation as a function of calendar month, latitude and year. Nevertheless, the forcing applied to the model is the total departure from current insolation computed via Berger [1978]’s code, without EOF truncation. The latitude grid is restricted to the tropical band [29◦ S; 29◦ N], and the time grid spans 1 million years, necessary to cleanly isolate important orbital periodicities. In Fig 3.1 we show the first 3 EOFs (accounting for 99.7% of the variance over the Holocene), the associated principal components (PCs) and their spectral density. The first two EOFs are clearly associated with precession, with a peak at a period of 23 kiloyear (ky), zero annual mean and weak dependence on latitude. EOF1 is associated with the summertime/wintertime insolation contrast near the equator. Similarly, EOF2 can be described as the spring-fall insolation contrast at the equator. Although the two PCs are, by construction, orthogonal over the last million years, they are significantly correlated (ﬂ ≥ 0.5) over the Holocene. The third EOF is associated with obliquity changes, with a period of 43ky, and the two hemispheres out of phase. Although it only accounts for 0.84% of the overall variance, the annualmean contribution of obliquity is non-zero, in contrast to precession. Indeed, these changes are mostly responsible for the increase of ≥ 1 Wm≠2 at the equator since the early Holocene (changes in eccentricity are negligible). Overall, these three EOFs show that the northern hemisphere summer-winter contrast has kept decreasing since the early Holocene, and so has the fall-spring contrast since about 5000 B.P, while the annual mean has slowly kept rising.

3.2.2

Solar Irradiance Forcing

As emphasized in the Introduction, reconstructions of past solar irradiance variations are a matter of considerable debate and vexingly large uncertainties. The reconstructions rely on sunspot observations for recent centuries, and on paleoproxy records of cosmogenic nuclides (14 C ,10 Be , 36 Cl ) for the longer record. The latter are directly influenced by changes in magnetic flux from the Sun, not changes in irradiance. A relationship between the two must be created by extrapolating from the short record of radiometric measurements, inferring a low-frequency irradiance component from observations of the group sunspot number gathered since the invention of the telescope (see Fröhlich and Lean [2004] and references therein). There is no obvious way to perform this extrapolation. El Niño and the Earth’s climate: from decades to Ice Ages.

3.2. Climate Forcing over the Holocene

77

By consistency with Bond et al. [2001], we use the detrended 14 C production rate (from INTCAL98, Stuiver et al. [1998]) as a proxy for solar activity, after applying a 40-year lowpass filter to remove high-frequency fluctuations, which makes the scaling more meaningful (these periods are too short to aﬀect our model). In Fig (3.2) we show the forcing and an estimate of its spectrum. The record clearly contains the documented centennial variability of the Gleissberg (≥ 88 yr) and DeVries (≥ 205 yr) cycles [Peristykh and Damon, 2003; Wagner et al., 2001], as well as significant power around 500 years, and a broad band around 1000 years. These centennial- to millennial-scale fluctuations are also present in several records of 10 Be accumulation (not shown), so that confidence can be gained that both nuclides were recording production-related changes. Indeed, Be and C have such diﬀerent geochemical cycles that their coherent behavior must not reflect climate eﬀects but a common external source: nuclide production. For periods shorter than about 3000 years (but longer than a few decades), it is a fair assumption to neglect changes in the geomagnetic field, and changes in production are commonly attributed to the Sun’s magnetic activity [Bard et al., 2000; Muscheler et al., 2006]. Nonetheless, the existence of millennial solar cycles is not firmly established [Marchal , 2005; Saint-Onge et al., 2003] and some of our results rest on the assumption that they are real.

There remains the problem of translating the loosely defined ”solar activity” into irradiance. Though sophisticated techniques have been applied to this end [Mordvinov et al., 2004], no such reconstruction is available for the Holocene at the time of publication. We therefore apply the linear scaling of Bard et al. [2000]: the reference scale (∆F ) here is the diﬀerence in TSI/4 (total solar irradiance, divided by 4 because of spherical geometry) from the Maunder Minimum (roughly 1645 to 1715 A.D.) to the ”present” (1950 A.D.). It is essentially the sunspot number diﬀerence multiplied by the slope of the scatterplot of irradiance versus sunspot number. The latter, as discussed above, is only based on about 20 years of reliable radiometric data. Since published estimates of the diﬀerence [Fröhlich and Lean, 2004] range from ∆F = 0.05% to 0.5% of the solar ”constant” (S◦ = 1366 Wm≠2 for consistency with Berger [1978]), we consider these two extreme cases, along with the intermediate case of 0.2%, corresponding to peak-to-peak diﬀerences of, respectively, 0.17, 0.68 and 1.7 Wm≠2 . The 0.2% case is close to the value used by Crowley [2000] and Weber et al. [2004]. It is worth emphasizing that most recent estimates are on the lower end of this interval [Foukal et al., 2006; Fröhlich and Lean, 2004], though the solar physics community is far from having reached a consensus on the issue. Also, these long-term changes are thought to have a marked maximum in the UV domain, but recent GCM experiments show that the atmosphere’s response is somewhat indiﬀerent to the spectral signature of the forcing [Rind et al., 2004].

78

Chapter 3. El Niño and the Sun

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Figure 3.2: Spectral analysis of the 14 C production rate record. a) 14 C timeseries from Bond et al. [2001], converted to Wm≠2 for the intermediate scaling (a Maunder Minimum solar dimming of 0.2% ◊ S◦ , see text for details). b) Multi-taper spectra and 99% confidence level for rejecting the null hypothesis that the series is pure ”red noise” (AR(1) process). This follows the methodology of Mann and Lees [1996].

El Niño and the Earth’s climate: from decades to Ice Ages.

3.3. Experimental Setting

3.3 3.3.1

79

Experimental Setting The Model

We use the intermediate-complexity model of Zebiak and Cane [1987]. It is a model with linear shallow-water dynamics for the global atmosphere [Gill , 1980; Zebiak, 1982] and the Tropical Pacific ocean [Cane and Patton, 1984], coupled by non-linear thernodynamics, which give the model self-sustained ENSO variability. The ocean model domain is restricted to [124◦ E-80◦ W; 29◦ S-29◦ N], which means that only tropical processes are considered. The model is linearized around a constant climatology [Rasmussen and Carpenter , 1982]. We employ the same configuration as Clement et al. [1999], in the model version written by Takashi Kagimoto at the International Research Institute for Climate Prediction. Radiative forcing anomalies are included as a source term of the (prognostic) equation for sea surface temperature (SST). Conversion is made from the top-of-theatmosphere pertubation to a surface flux by multiplying by (1 ≠ 0.62 C + 0.0019–) where C is the cloud fraction and – is the noon solar altitude [Reed , 1977]. Consistent with the absence of radiative scheme in the model, we hold the cloud fraction constant, 50%. As in Mann et al. [2005], the solar forcing estimates are multiplied by a factor of ﬁ/2, since the model represents only the Tropics.

3.3.2

Representation of Weather Noise

The tropical Pacific ocean-atmosphere system is the stage of considerable interannual and intraseasonal variability. Whether one is the child of the other is a question beyond the scope of this chapter. The question relevant to the present study is whether the ENSO system would notice solar irradiance perturbations in the presence of a physically realistic amount of weather noise. The latter concept encompasses all wind fluctuations that are external to the coupled subsystem, which our model is designed to represent. The simplest way to parameterize this phenomenon is to model it as a uniform patch of westerlies over the western equatorial Pacific (hereafter WP, spanning [ 165◦ E-195◦ E, 5◦ S-5◦ N]). Its behavior in time can be described by a statistical model that crudely approximates the low-order moments of the observed zonal wind stress (τx ). An autorregressive model of order 1 [AR(1)] seems appropriate for such a process. The amplitude of this random wind forcing (its time-integrated variance ‡N 2 ) can be defined as the fraction of monthly τx variability that is not accounted for by a direct response to SST forcing: ‡N = ¸ ‡NCEP , where ‡NCEP is the observed monthly windstress in the NCEP reanalysis [Kalnay, 1996]. Multi-member ensemble experiments with a state-of-the-art coupled ocean - atmosphere general circulation model (OAGCM) suggest that ¸ ƒ 40% (A. Wittenberg, personal communication), corresponding to a noise variance of 16% of the total. The AR(1) parameter is the lag-1 autocorrelation of monthly τx over the WP, estimated from NCEP data at – = 0.73.

80

Chapter 3. El Niño and the Sun Table 3.1: Summary of the numerical experiments used in this study.

Set Solar

Scale Noise level Name 0.5 40% Sol0.5 0.2 40% Sol0.2 0.05 40%, 0% Sol0.05 Orbital N.A. 40%, 0% Orb Orbital & Solar 0.5 40% Orb_Sol_0.5 0.2 40% Orb_Sol_0.2

The AR(1) processes X(t) are generated numerically, and the wind noise τxN (t) = ¸ X(t) is then applied uniformly onto the WP box for the whole length of the simulation. We summarize in Table 3.1 the diﬀerent numerical experiments conducted in this study.

3.4 3.4.1

Results Solar

In the following, our diagnostic variable of choice is the ensemble-mean zonal SST gradient along the equator (EW, for East-West), which is the diﬀerence between the WP index (average SST over the aforementioned western Pacific box) and the NINO3 index (average SST over [150◦ E-90◦ W, 5◦ S-5◦ N]). This procedure removes any zonallyuniform temperature change and reduces the noise significantly. A positive EW means that the gradient is strengthened, indicative of La Niña-like conditions. In Fig 3.3 we present the results of the model forced by reconstructed solar irradiance (∆F = 0.2%So ), in a 6-member ensemble. As is apparent from panel (a), the 40-year low-passed EW responds almost linearly to the irradiance forcing, with an amplitude of 0.3◦ C. While this may look insignificant at first sight, recent research on the origin of North American drought has demonstrated, using two diﬀerent general circulation models, that La Niña-like anomalies of such amplitude generated the sequence of severe droughts that visited the American West since the mid-nineteenth century, including the 1930s [Schubert et al., 2004; Seager et al., 2005b; Herweijer et al., 2006]. SST variations this small, if persistent enough, are suﬃcient to alter extratropical atmospheric circulation and perturb local hydroclimates in the Western US, South America, and elsewhere [Herweijer and Seager , 2007]. Panel (b) shows the wavelet spectral density of the same EW index, which is a convenient way of visualizing the evolution of a power spectrum through time. Its application to climate timeseries has been developed by Torrence and Compo [1998]. Though non-stationary, the signal generally shows the highest power in the ENSO El Niño and the Earth’s climate: from decades to Ice Ages.

3.4. Results

81

band (2 to 7 yr period, centered around 4 yr) and the centennial to millennial band (≥ 200 to 1000 yr) where the solar forcing displays its maximum variance. However, variability in this band could be entirely due to the model’s internal chaotic dynamics, as shown by Clement et al. [1999]. We therefore devise the following test: from a 150,000 year long unforced run of the model, we extract 400 timeseries of the same length as the simulations of interest (i.e. 10,000 years), with starting times picked at random more than 100 years apart. We perform the wavelet analysis on each of those timeseries, compute their global wavelet spectrum and for each scale, sort the spectra in increasing order. The upper 20 thus define the 95% confidence level. From this we can see on panel (c) that only in the 500 and 1000-yr bands does the model response exceed its level of natural variability at the 95% level. Interestingly, the model internal variability does exhibit a weak peak in the millennial band, though it knows of no numerical constant or physical process that could have introduced such a timescale. It is an illustration that the nonlinear atmosphere/ocean feedbacks it embodies can generate variability at unexpectedly long periods. The fact that it also responds to forcing at such frequencies could be perceived as a form of damped resonance, but this is not the case: perturbing the model by a white-noise radiative forcing with the same variance as the ∆F = 0.2%So case, we find that variability is raised uniformly at all frequencies, and that the millennial scale is not favored. Note that this approach implicitly assumes that the timeseries extracted from the unforced run are statistically independent, which may seem contradictory as they are part of the same realization of a numerical dynamical system. We assert that independence is true for all practical purposes, as predictability studies with the same model [e.g. Karspeck et al., 2004] show that its NINO3 index is of very limited predictability even a decade or two in advance. Why does the model respond with increased SST gradient to positive radiative forcing? This may be understood as follows [Clement et al., 1996]: if there is heating over the entire tropics, then the Pacific will warm more in the west than in the east because the strong upwelling and surface divergence in the east moves some of the heat poleward. Hence the east-west temperature gradient will strengthen, causing easterly winds to intensify, further enhancing the zonal temperature gradient (the Bjerknes [1969] feedback). This process leads to a more La Niña-like state (positive values of the EW index) in response to increased irradiance. Such an adjustment typically occurs over a few years to a decade, so that on millennial timescales, it looks virtually instantaneous. The dynamical feedback that makes the SST harder to change in the east has earned the name ”thermostat” to this mechanism. Quantitatively, we find the intermediate (∆F = 0.2%So ) scaling suﬃcient to trigger these feedbacks, while the weaker one (∆F = 0.05%So ) is not: at least in our model, a forcing that small would not generate a noticeable response. Finally, we present in panel (d) the probability of a strong El Niño event (NINO3 > 2 K for a year) on a 200-year window, as a measure of ENSO variability per se. Indeed, this quantity is more closely related to rainfall proxies from central and South America [e.g. Moy et al., 2002; Rein et al., 2004]. The index does show centennial

82

Chapter 3. El Niño and the Sun

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El Niño and the Earth’s climate: from decades to Ice Ages.

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3.4. Results

83

to millennial cycles, but no obvious trend, unlike the orbitally-forced model, as we shall see. Not surprisingly, it is significantly anticorrelated with EW, since the latter is equal to WP ≠ NINO3, with WP exhibiting much weaker variations than NINO3. In turn, periods of higher NINO3 are synonymous with an increased likelihood of large ENSO events.

3.4.2

Orbital

In Fig 3.4 we show the same quantities as before, in the case of the orbitally-forced run. High wavelet spectral density is expected at orbital timescales, but its exact value is unreliable in this calculation, as it mostly lies within the ”cone of influence” [Torrence and Compo, 1998]. Notice the small centennial-to-millennial power in this case, in contrast to the solar case. The salient feature is the growing intensity of ENSO activity from the mid-Holocene onwards, which can be seen either in the wavelet spectrum (b) or the probability of large ENSO events (d). The latter features a prominent upward trend, with the probability of a strong El Niño gaining 50% over the Holocene. A similar finding was noted by Clement et al. [2000] and qualitatively supported by a flood proxy from Lake Pallcacocha [Moy et al., 2002], high-resolution coral ” 18 O measurements from the Huon Peninsula [Tudhope et al., 2001], and oxygen isotope ratios in deep-sea sediment cores from the ENSO source region [Koutavas et al., 2006]. The dynamical explanation for why ENSO has a low variance at times of stronger seasonality is given by Clement et al. [1999]. The reason is that the seasonal migration of the inter-tropical convergence zone (ITCZ) modulates the eﬀective coupling strength [Zebiak and Cane, 1987], so that the system is most responsive to radiative anomalies centered around August/September: an increased insolation at that time of the year is then translated as a cooling in the eastern equatorial Pacific via the ”thermostat” mechanism described above. This tends to suppress the growth of large El Niño events at times where the summertime insolation was much stronger than now – such as the early Holocene. As this seasonal contrast wanes over the course of the Holocene, ENSO variance steadily grows towards modern-day values.

3.4.3

Orbital & Solar

We now consider the model response when solar and orbital forcing act together. In this we neglect the interaction between solar and orbital forcing anomalies, i.e. the modulation of irradiance perturbations exerted by the departure from today’s orbital configuration, since the product is too small to be of significance. The total radiative forcing is therefore, to a very good approximation, the sum of the two previously applied forcings (solar plus orbital). The model response is presented in Fig 3.5, with the same conventions as before, but with ∆F = 0.5%S◦ . The overall result, clearly visible in panel d) is that both

84

Chapter 3. El Niño and the Sun

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3.4. Results

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eﬀects (slow orbital growth over the Holocene, important solar-induced variance at 500-1000 yr scales) are superimposed, yet the model response is nonlinear. With a weaker ∆F = 0.2%S◦ , the model produces centennial and millennial changes that are not quite large enough to pass the same significance test. They are, however, still visible in the probability of strong events, albeit weaker. This is because in the early part of the Holocene, orbital forcing weakens the eﬀective air-sea coupling (as discussed above), which makes it harder for solar forcing to excite a thermostat type of response. Solar variability at centennial to millennial scales is thus subdued in this early part of the record, and only emerges in the second half of the Holocene. It is noteworthy that although solar forcing has peak-to-peak variations of ≥ 2 Wm≠2 even in the strong scaling case, much smaller than the summer-winter insolation difference (peaking at ≥ 40 Wm≠2 ), their eﬀect is disproportionately large: EW temperature responses are of similar amplitude for the two forcings. This is because the annual-mean signal in insolation is of the same order as the solar forcing perturbation, about 1 Wm≠2 . How much of the ENSO variability can be linearly predicted from knowledge of

86

Chapter 3. El Niño and the Sun

solar irradiance and the Earth’s orbital parameters? We consider the 6 realizations of the Orb_Sol_0.5 experiment, and perform a multivariate regression of the smoothed, ensemble-mean EW timeseries over three variables: PC1 and PC2 from the EOF analysis presented in Fig 3.1 and the solar irradiance Fo from Fig 3.2. The EW gradient was lowpass-filtered at periods longer than 40 years with a Gaussian window prior to normalization, to ease comparison with Figs 3, 4 and 5, panel a). The result is shown in Fig 3.6: the upper panel presents the dependent variable and its predictors ; the lower panel shows the result of the regression. The linear correlation coeﬃcient between predicted and ”observed” timeseries is high (ﬂ ƒ 0.70). Such a correlation means that about half the timeseries variance can be explained by the linear response to the forcing, with orbital forcing accounting for 14% and irradiance fluctuations for 35%. This ratio does change qualitatively over a wide range of cutoﬀ frequencies, since, as expected, the higher the cutoﬀ, the lesser the fraction of variance explained by the relatively small scales characteristic of solar forcing. What if the latter was weaker? With ∆F = 0.2%So , ﬂ drops to 0.51 (ﬂ2 = 26%). In that case the orbital part is nearly the same (12%), while the solar part is reduced to 14%, proportional to the reduction in irradiance. We conclude that in our model, solar perturbations of mid-range amplitude are suﬃcient to generate persistent SST anomalies of a fraction of a degree on millennial timescales, via the thermostat mechanism, reflected in the likelihood of strong El Niño events. Hence, ENSO may have acted as a recipient and transmitter of solar influence. The question is now: could such changes influence other parts of the globe, and is the global paleoclimate record consistent with this idea?

3.5

Global implications

We turn to the paleoclimate record to test the idea of a solar-induced ”thermostat”. Mann et al. [2005] show that their result is consistent with the Palmyra ENSO record of Cobb et al. [2003]: at times of increased irradiance, such as the Medieval Warm Period (900-1300 AD), the average conditions were colder in the eastern equatorial Pacific (La Niña-like). Conversely, they were comparatively warmer (El Niño-like) during the Little Ice Age (1600-1850 AD), when solar irradiance was weaker. Does this relationship extend throughout the Holocene and is it consistent with climate signals in remote regions?

3.5.1

Solar-induced ENSO and North America

North America is one of the regions of the world with the strongest teleconnection pattern to the tropical Pacific. The same drought patterns linked to tropical Pacific SSTs in the instrumental period are also found in tree-ring reconstructions of Palmer Drought Severity Index from the North American Drought Atlas for the medieval climate anomaly and Little Ice Age [Cook et al., 2004, 2007]. Herweijer et al. [2007] El Niño and the Earth’s climate: from decades to Ice Ages.

3.5. Global implications

87

EW and its predictors Standardized variables

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88

Chapter 3. El Niño and the Sun

review additional evidence for a La Niña-like global hydroclimate during the medieval climate anomaly. Consistent with our result, recent data by Asmerom et al. [2007] support the notion of an anticorrelation between solar activity (tree-ring ∆14 C ) and oxygen isotopic composition of uranium-series dated speleothems in the American Southwest, taken as a proxy for ENSO-related precipitation over the entire course of the Holocene. Given that the model only predicts the ensemble average SST gradient to closely follow the forcing, and that volcanic perturbations are absent from the latter, one would not expect the single realization provided by nature to match it exactly. On the contrary, the observed correspondence is unexpectedly high.

3.5.2

Solar-induced ENSO and the North Atlantic

We now go back to the original observation that motivated this work, and ask whether this theory can explain the Holocene record of ice-rafted debris (IRD) in the North Atlantic [Bond et al., 2001]. They argue that synchronous increases in percentages of particular IRD grain types from three sites in the North Atlantic demonstrated not only basin-wide cooling, but changes in atmospheric and oceanic circulation (see also Bond [2005]). Hematite-stained quartz grains, for example, must have been advected directly south of Iceland to produce the record at Feni Drift, an ice transport pattern inconsistent with a strong modern Icelandic Low centered near the Greenland-Faeroes ridge. This is in contradiction with the negative NAO pattern required by previous theories of sun-induced climate change [Shindell et al., 1999, 2001; Shindell et al., 2003]. In contrast, we propose here that a wind pattern consistent with such ice drift can be driven from the tropics. The idea that Indo-Pacific SSTs can alter the climate of the North Atlantic was recently advanced by Hoerling et al. [2001], who used an atmospheric general circulation model (GCM) forced by historical SSTs in various basins (namely, the whole globe (GOGA) or solely the Tropics (TOGA)). They attributed the late twentieth century upward trend of the North Atlantic Oscillation (NAO) to the SST warming trend of the western equatorial Pacific and Indian Oceans, most likely due to anthropogenic greenhouse forcing. Accordingly, in our theory, increased solar irradiance would warm the Western equatorial Pacific more than the east, which on these grounds would then be expected to push the NAO into a more positive phase. The search for stable correlations between the tropical Pacific and the North Atlantic has long been elusive [e.g. Rogers, 1984], but recent studies appear to capture them. Longer records have allowed such teleconnections to be established with instrumental data, also documenting them in several atmosphere models [Toniazzo and Scaife , 2006; Brönnimann et al., 2007; Bulic and Brankovic , 2006]. Here we document the association of northerly winds over the northern North Atlantic with El Niño-like states of the tropical Pacific, which we diagnose in the extended instrumental record and explain via state-of-the-art climate models. The details of the procedure are given in Appendix B and the result is shown in Fig 3.7. It can be seen that all three datasets El Niño and the Earth’s climate: from decades to Ice Ages.

3.5. Global implications

89

concur to show that ENSO states tend to coincide with northeasterly winds over the Fram and Denmark Straits, with a pattern broadly reminiscent of (but not identical to) a negative NAO. This is consistent with Toniazzo and Scaife [2006] and Brönnimann et al. [2004].

We note that the changes shown here are of subtle magnitude, and may be an imperfect analog to millennial changes relevant to the interpretation of the IRD record. Nevertheless, they hint at the possibility that ENSO may be driving surface ocean circulation over the North Atlantic, in the direction required to produce IRD discharge events. It is likely that feedbacks must be invoked to generate a more sizable response: the ENSO-induced south-westward winds at high latitudes would cool the North Atlantic and trigger a southward ice-drift, which would also lower the local sea surface salinity. This would weaken the buoyancy-driven circulation and its associated heat transport, further cooling the area. Recent modeling experiments [Vellinga and Wood , 2002; Chiang et al., 2003; Zhang and Delworth, 2005] have suggested that such SST anomalies in the Atlantic would shift the Pacific inter-tropical convergence zone southward, reducing the mean SST gradient along the equator, which would further intensify the El Niño-like anomaly. Thus it is plausible that such ENSO-induced perturbation in the North Atlantic would reverberate back into the Tropical Pacific: a positive feedback. The important idea is that solar forcing, weak though it is, is persistent enough to seed these changes into the Tropics, from which they can be exported to high latitudes, and further amplified by feedbacks involving sea-ice and the thermohaline circulation. Though much work remains to be done to establish a quantitative relationship between tropical climate and ice-rafting in the North Atlantic, we have outlined here a physical mechanism that could account for such a link.

3.5.3

Solar-induced ENSO and the Monsoons

Numerous studies have shown a significant simultaneous association between El Niño and weaker monsoon rainfall over India and southeast Asia [e.g. Pant and Parthasarathy, 1981; Rasmussen and Carpenter , 1983; Ropelewski and Halpert , 1987]. It is therefore natural to expect persistent anomalies of eastern Pacific SST to have a noticeable influence on the Indian and Asian Monsoons – though this could possibly involve a feedback between the two oscillations [Chung and Nigam, 1999]. The activity of these monsoons has been documented on a broad range of timescales, and recently been tied to abrupt climate change in the North Atlantic [Vellinga and Wood , 2002; Zhang and Delworth, 2005]. Speleothem records from northern Oman [Neﬀ et al., 2001], southern Oman [Fleitmann et al., 2003], the Chinese cave of Dongge [Wang et al., 2005] and anoxic sediments oﬀ the coast of Oman [Gupta et al., 2003], converge to a coherent depiction of the Indian and Asian Monsoon: in all these records, there is a millennial-scale correlation of weaker monsoons with IRD deposits

90

Chapter 3. El Niño and the Sun

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El Niño and the Earth’s climate: from decades to Ice Ages.

3.6. Discussion

91

in the North Atlantic [Bond et al., 2001]. This is consistent with periods of lower irradiance inducing an El Niño-like response.

3.6 3.6.1

Discussion Summary

We have found that solar and orbital forcing combine in a way that produces ENSOlike variance at centennial-to-millennial timescales, well above the model’s level of internal variability. The physics of the ocean-atmosphere system embodied in the model are able to pick out solar irradiance pertubations of intermediate amplitude (∆F = 0.2%So ), in the presence of orbital forcing and remarkably, in all cases, in the presence of a realistic amount of weather noise. For weak scalings of the solar irradiance (∆F = 0.05%So ), however, the response is indistinguishable from the variability of the unforced system. The results confirm the importance of orbital forcing in creating conditions favorable to the growth of ENSO variance over the Holocene, and suggest that solar irradiance variability may add centennial- to millennial-scale ENSO variance. We find qualitative agreement with high-resolution paleoclimate data and propose that ENSO mediated the response to solar irradiance discovered in climate proxies around the world.

3.6.2

Limitations of the Model Arrangement

The simplicity of the model is what allows the study of the coupled system over such long timescales, yet it creates caveats that are inherent to the model’s formulation [Clement et al., 1999]. While the chain of physical reasoning linking solar forcing to equatorial SSTs (the ”thermostat” mechanism) is certainly correct as far as it goes, the climate system is complex and processes not considered in this argument might be important. Perhaps cloud feedbacks play a substantial role, although it is still unknown whether the feedbacks associated with solar forcing would be positive or negative [Rind , 2002]. In a time of enhanced solar heating, the oceans should generally warm everywhere, including the subduction zones of the waters which ultimately make up the equatorial thermocline [McCreary and Lu, 1994]. This mechanism would complete a loop from equatorial SSTs through the atmosphere to midlatitude SSTs and then back through the ocean to equatorial SSTs. However, careful studies of Pacific SST variations in recent decades have shown that the oceanic pathway is ineﬀective because the midlatitude anomalies are diluted by mixing, especially as they move along the western boundary on their way to the equator [Schneider et al., 1999]. Still, since subduction and advection of midlatitude waters are the ultimate source of the equatorial thermocline, this oceanic mechanism must become eﬀective at some longer timescale, and alter the operation of the thermostat [Hazeleger et al., 2001].

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Further, this study does not preclude the response of other components of the climate system independently capable of responding to external forcing (e.g. stratospheric ozone, the Atlantic meridional overturning circulation, monsoons). Indeed, ENSO could have been just part of a global response. Whether these subsystems acted in synergy will be left for future work. It is hoped that more complete models will soon be able to clarify their respective roles on such timescales.

3.6.3

Forcing Uncertainties

Since the SST response to the moderate forcing (∆F = 0.2%So ) is just at the magnitude of the drought patterns of recent times [Seager et al., 2005b], any reduction in the estimate of irradiance forcing makes the Sun an implausible cause of tropical Pacific climate change, let alone global climate change. So while there is a reasonably convincing empirical correspondence between proxies for solar output and tropical Pacific SSTs, the great uncertainties in solar irradiance forcing raise doubts about explanations of these SST variations as responses to solar forcing. Further, the hypothesis of a solar origin of millennial climate fluctuations is incumbent on the assumption that the corresponding signal in cosmogenic isotope records is indeed due to the Sun. We note that the most recent radiocarbon calibration eﬀort, INTCAL04, displays weaker millennial cycles [Reimer and & Coauthors, 2004], though the production curve is still quite similar to INTCAL98, and such cycles are also present in a 10 Be record from Greenland [Yiou et al., 1997]. In any event, their irradiance scaling may not be known with satisfactory accuracy for a long time. Amidst such an array of uncertainties, a useful inference can still be made: for moderate to strong scalings of solar variability, it is physically plausible that ocean-atmosphere feedbacks amplified those changes above the level of internal ENSO variability, but weak scalings are unable to produce the necessary changes. A major caveat, as stated before, is the absence of volcanic aerosol forcing in the present study. The results need to be reassessed once such a timeseries becomes available.

3.6.4

Theoretical Implications of a Solar-Induced ENSO-like Variability

Our theory implies other predictions that should be testable with existing or future data: • Tropical Pacific SSTs: Periods of increased solar irradiance should be more La Niña-like, in the absence of other radiative perturbations (e.g. volcanoes). The development of better reconstructions of solar irradiance, as well as high-resolution coral and sedimentary proxy records, will prove crucial for testing this hypothesis, during the past millennium and beyond. El Niño and the Earth’s climate: from decades to Ice Ages.

3.7. Conclusions

93

• Hemispheric Symmetry: Tropical SSTs can influence mid and high-latitudes via Rossby-wave teleconnections [Hoskins and Karoly, 1981; Horel and Wallace, 1981] or the transient eddy response to SST-induced variations of subtropical jets [Seager et al., 2003, 2005a]. Both cause climate anomalies with clear hemispheric symmetry. Consequently, if solar-induced ENSO variability did actually occur, it should appear in Southern Hemisphere climate records, e.g. tree-ring records of droughtsensitive regions of South America. This is in contrast to the predictions of waterhosing experiments in the North Atlantic [Zhang and Delworth, 2005], which have asymmetric responses about the equator in the Pacific. It is hoped that high-resolution proxy data from the Southern Hemisphere will soon enable us to distinguish between these competing paradigms of global climate change.

3.7

Conclusions

We propose that, given a mid-to-high-range amplitude of Holocene solar irradiance variations, ENSO may have acted as one of the mediators between the Sun and the Earth’s climate. The reasoning goes as follows: air/sea feedbacks amplified solar forcing to produce persistent, El Niño-like SST anomalies at times of decreased irradiance – the thermostat mechanism. In so doing, the ENSO system weakened the intensity of the Indian and Asian monsoons , and triggered IRD discharge events in the North Atlantic, generating global climate variability on centennial to millennial timescales. It is likely that other feedbacks were involved in this process, such as the wind-driven and thermohaline circulation of the ocean, and cloud feedbacks. So far, data from the past millennium and the longer Holocene seem to support our view. As more complete – and presumably more accurate – climate records become available, especially from the Southern Hemisphere, we hope that our mechanism can be tested in greater detail and on longer periods.

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Chapter 4 El Niño in the Icehouse: ENSO Teleconnections During the Last Glacial Maximum “Time is the longest distance between two places.” Tennessee Williams

4.1

Introduction

As mentioned in the opening chapter of this book, there is now increasing appeal in theories that address the tropical origin of global climate change. This stems from recent observations of the interhemispheric near synchroneity and symmetry of glacial /interglacial changes, and from the inability of the “THC” theory of climate change to satisfactorily explain observations of abrupt and millennial climate change [Cane and Clement , 1999; Clement and Peterson, 2006]. In contrast, tropical theories of global climate change have traditionally received less attention, which motivates the current eﬀort. We know that the tropical oceans are currently the stage of important SST variability and that they can export it to higher latitudes via atmospheric wave propagation. This concept of “teleconnections,” dates back to Angstroem [1935] and its refinements are discussed, for instance, in Trenberth et al. [1998]; Alexander et al. [2002]. A complete theory of climate change must address how both aspects changed under diﬀerent boundary conditions. If one wants to understand the last deglaciation, for instance, it is crucial to understand how diﬀerent teleconnections were at that time, and why. A period of particular interest is the Last Glacial Maximum (LGM), for 3 reasons [Hewitt et al., 2003]:

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1. The changes are known to have been large (high signal to noise ratio) 2. The forcings are believed to be well known 3. There is an abundance of data with which to test the theories, growing and improving every year. Indeed, the LGM is a period of the Earth’s history that has been the target of considerable modeling eﬀorts. It provides a critical test of our understanding of current climate dynamics, which is embodied in general circulation models. Our inability to sample the atmosphere of the past condemns us to look at this problem in the context of numerical simulations of the Earth’s climate. The exercise, however, is still of great interest because internal variability is often an overlooked aspect of the complex behavior of said models. Yet it is crucial to understand their response to external forcing. A second motivation stems from the prediction by Yin and Battisti [2001] that even SST changes on the small end of available LGM reconstruction [CLIMAP Project Members, 1981] were suﬃcient to fundamentally reorganize the structure of jets and storm tracks, thereby inducing a very diﬀerent atmospheric circulation at the Last Glacial Maximum. The study, however, used a forced atmospheric general circulation model (AGCM) coupled to a slab ocean, which raises the question of how their mechanism would fare in a coupled ocean-atmosphere context. Thirdly, much of the interpretation of paleoclimate proxies relies on the principle of actualism: “The present is the key to the past”. As most proxies are used to describe non-local processes, paleoclimatologists rest heavily on the assumption that the statistical correlation between a climate signal and its expression in a particular geological object has remained approximately constant over time. In other words, we make the assumption of constant teleconnections. The climate modeling community is only beginning to address the potential consequences of altered teleconnections in the confrontation of their model results to paleoclimate data (see, for instance, Otto-Bliesner et al. [2003]), for which a good physical understanding is required. This chapter is structured as follows. In section 2 we describe the climatology of the two GCMs, comparing their simulation of the LGM, and their performance at reproducing the current climatology. Then we proceed to analyze teleconnections in the two GCMs and current observations (section 3). It will be shown that there is little consensus between models and that the sources of discrepancies are multiple. But both show interesting behavior at LGM, which begs for a physical interpretation. In section 4 we turn to a simpler class of dynamical models to understand key aspects of these changed teleconnections. It will be shown that the altered mean state and tropical forcing profoundly influence stationary wave propagation, but that these features are unable to fully explain the observed discrepancies. Discussion follows in section 5. El Niño and the Earth’s climate: from decades to Ice Ages.

4.2. The Climate of the Last Glacial Maximum

4.2

103

The Climate of the Last Glacial Maximum

The salient aspects of the LGM climate known at present are [Kohfeld and Harrison, 2000; Cane et al., 2006]: • a strong polar cooling (generally > 10◦ C, ≥ 20◦ C over Greenland) , and a moderarate tropical cooling (< 3◦ C over the ocean, < 5 ≠ 6◦ C over land). It is generally believed that these two eﬀects combined to enhance the baroclinicity of the midlatitude atmosphere, which is central to the dynamics of teleconnections. • the presence of 3 to 4 km ice sheets over northern hemispheric continents [Peltier , 2004], believed to have drastically reorganized the subtropical jets and planetary wave patterns through the combined influence of orographic and thermal forcing (increased albedo over land). • A tendency for a drier climate overall, especially in the Tropics, though some areas did get wetter [Kohfeld and Harrison, 2000]. Combined with the surface cooling, this decrease in tropospheric water vapor is likely to have decreased the static stability of the glacial atmosphere, though almost certainly not uniformly. There exists a wealth of other pertinent information [see Broecker , 2002], which we shall not delve into here, as it is not immediately relevant to describe the atmospheric mean state. Although considerable progress has recently been made in simulating those features in climate models [Cane et al., 2006], the LGM still presents GCMs with outstanding challenges, like accurately simulating tropical cooling and changes in the thermohaline circulation. Some coupled AOGCMs do tend to produce a stronger (more realistic) tropical cooling than AGCMs coupled to a slab ocean, an indication that ocean dynamics are a crucial element of the climate response [Hewitt et al., 2003]. However, there is no agreement between models as to many important aspects of this response, including the sign of the change in Atlantic meridional overturning circulation (cf Hewitt et al. [2003] vs Shin et al. [2003]), or whether tropical Pacific SSTs were more El Niño or La Niña-like [Pinot et al., 1999]. This will prove an important point, as this change in the tropical mean state does aﬀect the simulated ENSO and therefore its teleconnections. It has long been known that confidence in climate simulations can only arise through consensus. It is the driving force behind endeavors such as the Paleoclimate Modeling Intercomparison Project (PMIP, http://www-lsce.cea.fr/pmip2/. While a description of LGM teleconnections in all available GCM simulations is beyond the scope of this work, we deemed it important not restrict ourselves to a unique view of the LGM climate. Thus we consider two LGM simulations, using state-of-the-art land-ocean-ice-atmosphere GCMs: the Climate System Model (NCAR-CSM) * and the Hadley Center Climate Model (HadCM3) † , which we briefly describe below. * http://www.ccsm.ucar.edu/models/ccsm3.0/ † http://www.metoffice.com/research/hadleycentre/models/HadCM3.html

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Chapter 4. El Niño in the Icehouse

The CCSM3 Simulations

The NCAR CCSM3 is a global, fully coupled climate model. A detailed description of the simulations is given in Otto-Bliesner et al. [2006]. The atmospheric model is the NCAR CAM3, a three-dimensional primitive equation model solved with the spectral method in the horizontal and with 26 hybrid-coordinate levels in the vertical [Collins and Coauthors, 2006]. For these paleoclimate simulations, the atmospheric resolution is T42 (an equivalent grid spacing of approximately 2.8◦ in latitude and longitude). The land model includes a river routing scheme and specified but multiple land cover and plant functional types within a grid cell [Dickinson et al., 2006]. The ocean model is the NCAR implementation of POP (Parallel Ocean Program), a three-dimensional primitive equation model in spherical polar coordinates with vertical z -coordinate [Gent et al., 2006]. For these paleoclimate simulations, the ocean grid is 320x384 points, and 40 levels extending to 5.5 km depth. The ocean horizontal resolution corresponds to a nominal grid spacing of approximately 1◦ in latitude and longitude, with greater resolution in the tropics and North Atlantic. The sea ice model is a dynamic-thermodynamic formulation, which includes a subgrid-scale ice thickness distribution and elastic-viscous-plastic rheology [Briegleb et al., 2004]. Two simulations are considered here: 1. The control simulation, with pre-Industrial values for greenhouse gases and current land-sea-ice configuration (hereafter referred to as CTL). 2. The Last Glacial Maximum (LGM), with lowered greenhouse gases, altered orbital configuration, and glacial topography (ICE-5G reconstruction as in Peltier [2004]) and bathymetry (lowering of sea-level by 120m). The glacial boundary condition for those simulations was prescribed in compliance with the most recent specifications of PMIP (http://www-lsce.cea.fr/pmip2/).

4.2.2

The HadCM3 simulations

The simulations are described by Hewitt et al. [2003]. Succinctly: the AGCM, HadAM3, has a horizontal resolution of 2.5◦ by 2.75◦ and 19 vertical levels and is described in detail in Pope et al. [2000]. The OGCM, HadOM3, is based on the GFDL “Cox” ocean model [Cox , 1984]. Several modifications have been made to the original GFDL ocean model [see Gordon et al., 2000]. HadOM3 has a horizontal resolution of 1.25◦ by 1.25◦ and there are 20 depth levels. River runoﬀ is included in the model using predefined river catchments, and the runoﬀ enters the ocean at coastal outflow points. The sea ice model includes a simple thermodynamic budget and the ice thickness, concentration and snow depth are advected using the surface ocean current. Ice rheology is only crudely represented by preventing convergence of ice once the ice thickness reaches 4 m. This is a more dated coupled GCM, but it is widely believed to have less climatological biases than CCSM3. El Niño and the Earth’s climate: from decades to Ice Ages.

4.2. The Climate of the Last Glacial Maximum

105

The LGM boundary conditions are sensibly the same as for CCSM3, but for a much older version of Peltier’s ice-age topography [Peltier , 1994], with a slightly weaker sea-level lowering of 105 meters. The control case (CTL) refers to pre-industrial conditions, directly comparable to their CCSM3 counterpart.

4.2.3

Intercomparison of Simulated LGM Climates

Understanding diﬀerences between LGM simulations is not a simple matter (see, for instance, Braconnot [2004]). In this case, causes for discrepancies lie in the slightly diﬀerent boundary conditions, notwithstanding the usual factors of resolution, model physics and spin-up procedure. Nevertheless, it will be seen that both models do concur, at least qualitatively, on several aspects of LGM climate – which gives credence to their reliability. In the following, we will focus exclusively on the Northern Hemisphere winter season (December-January-February, DJF), since it is currently the one where ENSO and its teleconnections reach their peak. An analysis and modeling of the Northern Hemisphere summer will be left for future work. The most notable diﬀerences are in surface temperature, which alters the structure of the jets and absolute vorticity contours. In Fig 4.1 we show the surface temperature distribution in: (a) the present climate, taken from the NCEP/NCAR Reanalyses [Kalnay, 1996] (b) HadCM3 CTL (c) CCSM3 CTL. Though the general features of the observed temperature field are well reproduced by the models, each shows important diﬀerences, in particular over the tropical oceans. The eastern Pacific “cold tongue” extends too far west in those models, and both have a double maximum on either side of the equator associated in some seasons with a tendency for a double intertropical convergence zone (ITCZ). These flaws strongly aﬀect the simulation of ENSO, as we shall see. However, these diﬀerences pale in comparison to the anomalously warm temperatures over northern Eurasia and the Arctic (up to 12◦ C) in HadCM3 CTL compared to NCEP (d), and similarly in CCSM3 CTL (not shown). The glacial/interglacial changes (Panels E and F) are large – about twice this highlatitude bias. Both models do show a strong high latitude cooling, of up to 24◦ C over and downstream of the continental ice sheets in CCSM3. This change is overall much larger than in HadCM3, probably because of the higher glacial topography used in CCSM3 (Peltier [2004] vs Peltier [1994]). Both models agree on a weak tropical cooling (≥ 2 ◦ C on zonal average), and therefore a much increased equator-to-pole gradient (by 12 ◦ C in HadCM3, 13 ◦ C in CCSM3). By virtue of the thermal wind balance, this greatly enhances the baroclinic wind shear in midlatitudes. We choose to only show the upper tropospheric zonal wind in Fig 4.2, taken at ‡ = 0.257 (close to the 250 mb pressure level). Again, the two GCM simulations produce a realistic pattern to first order. However Panel D reveals that the HadCM3 subtropical jets are shifted too far south at almost every longitude, and are imperfectly separated. The CCSM3 control run is much more realistic in this respect. The situation changes markedly at the LGM: in HadCM3 the Asian Jet shifts north, while a jet appears downstream of the Laurentide ice sheet (with velocities up

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106 Chapter 4. El Niño in the Icehouse

Figure 4.1: Intercomparison of GCM Climatologies: Surface Air Temperature. (a) Present climate, taken from the NCEP/NCAR Reanalyses [Kalnay, 1996] ; (b) HadCM3 CTL ; (c) CCSM3 CTL ; (d) [b -a] ; (e) HadCM3 LGM (f ) CCSM3 LGM

El Niño and the Earth’s climate: from decades to Ice Ages.

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4.2. The Climate of the Last Glacial Maximum 107

Figure 4.2: Intercomparison of GCM Climatologies: Upper Tropospheric Zonal Wind. (a) Present climate, taken from the NCEP/NCAR Reanalyses [Kalnay, 1996] ; (b) HadCM3 CTL ; (c) CCSM3CTL ; (d) [b -a] ; (e) HadCM3 LGM (f ) CCSM3 LGM. (The color scales and contour intervals are the same within a row).

108

Chapter 4. El Niño in the Icehouse

to 15 ms≠1 ), over the subtropical North Atlantic. There is great disagreement between the two models over this region and much of North America. A jet also appears over the Atlantic, albeit which much higher velocities, and shifted southward, while latitudes around 45◦ N experience a massive deceleration (up to ≠15 ms≠1 ). Much of the area surrounding North America sees its upper tropospheric zonal wind field radically modified. Still, remarkably, changes are minimal around the Asian jet exit region. The reason for this considerable discrepancy, again, is likely to be the diﬀerence in cryotopography (Peltier [2004] vs Peltier [1994]).

4.3 4.3.1

Characterizing Ice Age Teleconnections Theory

Before we describe how they changed at the last Ice Age, we should unequivocally define teleconnections between the tropical oceans and the global or hemisphericscale atmospheric circulation. Instructed by the immense body of work existing on the subject, tropical SSTs and the upper tropospheric geopotential height (say at the 250 millibar level), will be the variables of choice. Now that we have narrowed the fields, how shall we describe their interrelations? Again, the choice is vast, so we will limit ourselves to a powerful technique that isolates patterns of covariance, the singular value decomposition of climate signals (SVD). The relative merits of this method are described, for instance, in Bretherton et al. [1992]. Implicit in our use are two physically-based assumptions: First, that tropical SSTs force the upper atmospheric motion, and second, that this response is approximately linear in the amplitude of the forcing. Both turn out to be quite good [Held et al., 2002]. For this analysis it is worth recalling a few of the properties of SVD, keeping the notation of Bretherton et al. [1992] for clarity. For two fields depending on space and time, say s(t, x) (SST) and z(t, x) (geopotential height), the goal is to find two sets of patterns pk (x) and qk (x) (k ∈ [1, N ≠ 1], where N is the length of the time interval), that maximize the covariance between the fields. Thus we write: s(t, x) = z(t, x) =

N ≠1 ÿ k=1 N ≠1 ÿ

ak (t)pk (x)

(4.1)

bk (t)qk (x)

(4.2)

k=1

ak (t) and bk (t) are called the expansion coeﬃcients, obtained by projecting each field El Niño and the Earth’s climate: from decades to Ice Ages.

4.3. Characterizing Ice Age Teleconnections

109

onto the kth pattern according to the following: ak (t) = pTk s(t, x) bk (t) = q Tk z(t, x)

(4.3) (4.4)

It turns out that pk and q k are simply the left and right singular vectors, respectively, of the covariance matrix Csz = Ès(t)z T (t)Í, and are obtained through the decomposition: Csz = USVT (4.5) Here we used the standard svd algorithm from Matlab to carry out this decomposition. U is the matrix containing the left singular vectors pk as its columns, V is the matrix containing the right singular vectors q k . Both are orthogonal, so that pTj pi = ”ij and similarly for q k . S is a diagonal matrix containing the so-called singular values, ‡k , k ∈ [1, N ≠ 1], which are the square-root of the eigenvalues of the matrix CTsz Csz . Thus ‡k2 represents the total amount of covariance accounted for by the kth SVD mode. A more useful metric is the squared covariance fraction (SCF): ‡k2

SCFk = 100 qN ≠1 n=1

‡n2

(4.6)

which is the fraction of the total covariance attributable to mode k. However, SCF does not give an idea of how important the mode is in describing the total variance of either of the two fields: for this we need to introduce another metric, the fraction of variance (FOV). To this end we use the expansion coeﬃcients. For the field z(t, x), say, one can use bk (t) to find how much variance is associated with mode k: Èbk (t), bk (t)Í Èbk (t), bk (t)Í FOVz (k) = qN ≠1 = var[z(t, x)] n=1 Èbn (t), bn (t)Í

(4.7)

(and similarly for s(t, x)) The last equality stems from the fact that the q k patterns form a complete orthonormal basis. Therefore the total variance is recovered from the sum over all modes (with a relative accuracy of 3 decimal places). In any event, care must be taken in interpreting FOV. A high fraction of variance means nothing more than a strong projection of the original field onto a particular spatial pattern. As in EOF analysis, this may have nothing to do with the underlying dynamics of the system. On the other hand, if a mode is identified with a high SCF, then it is likely to be associated with an important process of covariability, which makes it then interesting to look at its associated FOV. How can we visualize the mode? Once the expansion coeﬃcients have been obtained, it is straightforward to compute regression maps of the field onto them. In the following, the SVD pattern k for SST will be Ès(t)ak (t)Í (the so-called “homogeneous correlation map” in the terminology of Bretherton et al. [1992]) , while for Z250 we will display their “heterogeneous correlation map” Èz(t)ak (t)Í, though the high correlation that generally exists between ak and bk makes this distinction somewhat

110

Chapter 4. El Niño in the Icehouse

unimportant. The rationale for choosing the heterogeneous one for z is that we are primarily interested in the patterns of geopotential height field that accompany SST excursions. To get a feel for the method’s performance, let us apply it to the diagnosis of present day teleconnections, which we derive from the ERSST dataset for s [Reynolds and Smith, 1994] and NCEP Reanalysis dataset for z [Kalnay, 1996]. The SST data was limited to the tropical domain [30◦ S,30◦ N], while the geopotential height data includes only the Northern Hemisphere. The season considered is, as before, Northern Hemisphere winter (DJF). The variables were suitably transformed into anomalies and multiplied by the square-root of the cosine of latitude, in order for variance integrals to be representative of geometric areas [North et al., 1982]. The first mode is displayed in Fig 4.3. It accounts for an overwhelming fraction of the covariance (83%). Panel A shows its very distinctive El Niño SST pattern, as expected. The associated heterogeneous correlation map for Z250 (Panel B) displays the familiar Pacific North American (PNA) pattern [Wallace and Gutzler , 1981] that has long been recognized as the main ENSO teleconnection pattern. Both expansion coeﬃcients are well correlated (0.69, p < 0.01), and would also share a lot of variance with most ENSO indices. It is instructive to look at the second mode, displayed in Fig 4.4. It only explains 7% of the covariance, and should thus be interpreted cautiously. This time, the SST pattern is reminiscent of the broad horseshoe shape characteristic of the Pacific Decadal Oscillation (PDO) [Zhang et al., 1997], remarkably symmetric about the equator, though it is more localized in the central Pacific and has the opposite sign. It is associated with a general cooling of the Indian ocean and a cross-equatorial dipole in the tropical Atlantic. The geopotential height pattern features a deep Aleutian low that is consistent with the central equatorial Pacific warming, but has a strong zonally symmetric component in high latitudes, strongly projecting onto the Northern Annular Mode [Thompson and Wallace, 2000]. The expansion coeﬃcients have very little variance in the 1960’s and strong variance in the 80’s and 90’s consistent with what we know of the decadal modulation of ENSO [e.g. Fedorov and Philander , 2001; Cane , 2005], but the SST pattern does not purely reflect this. Overall, this leads to the hypothesis that several physical oscillations might have been simultaneously captured by this statistical mode. Nevertheless, the large amplitude in the central Pacific, in conjunction with the fact that the strong La Niña events of 88/89 and 98/99 feature prominently in the expansion coeﬃcient, suggest that this mode is dominated by the asymmetry between the warm and cold phases of ENSO, El Niño and La Niña, which has been proposed as the cause of the horseshoe shape of the PDO [Rodgers et al., 2004]. Thus, some ENSO events are combinations of mode 1 and 2, but one cannot say that the squared covariance fraction associated with ENSO is the sum of the two SCFs. All that can be said is that ENSO accounts for at least 83% of the covariance in this case. The lesson is thus threefold. First, SVD reliably picks out ENSO as the first mode of ocean-atmosphere covariability, as expected on physical grounds. Second, this is El Niño and the Earth’s climate: from decades to Ice Ages.

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4.3. Characterizing Ice Age Teleconnections 111

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El Niño and the Earth’s climate: from decades to Ice Ages.

4.3. Characterizing Ice Age Teleconnections

113

not suﬃcient to guarantee that all ENSO signals end up in one mode, for they could be spread across several of them (modes 1 and 2 in this case). Third, modes may lump together several physical oscillations and trends, so care must be taken in equating statistical modes with climatic oscillations. With these caveats in mind, we can now characterize teleconnections in the aforementioned GCM simulations.

4.3.2

Results: Glacial Teleconnections Patterns

CCSM3 Teleconnections In Fig 4.5 we present the case of the control climate (CTL) in CCSM3. The first observation is that ENSO is extremely regular, with a period close to 2 years (Panel C). The spatial pattern (Panel A) is somewhat too localized within the equatorial waveguive, extending much too far west, as is typical of non-flux-adjusted GCMs, where air-sea interactions tend to produce a cold bias in the Cold Tongue/Trade Wind system [Delecluse et al., 1998]. Less commonplace, but equally unrealistic, is the extreme sharpness of the meridional scale of the SST anomaly. The atmospheric teleconnection pattern (Panel B) is a canonical Rossby wave train extending from the western Pacific to a series of troughs and crests reminiscent of the PNA pattern seen earlier. However, this pattern fails to reproduce several aspects of Fig 4.3b in the high latitudes and accounts for a much lower part of the squared covariance fraction (only 12% of the Z250 variance, vs 19% in NCEP/ERSST). Overall, its amplitude is a factor of two weaker than observed, which stems in part from the weaker ENSO SST variance (for the NINO34 index, ‡CCSM3 = 0.72, while ‡ERSST = 0.83 over 1880-2006). We should also note that it has comparable amplitude in the North Pacific and North Atlantic, in contrast to observations. In Fig 4.6 we do the same for the LGM. ENSO decreases slightly in intensity at the LGM, but its period increases to 3-4 years. The LGM sees a radical shift in the geopotential height teleconnection pattern which assumes the rough shape of a scorpion, its “claws” circling a high over western Europe and its tail over North America. The SST pattern is somewhat diﬀerent from CTL, but if anything, closer to the observed ENSO pattern (Fig 4.3a). The SCF is higher in this case (65%), as is the FOV for Z250 (18%), indicating that ENSO teleconnections intensified in this simulation. The second mode is a central equatorial cooling (associated with a widespread cooling of about ≥ 0.1 ≠ 0.2◦ C over the tropical oceans (not shown). HadCM3 Teleconnections The control case can be seen in Fig 4.7. The first SST mode is ENSO again, with a broader meridional scale than in CCSM3 (and a realistic coastal warming near Peru), but as before extending much too far west. The Z250 teleconnection pattern also bears some resemblance to Fig 4.3b, but has a much more zonally symmetric component. In contrast to CCSM3, it correctly depicts the ratio between North Pacific and Atlantic values. The mode accounts for 86% of the SCF, and 19% of the Z250 variance, close

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El Niño and the Earth’s climate: from decades to Ice Ages.

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4.3. Characterizing Ice Age Teleconnections 115

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116

Chapter 4. El Niño in the Icehouse

to the NCEP/ERSST values. Again the simulated ENSO is unrealistically regular, this time with a period of 2-3 years. At the LGM, the SST pattern remains essentially the same: The Z250 pattern breaks up into 5 negative centers of action, though it retains much more similarity to its CTL counterpart than CCSM3 does. In addition, the mode loses some of its prominence (SCF=77%), and so does the FOV (13%). One aspect that is common with CCSM3 is that the LGM ENSO gains a longer period and a less periodic character. Summary In Table 4.1 we present the results of this analysis in five cases. The Present Day climate is as described in section 4.3.1. Other cases are from the coupled GCM integrations described before. In all cases, the first SVD mode has an SST expansion coeﬃcient very highly correlated with ENSO indices (NINO34, say) , and the Z250 correlation map is therefore very close to the pattern one would obtain by regressing the field onto such an index (not shown).

Total Variance SVD mode # SCF (%) f.o.v. SST (%) Õ f.o.v. Z250 (%)

1 83 46 19

Present Day 5.99 2 3 7 3 8 5 14 8

CCSM3

4 2 4 10

1 40 25 12

CTL 3.61 2 3 22 9 8 5 17 12

4 8 4 12

1 65 30 18

HadCM3 LGM 2.76 2 3 11 6 6 4 13 13

4 5 6 8

1 86 50 19

CTL 3.52 2 3 5 2 5 5 17 7

4 2 2 10

1 77 48 13

LGM 4.88 2 3 11 3 5 3 28 10

4 3 4 11

Table 4.1: Variance analysis of Northern Hemisphere winter geopotential height. The total variance is the integral of 250 millibar geopotential height variance over the Northern Hemiss Õ 2 ÍdA, in 106 m2 . Then shown, for each mode, are the squared covariance sphere NH ÈZ250 fraction (SCF), in percent of the total covariance between SST and Z250 , and the fraction of the total variance in the field explained by the projection onto a given mode (FOV) . Only modes 1 through 4 are shown for brevity. (See text for details.)

The results are the following: • Both models show a drastic change of ENSO teleconnection pattern from CTL to LGM. In CCSM3 the first mode shifts from a PNA-like pattern to a “scorpion” pattern. In HadCM3, the shift is from a somewhat diﬀerent PNAlike pattern to a wavenumber 5 type of pattern. • There are more diﬀerences than similarities between the 2 GCMs. For example, the variance in NINO34 decreases in CCSM3 (‡CTL = 0.78 vs ‡LGM = 0.59◦ C), whereas it stays virtually constant in HadCM3 (0.98 vs 1◦ C). The variance in Northern Hemisphere winter geopotential height decreases by about 24% in CCSM3, while it increases by 38% in HadCM3, accompanied by a decrease in the variance explained by ENSO teleconnections. There is no reason to believe one model more than the other, as consistency would be our only proxy El Niño and the Earth’s climate: from decades to Ice Ages.

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4.3. Characterizing Ice Age Teleconnections 117

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El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

119

for plausibility. We are therefore condemned to explain both teleconnection changes. • However, both GCMs agree in producing a longer period ENSO at the LGM: the main period switches from 2 years to 3-4 years. Even though the models disagree on the pattern of teleconnection and the fraction of variance it explains, it is important to understand the cause of both changes. The question we wish to ask is the following: do LGM teleconnections diﬀer because of 1. the structure of tropical heating (changing ENSO pattern)? 2. the medium of propagation (a changed basic state)? 3. the interaction with transient eddies in the subtropics and midlatitudes? In order to answer these questions, we now turn to simpler models of the Earth’s atmosphere, aimed at simulating the stationary wave response of the atmosphere to diabatic heating perturbations. Because these questions involve various degrees of non-linearity, two models will be considered – a non-linear (NLIN) and a linear one (ELM).

4.4

Modeling Ice Age Teleconnections

A review of ENSO teleconnections is beyond the scope of this book. The observational evidence is outlined in Bjerknes [1969]; Horel and Wallace [1981], while the theoretical foundations were laid out by Hoskins and Karoly [1981]; Simmons [1982]; Simmons et al. [1983]; Schneider and Watterson [1984]; Sardeshmukh and Hoskins [1988]. For recent reviews, see Alexander et al. [2002]; Hoerling and Kumar [2002]; Liu and Alexander [2007]. An instructive history of the evolution of this important subfield of climate dynamics is given in Trenberth et al. [1998], starting from the illuminating barotropic model of Hoskins and Karoly [1981] to a much more quantitative understanding involving ensemble GCM integrations. In spite of the numerous subtleties involved, the upshot is that the “protomodel” of Hoskins and Karoly [1981] still gives a useful qualitative understanding of the dynamics. While the quantitative refinements can be obtained with more complete stationary wave models (see also Held et al. [2002] and articles in the same issue), these are still much less complex than full GCMs. The subject of glacial stationary wave patterns has been previously explored by Cook and Held [1988], albeit with a much less convincing simulation of the LGM climate. Also, the study used a steady-state model linearized about the zonal average of the flow, whereas it has since been established that zonal asymmetries of the basic state play a paramount role in shaping the response [Ting and Held , 1990; Ting and Sardeshmukh, 1993]. It is therefore worthwhile to take a similar look at the problem with the basic states described in Section 4.2 and a non-linear stationary wave model.

120

4.4.1

Chapter 4. El Niño in the Icehouse

A Nonlinear Model of Stationary Waves (NLIN)

This model is made up of the governing dynamical equations of atmospheric flow (the so-called primitive equations) in ‡ coordinates: it is essentially the dynamical core of a GCM, devised to compute the response of the global circulation to prescribed heating and momentum fluxes given a background state. The latter is defined by five variables: the wind field in ‡ -coordinates (u, v, ‡) ˙ , temperature (T ) and surface pressure (Ps ). The model computes perturbations to such quantities, by producing divergent motion at upper levels, which excite Rossby waves that generate rotational motion across the globe, propagating primarily along great circles. The model is described in detail by Ting and Yu [1998], but we hereby recall a few of its properties. A semi-implicit time integration scheme is used for time marching [Hoskins and Simmons, 1975] with a halfhour time step, and a meaningful stationary wave solution is ensured by suppressing the growth of baroclinic eddies through a high Rayleigh damping and Newtonian cooling concentrated near the boundary layer‡ . The model is spectral in the horizontal, using an R30 (rhomboidal) truncation, and has 14 vertical levels located at ‡ = 0.015 , 0.050 0.100, 0.170 , 0.257, 0.355 , 0.460 , 0.568, 0.675, 0.777, 0.866, 0.935, 0.979, 0.9970. A rigid-lid boundary condition is applied at model top (‡ = 0) and the surface (‡ = 1). The advantage of this model is that it retains the full nonlinearity of the equations of motion (interactions between diﬀerent wavenumbers), but allows disentangling of results, because the background state and diabatic heating can be specified independently of each other, unlike a full GCM. However, the suppression of baroclinic instabiliy means that it cannot simulate interactions between stationary and transient eddies. Also, its formulation prohibits wave-mean flow interactions. Nevertheless, is has proven a useful tool in analyzing ENSO teleconnections, by isolating the essential forcing agents of certain extratropical circulation anomalies [Ting and Yu, 1998], which is what we purport to do here. Usually this forcing is the diabatic heating field due to SST anomalies, together with the indirect eﬀect of transient eddy heat fluxes. For the present application, we start from a specified background state composed of the three-dimensional climatological flow field, temperature and surface pressure of the CCSM3 or HadCM3 simulations in Northern Hemisphere winter (DJF). We then prescribe a three-dimensional heating perturbation approximating the anomalous diabatic heating Q due to ENSO SST anomalies (It is approximate as the full modeled diabatic heating was not available for this analysis, and had to be indirectly obtained through the precipitation field). This typically takes the form: Q = AV (‡)H(⁄, „)

(4.8)

Here ⁄ and „ are the geographical longitude and latitude, and A some amplitude. Unless the full tridimensional heating was available (see Sec 4.4.1), it is estimated as follows: since the horizontal heating distribution is so akin to the precipitation ‡ more

precisely, the damping timescale decreases from 15 days in the free troposphere to 0.3 days at the surface El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

121

anomalies associated with El Niño, a good proxy for H(⁄, „) is to regress the model’s precipitation field onto some ENSO index – in this case, the left expansion coeﬃcient a1 (t) of the SVD analysis seen earlier (Section 4.3.2). As is common practice (see, e.g. Gill [1980]), we approximate the vertical distribution of the heating by a sinewave: V (‡) = s 1 0

sin(ﬁ‡) sin(ﬁ‡)d‡

(4.9)

We start by evaluating the model’s performance in the current climate state, again for the DJF season. NCEP Basic State Typically, the model is run for fifty days, and the average of the output over the last twenty days reproduces stationary features quite well. As an example, we show in Fig 4.9 the response of the NLIN model to a three-dimensional diabatic heating perturbation associated with El Niño. The latter is diagnosed from the NCEP/NCAR Reanalyses Kalnay [1996] and displays a strong heating anomaly (≥ 1 Kday≠1 ) in the central equatorial Pacific east of the dateline, and a horseshoe-shaped cooling of similar amplitude around it. Both are direct consequences of the shift in convective precipitation that accompanies El Niño events (see, for instance, Seager et al. [2005], their Fig 1). Anomalies are present over the storm track regions and represent the anomalous latent heating due to the transient eddy response to altered stationary wave patterns during El Niño, though the compositing method remains an imperfect way of isolating those. Overall, the composite heating is an order of magnitude larger in the Tropics as in the midlatitudes. Similarly diagnosed was the stationary wave streamfunction at 250 mb anomalies for El Niño years (Ting, personal communication), shown in Panel C. The model (Fig 4.9b) satisfyingly reproduces the Rossby wavetrains emanating from the western equatorial Pacific in both hemispheres. However, its amplitude over the PNA route worsens downstream, and the pattern over North America ends up bearing only slight resemblance to the observations (Fig 4.9c). This is a sign that the transient eddy momentum fluxes (not included here) play a significant role in those areas. Which geographical locations matter most in creating the response? The question can be investigated with idealized heating patterns. In Fig 4.10 we gauge how much of this response can be obtained by: 1. Restricting this heating to the tropical Pacific 2. Specifying a bivariate Gaussian heating centered at the equator and 170◦ W. Comparison of Panels A and B with the previous figure will reveal that much of the simulated (and observed) streamfunction anomalies can be attributed to the tropical Pacific heating – in particular, the Pacific basin and its surroundings, and even much of

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El Niño and the Earth’s climate: from decades to Ice Ages.

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4.4. Modeling Ice Age Teleconnections

123

the North and South American continents. Not surprisingly, the comparison is worse in those locations where local heating is known to be important, i.e. the Northern Hemisphere storm tracks. It is instructive to consider an idealized heating – one described by (4.8) with A = 2 Kday≠1 and a bivariate Gaussian structure: A B  ⁄≠⁄ 2

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with half-widths of ∆⁄ = 30◦ and ∆„ = 10◦ (since we are interested in the response to a large-scale heating). In this case ⁄c = 170◦ E and „c = 0◦ N. The response to such heating (Panel D) is larger than before, because the total heating is commensurably larger (In this range of values, the response is quite linear in the amplitude of the heating, a fact that we shall exploit later). The pattern is the familiar PNA route along a great circle, as in Hoskins and Karoly [1981], though it is shifted further west here, as is the forcing. Also apparent is a pair of anticyclones just west of the date line, straddling the equator, and a pair of cyclonic anomalies east of it, qualitatively similar to the El Niño-forcing case. This is a confirmation that this part of the response is fairly insensitive to the geographic location of the forcing, but rather, is primarily determined by the zonal asymmetries of the basic state [Simmons et al., 1983] (hereafter SWB). The message is thus threefold: 1. NLIN produces a realistic response to tropical heating anomalies given the proper basic state. 2. In the case of ENSO anomalies, most of this response comes from the tropical Pacific. 3. This stems in part from the prominence of a modal behavior of the SWB type. We now turn to a similar analysis of the GCM experiments. CCSM3 Basic State In Fig 4.11 we present the response of NLIN to the El Niño-induced diabatic heating fields in the presence of the appropriate basic state (CTL or LGM, Northern Hemisphere winter). The model does reproduce the PNA-like pattern (panel b), as in Fig 4.5, and to a lesser extent Fig 4.10. However, it produces a center of action over Scandinavia that has no counterpart in either figure. The clear Rossby wave train is seen to originate from the far western Pacific, where the forcing is much stronger than in the Reanalyses, which is a strong reason why the CCSM3 teleconnection pattern should not be expected to perfectly match that in Fig 4.10 or Fig 4.3. The LGM case (Panel D) is nothing like the corresponding SVD mode – we interpret this failure of the theory as a sign that transient eddy fluxes are essential in shaping

124

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El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

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LGM teleconnections. Nevertheless, it is interesting to understand why the CTL and LGM patterns (Panels B and D) diﬀer so much. The reason lies in the distribution of the forcing: experiments with swapped forcing (CTL basic state with LGM heating, and vice versa) show that the heating mostly governs the amplitude of the tropical and subtropical response, as well as whether it excites a significant extratropical planetary wave train. Still, the shape of the latter is primarily governed by asymmetries in the basic state. Thus, we have the circumstance that even for a fixed basic state, two apparently similar forcings give rise to a very diﬀerent response – a result we shall try to understand in section 4.4.2. El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

127

HadCM3 Basic State In Fig 4.12 we present same analysis as Fig 4.11, but for HadCM3. Again, the heating fields are seen to be displaced too far west into the maritime continent, and to have anomalously sharp meridional scales, though less so than in CCSM3. However, this model suﬀers the additional problem that the heating maximum is concentrated along the edge of the model’s South Pacific Convergence zone, a result not supported by present observations. Nonetheless, the simulated geopotential height response is reminiscent of the teleconnection pattern in Fig 4.7: a great circle encompassing Siberia with a Canadian low somewhat elongated eastward. The disagreement is significant over East Canada and Greenland, but the similarity suggests that the combination of forcing and basic state is enough to produce the rough outlines of this pattern without invoking transient eddies. We will better isolate the cause in the next section. Though the LGM response is very far from reproducing Fig 4.8b, it is radically diﬀerent from the CTL case. Let us know explain why. We wish to uncover the regions where it is most eﬃcient to force this model. One way to do this is to evaluate numerical Green’s function, with an idealized pattern of heating displaced around the globe, in order to see where the largest response occurs, as in Ting and Yu [1998]. For computational reasons, it is prohibitively costly to do this with the nonlinear, time-stepping model. However, the aforementioned paper demonstrated that the nonlinearities in the response to heating (as opposed to orography) are weak enough that a linear, steady-state model approximates the response quite well. Moreover, such a computation is only sensible in a linear context.

4.4.2

A Linear, Steady-State Model of Stationary Waves (ELM)

The Exact Linear Model (ELM) is a linearization of the dynamical core of the R30 spectral GFDL GCM (the so-called “Manabe model”) with the same horizontal and vertical resolution as before. Given a mean state characterized by the three dimensional flow field in sigma coordinates (u.v, ‡) ˙ , temperature and surface pressure, it computes the large-scale, steady-state atmospheric response to a given heating anomaly. A rigid-lid boundary condition is also applied at the top (‡ = 0) and at the surface (‡ = 1) of the model atmosphere. The basic equations are those for vorticity, divergence, temperature, surface pressure, geopotential height, and ‡ -coordinate vertical velocity (‡˙ ). These equations are linearized about the fully zonally varying basic state. The model uses spherical harmonics with rhomboidal truncation at 15 wavenumbers (R15) in the horizontal and finite diﬀerence in the vertical. A complete description of the linear model and the numerical scheme used to solve the linear system can be found in Ting and Held [1990]. Several dissipations are applied to ensure a meaningful solution. In this case, we used Rayleigh friction and Newtonian cooling in the vorticity, divergence, and temperature equations, with a timescale increasing from 15 days in the free troposphere up to 0.3 days near the surface. In addition, a biharmonic diﬀusion with coeﬃcient

128

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1 ◊ 1017 m4 s≠1 , corresponding to an e-folding time of about 5 hours on the smallest

resolvable scale, is also applied to the vorticity, divergence, and temperature equations. These dampings are found necessary for the steady linear model, which otherwise produces resonant solutions with unrealistic magnitude. The relevance of such a model has been highlighted by Ting and Yu [1998] and Held et al. [2002], who showed that, as far as reasonable amplitudes of the diabatic heating were concerned, it captured the non-linear solution to a surprisingly thorough extent. Here we consider a forcing as given in (4.8), that is to say, a first baroclinic mode in the vertical, with A = 1 Kday≠1 and a bivariate Gaussian for H as in (4.10)). The forcing is then displaced longitudinally every 30◦ of longitude, and latitudinally every 2◦ of longitude from 28◦ S to 28◦ N, adding up to 312 cases. Obviously, these socalled Green’s functions are not orthogonal, but we are limited by the model’s design (solving for a stationary, large-scale solution), which implies that the forcing must have accordingly large scales, preventing the reduction of H to a pointwise forcing. While this method can eﬀectively find the favored locations of the forcing, it does not permit the complete reconstruction of the response to an arbitrary forcing via a simple convolution operation. One can think of the location index i ∈ [1; 312] as analogous to the time dimension of a 2D climate field. We can perform an EOF analysis on this variable as in Ting and Yu [1998], which gives an idea of the preferred response pattern (EOF) and the favored locations (PC) to force it from the tropics. Then, the index is easily reverted back to a geographical location for graphical representation. CCSM3 Basic State In Fig 4.13 we present such an analysis performed on the geopotential height field, for easier comparison with the SVD analysis. It is found that the first mode (48% of the variance) is a canonical Rossby wave train along a great circle route from the western tropical Pacific to the southeastern US, reminiscent of the PNA pattern. The associated PC shows that it is preferentially excited from the northern part of the western tropical Pacific, or negatively excited in the Indian Ocean. It is very close to a SWB mode, which explains the propensity of the latter to arise in response to realistic or idealized forcings in NLIN (Section 4.4.1). The second mode is roughly symmetric about the equator, and antisymmetric about the dateline. This mode seems to be a more local response to the shifting of the forcing along latitude circles, as the near coincidence of centers of action in the EOF and PC suggests. Modes 3 and 4 are not shown because of the low variance they explain. A comparison to a similar EOF analysis performed with the NCEP basic state in ELM (not shown) reveals essentially the same EOF patterns and PCs, only with a diﬀerent variance fraction (see Table 4.2), which helps explain the similarity between Fig 4.11b and Fig 4.5b or Fig 4.3b, regardless of the diﬀerence in forcing. In Fig 4.14 we present the same analysis for the LGM basic state. The patterns are essentially the same, except that the changes in the Asian Jet deflect the Rossby train El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

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130

Chapter 4. El Niño in the Icehouse

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El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

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slightly southward, and the mode loses some of its prominence (34% of explained variance vs 48%), which means that the forcing becomes relatively more important in shaping the response. We can now return to the question posed earlier, of why the response of the nonlinear model seems so diﬀerent at LGM despite the apparent similarity in the pattern of the forcing. In Fig 4.15 we plot the glacial-interglacial change in ENSO heating, which shows that the biggest diﬀerences are concentrated north of the equator and in the east of the basin, which has a strongly negative projection onto PC2. As a result, the pattern correlation of the response with the second EOF is much larger at LGM (≠0.32) than for CTL (≥ O(10≠3 )). This explains why the direct response to heating (EOF2) – as opposed to the modal behavior (EOF1) – is more important in the LGM case, and why a seemingly small diﬀerence in the pattern thereof leads to a very diﬀerent pattern of the response. In contrast, the dominance of the modal behavior at CTL (Table 4.2) means that it is relatively insensitive to the forcing location.

132

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El Niño and the Earth’s climate: from decades to Ice Ages.

4.4. Modeling Ice Age Teleconnections

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HadCM3 basic state An identical analysis for HadCM3 is displayed in Fig 4.16 and Fig 4.17. The CTL case is characterized by a similar Rossby wave pattern, though closer to a latitude circle, which is reminiscent of the pattern in Fig 4.12b. The modal behavior is very strong (74% of the variance) and is expected to dominate the total response, since the prescribed ENSO heating (Fig 4.12a) projects strongly onto the first PC. Surprisingly, the first mode radically changes character at the LGM (Fig 4.17a), switching to a dipole with a center of action over the Siberian peninsula and one of opposite sign over the Norwegian Sea. Now comparing Fig 4.17a to Fig 4.12d – and recalling that the sign of the EOF pattern is arbitrary – we can see a striking resemblance. This means that the response of the non-linear model was dominated by a modal behavior (SWB). If true, this would imply that the same pattern could be obtained by using solely the tropical part of the heating, and this is indeed the case (not shown). Though the study of Simmons et al. [1983] only considered a barotropic model on the sphere, similar results have been obtained in more complete ones – including this

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baroclinic model. A physical explanation is that, for a reasonable upper-level tropical divergence, the upper-tropospheric contours of absolute vorticity determine the Rossby wave source to leading order, thus inducing a similar Rossby wave response even for rather diﬀerent near-equatorial SST anomalies [Sardeshmukh and Hoskins, 1988]. It is an item of experience that barotropic models do a surprisingly good job at describing this propagation, provided the linearization is done about the ambient flow field close to the equivalent barotropic level [Ting , 1996]. Since the strongest vorticity gradients are found in the upper troposphere near the Asian Jet exit region, any forcing in its vicinity will tend to excite such a mode. The corollary is that it is necessary for the GCMs to accurately simulate the jet structure (and its change at LGM) in order to produce realistic teleconnections. Summary In Table 4.4.2 we summarize the variance explained by the various modes previously described. In all cases but HadCM3 LGM, the first mode is a Rossby wave train of the SWB type. In both models, the fraction of variance explained by the first mode decreases significantly at the LGM, which means that the location of the heating gains more importance. This may partially explain why NLIN does better at reproducing the current teleconnection patterns – even with a deeply unrealistic heating field – than it does at the LGM. The analysis confirms the great sensitivity of the stationary wave response to the mean state, consistent with Ting and Sardeshmukh [1993]. In some instances, this sensitivity seems to dominate the forcing, to the point that realistic teleconnection patterns can be excited by erroneous forcings provided the basic state favors a realistic SWB mode. Case \ EOF rank NCEP CCSM3 CTL CCSM3 LGM HadCM3 CTL HadCM3 LGM

1 39% 48% 34% 74% 66%

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3 11% 9% 10% 5% 5%

4 9% 8% 9% 4% 5%

Table 4.2: EOF analysis of the sliding tropical forcing experiments in ELM. Numbers shown here are the fraction of variance explained by each mode for geopotential height at the ‡ = 0.257 level (close to 250 mb). Only modes 1 to 4 are shown for brevity. See text for details.

Overall, this linear analysis sheds light on the behavior of NLIN by disentangling the influence of the forcing and the basic state in the nonlinear response. It also confirms Ting and Yu [1998]’s observation that for realistic amplitudes of forcing, say O(1 Kday≠1 ), the essence of the non-linear response is captured by the linear model. However, both models are a far cry from the GCM’s LGM teleconnection patterns, a topic to which we now turn our attention. El Niño and the Earth’s climate: from decades to Ice Ages.

4.5. Discussion

4.5

135

Discussion

We have used two simplified, stationary-wave models to understand the causes for diﬀerent ENSO teleconnection patterns in glacial times, as simulated by two coupled GCMs. We were motivated by the importance of ENSO teleconnections in the current climate, and the possibility that their reorganizations at the LGM might have important implications for ice sheet mass balance. Given the basic state and some estimate of ENSO-related diabatic heating, the models simulate the large-scale dynamical response of the atmosphere without transient eddy feedbacks. The non-linear model (NLIN) proves successful at simulating current stationary wave patterns associated with ENSO at present (NCEP basic state), and the simulated geopotential height field bears some resemblance to the teleconnection patterns observed in both control simulations (CCSM3 and HadCM3). This resemblance, however, is virtually non-existent when it comes to reproducing glacial teleconnections. A linear, steadystate model (ELM) is then employed to understand this behavior. It is found that the relative success of NLIN at CTL hinges on the modal character of the response (given a realistic background flow field). At LGM, both GCMs simulate a rather diﬀerent ambient flow – diﬀerent from their CTL counterpart and diﬀerent from each other. The linear analysis informs us that the modal character of the response is diminished at the LGM, and thus the sensitivity to the forcing is enhanced. This is the first main diﬃculty in simulating the glacial teleconnections. One should note, however, the diabatic heating had to be indirectly backed out from the precipitation field§ , assuming a vertical structure peaking in the mid - troposphere. This proves to be a rather good approximation in the control case and within the tropics, but the heating may have been peaked at higher altitudes by virtue of the decreased static stability of the Glacial tropical atmosphere. Also, this vertical structure is appropriate for latent heat release associated with deep convection – not the shallow heat release associated with precipitation in the storm track regions, where baroclinic instability (“slanted convection”) prevails. Thus we propose that the relative failures of NLIN are to be blamed on the incorrect specification of the heating over the storm track regions. More work is therefore needed to extract this information from the GCMs and quantify its importance. Nonetheless, we expect this limitation to pale in comparison to the absence of transient eddy feedbacks, lacking from either model. It is known that El Niño-induced changes in the latitudinal positions of the jets trigger changes to the transient eddy momentum fluxes in midlatitudes, which induce equatorward low-level flow at high latitudes, with a noticeable zonally-symmetric component [Seager et al., 2003, 2005]. Clearly, the neglected transient eddy fluxes of heat and momentum must play a key role in establishing the response to tropical forcing described in Section 4.3.2. How might one asses their role? To this end, it would be instructive to use a nonlinear model of Northern Hemisphere winter storm tracks, such as devised by Chang [2006]. The latter study presents § monthly

values for this field in both GCMs were not available for this work

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an impressively realistic simulation of transient eddy statistics over the Atlantic and Pacific storm track regions. It has not been used in the present work, because it remains to be established whether such a model can accurately reproduce the interannual variability of the storm tracks in response to tropical heating. If this can be achieved, we propose to force this model with ENSO-related heating anomalies and quantify how stationary waves, jet streams and transient eddies conspire to bring about vastly diﬀerent teleconnection patterns at the LGM. It will undoubtedly deepen our understanding of the dynamics at work in the current generation of climate models and hopefully shed light on how these elements interacted in nature, bringing us closer to solving Ice Age puzzles. Another aspect of ENSO teleconnections neglected in this study is their potential change over the Southern Hemisphere. Traditionally overlooked, there is now increasing evidence that the latter is the stage of processes governing many aspects of the global ocean circulation. Most notably, it has been proposed that the Atlantic meridional overturning circulation (MOC) is driven by the upwelling of North Atlantic Deep Water with the recirculation cells of the Southern Ocean, thought to be primarily controlled by the wind field over the Drake Passage [Toggweiler and Samuels, 1993, 1995, 1998; Gnanadesikan, 1999]. Therefore, any sizable change in surface winds over the area could aﬀect the Atlantic MOC to some extent. The impacts of ENSO over the Southern Ocean are important in the current climate, in particular in terms of sea-ice concentration and extent [Yuan et al., 1996; Yuan and Martinson, 2000]. Their change in a glacial world can conceivably participate in reorganizing the sea-ice field, thereby strongly aﬀecting the local winds and the Southern Ocean’s density structure. Another noteworthy impact of ENSO over the Southern Hemisphere is its ability to shift westerly wind belts equatorward over the ocean during El Niño years [Seager et al., 2003]. Seager et al. [2007] point out that, were such changes to persist, these would markedly reorganize the salt export associated with the Agulhas retroflection, crucial to the salinity balance of the Atlantic basin [Gordon, 1985]. Large glacial-interglacial fluctuations in this export have been documented over the past 5 cycles [Peeters et al., 2004] and are hypothesized to have played a significant role in the fluctuations of NADW production over those timescales. Seager et al. [2007] propose that ENSO might remotely drive this salt export, thereby partially controlling the fluctuations of the Atlantic MOC on centennial timescales. Currently, most climate models used at the LGM have too crude a grid size to adequately resolve such a retroflection. It would thus be worthwhile to explore if they can simulate ENSO-related changes in the surface wind field that support such a tropical mechanism for the resumption of the Atlantic MOC after the LGM. Hence, once the changes in ENSO teleconnections have been understood over the Northern Hemisphere, there will remain a wealth of interesting problems to tackle over the Southern Ocean, which we shall leave for future work.

El Niño and the Earth’s climate: from decades to Ice Ages.

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143

Conclusion “We are not certain, we are never certain. If we were, we could reach some conclusions and we could, at last, make others take us seriously.” Albert Camus

Summary The goal of this book has been the exploration of some mechanisms of low-frequency climate change in the tropical Pacific and of their impacts on the rest of the globe. Its approach was reductionist in essence, aiming at isolating the relevant physical processes through simple models of the ocean and atmosphere. The problem was broken up into four chapters, which correspond to the four spectral bands under investigation. Chapter 1 focused on decadal variability. We built upon the rich tradition of reduced-gravity ocean models and extended linear equatorial wave theory by computing the Green’s function of the problem. This allowed us to rigorously gauge the relative importance of tropical and extratropical wind forcing in generating thermocline motion at the equator. It was found that the sharp decrease of the Green’s function with latitude meant that tropical winds always had a relative advantage over extratropical winds, in spite of their lesser variance. We also pointed out the relative ineﬃciency of the oceanic ”modes” to pick out power from a white spectrum of the wind field, since they all are damped. Tropical winds are able to generate a strong equatorial response with periods of 10 to 20 years, while midlatitude winds can only do so for periods longer than about 50 years. We concluded on these theoretical grounds that the latter are unlikely to be responsible for the observed decadal variability in sea-surface temperature. In addition, we discussed other impediments to a modal behavior of the Pacific basin on those timescales – coastline geometry, dissipation and most importantly the energy loss to the barotropic eddy field – all of which weighed strongly against the possibility that baroclinic eigenmodes could be responsible for the decadal component of tropical Pacific SST records. In contrast, we exhibited alternative mechanisms relying on ocean-atmosphere coupling (whether local or not) that

144

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could more plausibly account for it. Beyond the mathematical contribution of formally unifying diﬀerent solutions to the low-frequency equatorial wave problem, this work makes a contribution to the field of climate dynamics, in that it helps narrow down the substantial set of mechanisms of Pacific decadal variability that have been oﬀered so far. We then turned to the behavior of ENSO over centennial to millennial timescales. Chapter 2 explored specifically the sensitivity of ENSO to volcanic forcing and its interaction with solar forcing over the past millennium (1000-1999 A.D.). We used a model of intermediate complexity with a simplified parameterization of the eﬀect of atmospheric radiation on SST. This allowed us to repeat simulations of the millennium up to 200 times, building a solid statistical base for assessing the impact of tropical volcanic eruptions on the likelihood of El Niño events. In accordance with previous studies [Mann et al., 2005], the model responded to increased radiation with a La Niña-like pattern, as predicted by the thermostat mechanism of Clement et al. [1996]. It was found that only forcings greater than about 4 Wm≠2 (i.e., larger than the two largest tropical eruptions of the past 150 years, Krakatau in 1883 and Mt Pinatubo in 1991) can push the likelihood and amplitude of an El Niño event above the model’s level of internal variability. This explained why Adams et al. [2003] could detect a statistical relationship between explosive volcanism and El Niño over the past 350 years, while on the other hand Chen et al. [2004] were able to predict El Niño events of the last 148 years without knowledge of volcanic forcing. This result an important step in the resolution of what was hitherto a paradox. If explosive volcanism can tip the dynamical balances towards an El Niño, then it was reasonable to expect that the strongest eruption of the millennium (1258 A.D.) may have done so. We peered into the array of high-resolution paleoclimate data to show that indeed, it is likely to have triggered a moderate-to-strong El Niño event in the midst of prevailing La Niña-like conditions induced by increased solar activity during the Medieval Climate Anomaly. In so doing, we developed a multiproxy method that is the first building block of a more comprehensive paleo-ENSO index over the past millennia, which is needed to more thoroughly test the thermostat mechanism. In Chapter 3, we explored the possibility that ENSO may have acted as a mediator of the much debated solar influence on climate. By using a range of scaling estimates between the amount of cosmogenic isotopes and solar irradiance, we bracketed uncertainties relative to the sensitivity of the ENSO system to solar forcing over the Holocene. The model proved remarkably sensitive to even modest changes in irradiance, which were able to generate a response in the east-west SST gradient that surpassed the model’s considerable level of internal variability, even in the presence of realistic amounts of weather noise. Combined with orbital changes in insolation, we found solar irradiance able to drive millennial oscillations in the tropical Pacific SSTs. Its subtle amplitude, accumulated over these longs timescales, could plausibly account for a multitude of climate anomalies detected across the globe, concomitantly with excursions in the concentration of cosmogenic isotopes. The influence of the Sun, albeit small, was non-zero when averaged over the seasonal cycle, while precessional forcing El Niño and the Earth’s climate: from decades to Ice Ages.

145 did average to zero. Remarkably, the corresponding SST response was of similar magnitude (a fraction of a degree) in both cases, despite the order of magnitude diﬀerence in peak-to-peak variations. As in Chapter 2, this Chapter assumed modern ENSO teleconnections and used the rich array of high resolution paleoclimate records (IRD, speleothems, corals, tree-rings, lacustrine sediments) to test our hypothesis, which we found supported by the available data under this scenario. If confirmed by subsequent studies, this would have important implications for understanding the climate of the past millennium. Indeed, it lended support to the notion that the Little Ice Age and the Medieval Climate Anomaly were just two of the most recent swings induced by solar activity over the Holocene, and possibly over more ancient epochs as well [Bond et al., 2001]. Nonetheless, the current tests were far from definite, so we detailed other predictions of the theory as specific targets of tests to come, based on data that we hope available to the climate community within a reasonable timeframe. With the recognition that these empirical tests all rely heavily on modern teleconnections patterns, we dedicated Chapter 4 to understanding how these may have varied in the past, especially at the Last Glacial Maximum (LGM). To this end we analyzed the LGM simulations of two state-of-the-art climate models, HadCM3 and CCSM3 and investigated how their teleconnections diﬀered from the present-day ones. While both models did a credible job of reproducing modern ENSO teleconnections, they showed very diﬀerent patterns at the LGM – diﬀerent from the preindustrial case and diﬀerent from one another. This must be partly due to the reduction in ENSO activity observed at LGM in CCSM3, not in HadCM3. While unhelpful in trying to understand natural climate change, this failure provided us with an opportunity to peer into the causes of discrepancies between coupled general circulation models (GCMs) via simplified models. We used primitive equation models with idealized damping to compute the atmospheric response to anomalies in tropical Pacific diabatic heating anomalies. Use of these models, which ignore transient eddy feedbacks, allowed for an exploration of the extent to which one can account for GCM teleconnections only on the basis of planetary wave propagation. Experiments confirmed the established fact (see Held et al. [2002] and references therein) that present-day ENSO teleconnections can largely be understood in terms of linear, stationary wave dynamics. A similar attempt proved unsuccessful for LGM teleconnections, leading us to suggest that the non-linear trilogy of jets, planetary waves and transient eddies must be invoked to explain the changes that occurred in the GCM simulations of the LGM.

Caveats and Future Work Although much insight can be gleaned through simple models, this simplicity comes at the expense of completeness. The model used in Chapter 1 is as idealized as they come: a single baroclinic mode, linear dynamics, straight coastlines, in the — -plane approximation, supplemented by the low-frequency long-wave approximation. It is

146

Conclusion

only meant to give a qualitative description of the Pacific basin. While this adiabatic model has proven surprisingly successful at describing observed interannual anomalies in tropical circulations [e.g. Cane, 1984] as to warrant operational forecasts of El Niño (T.Barnston, personal communication), its applicability to decadal studies fades as the thermal structure is assumed fixed and no dissipation was introduced. Furthermore, it is not coupled to the atmosphere, while we argued that coupling was most likely the key to this Pacific Decadal Variability. The immutability of stratification is an even more serious caveat as we consider the evolution of ENSO on timescales of centuries to millennia. It is known that the properties of ENSO are sensitive to the background state upon which the anomalies develop [Zebiak and Cane, 1991; Wittenberg , 2002]. Since the physics familiar to the interannual ENSO (the Bjerknes [1969] feedback) operate on all timescales, and also seem crucial in establishing the climatology [Dijkstra and Neelin, 1995], the definition of this background state is unclear: what is ENSO and what is not? To some extent, the model modifies its own background state, should the latter be defined on a 50 year average, say. Indeed, Wittenberg [2002] reduced the problem to understanding the response of ENSO to an El Niño- or La Niña-like climatology. It is clear, however, that the structure of the equatorial thermocline is not entirely determined within the Tropics and that the full tridimensional circulation of the upper ocean is involved in its establishment [Boccaletti et al., 2004]. While it now appears that decadal temperature anomalies subducted in the subtropics do not reach the equator with any appreciable amplitude [Schneider et al., 1999], thermocline waters are ultimately ventilated from higher latitudes where solar forcing would inevitably aﬀect their formation. Pycnocline waters are made up from subtropical mode waters with neutral densities between 25 and 26.5 kgm≠3 , which outcrop in the subtropics and midlatitudes [Johnson and McPhaden, 1999]. The formation regions of these mode waters tend to be localized in the western part of the subtropical gyre, while lower pycnocline waters originate from beyond the gyre boundary with more zonally-elongated outcrops [Hanawa and Talley, 2000]. It is therefore unclear, even in the absence of atmospheric feedbacks, how a uniform change in incoming solar radiation would modify the equatorial thermocline, not least because of the mixing and stirring of subducted waters by the eddy field below the mixed layer. It is an outstanding problem in oceanographic research, one that will undoubtedly mobilize the full array of observational, theoretical and modeling capabilities for its resolution. Even greater simplifications were made in the treatment of atmospheric radiation in our coupled model. It comprises no radiation scheme whatsoever, while the difference between top-of-the-atmosphere and surface downwelling shortwave radiation was only accounted for by a fixed cloud fraction. One might also find surprising that the simple model of Gill [1980] would even approximately simulate near equatorial surface winds despite its tremendously crude physics. Its success is an item of experience [Neelin et al., 1998], but for this problem the primary matter is the incoming radiation into the ocean mixed layer, which is obviously aﬀected by clouds – absent in this simple model. Unfortunately, cloud physics are known to be the Achilles’ heel of El Niño and the Earth’s climate: from decades to Ice Ages.

147 the most comprehensive GCMs. Marine stratus clouds, especially, are crucial to the sign (let alone the magnitude)of the climate response to radiative perturbations [e.g. Bony et al., 2006]. Moreover, there is considerable controversy as to how they would respond to solar forcing, as some have suggested that their formation may be influenced by galactic cosmic rays [Marsh and Svensmark, 2000; Carslaw et al., 2002]. The absence of an explicit moisture equations also means that no water vapor feedback can occur, while Pierrehumbert [1999] has argued that it should be instrumental in producing global climate change on millennial timescales. In short, while the model emphasizes the dynamical adjustment of the ocean via the Bjerknes feedback, it is still unknown how these eﬀects would fare in comparison to the change that solar irradiance would impose on the atmosphere and the basin-wide ocean circulation, either by direct radiative forcing or indirect forcing via air/sea fluxes. Only a model with a realistic representation of all these elements can inform us about these interactions, which constrains us to use coupled GCMs. Yet, the abundant evidence of their flaws in simulating the present-day tropical climatology [Delecluse et al., 1998] or LGM climate (Chapter 4) does not bode well for such an exercise. At present, there is still no consensus on the ENSO response to greenhouse gas forcing amongst GCMs [Collins, 2005]. Hence the rationale for using our simpler model, whose dynamical thermostat behavior seems supported by the observation of an increased SST gradient along the equator over the twentieth century [Cane et al., 1997]. At this point, it is also premature to expect consensus amongst GCMs in their response to solar perturbations. Further, it seems that some GCMs respond diﬀerently to solar and greenhouse gas forcing, a puzzling fact which has yet to be explained (A. Clement, personal communication). This issue partly motivated our Chapter 4, since the past provides a critical testbed for coupled GCMs and their simulation of the tropical Pacific. The disagreement between the 2 GCMs proved substantial, albeit not unexpected. We saw that both models produced an ENSO extending too far west into the warm pool, which contributed to the diﬀerence between simulated and observed present-day teleconnections. Why did the latter diﬀer at LGM? While the divergence in ENSO behavior between models undoubtedly played a role, we also had to make an assumption regarding the vertical distribution of heating and how it scaled with precipitation. This assumption was arguably acceptable in the Tropics, not over the storm tracks. Unfortunately, the full three-dimensional diabatic heating fields were not available for this study, which suggests an obvious area for improvement. Equally important are the transient eddy heat and momentum fluxes, which are typically not saved in long GCM integrations. It is hoped that those will be made available in future integrations of coupled GCMs for the purpose of such analyses. More fundamentally, it was shown that transient eddies are instrumental in shaping the ENSO teleconnection pattern at the LGM, and this is the most pressing point to address. In addition, we should point out that stationary models are tuned to the current climate (inasmuch as the specified damping is meant to account for mixing by transient eddies), which could partly explain their poor performance in the LGM climate.

148

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Finally, a word should be said about uncertainties in the forcing: while these are believed to be relatively small for decadal variability and the LGM, this is not the case over the Holocene. Specifically, we are tracking either minute changes in solar irradiance over long timescales – which some argue are insignificant [Foukal et al., 2006] – or large, abrupt changes in stratospheric aerosol loading, which are only indirectly recorded in ice cores and often with large error bars. Furthermore, no dataset of Holocene volcanic forcing was available for the study in Chapter 3, though the upshot of Mann et al. [2005] is that it is at least as important as solar forcing, even over centennial timescales. These limitations leave ample room for progress.

Outlook With some appreciation gained from these successes and failures, we can now formulate questions for future research: • How do coupled GCMs with a realistic ENSO cycle react to volcanic perturbations? Is the thermostat mechanism operating in them and with which amplitude? • How do such models react to centennial perturbations in solar irradiance? Is that response qualitatively diﬀerent from that to greenhouse gases? If so, why? • How might one construct an objective multiproxy index of ENSO intensity over the past millennium? • If ENSO is indeed a mediator of the solar influence on climate, and if the mechanism of Shindell et al. [2001] also contributes, what is the relative importance of the two? Could they reinforce one another? • What is the role of the tridimensional ocean circulation in determining the equatorial Pacific thermocline? In particular, how does the Atlantic MOC influence it, and how? Conversely, how do tropical Pacific SSTs influence the North Atlantic? Can a positive feedback exist between the two systems, as suggested in Chapter 3? • If at least one of these two positive feedbacks operates, might this non-linearity lead to bifurcations that could explain some aspects of abrupt climate change? • Why do LGM simulations of ENSO and its teleconnections diﬀer so much? Can idealized models of the storm tracks help explain this diﬀerence? How might this knowledge be used to improve long-range climate forecasts? It is hoped that answers to these questions will be found within a few years and that they will empower us with a greater ability to predict the future of our climate.

El Niño and the Earth’s climate: from decades to Ice Ages.

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151

Appendix A Pacific Decadal Variability: Boundary-Layer Correction When the forcing reaches the poleward boundaries of the domain, the forced solution (1.32) has to be amended. Our solution holds within a distance ‘ of the northern wall, so that we can write the ”interior” western boundary mass flux : UI = 2i„

⁄

yN ≠‘

0

F (y)E(„y 2 )dy

(A.1)

Far from the equator, the PGPV solution holds to lowest order : h=

A

F y

B C y

1 ≠ ei„y i„

2›

D

(A.2)

and the boundary layer zonal mass flux can be computed using geostrophy : 1 u = ≠ hy y

so that :

C

1 U‘ = ≠ hy y

DyN

+

yN ≠‘

(A.3)

⁄

yN

yN ≠‘

h dy y2

(A.4)

Taking F = 0 at y = yN ≠ ‘ since it is already included in the interior integral, performing another integration by parts, and using previous formula for UI , the boundary-layer return flow then writes : C

D

⁄ yN hN FN 1 ≠ e≠i◊N U‘ = ≠ + ≠ 2i„ F (y)E(„y 2 )dy yN yN i◊N yN ≠‘

(A.5)

where FN = F (yN ). We can ignore the integral, which is approximately ≠2i„ ‘ FN E(◊N ) ≈ O(‘) . Again using (A.2) to compute the compute the meridional mass flux into the

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Appendix A. Pacific Decadal Variability: Boundary-Layer Correction

northern wall : ⁄

1 VN = v d› = yN ≠1 0

5⁄

0

≠1

h› d› ≠

⁄

0

≠1

6

F d› =

hN ≠ FN yN

(A.6)

Therefore the total boundary layer correction is : C

FN 1 ≠ e≠i◊N U‘ + VN = ≠ 1≠ yN i◊N

D

(A.7)

So that for a symmetric basin, the total mass flux is : I

IF = ≠ 2i„

⁄

0

yN

C

FN 1 ≠ e≠i◊N F (y)E(„y )dy + 2 1≠ yN i◊N 2

DJ

(A.8)

which reduces to (1.32) if the forcing vanishes at the boundary (FN = 0). For ◊N Ø 1, one can obtain a crude estimate of the importance of the boundary forcing goes as follows : FB ≥ FyNN , FI = 2i„yN F (using E = O(1)), so that : FB 1 ≥ Æ1 FI ◊N

(A.9)

which confirms the intuitive result that for basins suﬃciently big, the eﬀect of the northern and southern boundary mass fluxes is lesser than that of the interior mass flux.

El Niño and the Earth’s climate: from decades to Ice Ages.

153

Appendix B ENSO Impacts on North Atlantic Winds We show evidence of a link between ENSO and surface winds over the northern North Atlantic. We use wind field data from three sources : surface observations, a coupled general circulation model (GCM), and a forced atmospheric GCM. The idea is to progressively strip down the physics to isolate the mechanism responsible for the linkage. The data sources are : • Our best observational estimate of surface winds over the North Atlantic. Since wind stress estimates are unfortunately unavailable before 1949, the wind velocity field was taken from the analysis of Evans and Kaplan [2004], which uses an optimal interpolation (OI) of ICOADS winds [http://icoads.noaa.gov/, Worley et al. [2005]]. This has the eﬀect of retaining the large-scale features of the field, which are most relevant for our study. • the GDFL coupled model (version 2.1) simulation H1 (http://nomads.gfdl. noaa.gov/CM2.X/CM2.1/data/cm2.1_data.html). This is a state-of-the-art ocean-atmosphere general circulation model in the configuration used for the Fourth Assessment report of the Intergovernmental Panel on Climate Change. The forcing is a reconstruction of natural and anthropogenic radiative perturbations over the period 1860-2000. This particular simulation has a vigorous, self-sustained ENSO with variance comparable to that observed. but very similar results were obtained with other ensemble members H2 and H3. • POGA-ML simulations with the NCAR CCM3 model, as used in Seager et al. [2005b]. The AGCM is coupled to a two-layer, entraining, mixed-layer ocean model, with historical SSTs [Kaplan et al., 1998] prescribed only in the tropical Pacific (computed elsewhere). The results analyzed are the average of a 16member ensemble, which isolates the influence of the boundary conditions - in this case, tropical Pacific SSTs over the period 1860-2000. The data can be found

154

Appendix B. El Niño and the North Atlantic at http://kage.ldeo.columbia.edu:81/expert/SOURCES/.LDEO/.ClimateGroup/. MODELS/.CCM3/.PROJECTS/.poga-ML/.poga-ML-mean/. In both models we analyzed the wind stress, since it is the most relevant to surface ocean dynamics.

The period of analysis was the longest common to all datasets, 1860-2000. All fields were smoothed by a 3-month running average. They were then regressed onto the corresponding NINO3 index : for historical SSTs, we used the extended SST analysis of Kaplan et al. [1998], while the model-generated NINO3 index was computed in the second example (GFDL H1). Results are shown in Fig 3.7 : the left-hand panels show the regression patterns of surface wind-stress (or velocity when analyses of stress were not available) on the normalized NINO3 index, and the right-hand ones show the linear correlation maps of the meridional component with NINO3. All datasets are in broad agreement that northeasterly winds tend to occur over the area of interest during periods of high NINO3. Nonetheless, the amplitudes are weak and it is necessary to establish whether any of these correlations are statistically significant. For the period 1860-2000, with monthly data smoothed over 3-months intervals, N ≥ 500, so the significance 95% threshold is |ﬂ| ≥ 0.1. We found that correlations are significant at the 95% level everywhere in the POGA-ML ensemble mean (Fig 3.7, 2b), which very eﬀectively isolates the response to tropical SST variability. The correlation is consistently high in this case, because of a dynamical linkage between the two basins : El Niño-induced changes in the latitudinal positions of the jets trigger changes to the transient eddy momentum fluxes in midlatitudes, which induce equatorward low-level flow at high latitudes, with a noticeable zonally-symmetric component [Seager et al., 2003, 2005a]. In nature, however, this signal is potentially swamped by atmospheric dynamics independent of ENSO. Indeed, we find in the surface wind analyses (3b) that the ENSO/North Atlantic connection is very weak north of ≥ 48◦ N . Repeating this analysis for five 50-year periods between 1860 and 2000 (sliding the window by 18 years each time), we found that this was due to a strong non-stationarity of the correlation in the northern parts of the basin : well above the 95% level in some decades, well below in some others. This result was also obtained for geostrophic wind fields derived from the sea-level pressure (SLP) data of Kaplan et al. [2000]. This could be due either to observational error (in SST, winds, as well as SLP) or to noise. However, we found that a similar non-stationarity occurred in the GFDL simulations H1, H2 and H3, which have no measurement error. Therefore local variability is to blame in lowering the observed correlation to NINO3. This therefore suggests the following interpretation : a link between the tropical Pacific and the North Atlantic is at work in nature as in the two GCMs, but it is of modest amplitude compared to the natural climate variability of the North Atlantic, which is quite energetic in the multidecadal spectral range. The consequence is that the statistical link only emerges on long timescales. The simulated and instrumental SLP data are consistent with this idea, albeit too short to be conclusive, and perhaps El Niño and the Earth’s climate: from decades to Ice Ages.

BIBLIOGRAPHY

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veiled by the confounding influence of anthropogenic greenhouse gas increase.

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