UNIVERSITY of CALIFORNIA, SAN DIEGO Temperature Reconstruction

UNIVERSITY OF CALIFORNIA, SAN DIEGO

Temperature reconstruction at the West Antarctic Ice Sheet Divide, for the last millennium, from the combination of borehole temperature and inert gas isotope measurements.

A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy

Oceanography

Anais J. Orsi

Committee in charge:

Jeffrey P. Severinghaus, Chair Bruce D. Cornuelle Helen Fricker Dan Lubin Lynne D. Talley William Trogler

Chair

University of California, San Diego

2013

iii EPIGRAPH

Fortitudine Vincimus By endurance we conquer - Ernest Shackelton

iv TABLE OF CONTENTS

Signature Page...... iii

Epigraph...... iv

Table of Contents...... v

List of Figures...... xii

List of Tables...... xv

Acknowledgements...... xvi

Vita, Publications, and Fields of Study...... xix

Abstract of the Dissertation...... xxi

Chapter 1 Introduction...... 1

Chapter 2 Magnitude and Temporal Evolution of DO 8 Abrupt Temperature Change Inferred From Nitrogen and Argon Isotopes in Greenland Ice Using a New Least-Squares Inversion...... 4 2.1 Introduction...... 5 2.1.1 Reconstructing polar surface temperature...... 5 2.1.2 Abrupt climate changes...... 6 2.1.3 Noble gas isotopes...... 8 2.1.4 Temperature reconstruction...... 9 2.2 Methods...... 9 2.2.1 Laboratory measurements...... 9 2.2.2 Timescale...... 10 2.2.3 Isolation of the thermal signal...... 12 2.2.3.1 Gas loss correction...... 13 2.2.3.2 Using two pairs of isotopes...... 14 2.2.3.3 Using a densiﬁcation model...... 16 2.2.4 Forward densiﬁcation and heat diffusion model... 16 2.2.4.1 Improvement of the Goujon model.... 18 2.2.4.2 Linearization of the forward model.... 18 2.2.4.3 Linearity of the model...... 19 2.2.4.4 Choice of the basis functions...... 20 2.2.5 Inverse model...... 22 2.2.5.1 Least-squares inversion...... 22 2.2.5.2 Uncertainty estimation...... 24

v 2.2.5.3 Influence of the parameters used in the inversion...... 25 2.3 Results...... 25 15 2.3.1 First, and simplest, approach with δ Nxs ...... 27 2.3.2 Second approach, with a diffusive column height fit to data...... 27 2.3.3 Third approach, with a densification model..... 29 2.3.3.1 Accumulation rate scenarios...... 29 2.3.3.2 Surface temperature reconstruction.... 30 2.3.3.3 Gas Age calculation...... 32 2.4 Discussion...... 34 2.4.1 Accumulation history...... 34 2.4.2 Amplitude of the warming...... 36 2.4.3 Calibration of the δ18O thermometer...... 37 2.5 Sensitivity analysis...... 39 2.5.1 Sensitivity to the initial conditions...... 39 2.5.2 Sensitivity to the initial temperature history..... 39 2.5.3 Comparison of the Goujon and Spencer densification models...... 40 2.5.4 Sensitivity to the accumulation history...... 43 2.5.5 Sensitivity to the convective zone...... 43 2.5.6 Sensitivity to the lock-in depth...... 44 2.6 Conclusions...... 47

Chapter 3 Little Ice Age Cold Interval in West Antarctica: Evidence from Borehole Temperature at the West Antarctic Ice Sheet (WAIS) Di- vide...... 48 3.1 Introduction...... 49 3.1.1 The last 1000 years...... 49 3.1.2 Site description...... 49 3.2 Method...... 51 3.2.1 Sampling method...... 51 3.2.2 Forward model...... 51 3.2.3 Inverse model...... 53 3.2.3.1 Linearization...... 55 3.2.3.2 Least-squares regression...... 56 3.2.4 Uncertainty estimation...... 57 3.2.4.1 Uncertainty associated with the least- squares optimization...... 57 3.2.4.2 Uncertainty in the timing of the temperature minimum...... 58 3.2.4.3 Uncertainty associated with the boundary conditions...... 58

vi 3.2.4.4 Uncertainty associated with the model parameters...... 58 3.3 Results and discussion...... 59 3.3.1 Seventeenth century minimum...... 59 3.3.2 Recent warming...... 62 3.4 Sensitivity analysis...... 64 3.4.1 Influence of the initial boundary conditions..... 64 3.4.2 Influence of the bottom boundary conditions.... 64 3.4.2.1 Bottom temperature...... 65 3.4.2.2 Bottom temperature gradient...... 65 3.4.2.3 Bottom depth...... 65 3.4.3 Influence of the vertical velocity parameterization.. 67 3.4.4 Influence of the accumulation rate...... 67 3.4.5 Influence of the thermal conductivity of the ice... 69 3.4.6 Influence of the basis functions used in the inversion. 69 3.4.6.1 Influence of the prior covariance of the model parameters...... 69 3.4.6.2 Influence of the signal to noise ratio.... 73 3.4.6.3 Influence of the basis functions...... 73 3.4.7 Uncertainty in the measurements...... 75 3.4.7.1 Uncertainty in the calibration...... 75 3.4.7.2 Systematic biases...... 76 3.4.7.3 Random noise...... 77 3.5 Conclusion...... 77 Appendix 3.A Forward model description...... 78 3.A.1 Model parameters...... 79 3.A.2 Boundary conditions...... 79

Chapter 4 Analytical Methods...... 81 4.1 Introduction...... 82 4.2 La Jolla Air standard...... 83 4.2.1 Pier extraction...... 84 4.2.2 Aliquot extraction...... 85 4.2.3 Working standard...... 85 4.2.4 Stability of the standard...... 86 4.3 Nitrogen and argon isotope measurements...... 87 4.3.1 Set up description...... 89 4.3.2 Oxygen removal...... 90 4.3.2.1 Optimisation of the oxygen removal process with hot copper...... 90 4.3.2.2 Tests with Ridox...... 91 4.3.3 Air extraction from ice samples...... 92 4.3.3.1 Flask design...... 92

vii 4.3.3.2 Evacuation time...... 93 4.3.3.3 Melting and stirring...... 94 4.3.4 Mass spectrometry...... 96 4.3.4.1 Gas conﬁguration...... 96 4.3.4.2 Source focusing...... 96 4.3.4.3 Aliquot expansion...... 97 4.3.4.4 Quality Control...... 99 4.3.4.5 Argon isotopes...... 101 4.3.4.6 Nitrogen isotopes...... 104 4.3.4.7 Ar/N2 ratio...... 105 4.3.4.8 Kr/N2 ratio...... 109 4.3.5 Ice core measurements of WDC05A...... 110 4.3.5.1 WDC05A samples...... 110 4.3.5.2 Evaluation of the precision...... 111 4.3.5.3 Gas loss...... 113 4.3.5.4 Argon isotopic offset...... 114 4.3.5.5 Comparison with the getter method.... 114 4.3.5.6 Comparison with WDC06A...... 117 4.4 Noble gas measurements in ﬁrn air...... 117 4.4.1 Experimental protocol...... 118 4.4.2 Mass Spectrometry...... 120 4.4.2.1 Optimisation of the performance of the MAT-253...... 120 4.4.2.2 Sample handling...... 122 4.4.2.3 Standard...... 122 4.4.2.4 Argon isotopes...... 124 4.4.2.5 Krypton isotopes...... 124 4.4.3 Elemental ratios...... 125 4.5 Noble gas measurements in ice cores...... 126 4.5.1 Sample preparation...... 127 4.5.1.1 Ice extraction...... 127 4.5.1.2 Gettering...... 127 4.5.2 Mass spectrometry...... 129 4.5.2.1 Background...... 129 4.5.2.2 Pressure imbalance sensitivity...... 129 4.5.2.3 Chemical slope...... 130 4.5.3 WDC05A samples...... 131 4.5.3.1 La Jolla Air calibration...... 131 4.5.3.2 Evaluation of the precision...... 133 4.5.3.3 Fractured ice...... 133 Appendix 4.A Protocol for extracting La Jolla Air...... 134 4.A.1 In the laboratory...... 134 4.A.2 At the pier...... 134

viii 4.A.3 Take down...... 135 Appendix 4.B Protocol for ﬁlling working standard cans..... 136 4.B.1 Ar-N2 standard...... 136 4.B.1.1 Preparation...... 136 4.B.1.2 Addition of argon...... 136 4.B.1.3 Addition of nitrogen...... 137 4.B.1.4 Correct the Ar/N2 ratio by adding Ar... 138 4.B.2 Ar-Kr-Xe standard...... 139 4.B.2.1 Handling of Kr and Xr tanks...... 139 4.B.2.2 Setup...... 139 4.B.2.3 Calculations...... 140 4.B.2.4 Operation...... 140 4.B.2.5 Notes...... 141 Appendix 4.C Protocol for extraction of Ar and N2 in ice samples: Copper method...... 142 4.C.1 Preparation of the method...... 142 4.C.1.1 Chest freezer...... 142 4.C.1.2 Getting the ﬂasks ready...... 142 4.C.2 The night before...... 142 4.C.3 In the freezer...... 143 4.C.4 In the lab...... 143 4.C.5 Clean up...... 147 4.C.6 Mass spectrometry...... 148 Appendix 4.D Notes on Focusing the MAT-252...... 149 4.D.1 Settings that should be left alone...... 149 4.D.2 Settings that should be adjusted...... 149 Appendix 4.E Protocol for the measurement of noble gases in ice samples...... 152 4.E.1 The day before...... 152 4.E.2 Before going down to the freezer...... 153 4.E.3 In the freezer:...... 153 4.E.4 Sample preparation for the line...... 154 4.E.5 Pumping out ambient air...... 154 4.E.6 Preparing the vacuum line for transfer...... 155 4.E.7 Extraction and transfer...... 156 4.E.8 Gettering...... 158 4.E.9 At the end of the day...... 159

Chapter 5 Constraints on the recent warming in West Antarctica...... 160 5.1 Introduction...... 160 5.1.1 Site location...... 161 5.1.2 Variability in the atmospheric circulation and teleconnections with the central tropical Paciﬁc..... 163

ix 5.1.3 Evidence for widespread warming in West Antarctica 164 5.2 Paleo-temperature measurements...... 165 5.2.1 Borehole temperature...... 165 5.2.2 Inert gas isotopes...... 165 5.2.3 Water isotopes...... 170 5.3 Results...... 171 5.3.1 Temperature reconstruction...... 171 5.3.2 Comparison with reconstructions based on satellite and weather station data at WAIS-Divide...... 174 5.3.3 Is it normal?...... 178 5.4 Conclusion...... 178

Chapter 6 Surface temperature reconstruction using inert gas isotopes.... 182 6.1 Introduction...... 182 6.2 Analysis of the raw data...... 184 6.2.1 Nitrogen and Argon isotope data in the WDC05A ice core...... 184 6.2.1.1 Gas loss...... 184 6.2.1.2 Disequilibrium...... 186 6.2.2 Source of the scatter in the data...... 187 6.2.3 Separation of gravitational and thermal component. 189 6.3 Firn thickness and ∆age...... 193 6.3.1 Firn thickness and diffusive column height..... 193 6.3.2 Modeling the lock-in depth...... 195 6.3.2.1 Lock-in depth parameterization...... 195 6.3.2.2 Variability in the diffusive column height. 196 6.3.2.3 Densiﬁcation model description...... 197 6.3.2.4 Inputs to the densiﬁcation model..... 198 6.3.2.5 Results...... 200 6.3.3 Gas age calculations...... 203 6.4 Temperature reconstruction...... 205 6.4.1 Analysis of the temperature difference ∆T ..... 205 6.4.2 Dual inversion of ∆T firn and borehole temperature. 205 6.4.3 Description of the surface temperature record.... 209 6.5 Discussion...... 211 6.5.1 Comparison with Northern Hemisphere records... 211 6.5.2 Solar Forcing...... 213 6.6 Conclusion...... 215

Chapter 7 On bubble-free layers in the WAIS-Divide ice core...... 216 7.1 Introduction...... 216 7.2 Analysis of bubble-free layers...... 217

x 7.2.1 Description...... 217 7.2.2 Are bubble-free layers caused by ice melt?..... 218 7.2.3 Do bubble-free layers impede gas ﬂow?...... 222 7.3 Discussion...... 222 7.4 Conclusion...... 224

Chapter 8 Conclusion and perspectives...... 226 8.1 Borehole temperature...... 226 8.2 Inert gas isotope measurements...... 227 8.3 Inverse method...... 227 8.4 Surface temperature reconstruction...... 228 8.5 Bubble-free layers...... 229 8.6 Perspectives...... 229

References...... 230

xi LIST OF FIGURES

Figure 2.1: Overview of polar climate history of the last glacial period.....7 Figure 2.2: Layer thickness...... 11 Figure 2.3: Gas Isotope Data...... 15 Figure 2.4: Output of the Goujon model...... 17 Figure 2.5: Estimation of the magnitude of the non-linear component of the model 21 Figure 2.6: Inﬂuence of the set of basis functions...... 26 Figure 2.7: Surface temperature reconstruction with prescribed gravitational fractionation...... 28 Figure 2.8: Accumulation Scenarios...... 30 Figure 2.9: Surface temperature reconstruction with accumulation scenarios.. 31 Figure 2.10: Gas age - ice age difference...... 33 Figure 2.11: Temperature change for all scenarios...... 38 Figure 2.12: Sensitivity to the initial history...... 40 Figure 2.13: Comparison of the Spencer and Goujon models...... 41 Figure 2.14: Sensitivity to the deﬁnition of the LID...... 46

Figure 3.1: Location of WAIS-Divide: at the center of West Antarctica, 160 km from the Byrd ice core site...... 50 Figure 3.2: WAIS-Divide borehole temperature data...... 52 Figure 3.3: Smoothing function...... 54 Figure 3.4: Surface temperature reconstruction...... 60 Figure 3.5: Timing of the coldest 20 year and Temperature difference between the average over the time period 950-1250 (Medieval Warm Period), and the average over 1400-1700 (Little Ice Age)...... 61 Figure 3.6: Temperature reconstruction over the last 50 years...... 63 Figure 3.7: Sensitivity to the bottom boundary conditions...... 66 Figure 3.8: Sensitivity to the vertical velocity parameterizations...... 68 Figure 3.9: Inﬂuence of the accumulation rate...... 70 Figure 3.10: Sensitivity to the thermal conductivity...... 71 Figure 3.11: Inﬂuence of the prior covariance and basis functions used in the linearization...... 74

Figure 4.1: Schematics of the set up to extract La Jolla Air standard...... 84 Figure 4.2: Long term stability of the standard...... 87 Figure 4.3: Schematics of the set up to measure N2 and Ar isotopes in ice... 89 Figure 4.4: Vessel design...... 93 Figure 4.5: Pressure as a function of time during the initial pump down time.. 94 Figure 4.6: Beam intensity on 40Ar as a function of extraction voltage..... 97 Figure 4.7: Sensitivity to the equilibration time...... 98 Figure 4.8: Scan...... 100

xii Figure 4.9: Sensitivity of the Pressure Imbalance Sensitivity (PIS) to the target voltage...... 103 Figure 4.10: Chemical Slope for Ar and N2 ...... 104 Figure 4.11: Pressure imbalance as a function of the peak center offset...... 105 Figure 4.12: Peak shape...... 106 Figure 4.13: Ar/N2 residuals...... 115 Figure 4.14: Comparison between firn air data and ice core data, near the firn ice transition...... 116 Figure 4.15: Method comparison...... 116 Figure 4.16: Comparison between WDC05A and WDC06A...... 117 Figure 4.17: Experimental set up for the getter method, with air flasks...... 119 Figure 4.18: Pressure in the line as a function of time during gettering...... 120 Figure 4.19: Trend due to capillaries...... 122 Figure 4.20: Beam Stability...... 123 Figure 4.21: Krypton isotopes in firn air in the lock-in zone at WAIS-Divide... 125 Figure 4.22: Experimental setup for the extraction of noble gases...... 128 Figure 4.23: Chemical slope measurements for krypton isotopes...... 131 Figure 4.24: Argon isotope measurements...... 132 Figure 4.25: Krypton isotope measurements...... 132 Figure 4.26: Schematics of the set up to extract La Jolla Air standard...... 135 Figure 4.27: Setup for adding Ar to an Ar-N2 standard...... 136 Figure 4.28: Setup for adding N2 to an Ar-N2 standard...... 137 Figure 4.29: Setup for building a Ar-Kr-Xe standard...... 140 Figure 4.30: Set up for the Ar-N2 method...... 144 Figure 4.31: Screenshot of the Ar method, highlighting where to find the rR indicative of the pressure imbalance...... 151 Figure 4.32: Experimental setup for the extraction of noble gases...... 152

Figure 5.1: Correlation between the annual mean temperatures at Byrd and the annual mean temperatures at every other grid point in Antarctica.. 162 Figure 5.2: Weather station data from Byrd and WAIS-Divide...... 163 Figure 5.3: Age distribution...... 166 Figure 5.4: Age distribution of a temperature pulse in the ice...... 166 Figure 5.5: WAIS-Divide measured borehole temperature proﬁle...... 167 Figure 5.6: Inert gas isotopic measurements in the WAIS-Divide ﬁrn air.... 167 Figure 5.7: Calibration of De in the convective zone with krypton isotopes... 169 Figure 5.8: Gas diffusion model validation...... 169 Figure 5.9: Surface temperature reconstruction...... 171 Figure 5.10: Data and model output...... 172 Figure 5.11: Data-model mismatch of the thermal component...... 173 Figure 5.12: Comparison of several published temperature reconstructions of the last 50 years at WAIS-Divide and Byrd station...... 175

xiii Figure 5.13: Comparison of several published temperature reconstructions of the last 50 years at WAIS-Divide and Byrd station, temperature gradients 176 Figure 5.14: Seasonal variability of the borehole temperature profile...... 177 Figure 5.15: Influence of interannual variability on the borehole temperature profile...... 177 Figure 5.16: Location map of the ITASE cores...... 179 Figure 5.17: How unusual is the recent warm period?...... 180

Figure 6.1: δ Ar/N2 and gas loss...... 185 Figure 6.2: Comparison between firn air with ice core data...... 186 Figure 6.3: Evidence for disequilibrium fractionation in the WAIS-Divide firn. 187 Figure 6.4: Scatter...... 188 Figure 6.5: Nitrogen Isotope data...... 189 Figure 6.6: Separation of gravitational and thermal fractionation...... 191 Figure 6.7: Sensitivity of the ∆T calculation to τ ...... 192 Figure 6.8: Diffusive column height...... 194 Figure 6.9: Density profile in the WDC06A ice core...... 196 Figure 6.10: Accumulation rate at WAIS-Divide...... 199 Figure 6.11: Densification model outputs 1...... 201 Figure 6.12: Densification model outputs 2...... 202 Figure 6.13: Age distribution of gases in the WAIS-Divide firn...... 204 Figure 6.14: Firn temperature gradient...... 205 Figure 6.15: Surface temperature reconstruction...... 208 Figure 6.16: Comparison of the WAIS-Divide temperature reconstruction with other climate indicators...... 209 Figure 6.17: Comparison of the Surface temperature reconstruction with North- ern Hemisphere records...... 211

Figure 7.1: Pair of bubble-free layers in the WDC05A core...... 218 Figure 7.2: Bubble free layer statistics...... 219 Figure 7.3: Melt Layer...... 220 Figure 7.4: Melt layer identiﬁcation...... 220 Figure 7.5: Hard surfaces (”crusts”) seen at WAIS-Divide...... 223

xiv LIST OF TABLES

Table 2.1: Accumulation scenarios...... 30 Table 2.2: Amplitude of the warming...... 37

Table 4.1: Mean values of La Jolla air flasks against the working standard ArN2-18...... 88 Table 4.2: Influence of the pumping time on the extraction...... 95 Table 4.3: Influence of stirring...... 95 Table 4.4: Resistor configuration of the MAT252 for Ar-N2 measurements... 96 Table 4.5: Sensitivity of the reproducibility of standard measurements to the equilibration time...... 98 Table 4.6: Sensitivity of the raw machine precision to the target voltage.... 101 Table 4.7: Chemical slope...... 103 Table 4.8: Precision of the copper method...... 111 Table 4.9: Precision of krypton isotopes...... 126 Table 4.10: Precision of elemental ratios...... 126 Table 4.11: Pressure Imbalance Sensitivity (PIS) for δ40Ar, δ86Kr, and elemental ratios in per meg per per mil...... 130 Table 4.12: Mean La Jolla air values used to normalize the results run against the working standard can...... 132 Table 4.13: Precision of the Kr-Ar method...... 133 Table 4.14: Fractured ice...... 133

Table 7.1: Analysis of bubble-free layers in the WDC05A ice core...... 221

xv ACKNOWLEDGEMENTS

The first step of a PhD is to get started. I would like to thank Mme Philippon, my very first Physics teacher in 8th grade, who sparked my interest in the subject. I still have very vivid memories of her and her perfectly hand-written notes. At the Ecole Polytechnique, Jean Marc Chomaz introduced me to geophysical fluid dynamics, and convinced my to apply to Scripps. Aurelien Ponte, Paola Cessi and Richard Somerville were instrumental in encouraging me to come. Richard, Guang Zhang, Uwe Send and Jeff Severinghaus supported me through my first year, and allowed me to take the time to explore what Scripps had to offer before I would choose a lab. Jeff Severinghaus became my adviser, and I immediately responded to his en- thusiasm for science. Through my years as a graduate student, I always came out of a meeting with him more hopeful and more motivated than when I entered his office. I would like to thank him for his patience and his encouragements when things became difficult. I also particularly appreciated being given the freedom to explore many as- pects of ice core science, teach and to participate in several field expeditions. These experiences had an important impact in my development as a scientist, and in the way that I can now shape my future. I would like to acknowledge my committee. Bruce Cornuelle provided essential guidance in inverse modeling. It has been a pleasure to learn from him. I particularly appreciated his availability, and the fact that he would always present information in chunks of the right size, so that I would not be overwhelmed. Lynne Talley and Dan Lubin helped me to broaden the scope of my research. Helen Fricker was an ally during committee meetings, and gave me precious advice on productivity. Bill Trogler provided timely assistance with the bureaucracy of graduation. I would also like to thank Naomi Oreskes for agreeing to be part of my committee, even though she could not stay till the end. I would like to thank my collaborators in the ice core community, especially Ken Taylor for his leadership in the WAIS-Divide project. The ice core community is a friendly and collaborative group, and it is partly thanks to him. He has also always cared about involving students in fieldwork, and I am indebted to him for letting me head the science party for two field seasons, in 2008-2009 and 2009-2010. I would like to thank

xvi Eric Steig for his early interest in my work, and his encouragement. I’d like to thank the field participants, core handlers and drillers, without whom we would not have ice of the same quality to work with, as well as the camp support staff from RPSC, which kept us warm and help keep the ice cold. I have shared a lot of fun times and interesting conversations with my fellow WAIS-Divide graduate students, Thomas Bauska, John Fegyveresi, T.J. Fudge, Bess Koffman, Jessica Lundin and Logan Mitchell. Kenji Kawamura is like an older brother to me. I benefited extremely from his experience in the lab, and I would look forwards to each of his visits. Kenji has always been very generous with his time, and has given me precious career advice. Ross Beaudette has provided technical (and musical) assistance every step of the way. I owe him special thanks for helping me, and getting into a sort of symbiotic relationship in 2012 when we were trying to finish the lab portion of my thesis. Ross is a dedicated scientist, and he brings a good atmosphere into the lab. I would also like to thank my fellow lab-mates, Vas Petrenko, Takuro Kobashi, Melissa Headly and Daniel Baggenstos. I would like to thank the SIO grad department, for taking care of mere mortal concerns, to the professors for being a source of inspiration an excitement. I would like to thank the SIO graduate students, Dian, Lauren, Lelia, Jim, Ha Joon, Kyla, Rob, and also Sylvia, Ben, Yvonne, Gordy, San, Aneesh, Mike, Shang, Kaushik, Daniel, and many more, who have made this chapter of my life about a lot more than science. The San Diego Mountain Rescue Team has given me many opportunities to escape the university bubble, and bring out a different side of me. The Dugas family, Dawn Christophe, Herv, Fafa, Katleen, Natalie and Gianna, made me feel at home in this far away land. My roommates, Ida, Celina, Jason, Gordy, Chad, Julie, Mimmi and Audrey, have shared their worlds with me. I’d like to thank Peter for smiling at me everyday. I would like to thank my family, who has always trusted me, and let me go out and explore the world from a young age. I’d like to acknowledge my uncle Jean-Pierre Puthot, who shared so many things about the alpine environment with me on our summer hikes, and who encouraged me to investigate the natural world. I did not get to share my Antarctic stories with him, but he has been present in thoughts throughout my time here.

xvii The support of my colleagues, friends and family has been essential not only to my success, but to my ability to project myself in the future. In this respect, this work is a little bit theirs.

Chapter2, in full, has been submitted for publication in Earth and Planetary Science Letters: Orsi, A. J., B. D. Cornuelle, and J. P. Severinghaus, Magnitude and Temporal Evolution of Interstadial 8 Abrupt Temperature Change Inferred From inert gas isotopes in GISP2 Ice Using a New Least-Squares Inversion, Earth and Planetary Science Letters, in review. The dissertation author was the primary investigator and author of this work. Chapter3, in full, is a reproduction of the material as it appears in Orsi A., B. Cornuelle and J. Severinghaus, Little Ice Age Cold Interval in West Antarctica: Evi- dence from Borehole Temperature at the West Antarctic Ice Sheet (WAIS) Divide, Geo- phys. Res. Let., 2012. The dissertation author was the primary investigator and author of this work. Chapter6 is being prepared for publication in a yet to be determined journal, as: Orsi, A. J., and J. P. Severinghaus, Temperature reconstruction for the last thousand years at the West Antarctic Ice Sheet Divide using inert gas isotopes. The dissertation author was the primary investigator and author of this work. Chapter7 is being prepared for publication in the Journal of Glaciology, as: Orsi, A. J., J. Fegyveresi and J. P. Severinghaus, On bubble free layers in the WAIS Divide ice core. The dissertation author was the primary investigator and author of this work.

xviii VITA

2002-2005 Bachelor of Engineering in Physics, Ecole Polytechnique, France

2005-2013 Graduate Student Researcher Scripps Institution of Oceanography University of California, San Diego

2006 Master of Science in Oceanography, University of California, San Diego

2013 Doctorate of Philosophy in Oceanography, University of Califor- nia, San Diego

PUBLICATIONS

Steig E.J. and Orsi A.J., Climate science: The heat is on in Antarctica, Nature Geo- science 6, 8788 (2013)

NEEM community members, Eemian interglacial reconstructed from a Greenland folded ice core, Nature, 493, 489494 (24 January 2013)

WAIS Divide community members, Deglacial warming on West Antarctica driven by both local orbital and Northern Hemisphere forcing, Nature, submitted

Orsi, A. J., B. D. Cornuelle, and J. P. Severinghaus (2012), Magnitude and Temporal Evolution of Interstadial 8 Abrupt Temperature Change Inferred From inert gas isotopes in GISP2 Ice Using a New Least-Squares Inversion, Earth and Planetary Science Let- ters, in review.

Petrenko V., et al., High-precision 14C measurements demonstrate production of in situ 14 14 cosmogenic CH4 and rapid loss of in situ cosmogenic CO in shallow Greenland ﬁrn, Earth and Planetary Science Letters, in review

Guillevic, M., et al., Spatial gradients of temperature, accumulation and δ18O-ice in Greenland over a series of Dansgaard-Oeschger events,Clim. Past Discuss., 8, 5209- 5261, 2012

Orsi A., B. Cornuelle and J. Severinghaus, Little Ice Age Cold Interval in West Antarc- tica: Evidence from Borehole Temperature at the West Antarctic Ice Sheet (WAIS) Di- vide, Geophys. Res. Let., 2012

Battle M. O., et al, Controls on the movement and composition of ﬁrn air at the West Antarctic Ice Sheet Divide, Atmos. Chem. Phys. Discuss., 11, 18633-18675, 2011

xix Buizert C. et al, Gas transport in ﬁrn: multiple-tracer characterisation and model intercomparison for NEEM, Northern Greenland, Atmos. Chem. Phys. Discuss, 11, 15975- 16021, 2011

FIELDS OF STUDY

Major Field: Oceanography

Studies in Paleoclimate Professors C. Charles and J. Severinghaus

Studies in Climate Sciences Professors P. Flatau, D. Lubin, J. Norris, V. Ramanathan, L. Russell, and R. Somerville

Studies in Data Analysis Professors D. Agnew, M. Buckingham, C. Constable, B. Cornuelle, R. Parker, and D. Rudnick

Studies in Geochemistry Professors D. Lal and R. Keeling

Studies in Glaciology Professors H. Fricker and B. Werner

Studies in Geophysical Fluid Dynamics Professors P. Cessi, R. Salmon and C. Winant

Studies in Physical Oceanography Professors M. C. Hendershott, D. Roemmich, L. D. Talley and U. Send

xx ABSTRACT OF THE DISSERTATION

Temperature reconstruction at the West Antarctic Ice Sheet Divide, for the last millennium, from the combination of borehole temperature and inert gas isotope measurements.

Anais J. Orsi

Doctor of Philosophy in Oceanography

University of California, San Diego, 2013

Jeffrey P. Severinghaus, Chair

The study of past climates informs us on the causes, amplitude and mechanisms of climate change, which is necessary to our ability to predict future changes, and build the necessary infrastructure to ensure the resilience of our society to these changes. Local climate records contain both large scale and local signals, from both external forcing, such as radiative forcing, and internal climate variability. In order to understand the response of the climate system to global drivers, we must average out the local signals into hemispheric or global variables. This process has been difﬁcult because we lack the spatial coverage in large areas of the Earth, including the oceans, and much of the Southern Hemisphere.

xxi The work presented here aims at improving our knowledge of the climate by producing a new temperature time series from the center of West Antarctica for the last 1000 years, a region previously unexplored. This temperature reconstruction is based on a new method, combining borehole temperature measurements with inert gas isotopes from the WAIS-Divide ice cores into a single inverse problem. Borehole temperature measurements constrain the long term changes in the climate, while inert gas isotopes record decadal to centennial scale changes. Together, they produce a temperature estimate that is independent of the traditional proxy δ18O of ice, and provide a way to calibrate it. WAIS-Divide experienced a long term cooling trend from 950 to 1850 A.D., which ended abruptly by warming by 2.3◦C in 30 years. More recently, WAIS-Divide has been warming by more than 1.5◦C since 1957, which refutes the idea that Antarctica would not experience the current warming seen elsewhere. The long term cooling trend was superimposed on centennial scale variations in the climate, including two warming events, notably between 1315 and 1395 A.D., 1596 and 1626 A.D., with a warming rate of 0.24 and 0.32◦C/decade. This evidence shows that the current rate of warming at WAIS-Divide, of 0.23◦C/decade for the last 50 years is rare but not unprecedented. This record is consistent with the idea that the decrease in solar radiation from 1400 to 1800 A.D. induced widespread cooling in mid and high latitudes of both hemispheres.

xxii Chapter 1

Introduction

Temperature is the most fundamental climate variable: for example, the equator to pole temperature gradient is the driving force of the general circulation of the atmosphere. Our understanding of the climate drivers depends on good temperature maps, and polar regions are especially important. Because both the Arctic and the Antarctic are hostile environments, there are very few direct temperature observations before the International Geophysical Year of 1957, which leads us to rely on paleoclimate proxies to estimate past temperature changes. Dansgaard[1954] found that the isotopic composition of precipitation is related to local temperature. This important discovery lead to the ﬁrst paleo-temperature reconstruction from an ice core, drilled at Camp Century in Greenland in 1966 [Dansgaard et al., 1969]. One strange feature of the glacial climate was a series of very sharp oscillations between cold and warm episodes. It took the extraction of four ice cores in Greenland to convince the community that these“abrupt climate changes” were indeed a real climate signal [Johnsen et al., 1992]. During these events, the temperature at the Summit of Greenland increased by more than 10◦C in less than 30 years. The analysis of one such event, 38 thousand years ago is presented in Chapter2. In Antarctica, their signature is very different: As Greenland warms abruptly, Antarctica starts cooling, and when Greenland cools back down, Antarctica warms again (see Chapter2). It is the study of both polar regions together that showed that these events must be related to abrupt shifts in the oceanic meridional overturning circulation [Blunier and Brook, 2001; Stocker and Johnsen, 2003].

1 2

Homo Sapiens have been present on Earth for two hundred thousand years, but the first traces of civilization (agriculture, buildings) only date back 10 thousand years, to the start of the Holocene, our current interglacial warm period. Although less spec- tacular than during the glacial period, there is evidence for abrupt climate changes during the Holocene [e.g. Kobashi et al., 2007]. The shifts in the climate, and especially prolonged droughts, have tested the resilience of early human civilizations [e.g. Zhang et al., 2005; Hodel et al., 1995]. As we are currently going through an important shift in our climate, it is interesting to investigate past climate changes of similar magnitude, and their impact on the biosphere. The most recent significant shift in the climate dates back to the 1800s. There is ample evidence of a cool period from 1400 to 1800 A.D. in the Northern mid and high latitudes, often referred to as the “Little Ice Age” (hereafter LIA) [Grove, 2004; Wanner et al., 2011]. Although a reduction in solar input [Mann et al., 2009a] and persistent volcanism [Miller et al., 2012] are coincident with this cold period, it is unclear how such a weak forcing would have caused the observed changes. The Southern Hemisphere is significantly under sampled, and the comparison of temperature trends between both hemispheres would help identify the cause and extent of the LIA. In particular, the reduction in solar forcing suggests that we should expect hemispheric synchroneity, whereas evidence of a southward shift of the Pacific Inter-tropical Convergence Zone, or deep ocean circulation changes would suggest a delayed or inverse response [Sachs et al., 2009; Keigwin and Boyle, 2000; Goosse et al., 2004; Broecker, 2000]. The purpose of this thesis is to make a robust reconstruction of surface temperature in West Antarctica for the last 1000 years, with decadal resolution . We achieved this by measuring inert gas isotopes (δ15N, δ40Ar and δ86Kr) in firn air and ice from the WAIS-Divide ice cores, and combined those measurements with borehole temperature from the same site to produce a precise surface temperature reconstruction. Borehole temperature measurements record long term temperature averages, while inert gas isotopes fractionate in response to decadal to centenial scale temperature variations. The combination of both types of complementary information into a single inverse problem allows us to improve the accuracy of temperature reconstruction from polar regions. Chapter2 details a new approach for reconstructing the surface temperature his- 3 tory from δ15N and δ40Ar, using the example of Dasgaard-Oeschger event 8, 38 thousand years ago, observed in the Greenland GISP-2 ice core. This method allows us to reconstruct the temporal variations of abrupt temperature changes, and clearly estimate the uncertainty in the reconstruction. The inverse method used in this chapter will be used in all of the other chapters. In Chapter3, we present the first unequivocal evidence of a cold period in West Antarctica during the Little Ice Age, based on the analysis of borehole temperature at WAIS-Divide (79◦S, 112◦W). Chapter4 is dedicated to the detailed description of laboratory methods used in the thesis. Chapter5 focuses on the warming trend of the last few decades. It combines borehole temperature measurements with firn air measurements of inert gas isotopes to evaluate the warming rate at WAIS-Divide. This reconstruction is compared to published estimates of the temperature trend over the last 50 years. Chapter6 is dedicated to the dual inversion of inert gas isotopes and borehole temperature to produce a temperature history at WAIS-Divide. It provides an estimate of the amplitude of multi-decadal temperature variability in West Antarctica, and provides a context for the observed warming trend. The study of inert gas isotopes at high precision also gives insights into the mechanisms of gas trapping in ice cores, which are relevant for the reconstruction of atmospheric composition from ice core data. Chapter7 describes the character of bubble-free layers in the WAIS Divide ice cores. It shows that these layers are not caused by melt, and that the presence of bubble- free layers does not affect the gas record. Instead, we hypothesize that they are created by water vapor transport at time of surface temperature inversion, and may be used in the future as a a proxy for such inversions. Chapter 2

Magnitude and Temporal Evolution of DO 8 Abrupt Temperature Change Inferred From Nitrogen and Argon Isotopes in Greenland Ice Using a New Least-Squares Inversion

Abstract

Isotopes of inert gases in air bubbles trapped in ice cores have proved to be useful indicators of past temperature changes. These isotopes fractionate as a result of gravity and temperature gradients in the firn. As a result, noble gas isotopes provide a method for estimating temperature that is completely independent from the traditional δ18O of ice. However, most prior studies have made assumptions about the shape of the temperature history. Here, we present a new numerical technique for inverting the noble gas isotopic signal, and employ it on a new data set from GISP2, Greenland, during Intersta- dial 8, 38.2 thousand years ago. Based on generalized least-squares, our inversion does not require specific assumptions regarding the shape of abrupt temperature changes. We find that Interstadial 8 at GISP2 had an abrupt warming of 10.63±0.64◦C, as-

4 5 sociated with a probable doubling to tripling of the accumulation rate. This warming was associated with an increase in δ18O of 3.99±0.9 , which corresponds to a temperature sensitivity α of 0.38 ± 0.1 /◦C, which is slightlyh larger than the glacial/interglacial value of 0.328 /◦C. h h 2.1 Introduction

2.1.1 Reconstructing polar surface temperature

Temperature is the most fundamental climate variable: as just one example, the equator to pole temperature gradient is the driving force of the general circulation of the atmosphere. When exploring past climates, an accurate temperature history is key to our understanding of atmospheric circulation and the mechanism of climate change, with relevance to predicting future climate. The most precise polar paleo-temperature estimates come from ice cores [Dahl- Jensen and Johnsen, 1986; Johnsen et al., 1995; Cuffey and Clow, 1997]. Past surface temperature at the ice core site is commonly inferred from measured water stable isotopes in the ice. The isotopes of oxygen and hydrogen in precipitation fractionate in a complex fashion, in response to the source temperature, the atmospheric pathway, and the condensation temperature at the ice core site [Dansgaard, 1954]. In polar regions, the condensation temperature is the dominant source of interannual variability in δ18O 18 of snow, and, with proper calibration, δ Oice can be used to reconstruct the atmospheric 18 temperature [Dansgaard, 1964]. The current spatial variability in δ Oice is well correlated with the surface temperature, but this “spatial” calibration is not consistent with 18 18 temporal variations δ Oice and temperature. As a result, δ Oice is generally calibrated using an independent measure of temperature, usually a borehole temperature record [e.g. Cuffey and Clow, 1997]. Borehole temperature proﬁles provide an absolute estimate of long term surface temperature changes. This method relies on the fact that the diffusion of heat through the ice is slow, and deep ice still retains information about the temperature at the time when it was at the surface. Short timescale changes are not resolved by this method, however, because the diffusion process destroys information. 6

18 Although δ Oice can be a faithful temperature proxy in times of relatively stable climate, it is challenging to calibrate it at times of large reorganization of the climate system, such as abrupt climate changes, because non-temperature effects on the isotopic fractionation become important. As a result, different values of dδ18O/dT have been used for different climate states. At GISP2 (Greenland Summit) for instance, the Holocene dδ18O/dT is 0.465 /◦C, and the glacial-to-interglacial value is 0.328 /◦C 18 [Cuffey and Clow, 1997]. Boreholeh temperature cannot be used to calibrate δ Ohice beyond the last glacial period, and there is mounting evidence that the glacial dδ18O/dT is not appropriate for abrupt climate changes such as Dansgaard-Oeschger events [Huber et al., 2006]. Here, we used isotopes of inert gases in ice cores to reconstruct temperature 18 changes independently of δ Oice. We present a new inverse method that produces a temperature history directly from gas isotope data, which allows us to ﬁnd an accurate 18 calibration of δ Oice during abrupt climate changes. This new method presents an important advance in the quantiﬁcation of past temperature changes in polar regions. It will provide a more accurate boundary condition for general circulation models, which will ultimately improve our understanding of potential tipping points in the climate system.

2.1.2 Abrupt climate changes

The last glacial cycle was characterized by a sequence of abrupt climate changes known as Dansgaard-Oeschger (DO) events, which occur approximately roughly every 1500 years. They were ﬁrst noticed in water isotope records from Greenland ice cores, as an abrupt warming of 8 to 16◦C in just a few decades, followed by a gradual cooling, and 1000 years later, a rapid cooling back to the cold conditions [Dansgaard et al., 1984, 1993; Alley et al., 1993; Taylor et al., 1993]. The cold episodes are called stadials, and the warmer episodes interstadials. The term “DO event” refers to the abrupt warming between a stadial and an interstadial. They are numbered from the most recent event to the oldest event (Figure 2.1). The ice core and paleoclimate record shows that the abrupt warming in Green- land was associated with large scale circulation changes [Voelker and workshop participants, 2002]: wetter conditions in the mid latitudes of Asia, a greening of the Mediter- 7

90 80 70 60 50 40 30 20 10 −34 Greenland21 19 17 15 13 11 9 7 5 3 1 −36 20 18 16 14 12 10 8 6 4 2

−34 −38

O, per mil −36 18

δ −40

−38 −42 O, per mil 18 δ −40 800 Antarctica 700 −42

600

500 Methane, ppb 400 Methane

90 80 70 60 50 40 30 20 10 time, thousand years BP

Figure 2.1: Overview of polar climate history of the last glacial period, showing measured δ18O in the GISP2 ice core (Greenland; blue), and in the Byrd ice core (Antarc- tica; red), and a composite atmospheric methane history (green) [Blunier and Brook, 2001]. The grey shading highlight the DO events, which are numbered. δ18O is a proxy generally representing temperature. When Greenland experiences an abrupt warming, Antarctica starts a cooling trend. The abrupt warming in Greenland is associated with a sharp increase in methane. 8 ranean, and a strengthening of the Asian monsoon system [Wang et al., 2001]. In Antarc- tica, the temperature history is very different: the abrupt Greenland warming coincides with the start of a cooling trend in Antarctica, and the rapid Greenland cooling with a warming trend in Antarctica [Blunier and Brook, 2001]. This observation led to the “bipolar see-saw” theory to explain these cycles: The oceanic meridional overturning circulation (MOC) transports heat from the Southern Hemisphere to the Northern Hemi- sphere in the Antlantic Ocean. During the stadials, the MOC is weak, and Greenland is cold, while Antarctica warms. During an interstadial, the MOC becomes stronger, warming Greenland, but cooling Antarctica [Stocker and Johnsen, 2003]. An abrupt slowdown of the MOC can be triggered by a large discharge of freshwater in the North Atlantic, however, there is still not a clear mechanism to explain how changes in the MOC could cause an abrupt warming at the start of a DO event, nor is there an identi- ﬁed external trigger of these events [Cane and Clement, 1999]. This paper focuses on Interstadial 8, one of the longest lived interstadials. It happened at a time of nearly invariant orbital forcing, which helps to clarify the role of unforced internal variability in these events. We present here a temperature reconstruction of the abrupt warming, 38.2 thousand years ago, at the Summit of Greenland (GISP2, 72◦34’ N, 28◦37’ W, 3216 m a.s.l.), from isotopic measurements of nitrogen and argon in the GISP2 ice core. This proxy provides a quantitative estimation of the amplitude and shape of the abrupt temperature change, and thus allows us to ﬁnd an 18 accurate calibration of δ Oice.

2.1.3 Noble gas isotopes

Isotopes of inert gases in air bubbles trapped in ice cores have proved to be useful indicators of past temperature change in polar regions [Severinghaus et al., 1998; Landais et al., 2004a]. The top of ice sheets is covered with a layer of firn ( >1 year old snow) that gradually becomes denser until it turns into solid ice. Firn is a porous medium where air can move mostly by molecular diffusion. Eventually, the pores close off, the air is trapped in bubbles in the ice, and its composition stops evolving [Schwander et al., 1993]. Ice cores provide a record of the atmospheric composition through the filtering of the firn: the gas composition in the ice core differs from the atmospheric composition 9 essentially because of fractionation by molecular diffusion in the diffusive zone. The two main causes of fractionation are gravitational settling, by which heavier elements are enriched with depth, and thermal fractionation due to temperature difference between the surface and the close off depth. The isotopic composition of atmospheric N2 and Ar does not change significantly for millions of years [Mariotti, 1983]. Therefore, any change in δ15N and δ40Ar in the ice cores is due to firn processes, namely thermal or gravitational fractionation. We can use a heat diffusion model to reconstruct the surface temperature history from isotopic fractionation of nitrogen and argon in the ice core. This method provides an estimate of surface temperature which is completely independent from the traditional δ18O of ice. In addition, this model can also be used to correct the gases that do change in the atmosphere for the fractionation happening in the firn [Buizert et al., 2012], and reconstruct the true atmospheric composition history from ice core measurements.

2.1.4 Temperature reconstruction

Most prior temperature reconstructions using inert gases assumed an idealized shape of the temperature history, often a step function, or relied on a scaling of δ18O. Here, we present a new technique for inverting the noble gas isotopic signal from GISP- 2 during Interstadial 8, 38.2 thousand years ago. Based on generalized least-squares, our inversion does not require speciﬁc assumptions regarding the shape of abrupt temperature changes. It allows us to create a completely independent temperature history at 18 the site. This history can then be used to calibrate δ Oice on timescales not resolved by borehole temperature.

2.2 Methods

2.2.1 Laboratory measurements

The samples are taken from the GISP2 ice core, near the summit of Greenland (72.6◦N, 38.5◦W), covering 24 discrete depths, between 2236.15 m and 2249.85 m, which corresponds to 37.91 to 38.42 k.a. BP (before 1950 C.E.). Two to 6 samples 10

were run at each depth for N2 (10 g samples) and Ar (50 g samples) isotopes. Ni- trogen isotopes were analyzed following the melt/refreeze procedure of Sowers et al. ◦ [1989]. Argon samples were exposed to a Zr/Al SAES getter at 900 C to remove N2,

O2 and other reactive gases, according to Severinghaus et al.[2003]. All samples were run on a MAT 252 mass spectrometer at Scripps Institution of Oceanography. A total of 66 discrete δ15N measurements were made in January and February 2000, with a pooled standard deviation of 7.7 per meg. A second set of 30 samples was measured in November 2001, but these samples were systematically lower in δ15N, possibly due to a calibration error or storage problem, and were rejected. Argon isotopes were measured in April and May 2001 in duplicates, and the pooled standard deviation of 48 δ40Ar samples is 13 per meg.

2.2.2 Timescale

The official timescale of the GISP2 ice core is from Meese et al.[1997]. Since then, a large effort has been made to improve on all Greenland deep ice core timescales, and provide a new layer-counted timescale, called GICC05 [Rasmussen et al., 2006; Andersen et al., 2006; Svensson et al., 2008], which can be tied to the GISP2 ice core (I. Seierstad, in prep). To maximize the compatibility with other records, we used the GICC05 age scale for the ice age, and used the Goujon firn densification model [Goujon et al., 2003] to estimate the gas-age ice-age difference, ∆age. The GICC05 tie points were interpolated using the Meese et al.[1997] annual layer thickness: the spacing of layers in between tie points was preserved, but the time they represent was adjusted by a scaling factor, in order to have the right number of years in between tie points. This method has the advantage of retaining some of the detailed information present in the original layer counted timescale, in contrast to a simple interpolation with respect to depth (Figure 2.2). Gases trapped in an ice core do not have the same age as the ice that is surrounding them. Atmospheric gases can move readily through the firn and only get locked into the ice at a depth of 70 to 100 m, where the ice is already several hundred years old. The lock-in depth depends on the details of densification of the firn, and changes when the temperature and accumulation rate change [Goujon et al., 2003]. An increase in tem- 11

Time, ka BP 46 44 42 40 38 36 34 0.04 Meese et al. (1997) 0.035 layer interpolation depth interpolation 0.03 tie points

0.025

0.02 Layer thickness, m 0.015

0.01 2350 2300 2250 2200 2150 Depth, m

Figure 2.2: Layer thickness for the Meese et al.[1997] timescale (green), GICC05 linearly interpolated in between tie points (blue), and GICC05, linearly interpolated while respecting the layer thickness distribution of Meese et al.[1997] in between tie points (red). The time is given in thousand years before the year 1950 C.E. The Meese et al.[1997] timescale is not accurate in this depth range, therefore we used the layer interpolated GICC05 timescale in this study (red curve). 12 perature will cause the ﬁrn to densify faster, and decrease the lock-in-depth, and consequently decrease ∆age. During a sharp transition, such as the abrupt climate change we are studying in this paper, ∆age is a parameter that needs to be modeled. At the beginning of the transition, the ∆age is 985 years, and it decreases during the warming event, to about 600 years. In order to maximize the internal consistency of our assumptions, ∆age is estimated separately by the Goujon model for each scenario of temperature and accumulation history [Goujon et al., 2003]. In other words, the age of the gases is a parameter that is estimated by the model, along with δ15N and δ40Ar. The observed depth of the abrupt transition into Interstadial 8 itself constitutes a useful tie-point for timescales. We found that the Meese et al.[1997] ice timescale was offset by 206 years from GICC05 at the transition. GICC05 places the date of DO-8 at 38.17±0.72 k.a. BP [Andersen et al., 2006]. This timing is consistent with radio-isotope dates from the Sofular speleothem record [38.14±0.1 k.a. BP; Fleitmann et al., 2009].

2.2.3 Isolation of the thermal signal

In the ﬁrn, isotopes are separated by two processes: gravitational fractionation and thermal fractionation. Thus we need to isolate the thermal signal in the isotopic measurements in order to reconstruct the temperature history, by correcting for gravitational fractionation. Gravitational fractionation is proportional to the depth of the diffusive ﬁrn column Z and to the mass difference between the isotopes in a pair ∆m.

∆mg δ15N = Z (2.1) g RT 15 15 δ Ng refers to the gravitational component of the measured δ N, g is the gravitational constant (9.82 m s−2), R the gas constant (8.314 J K−1 mol−1), and T the mean ﬁrn temperature in K. Thermal fractionation is proportional to the temperature difference between the top and the bottom of the diffusive column ∆T :

15 15 δ NT = Ω ∆T + (2.2) 13

15 15 δ NT refers to the thermal component of the measured δ N, and is a disequilibrium term, which can safely be neglected on timescales longer than a few decades. The thermal diffusion sensitivity Ω15 is determined precisely by laboratory measurements [Grachev and Severinghaus, 2003b]. Argon isotopes are also affected by gas loss fractionation, and the gas loss correction is detailed in Section 2.2.3.1. The thermal signal can then be isolated, either by using two pairs of isotopes (Section 2.2.3.2) or by using a ﬁrn densiﬁcation model to estimate the gravitational component (Section 2.2.3.3). Each method has its advantages and drawbacks, so we compared results obtained by both approaches.

2.2.3.1 Gas loss correction

Argon is a small atom that can leak out of air bubbles during storage [Sever- inghaus et al., 2003]. We corrected for the fractionation induced by gas loss using δ84Kr/36Ar. Gas loss mostly affects atoms and molecules with a diameter less than

3.6 A˚ [Severinghaus and Battle, 2006], and does not signiﬁcantly fractionate N2 (3.9 A˚ ) or krypton (3.66 A˚ ). We deﬁne k as the amount of gas loss, and γ as the ratio of gas loss fractionation between δ40/36Ar and δ84Kr/36Ar. The isotopic fractionation of gases can be written as follows [Grachev, 2004]:

 g  15 δ Nmeas = 1 Z + Ω15∆T  RT  g δ40Ar = 4 Z + Ω ∆T + γk (2.3) meas RT 40   g δKr/Ar = 48 Z + Ω ∆T + k  meas RT Kr

We can estimate the gas loss ratio γ during the constant climate of the stadial, where we suppose that ∆T = 0. In that case: 14

 g  15 δ Nstadial = 1 Z  RT  g δ40Ar = 4 Z + γk (2.4) stadial RT   g δKr/Ar = 48 Z + k  stadial RT

40 15 δ Arstadial − 4δ Nstadial γ = 15 (2.5) δKr/Arstadial − 48δ Nstadial We found a value of γ = 0.0062 ± 0.0001 / , which is in very good agreement with Severinghaus et al.[2003]. h h We can now solve the system of three equations (2.3), with three unknowns Z, ∆T , and k, and ﬁnd the gas loss corrected value of δ40Ar.

g δ40Ar ≡ δ40Ar − γk = 4 Z + Ω ∆T (2.6) glc meas RT 40 The gas loss fractionation occurs during the storage of the ice, and we do not expect it to have any correlation with the climate signal. Indeed, the gas loss correction to δ40Ar has a mean of 42 per meg, and a standard deviation of 7.8 per meg (Figure 2.3). We re-calculated the pooled standard deviation of replicates samples corrected for gas loss, and found that it dropped from 13 to 10.5 per meg.

2.2.3.2 Using two pairs of isotopes

Once the argon isotopes have been corrected for gas loss, we can separate out 15 the thermal and gravitational fractionation by deﬁning δ Nxs, which only depends on 15 temperature, and δ Ng which isolates the gravitational component:

 40 15 15 δ Arglc Ω40 δ Nxs = δ Nmeas − 4 = (Ω15 − )∆T  4 g (2.7) δ15N = Z = δ15N − Ω15 δ15N  g RT meas Ω xs  Ω − 40 15 4 15

Time, k.a.B.P. 38.73 38.26 38.02 37.88 Stadial δ15N N

15 0.5

δ 40 2.2 per mil δ Ar meas 2 0.4 40 δ Ar Ar, per mil glc 1.8 40

32 δ Ar 1.6

36 30 δKr/Ar Kr/ 28 per mil 84 δ 26 δ40Ar gas loss 0.05 0.04 k, per mil γ

0.03 Ar gas loss, 2250 2245 2240 2235 Depth, m

Figure 2.3: Gas Isotope Data: δ15N (blue), δ40Ar (red), and δKr/Ar (brown) data are shown, with their respective pooled standard deviations as error bars. The gas loss 40 40 component of δ Ar is shown in green, and the corrected δ Arglc is shown in magenta. The gas loss correction is nearly uniform along the whole data set, and does not produce any bias in the reconstruction of the temperature history. 16

15 The temperature history can be reconstructed by integrating δ Nxs. This method is advantageous because it is clearly independent of changes in accumulation, and it does not rely on an imperfect ﬁrn densiﬁcation model [Severinghaus and Brook, 1999]. However, the precision of the measurements can limit its application. Results from this method are discussed in Sections 2.3.1 and 2.3.2.

2.2.3.3 Using a densiﬁcation model

Alternatively, we can use a densification model to estimate Z. Densification is mainly controlled by temperature (a warmer firn densifies faster, yielding a smaller Z) and snow accumulation (the more accumulation, the thicker the firn). We used a coupled densification and heat transport model [Goujon et al., 2003] to determine the evolution of both the firn thickness Z , and the temperature difference between the top and the bottom of the diffusive column ∆T . The inputs of the Goujon model are the histories of temperature and accumulation, and a depth-age relationship for the ice core. The snow accumulation history can be estimated using observed annual layer thickness, coupled with a glaciological flow model to correct for layer thinning [Cuffey and Clow, 1997]. It is not known very well at the depth we are considering here, because of uncertainties in the size of the ice sheet at the time [Cuffey and Clow, 1997], and uncertainties in the layer-counted timescale [Svensson et al., 2006]. We used three different scenarios of abrupt changes in the accumulation, and used an inverse model to reconstruct the temperature history from the data. Results are discussed in Section 2.3.3.1.

2.2.4 Forward densiﬁcation and heat diffusion model

The Goujon model takes the history of temperature and accumulation as inputs, and outputs the δ15N and δ40Ar proﬁles, that we may compare to ice core data. In an abrupt climate change, both temperature and accumulation increase rapidly [Dansgaard et al., 1993]. Figure 2.4 shows the response of the forward model to a step increase in accumulation, from 5.45 to 13.6 cm/y in water equivalent, with an associated step increase in temperature. 17

no T change data δ T= 1°C 0.55 δ T= 2°C δ T= 5°C δ T= 8°C δ T= 10°C

N, per mil 0.5 δ T= 12°C 15 δ

0.45

−200 −100 0 100 200 300 400 Time after the change, years

Figure 2.4: Output of the Goujon model, with a step in accumulation from 5.45 to 13.6 cm/y (black), and an additional simultaneous step in temperature of 1, 2, 5, 8, 10 and 12◦C. The increase in accumulation deepens the firn column (black), whereas the increase in temperature first increases δ15N because of thermal fractionation, and then decreases δ15N because a warmer firn densifies faster, decreasing the lock-in depth. 18

2.2.4.1 Improvement of the Goujon model

The Goujon et al.[2003] firn densification model computes gas fractionation based on the depth and temperature gradients at the lock in zone (Equations (2.1) and (2.2)), and it does not take into account gas diffusion in the firn. Gas diffusion causes a broadening of the age distribution of the gases, and hence a smoothing of the gas isotope record [Schwander et al., 1993]. If we were to neglect this effect, it would lead us to under-estimate the magnitude of fast changes needed to fit the δ15N data. It is too time consuming to run a full gas diffusion model, but we can model gas diffusion by smoothing the raw δ15N data by a log-normal distribution (Equation 2.8)[Kohler¨ et al., 2010, 2011], where p is the probability density, t the time, and µ the mean of the distribution.

1 t − µ2 p(t) = √ exp − 0.5ln (2.8) (t − µ) 2π µ We matched the width of the log-normal probability density function to the width of the age distribution at the lock-in depth, obtained by running a gas diffusion model [Severinghaus et al., 2010; Buizert et al., 2012], which corresponds to µ = 7 years.

2.2.4.2 Linearization of the forward model

The functional space of temperature history can be expressed as a reference guess T0 plus a linear combination of basis functions bi(t):

X T (t) = T0(t) + xibi(t) (2.9) i

where T (t) is a history of temperature, t is the time, and xi the coefﬁcients of this linear combination. After discretization, in vectorial notation, Equation 2.9 becomes:

T = T0 + Bx with B = [b1 b2 ... bn] (2.10)

Discretized equations use bold lower case letters to designate vectors, and bold upper case letters to designate matrices, with the exception of T, which represents the vector of temperature with time. 19

Each basis bi(t) was added to T0(t) and run through the forward model to pro- 15 40 duce δ N and δ Ar values, yi(z). We deﬁne hi(z) = yi(z) − y0(z), with y0 the output 15 using our initial guess T0(t). If the model is approximately linear, any δ N proﬁle y(z) can be expressed as y0 plus a linear combination of the vectors hi(z), and a residual r:

y = y0 + H x + r with H = [h1 h2 ... hn] (2.11)

The matrix H is the linearized and discretized version of the forward model, expressed in the space described by B. It effectively depends on T, or x. For the first iteration, H = H(x0) with x0 = 0. We want to find a history of temperature T (t) that would fit our data d(z). This is equivalent to finding x so that

d − y0 = H x + r (2.12) with r and x as small as possible, and consistent with their uncertainties.

2.2.4.3 Linearity of the model

The heat advection-diffusion equation is not simply linear, because many parameters, including diffusivity, depend on temperature. We tested the linearity of the Goujon model, by looking at the size of the non- linear residual r. Equation 2.11 can be expanded to :

1 T ∂H 3 y = y0 + H(x0) δx + δx δx + O(|δx| ) (2.13) 2 ∂x x0

Where δx = x − x0 is a small perturbation, ∂H/∂x is the Jacobian matrix, and O(|δx|3) represents the higher order terms.

The non-linear residual, rnl(δx) = y(x0 + δx) − y(x0) − H(x0) δx , can be estimated by looking at the difference between opposite perturbations δx and −δx: Figure 2.5A shows an example of such a perturbation, when we choose for δx a step function of 8◦C. The mismatch between the two curves reﬂects the non- linearities. Figure 2.5B shows the magnitude of non-linear perturbation, (rnl(δx) + rnl(−δx))/(y(x0 + δx) − y(x0 − δx)), as a function of the amplitude of the perturbation δx. As expected, the non-linearities increase as the perturbation gets larger, but 20 they are weak enough in the range of temperatures we are considering to allow us to use a linearized model to reconstruct the temperature history (Figure 2.5B). Indeed, after the ﬁrst iteration, δx will be on the order of 1◦C or less, where the model is very linear, which will allow a rapid convergence towards the optimum solution.

2.2.4.4 Choice of the basis functions

The functional space of temperature history has inﬁnite dimension, and we need to truncate it for practical purposes. The size of the space that we consider will affect both the solution and the uncertainty estimation. We need enough functions to represent the space of temperature history completely, so that the solution will not be affected by the number of functions used. We also include basis functions that may not be needed: they do not affect the best solution found, but will allow us to estimate uncertainties accurately. If we had very few basis functions, the solution would wrongly appear well- determined. We used two different decompositions of the functional space of temperature history: Fourier components and piecewise linear functions. These two sets of basis functions represent two extremes in the representation of the functional space of temperature history: smooth and non-local, or non-smooth and local. The inversion was run on a time window of 2000 years, and the mean sampling rate was 27 years. To avoid enforcing periodicity, the Fourier components were evenly- spaced harmonics of a 4000 year fundamental period, extending up to 20 year period. The piece-wise linear components had a spacing of 20 years. Both sets of basis functions were normalized so each element had a maximum amplitude of 1◦C. Periods shorter than 20 years will not be included in the uncertainty estimate, or, in other words, the uncertainty estimation presented here is valid for 20-year average temperature. We have shown in this section that the Goujon model is weakly nonlinear for the range of perturbations we are considering here. As a result, we can use iterated linear inversions to solve Equation 2.12 and reconstruct the temperature history from gas isotope data. 21

A δ 0.1 T= 8°C −(δ T= −8°C)

0.05 N, per mil 15 δ

0 0 50 100 150 200 Time after the step in T, years

0.25 B 25 y 0.2 50 y 100 y 0.15

0.1

0.05

as a fraction of total perturbation 0 Amplitude of the non linear signal, 0 2 4 6 8 10 Amplitude of the perturbation, °C

Figure 2.5: Top: Output of the Goujon model for a step change in temperature of 8◦C, ◦ and -8 C. The perturbation (y(x0 + δx) − y(x0)) is plotted in blue, and the opposite perturbation (y(x0)−y(x0 − δx)) plotted in red. The mismatch between the two curves is due to non-linearities. Bottom: Estimation of the magnitude of the non-linear component of the model, shown as (rnl(δx)+rnl(−δx))/(y(x0 +δx)−y(x0 −δx)), calculated at 25, 50 and 100 years. Non linearities increase with the amplitude of the perturbation, but remain below 10% of the linear change, which allows us to iterate with a linearized model. 22

2.2.5 Inverse model

Diffusion smears out the details of the temperature history, which causes the problem to be under-determined: there are many possible temperature histories that would match the data perfectly. The most straightforward way to limit the number of unknowns is to assume a special shape for the temperature history, which depends on just one or two parameters, and ﬁnd these parameters by trial and error. Severinghaus and Brook[1999] used a step function to calculate the temperature change of the Younger Dryas, and Landais et al. [2004a] scaled the δ18O history. An alternative method [Kobashi et al., 2008a] relies on the fact that the thermal fractionation is proportional to the temperature difference between the lock in depth and the surface ∆T (Equation 2.2). At each time step, the surface temperature Ts can be adjusted to match this temperature gradient : Ts = Tbottom + ∆T . However, a shortcoming of this integrating method is that the error is cumulative: a small bias in the data can create a spurious trend in the temperature history, and a bad data point may create an offset for all earlier times. Here, we followed a different approach: instead of modeling the shape of the temperature history with a small number of parameters, we allow a large amount of freedom and handle the large number of unknowns by a least square inversion performed on the linearized forward model. This method allows us to reconstruct the evolution of temperature and not just the magnitude of the change. In addition, we are able to identify the undetermined dimensions of the problem, and understand the true uncertainty in the reconstruction. The solution is also independent of δ18O, and provides a good basis for comparison.

2.2.5.1 Least-squares inversion

We solved Equation 2.12 by least-squares optimization, minimizing the quadratic cost function

1 1 J = rT R−1r + xT P−1x (2.14) 2 2 23

where P is the inverse of the penalty weighting for model structure, which provides regularization, and R is the inverse of the penalty weighting for model-data misfit (residuals) r. In a Bayesian framework assuming Gaussian statistics, J is the negative of the log of the a-posteriori likelihood function, where P is the a priori covariance of uncertainty in the model parameters x, and R the covariance of uncertainty in the residuals r. P allows us to control the smoothness of the temperature history. For the Fourier series, the Fourier components were assumed to be uncorrelated and were given an assumed prior variance proportional to the square of their period. For the piece-wise linear functions, a cross-correlation was added. Its decorrelation scale was set to 300 years before the abrupt warming, 40 years during the abrupt warming, and 100 years after the warming. Both were scaled so that the a priori root mean square error was set ◦ to σx = 5 C. R represents not only the error in the data, but also the fact that the model may not be a perfect representation of reality, and may not be expected to fit the data perfectly. We assumed the uncertainty in the residuals to be uncorrelated in time, with time-independent variance and used a signal to noise ratio of 500, to set the noise level as a function of the signal. The least-squares inversion is not sensitive to the magnitude of P or R, but to the ratio between them, so it is useful to define R in terms of signal to noise ratio. The actual magnitude of P is important for the posterior uncertainty estimation (Section 2.2.5.2). The least-squares theory shows that the optimum solution to Equation 2.12 is [Wunsch, 1996, Chapter 3]:

T T −1 x1 = PH1 (H1PH1 + R) (d − yo) (2.15)

The same linearization exercise can be performed around T1 = T0 + B x1, with the output proﬁle y1, creating a matrix H2. Subsequent solutions take the form [El Akkraoui et al., 2008]:

n n−1 X T T −1 X xj = PHn (HnPHn + R) (d − yn−1 + Hn xj) (2.16) j=1 j=1 24

n−1 P The additional term Hn xj is there to keep a consistent constraint on T0(t). j=1 Without it, subsequent iterations could drift away from T0(t). The history of temperature is recovered using Equation 2.10.

2.2.5.2 Uncertainty estimation

The least-squares optimization provides an estimate of the covariance Pˆ of the uncertainty in the estimated model parameters :

ˆ T T −1 P = P − PHn (HnPHn + R) HnP (2.17)

The eigenvectors of Pˆ with the largest eigenvalues represent the dimensions least constrained by the data, which allows us to explore the statistics of the reconstruction. The 1-σ error on the reconstruction is given by the square root of the diagonal elements of S = BPBˆ T, but this metric neglects the covariance between the temperature at a certain time, and the temperature a few years before or after. An ensemble of solutions to Equation 2.12 can be created using the eigenvalue T th decomposition of Pˆ = UDU . The j trial solution xj takes the form:

√ xj = x + U D mj (2.18)

with mj a vector of Gaussian, independent and identically distributed random numbers with zero mean and unit variance, x the optimum least-squares solution, and √ D the element by element square root of the diagonal matrix D. For each scenario, we created a set of 100 solutions to the least-squares problem using Equation 2.18. These solutions allow us to explore the range of possibilities allowed by both the uncertainty in the data, and the unconstrained dimension of each scenario. We used these series of solutions to compute the uncertainty in the temperature change (Section 2.4.2). 25

2.2.5.3 Inﬂuence of the parameters used in the inversion

We performed the inversion independently with each set of basis functions (Fig- ure 2.6), using a prior P described in Section 2.2.5.1. The decorrelation scale is uniform in time for the Fourier series, and it decreases at the time of the abrupt changes for the piecewise linear functions. As a result, the “Fourier” output is somewhat smoother during the abrupt temperature jump, and fits the data less closely. Aside from the steepest increase, both solutions are very similar, and in particular, they produce the same overall amplitude for the event. We also performed the inversion with piecewise linear functions at a 10-year resolution (red curve in Figure 2.6), and found a temperature reconstruction very similar to that at 20-year resolution, with a small difference at 2237m where the 10-year resolution curve fits the data more closely. All three temperature reconstruction fit within the 1-σ error computed in Section 2.2.5.2. Overall, the temperature reconstruction is only weakly sensitive to the set of basis functions used, or to a reasonable choice of the prior P. For computational reasons, we present here results with piecewise linear functions at a 20-year resolution.

2.3 Results

The magnitude of the abrupt warming was determined by three methods with increasing complexity. Section 2.3.1 gives a direct estimate of the temperature change, 15 using δ Nxs. The second method (Section 2.3.2) also relies on both pairs of isotopes to separate gravitational and thermal fractionation, but uses a temperature diffusion model to determine the magnitude and temporal evolution of the event. These methods do not 15 need to rely on a complex model, but the error in δ Nxs is larger than the error in the δ15N and δ40Ar measurements, which limits the precision of the temperature reconstruction. Finally, Section 2.3.3 uses a densiﬁcation model to estimate the gravitational fractionation. 26

Sensitivity to the set of basis functions −35 Fourier series Piecewise linear, 20−y −40 Piecewise linear, 10−y error bar

−45 Temperature, °C −50

38.6 38.4 38.2 38 37.8 Time, ka BP

Data 0.55

0.5 N, per mil 15

δ 0.45

0.4 2250 2245 2240 2235 Depth, m

Figure 2.6: TOP: Surface temperature reconstruction, with different sets of basis functions used in the linearized inversion. Fourier series (in green) are smooth and non-local, and piecewise linear functions with 20 year (blue), and 10 year resolution (red) are non- smooth and localized in time. All yield a very similar reconstruction, showing that the basis on which we linearize the model does not signiﬁcantly affect the result. BOT- TOM: δ15N proﬁle corresponding to these histories. 27

15 2.3.1 First, and simplest, approach with δ Nxs

15 To first order, the abrupt change in δ Nxs can give us the magnitude of the abrupt temperature change (Equation 2.7). Indeed, abrupt climate changes are so fast that the temperature at the bottom of the firn TLID does not have time to change, and the 15 change in δ Nxs directly reflects the change in surface temperature Tsurf :

15 15 δ Nxs(2) − δ Nxs(1) = Ω h = (Ω − 40 ) T (2) − T (2) 15 4 surf LID i − Tsurf (1) − TLID(1) Ω h i ≈ (Ω − 40 ) T (2) − T (1) (2.19) 15 4 surf surf

If the temperature change was not instantaneous, then, for an abrupt warming, we would have TLID(2) > TLID(1), and this method would under-estimate the actual warming. For a quantitative estimation of this effect, see Landais et al.[2004a]. 15 We estimated the stadial value of δ Nxs by taking the mean of the five 15 oldest samples: δ Nxs(1) = −0.00008 ± 0.004 , and took the maximum value 15 of δ Nxs(2) = 0.042 ± 0.004 to calculate theh magnitude of the abrupt change. ◦ ◦ ◦ With Ω15 = 0.0142 / C and Ωh40 = 0.0381 / C at -50 C, we find that ∆Tsurf = ◦ 15 8.5 ± 1.0 C. If instead,h we choose the interstadialh value of δ Nxs to be the mean value between 2240 and 2244 m, which represents 60 to 200 years after the abrupt event, we 15 ◦ find δ Nxs(2) = 0.033 ± 0.004 , which corresponds to ∆Tsurf = 6.8 ± 1.0 C. This first approach is appealingh because of its simplicity. However we know that ◦ TLID(2) is not equal to TLID(1). Fifty years after the start of an 8 C step increase in ◦ ◦ temperature, TLID has already increased by 1 C. This estimate of 6.8 C is therefore a lower bound.

2.3.2 Second approach, with a diffusive column height ﬁt to data

As a second approach, we followed the same idea of separating nitrogen and argon isotopes into their thermal and gravitational components (Equation 2.7), and used 28

−35 A δ18O/0.356+67.5 −40 Scenario A Scenario B −45

−50 Temperature, °C

−55 38.6 38.5 38.4 38.3 38.2 38.1 38 37.9 Time, ka BP, GICC05

Gas age, ka BP Gas age, ka BP 38.8 38.3 38.0 37.9 38.8 38.3 38.0 37.9 B 0.04 D 0.55 0.02

0.5 , per mil xs N, per mil 0.45 N 0 15 15 δ δ −0.02 2.2 0.5 C E 2 0.45 , per mil g Ar, per mil

1.8 N 40 15 0.4 δ 1.6 δ 2250 2245 2240 2235 2250 2245 2240 2235 Depth, m Depth, m

Figure 2.7: Surface temperature reconstruction with prescribed gravitational fractionation. Plot A shows the reconstructed temperature history, in color for each of 15 18 the δ Ng scenarios. The black line is the translation of δ Oice into temperature with α =0.356 /◦C, following Grachev[2004]. For plots B-E, the black symbols represent the data, withh its analytical error bar. The colored lines represent 2 scenarios. Plot B 15 40 15 shows δ N. Plot C shows δ Ar. Plot D shows the thermal component, δ Nxs . Plot 15 E shows the gravitational component, δ Ng, along with the fit corresponding to each scenario. 29 the inverse method to find the optimal history matching the data, while prescribing 15 15 15 15 40 δ Ng. Both δ Nxs and δ Ng are noisier than δ N and δ Ar, and we do not expect all of the structure in the data to be a true reflection of the climate. We used two 15 different fits to δ Ng (shown in Figure 2.7E), and used that as an input into the Goujon model to define the lock in depth (Figure 2.7). We found a warming of 10.4 ±0.5◦C. Although we used the Goujon model to find this temperature history, we do not rely on the densification scheme to get the gravitational fractionation. The model helps us get an accurate temperature advection-diffusion through the firn, and provides an accurate ∆age.

2.3.3 Third approach, with a densiﬁcation model

As a third approach, we ran the Goujon et al.[2003] firn densification model to estimate changes in the firn thickness, and consequently the amount of gravitational fractionation (Equation 2.7). The firn thickness depends both on the temperature and the accumulation. During an abrupt warming, the accumulation also increases [e.g. Thomas et al., 2009]. Both effects are competing: the increase in accumulation tends to increase the thickness of the firn, but the warming will have a tendency to decrease the firn thickness (Figure 2.4). For this reason, the temperature history found by the inverse method will also affect the amount of gravitational fractionation, and it is important to keep running the densification model with an updated temperature history in order to get the correct amount of gravitational fractionation. We specified a suite of scenarios of the accumulation history, and for each of these scenarios, ran the inversion in order to find the optimal temperature history.

2.3.3.1 Accumulation rate scenarios

The change in the accumulation rate is not very well constrained by the data [Svensson et al., 2006]. We chose to use a step increase in the accumulation rate, in a 15 ◦ range compatible with the δ Ng data. We used a step increase in temperature of 6.5 C, and a synchronous step increase in accumulation corresponding to 2x, 2.5x and 3x the initial accumulation rate of 0.0545 m/yr (see Table 2.1). In addition, we scaled the layer thickness derived from the depth-age scale to match the stadial accumulation rate, and 30 produced another accumulation history (Scenario 5). Results are shown in Figure 2.8.

Table 2.1: Accumulation scenarios, in m/y water equivalent

Scenario 1 2 3 Stadial 0.0545 0.0545 0.0545 Interstadial 0.1090 0.1362 0.1635

0.5 Data Scenario 1 Scenario 2 0.48 Scenario 3

0.46 , per mil g

N 0.44 15 δ 0.42

0.4

2250 2245 2240 2235 Depth, m

Figure 2.8: Accumulation Scenarios: Gravitational fractionation for three accumulation scenarios, described in Table 2.1, with a temperature increase from -48◦C to - 41.2◦C. The scenarios with a 2.5-fold (green) to 3-fold (red) increase in the accumulation rate are the most consistent with the data.

2.3.3.2 Surface temperature reconstruction

We reconstructed the temperature history using the Goujon model and the linearized inverse method detailed in Section 2.2.5, with three accumulation scenarios described in Table 2.1. These three scenarios produce a temperature change of 10.7 to 11.2◦C, taking about 130 years to reach the maximum (Figure 2.9). 31

−35 A δ18O/0.356+67.5 Scenario 1 −40 Scenario 2 Scenario 3 −45

−50 Temperature, °C

−55 38.6 38.5 38.4 38.3 38.2 38.1 38 37.9 Time, ka BP, GICC05

Gas age, ka BP Gas age, ka BP 38.73 38.26 38.02 37.88 38.73 38.26 38.02 37.88 B 0.04 D 0.55 0.02

0.5 , per mil xs N, per mil

N 0

15 0.45 15 δ δ −0.02 2.2 0.5 C E 2 0.45 , per mil g Ar, per mil 1.8 N 40 15

δ 0.4 δ 1.6 2250 2245 2240 2235 2250 2245 2240 2235 Depth, m Depth, m

Figure 2.9: Surface temperature reconstruction with accumulation scenarios. Plot A shows the reconstructed temperature history, in color for each one of the 3 accu- 18 mulation scenarios. The black line is the translation of δ Oice into temperature with α =0.356 /◦C, following Grachev[2004]. For plots B-E, the black line represents the data, withh its analytical error bar. The colored lines represent the ﬁt to the data for the optimal solution found for each of the three scenarios described in Table 2.1. Plot B 15 40 15 shows δ N. Plot C shows δ Ar. Plot D shows shows the thermal component δ Nxs. 15 Plot E shows the gravitational component δ Ng. 32

The firn column does not respond immediately to changes in the accumulation: the first few data points in the increase in δ15N are solely a reflection of temperature changes in the firn, and show a good agreement between all scenarios (see also Figure 2.11). If we overestimate the increase in the accumulation rate, the model will compensate it with a faster increase in temperature: scenario 3 produces a higher temperature, and earlier temperature increase, than scenario 1. The increase in temperature advection at the bottom of the firn from a higher accumulation scenario is only on the order of 0.04◦C, for the first 300 years, which represents less than 1% of the temperature increase, and it is not significant. Therefore, changes in accumulation do not contribute noticeably to thermal fractionation. The temperature diffusion to the bottom of the firn reduces ∆T as time pro- gresses. This effect causes a reconstructed slow temperature change to have a higher amplitude than a faster temperature change for the same isotope data [Landais et al., 2004a]. Therefore, forcing the temperature history to have a step function will tend to under-estimate the real change in temperature, and a slow increase will over-estimate the change. The least-squares optimization used here produces the smallest integral of the amplitude of the event, and finds a balance between the speed and amplitude of the event. The timing of the increase in temperature is not very well constrained by this method, especially when we do not have a strong constraint on the accumulation history. 18 Thus, δ Oice is a better proxy for the timing and speed of the abrupt change. The accumulation scenarios do not allow the model to match the sharp decrease 15 15 in δ Ng above 2240 m (Figure 2.9E), which leads to an under-estimate of δ Nxs. All 15 three scenarios produce a surface cooling, which is not in agreement with δ Nxs above 2240 m, even though the fit to both δ15N and δ40Ar is good (Figure 2.9). The scenarios 15 with a prescribed δ Ng do not produce such sharp cooling (Figure 2.7), which indicates that it may be an artifact, caused by the rigidity of the accumulation scenario, or the densification process.

2.3.3.3 Gas Age calculation

The accumulation scenarios inﬂuence the calculation of ∆age (Figure 2.10). All three scenarios have an accumulation rate during the stadial that is compatible with the 33

1200

1000

Bender ∆ age ∆ 800 measured age

age, years Scenario 1

∆ Scenario 2 Scenario 3 Scenario A 600 Scenario B GICC05 scaled accum

2250 2245 2240 2235 Depth, m

Figure 2.10: Gas age - ice age difference: The black line shows ∆age as published by Bender et al.[1994b]. The (+) sign is the ∆age at the start of the abrupt warming, determined from the data, and the colored lines represent ∆age produced by the Goujon model for each of the scenarios. The light blue line represents the output of the Goujon model for an accumulation scenario resulting from the scaling of the layer thickness derived from the GICC05 timescale. The uncertainty in the accumulation rate generates an error of up to 100 years in ∆age. 34 measured ∆age at the start of the abrupt change. As the accumulation increases, ∆age decreases. At the end of our data set (2235 m), Scenario 3 produces a ∆age that is 100 years smaller than Scenario 1 (Figure 2.10). As a result, the increase in temperature is more compressed for Scenario 3 than for Scenario 1 (Figure 2.9A). An accumulation scenario can also be calculated by scaling the annual layer thickness produced by the age model, GICC05. The ∆age produced by such an accumulation history (light blue curve in Figure 2.10) is within the range of our three accumulation scenarios, which conﬁrms that we have sampled a large enough parameter space to estimate ∆age. The values of ∆age published by Bender et al.[1994b] were obtained by syn- 18 chronizing GISP2 to Vostok using δ Oatm of atmospheric O2, which was difﬁcult during D/O 8 because both the GISP2 ice age scale and the Vostok gas ages were ques- tionable at that time [Bender et al., 1994b; Svensson et al., 2008]. Considering this, the differences between the Bender et al.[1994b] ∆age and our estimate are within the known uncertainty. To sum up, this work presents an improvement on the gas age scale from the previously published data. The uncertainty in the accumulation produces an uncertainty in ∆age of up to 100 years.

2.4 Discussion

2.4.1 Accumulation history

The gravitational fractionation of inert gases gives us some constraints on the thickness of the firn, which is related to temperature and accumulation rate changes. We used a densification model with a step increase in temperature of 6.8 ◦C, consistent 15 with δ Nxs data, and explored the range of increase in the accumulation rate that would match the change in gravitational fractionation seen in the data. The data is compatible with a 2.5- to 3-fold increase in the accumulation rate (Figure 2.8). Cuffey and Clow[1997] have combined measured layer thickness from visual and chemical analysis with an ice flow model to produce an accumulation history, and found a 54 % increase in the accumulation rate at this event. However, the layer counting 35 became uncertain around this depth. This estimate is consistent with another study at NGRIP based on layer thickness, which also found an increase of the accumulation rate of ≈ 50%, synchronous within 2 years of the abrupt warming [Thomas et al., 2009]. The new timescale GICC05 gives an updated record of annual layer thickness for GISP2, and shows an increase in layer thickness from 0.012 to 0.024 m/y during the transition, which is consistent with a doubling of the accumulation rate (Figure 2.2). Our estimate of change in the accumulation is larger. One possible explanation is that the Goujon model is too sensitive to temperature: the firn would densify too fast after the abrupt warming, and it would need a higher increase in the accumulation rate to compensate for it. Most other models use a lower temperature sensitivity for densi- ties above 500 g/m3 : Spencer et al.[2001] uses 36 to 41 kJ/mol, Herron and Langway [1980] uses 10 to 21 kJ/mol, compared to 60 kJ/mol for Goujon et al.[2003]. Recent studies have shown that the lower temperature sensitivity fails to account for seasonal changes in densification [Arthern et al., 2010]. However, the controls of near-surface densification may be very different from those of the deeper firn. Indeed,H orhold¨ et al. [2011] have shown that temperature may not control densification below 30 m. The accumulation history may serve as an adjustable variable to mask our lack of understanding of the densification process. Another explanation for the larger change in the accumulation rate is a change in the convective zone [Severinghaus et al., 2010]. We used a 2 m convective zone throughout the record, but it is possible that at least half of the 10 m changes in the diffusive column height may be due to a thinning in the convective zone. Indeed, colder sites with lower accumulation can have a larger convective zone. The stadial conditions at GISP 2 are not unlike the modern climate at Vostok, which has a 12 m convective zone [Bender et al., 1994a]. Using a 5 m decrease in the convective zone would limit the increase in accumulation, with very little impact on the temperature reconstruction. However, the depth of the convective zone is unconstrained, and we would not gain much understanding by adding an unconstrained parameter to our reconstruction effort. For these reasons, the accumulation history serves here as an adjustable parameter input to the densification model, and the absolute value found should be used with caution. This uncertainty in the accumulation rate adds an uncertainty of 0.4◦C to the 36 amplitude of the warming (see Section 2.5.4, Table 2.2 and Figure 2.9). In contrast, the 15 use of δ Nxs circumvents this problem by not relying on any accumulation history or firn model and solely relies on thermal diffusion (Sections 2.3.1 and 2.3.2).

2.4.2 Amplitude of the warming

We assembled all of the scenarios to get the best estimate of the uncertainty in the warming. Scenarios 1-3 use upper and lower bounds of the possible change in the accumulation rate (Figure 2.8), and include the physics of firn densification. However, the densification model is unable to fit the last four data points (Figure 2.9E). Scenario A and B follow the data more closely (Figure 2.7) and do not rely on an accumulation scenario or a densification model (Section 2.3.2). The sharp decrease in δ15N at 2240 m is not likely to be caused by a change in the diffusive column height, but it could be a sharp change in the convective zone, or an analytical artifact. For each scenario, we computed the time of the transition as the middle of the time interval when the increase in temperature is 1 to 6◦C warmer than the stadial temperature. The stadial temperature was computed as the mean temperature between 200 and 100 years before the abrupt warming. The mean interstadial temperature was computed as the mean temperature between 100 and 200 years after the transition. These intervals were chosen to be out of the fast transition, so that any slight difference in the timing of the abrupt change would not affect the result. For each scenario, we found 100 solutions to the least-squares problem, using Equation 2.18. All 500 solutions were used to estimate the uncertainty in the amplitude of the abrupt change. The probability of a solution having a given temperature is shown in the shading of Figure 2.11A, and each best solution is shown in the colored line. For each scenario, we computed the amplitude of the event, defined as the difference between the mean temperature 200 to 100 years before the event, and the mean temperature 100 to 200 years after the event. The distribution of the amplitude is shown in Figure 2.11B and the mean and standard deviation in Table 2.2. The reconstruction for each scenario has an uncertainty of about 0.4◦C. The temperature change is larger for a smaller change in the accumulation rate (scenario 1), as expected, and our lack of knowledge of the true accumulation history therefore 37

Table 2.2: Amplitude of the warming, for each scenario. Scenario 1-3 used a doubling to tripling of the accumulation rate. Scenario A and B used a prescribed amount of gravitational fractionation. The values reported here are the mean and standard deviation of 100 solutions for each scenario, obtained from Equation 2.18.

Scenario mean (◦C) st. dev. (◦C) 1 11.12 0.36 2 11.20 0.30 3 10.70 0.34 A 9.80 0.40 B 10.31 0.46 1-3 11.0 0.40 A-B 10.06 0.50 all 10.63 0.64 generates an uncertainty of 0.40◦C. The uncertainty in the magnitude of the temperature change is represented by the standard deviation between all reconstructions from all scenarios, and it is 0.64◦C. This ﬁgure includes both the uncertainty in the isotope data, and the uncertainty in our knowledge of the densiﬁcation process. Finally, we conclude that the abrupt warming at the start of Interstadial 8 was 10.63±0.64◦C.

2.4.3 Calibration of the δ18O thermometer

Cuffey and Clow[1997] calibrated the overall relationship between δ18O and temperature during the transition from the last glacial to the present with the following equation:

δ18O T = + 75.4 ,in◦C (2.20) 0.328 This calibration would lead to a DO-8 magnitude of 11.0±3◦C, which is slightly higher than the temperature change found in this study, although within error. We computed the change in δ18O between stadial and interstadial in the same way we calculated the change in temperature (Section 2.4.2), and found ∆(δ18O) = 3.99 ± 0.9 . Using ∆T = 10.63 ± 0.64◦C, we ﬁnd : h

dδ18O α = = 0.38 ± 0.1 /◦C. (2.21) dT h 38

12 A 150 10 8 100 6 4 2 50

0 Number of Solutions Temperature change, °C −2 0 −200 −100 0 100 200 300 Time after the abrupt warming, years

80 B 60 Scenario 1 Scenario 2 Scenario 3 40 Scenario A Scenario B 20 all Number of Solutions 0 8 9 10 11 12 13 Warming Amplitude, °C

Figure 2.11: A: Temperature change for all scenarios. The grey shading represent the number of models having a certain temperature at a certain time, using 100 solutions per scenario. The colored lines are the optimal solutions found for each scenario. B: Distri- bution of the amplitude of the warming, for 100 solutions per scenario. See main text for details. Scenario 1, which has the lowest increase in the accumulation rate, produces the largest warming. Scenario A and B, which ﬁt the data most closely, have a lower increase in temperature. Overall, the abrupt warming has an amplitude of 10.63±0.64◦C. 39

This ﬁnding is consistent with the study by Landais et al.[2004a] which found, during DO/12 at GRIP a value of α=0.4 /◦C slightly larger than the glacial/interglacial value of 0.32 /◦C. h h 2.5 Sensitivity analysis

2.5.1 Sensitivity to the initial conditions

The initial temperature and accumulation rates were chosen so that the ﬁrn depth produced by the Goujon model matches δ15N during the stadial. Changing the initial temperature by 1◦C does not have a measurable impact on our reconstruction: the model runs for 2000 years before the abrupt DO warming, which is enough time to re-adjust the temperature. If we change the accumulation rate by 10% (from 6 cm/yr to 5.5 cm/yr), it affects the timing of the event. We ﬁxed the depth at which the event is observed in the gas phase of the ice. A 10% smaller accumulation rate increases ∆age by almost 100 years, and the solution found is incompatible with the timing of the event as seen in δ18O of the ice, using the GICC05 timescale. The validity of the timescale is discussed in section 2.2.2. In other words, the initial input accumulation rate is well constrained by the data, and does not contribute to uncertainties in the temperature reconstruction. Nonetheless, its absolute value may be model dependent (See Section 2.4.1).

2.5.2 Sensitivity to the initial temperature history

The least square inversion produces a solution that has the smallest amount of change from our initial temperature history T0. We chose a constant temperature history, so that the values that we present in this paper are the smallest possible change from the null hypothesis of a constant climate. If however, we suppose that the climate must have undergone an instantaneous warming, the optimum solution found will be somewhat different. Figure 2.12 shows the optimum solution found for (1) a constant initial temperature, and (2) a step function of 10 ◦C (hereafter Scenario 6). Scenario 6 shows a fast warming for the ﬁrst half of the trend, followed by a more gradual warming, with a 40 slope very similar to the one of the ﬁrst scenario (Figure 2.12). Past 38.1 k.a. bP, both reconstructions show cooling: this feature of the reconstructed history is mandated by the data, and is not an expression of the relaxation towards the null hypothesis. Indeed, the later part of the reconstruction shows both curves diverging to their respective initial guess: the least-squares optimization will relax to the initial history T0(t) in the absence of information. This cooling trend may be caused by inappropriate gravitational correction, and should be interpreted with caution (see Section 2.4.1). The maximum amplitude of the warming from stadial conditions differs by 0.8 ◦C. Scenario 1 can be thought of as the scenario producing the minimum of warming, while scenario 6 would produce the maximum warming.

−35 initial 1 Unconstrained initial 2 −40 best 1 best 2 −45 Temperature, °C

−50 38.6 38.4 38.2 38 37.8 37.6 Time, ka BP

Figure 2.12: Sensitivity to the initial history: Dashed lines show two initial temperature histories, and solid lines their corresponding best reconstruction, for (1) a constant temperature history, and (2) a step of 10◦C.

2.5.3 Comparison of the Goujon and Spencer densiﬁcation models

The Goujon model is one of the most sophisticated densiﬁcation models. The densiﬁcation process is divided in three stages, each using a different type of physics 41

105 Spencer model, T = − 45.7°C 1 Goujon model, T = − 45.7°C 1 Goujon model, T = − 47.5°C 100 1

85 Diffusive column height, m 80

0 100 200 300 400 500 Time, years after the abrupt change

Figure 2.13: Comparison of the Spencer and Goujon models: Changes in the Diffu- sive Column Height (DCH) with input temperature increasing in a step from -45.7◦C to -37.2◦C, and accumulation increasing from 0.0586 to 0.1758 m/y, for the Spencer model and the Goujon model. The third curve shows the Goujon model, with temperature increasing from -47.5 to -39◦C, and with the same step in accumulation rate. The Goujon model is more sensitive to temperature than the Spencer model, although their transient response is similar. 42 to control the densification rate. The first stage of densification results mostly from grain boundary sliding [Alley, 1987]. The following stages use a hot-isostatic power- law creep, that was initially used for hot pressure sintering of ceramics and metals. The second stage uses power-law creep for spherical grains [Arzt, 1982; Arzt et al., 1983]. The third stage, where the pressure in the bubbles starts increasing, uses the Wilkinson and Ashby[1975] formula. We compare the Goujon model to the Spencer et al.[2001] densification model, which uses an empirical parameterization of the Wilkinson and Ashby[1975] power- law creep based on the analysis of 38 modern density profiles spanning a large range of temperature and accumulation. Both models have added an Arrhenius-type dependence on temperature on the densification rate, with an activation energy of 60 KJ/mol for the Goujon model and 30 to 47 KJ/mol for the Spencer model, depending on the stage. 60 KJ/mol is the commonly used value for ice diffusion. Recent measurement campaigns have shown that low values such as those used by Herron and Langway[1980] (11 to 21 KJ/mol) under-estimate the observed seasonal changes in densification in the shallow firn [Arthern et al., 2010; Zwally and Jun, 2002]. For an equilibrium temperature of -45.7◦C, and an accumulation rate of 5.84 cm/y, the diffusive column height predicted by the Spencer model is 84.4 m, 5.7 m deeper than the one predicted by the Goujon model (78.8 m, Figure 2.13). It is essentially a reflection of the different temperature sensitivity of the models: The Goujon model is more sensitive to temperature than the Spencer model. In the range of temperatures we are considering here (-50 to -35◦C), the Goujon model has a shallower firn for the same temperature, and the abrupt increase in temperature will have be felt sooner at the bottom of the firn. In order to match the firn depth during the stadial, the Goujon model needs to be 2◦C colder (Figure 2.13). To sum up, the Goujon model used in most of this study may be too sensitive to temperature, and may overestimate the decrease in firn thickness associated with the abrupt warming. 43

2.5.4 Sensitivity to the accumulation history

The surface temperature reconstruction for three accumulation histories is presented in Figure 2.9A. A larger increase in the accumulation (red curve in Figure 2.9A) leads to an earlier and faster increase in inferred temperature. A larger accumulation rate will also decrease ∆age (Figure 2.10). All three scenarios produce an estimate of ∆age at the start of the transition which is within the stated error of the GICC05 Chronology [Andersen et al., 2006]. A faster increase in the accumulation rate triggers a faster increase in the diffusive column height. If this change is too large, the model will tend to increase the temperature in order to decrease the DCH to the right level. In summary, the uncertainty in the accumulation rate translates into a 0.4◦C uncertainty in the magnitude of the warming, and up to 100 year uncertainty in ∆age (Figure 2.10).

2.5.5 Sensitivity to the convective zone

The first few meters of the firn are porous enough that wind and pressure gradients can trigger bulk motion of the air. This convective movement prevents diffusive fractionation from occuring, incuding gravitational settling. The depth of the convective zone depends on the site, but it is usually less than 5 m for sites with an accumulation above 5 cm/y [Compilation by Landais et al., 2006], and could be as much as 10 or 12 m in very cold sites like Vostok or Dome F, which have an accumulation rate of less than 2 cm/y. In places with near-zero accumulation rate, macro-cracks may form and create a very large convective zone, which may be as deep as 30 m [Megadunes, Antarctica: Severinghaus et al., 2010]. An abrupt change in the depth of the convective zone would create a change in the gravitational fractionation that would be independent of changes in the firn thickness. In modern times, the convective zone is often larger when the accumulation rate is smaller [Landais et al., 2006]. During an abrupt warming, we expect the convective zone to decrease, which would create an increase in the diffusive column height, Z. The data show an increase in Z of 9.2±2.4 m. It is possible that the convective zone may have decreased by as much as 5 m. We do not have any proxy for the depth of the 44 convective zone at present, and considered it constant at 2 m in our calculations. As a result, we may overestimate the increase in the accumulation rate to fit the data. The uncertainty in the convective zone can be circumvented by using two pairs of isotopes, as presented in Section 2.3.2, and Figure 2.7. Although it is important for the estimation of the accumulation rate, and ∆age, the uncertainty associated with the convective zone does not increase the error in the surface temperature reconstruction beyond what is already taken into account as uncertainty associated with the accumulation rate. This uncertainty was on the order of 0.4◦C (Section 2.5.4).

2.5.6 Sensitivity to the lock-in depth

The Lock In Depth (LID), the depth at which diffusion stops, is a key parameter in this study. It is calculated in the Goujon model by a semi empirical formula, based on the observations of firn closed porosity and total air content from many ice core sites [Goujon et al., 2003]. Martinerie et al.[1994] have found that there is an empirical correlation between the temperature of an ice core site, and the density of the firn at which the gases become trapped. The density at which bubbles and macro-pores are sufficiently closed that the pressure starts increasing in the pores is called the close off density ρc:

1 1 = + 6.95 × 10−4T (K) − 0.043(cm3g−1) (2.22) ρc ρice

where ρice is the density of ice, and T the temperature of the close off depth at the site. However, this is not the relevant parameter for gas diffusion: Some layers of firn densify faster than others. A dense layer may create a lid preventing layers below that from exchanging air with the rest of the firn column, effectively stopping the evolution of gas fractionation, even though the mean density of the firn may still be quite low. The LID is the depth at which gravitational enrichment of δ15N stops. It is parameterized as a threshold of the amount of closed porosity.

The closed porosity Pclosed is expressed as [Goujon et al., 2003]: 45

P −7.6 Pclosed = 0.37 × P (2.23) Pc ρ ρc with P = 1 − and Pc = 1 − (2.24) ρice ρice

This expression was established by measurements of firn porosity and total gas content at three ice core sites ( J.M. Barnola, unpublished). At the close-off depth, the ratio of closed porosity to total porosity is 37%. At the lock in depth, this ratio is smaller, and depends on the site. At a cold site like Vostok, (Pclosed/P )LID = 0.21; at GISP2, it is 0.13. These values are determined by looking at the firn density at the lock in depth in modern firn air analyses. The parameters affecting the LID are poorly understood. Data from firn air campaigns in Greenland and Antarctica have shown that warmer sites usually have a lower lock-in density than colder sites [Landais et al., 2006]. It is thought that a warmer firn is typically more layered. Recent analysis of high resolution density show however that the amount of impurities in the ice may be a better predictor of its density than temperature [Horhold¨ et al., 2011]. In the modern world, the colder sites are located in Antarctica, and are also less dusty. However, during glacial times, cold stadial conditions were more dusty than interstadial or modern times. Our limited understanding on the controls of densification could trigger errors in the modeling of the firn depth. How- ever, because gases are closed off in bubbles within ice that is older, the DO warming presented here happens solely within older stadial ice, and we should not expect a large change in ice properties near the lock in zone at the transition. Therefore, the model may create a bias in the firn depth, but this bias should be uniform across the data set, and will be compensated for by using a different absolute value of the accumulation rate and temperature.

We explored the magnitude of the variations in the lock in density ρLID through the data set (Figure 2.14). We ran a ﬁrst sensitivity test considering a constant density at lock-in, by disabling the Martinerie et al.[1994] parameterization. Changes were minimal (Figure 2.14, blue and green lines), suggesting that, although the relation between

ρc and temperature is purely empirical and poorly understood, we do not expect large 46

Sensitivity to the definition of the LID 105 A δ15N data xs 100 Changing LID Constand Density LID Constant Depth LID 95 8 C

Lock In Depth 90 6

85 2250 2245 2240 2235 4 depth, m 0.91 B 2 0.9 0 0.89

0.88 Temperature difference −2 between surface and LID 0.87 −4 0.86 Lock In Relative Density 0.85 −6 2250 2245 2240 2235 2250 2245 2240 2235 depth, m depth, m

Figure 2.14: Sensitivity to the definition of the LID. Model output for three scenarios: Scenario 2 (table 2.1, green), a constant lock-in density (dashed blue), and a constant lock-in depth (dashed red). Plot A shows the lock-in depth. Plot B shows the lock- in density. Plot C shows the temperature difference between the surface and the LID, 15 which is directly proportional to δ Nxs (Equation 2.7). Considering a constant density does not affect the results. Considering a constant depth leads to an over-estimation of 15 δ Nxs a the peak of the warming, but the change is still within the stated error. As a result, the estimation of thermal fractionation is robust to large uncertainties in the LID. 47 changes in the range of temperatures we are considering here, and our results remain robust. The depth of the lock in, however, increased by more than 10 m (Figure 2.14, top panel). Keeping the LID constant (red line in Figure 2.14) causes an over-estimate of the temperature difference between the surface and the LID, by at most 0.4◦C, or 12% of the signal, which is still within error. Changes in the firn depth not only affect the gravitational fractionation, but also, to a lesser extent, the thermal fractionation. Anal- 15 ysis of δ Nxs data without properly accounting for changes in firn depth can create a small bias in the reconstruction of the temperature history.

2.6 Conclusions

The abrupt warming at the start of Interstadial 8 had an amplitude of 10.63±0.64◦C, and was associated with a two to three fold increase in the accumulation rate. This increase in accumulation confirms that the layer counting of GISP2 is inaccurate in the vicinity of Interstadial 8: The accumulation derived from layer counting in Cuffey and Clow[1997] shows little change at the abrupt warming, which is in conflict with our finding, and with GRIP and NGRIP accumulation histories. This temperature reconstruction allows us to revisit the calibration of δ18O, and we found that α = 0.38 ± 0.1 /◦C, which is broadly consistent with the the glacial/interglacial value of 0.328 /◦C.h h Acknowledgement This chapter, in full, has been submitted for publication in Earth and Planetary Science Letters as: Orsi, A. J., B. D. Cornuelle, and J. P. Severinghaus, Magnitude and Temporal Evolution of Interstadial 8 Abrupt Temperature Change In- ferred From inert gas isotopes in GISP2 Ice Using a New Least-Squares Inversion, Earth and Planetary Science Letters, in review. The dissertation author was the primary investigator and author of this work. Chapter 3

Little Ice Age Cold Interval in West Antarctica: Evidence from Borehole Temperature at the West Antarctic Ice Sheet (WAIS) Divide.

Abstract

The largest climate anomaly of the last 1000 years in the Northern Hemisphere was the Little Ice Age (LIA) from 1400-1850 C.E., but little is known about the signature of this event in the Southern Hemisphere, especially in Antarctica. We present temperature data from a 300 m borehole at the West Antarctic Ice Sheet (WAIS) Divide. Results show that WAIS-Divide was colder than the last 1000 year average from 1300 to 1800 C.E. The temperature in the time period 1400-1800 was 0.52±0.28◦C colder than the last 100 year average. This amplitude is about half of that seen at Greenland Summit (GRIP). This result is consistent with the idea that the LIA was a global event, probably caused by a change in solar and volcanic forcing, and was not simply a seesaw-type redistribution of heat between the hemispheres as would be predicted by some ocean- circulation hypotheses. The difference in the magnitude of the LIA between Greenland

48 49 and West Antarctica suggests that the feedbacks amplifying the radiative forcing may not operate in the same way in both regions.

3.1 Introduction

3.1.1 The last 1000 years

The Northern Hemisphere experienced a widespread cooling from about 1400 to 1850 C.E., often referred to as the “Little Ice Age” (hereafter LIA) [Moberg et al., 2005]. The LIA was the latest of a series of centennial scale oscillations in the climate [Wanner et al., 2011]. Understanding the cause of this type of event is key to our knowledge of the variability in the climate system, and to our ability to forecast future climate changes. The LIA cooling was associated with a time of lower solar irradiance and increased persistent volcanism [Mann et al., 2009a]. This forcing must have been ampliﬁed by natural feedbacks, because the magnitude of the forcing by itself is too small to explain the observed response. It is still unclear whether the Southern Hemisphere high latitudes had a temperature response synchronous to that of the Northern Hemisphere: changes in the solar forcing would call for hemispheric synchroneity, but evidence from the southward movement of the Inter-tropical Convergence Zone in the Paciﬁc Ocean [Sachs et al., 2009], and from changes in the ocean circulation [Keigwin and Boyle, 2000] argue for a delayed [Goosse et al., 2004] or inverse response [Broecker, 2000].

3.1.2 Site description

We present here borehole temperature data from WAIS-Divide (79◦28’ S, 112◦05’ W, 1766 m a.s.l.), situated near the ﬂow divide at the center of West Antarctica (FIgure 3.1). The relatively low elevation of West Antarctica allows marine air masses to penetrate into the continent interior, bringing with them heavy precipitation and warmer temperatures [Nicolas and Bromwich, 2011]. WAIS-Divide has a mean annual ◦ air temperature of -28.5 C, and accumulation rate of 0.22 mice/yr, making it a good ◦ southern analog to the summit of Greenland (-29.5 C, 0.24 mice/yr [Shuman et al., 2001]), thus a good candidate for inter-hemispheric comparisons. WAIS-Divide is 50 also strongly connected to the climate of the South Paciﬁc [Ding et al., 2011], and is sensitive to El-Nino˜ Southern Oscillation [Mayewski et al., 2009; Fogt et al., 2011].

Figure 3.1: Location of WAIS-Divide: at the center of West Antarctica, 160 km from the Byrd ice core site.

Borehole temperature measurements take advantage of the advection and diffusion of heat through the snow and ice. Both the thickness of the ice sheet (3460 m) and the high accumulation rate allow the climate signal to be better preserved at WAIS- Divide than anywhere in central East Antarctica. We used a model of heat advection and diffusion in ice to quantify this process, and an inversion scheme to reconstruct the surface temperature history from the borehole measurements. 51

3.2 Method

3.2.1 Sampling method

The 300 m air-filled hole WDC05A (79◦28’ S, 112◦05’ W) was drilled in Jan- uary 2005, and sampled both in January 2008 and January 2009 with a single thermistor (Omega 44033) connected to a precision multimeter (Fluke 8846A, 6 1/2 digits) using the 4-wire measurement method. The thermistor was calibrated at Scripps Insti- tution of Oceanography against a secondary reference temperature standard, according to the Steinhart-Hart equation. The accuracy of the absolute temperature of this calibration is 0.1 K, and its relative uncertainty in the range of our borehole measurements is 0.0023 K. The inversion of borehole temperature measurements is not sensitive to the absolute temperature, but to the relative temperature difference between data points. Therefore, we are not as concerned about systematic biases in the whole profile as we are about errors that affect each data point, or each depth differently. A detailed error analysis is available in Section 3.4.7. In the field, the sensor was held stationary every 5 meters to equilibrate with the surrounding temperature for 20 min, and the resistance was integrated over 5 min. Logging was done both upwards and downwards, with 2 or 3 measurements at each depth. There is no significant difference between the profiles measured in 2009 vs 2008 below 30 m (Figure 3.2). The pooled standard deviation of all measurements, including both years, is 1.8 mK. This figure represents the reproducibility of the measurements, and may be taken as an estimate of the overall precision, which includes the noise from the instrument and local variability from air movement in the hole. The calibration is the leading source of uncertainty, and we consider the overall precision to be 2.3mK.

3.2.2 Forward model

The forward firn and ice model is based on the 1 dimensional heat and ice flow equation, discretized in an explicit finite difference scheme, following Alley and Koci 52

ï29.5 data 2008 ï29.98 ï29.6 data 2009 reconstruction ï30 ï29.7 ï30.02 ï29.8

ï29.9 ï30.04 Temperature, °C Temperature, °C ï30 ï30.06

ï30.1 20 40 50 100 150 200 250 300 0.01 0.02 5000 0.01 0 2500 1000 0 500 misfit,°C misfit,°C ï0.01 difference 2009ï2008 ï0.01

10 nb of models ï0.02 modelïdata misfit ±2 mK error bar 1 ï0.03 ï0.02 20 40 50 100 150 200 250 300 Depth, m Depth, m

Figure 3.2: Top: WAIS-Divide borehole temperature data, measured in a dry 300 m hole. There is no significant difference between the measurements made in 2008 and 2009. Bottom: Misfit between the best reconstruction and the data. In black is the stated 1-σ error in the data. The red symbols (+) show the difference between data measured in 2008 and 2009. The light blue shading represents the probability of each of the 6000 solutions generated to have the stated misfit with the data. All solutions fit the data reasonably well. 53

[1990]:

∂T ∂ ∂T ∂T ρ c = k − ρ c w + Q (3.1) p ∂t ∂z ∂z p ∂z

where ρ is the density of firn/ice, k the thermal conductivity, cp the heat capacity, T the temperature, t the time, z the depth, w the downward velocity of the firn/ice, and Q the heat production term, taking into account ice deformation and firn compaction. WAIS-Divide is near the ice flow divide, and the horizontal advection of mass and heat are both negligible. The density and accumulation rate are taken from onsite measurements [Battle et al., 2011; Banta et al., 2008]. The vertical velocity of the firn or ice w is determined using a constant strain rate, following [Cuffey et al., 1994]. The heat capacity cp, thermal conductivity k and heating term Q are all determined according to the classical equations [Cuffey and Paterson, 2010, Chapter 9]. A detailed description of the model, and the uncertainties associated with each parameter is available in Section 3.A.

3.2.3 Inverse model

The diffusion process blurs the true temperature history, and this problem is classically underdetermined: there is an infinite number of possible temperature histories that would fit the data perfectly [Clow, 1992]. In addition, most of the parameters in Equation (3.1) depend on temperature, which makes the problem non linear. Finding a solution requires us to make assumptions about what we consider to be a plausible solution, so that we can reduce the dimensionality of the problem. The details of the inverse method will therefore have an impact on the “best” solution found [Shen et al., 1992]. At least three approaches have been used to overcome this problem. A Monte Carlo scheme can be used to explore the range of possible solutions [e.g. Dahl-Jensen et al., 1998]. Other types of data, like water isotopes, can be included as additional constraints on the temperature history [Cuffey and Clow, 1997]. A third approach is to linearize the problem and find a solution by a generalized least-squares method [e.g. MacAyeal et al., 1991; Muto et al., 2011]. This method has the advantage of providing 54 information about the unresolved dimensions of the problem. We chose here to use a generalized least-squares method, with the constraints highlighted below.

Smoothing function in the time domain

1493 1733 0.1 1807 1907 1962 1988 0.05 Normalized Amplitude 0 1200 1400 1600 1800 2000 1500 1000 500

smoothing 0 window, years 1200 1400 1600 1800 2000 time, year C.E.

Figure 3.3: Top: Smoothing function for select times. Bottom: Smoothing window, calculated as the width of the smoothing function at half maximum. As we go back in time, the borehole temperature reconstruction effectively calculates the weighted average temperature over the time period given by the smoothing function. The high frequency variability of the climate is blurred.

Figure 3.3 shows the unavoidable smoothing of the record as we go back in time. In 1800 C.E., we can only reconstruct a non-uniform 220 year “average” temperature [Clow, 1992]. With this in mind, we do not try to resolve high-frequency changes in past climate, but rather we extract long term changes. As a consequence, we will choose among the inﬁnite possibilities a solution with a small change in climate for a long timescale, rather than a short event of much larger amplitude. The net result is that all the extrema of temperature shown in this study are lower bounds of the actual climate history. It should also be noted that the method resolves high frequencies better as we get closer to the present: the reconstruction shows more details in the last 50 years (Figure 55

3.4B). For this reason, we caution that this study is not able to compare the warming of the last few decades to the longer term context.

3.2.3.1 Linearization

The forward model was linearized along an initial temperature history θ0(t), which allowed us to use a least-squares regression to ﬁnd the optimal solution [Wunsch, 1996, Chapter 3]. The functional space of temperature history can be expressed as a linear com- P bination of basis functions bi: θ(t) = θ0(t) + x(i)bi(t) where θ(t) is a history of i temperature, t is the time, and x(i) the coefﬁcients of this linear combination. In vector notation, we can write:

θ = θ0 + Bx with B = [b1 b2 ... bn] (3.2)

We used a Fourier decomposition for bi, with periods between 4000 years (twice our window) and 20 years, with an amplitude of 1◦C. Periods smaller than 20 years are quickly damped and do not contribute signiﬁcantly to the solution. We also used a piecewise linear basis as an independent comparison. The inﬂuence of the choice of the basis functions is discussed in Section 3.4.6.

Each basis function bi(t) was run through the forward model to produce a temperature profile yi(z). We define hi(z) = yi(z) − y0(z), with y0 the output of our initial guess θ0(t). If the model is approximately linear, any temperature profile y(z) can be expressed as a linear combination of the vectors hi(z). In vector notation:

y = y0 + H x with H = [h1 h2 ... hn] (3.3)

We want to find a history of temperature θ(t) that would fit our data d(z). This is equivalent to finding x so that

d − y0 = H x (3.4) 56

3.2.3.2 Least-squares regression

Of the many solutions to Equation (3.1), we are looking for the solution that satisﬁes the following assumptions:

1. The changes in the climate are as small as possible. Thus we chose θ0(t) to be a constant temperature, and used the least-squares algorithm to minimize the temperature difference.

2. The lower frequencies were allowed a larger variance than the higher frequencies, reﬂecting the preference for long term climate variations. This assumption is re- ﬂected in the a-priori error covariance matrix of the model parameters P, whose diagonal elements are: f(i)−2 P = σ2 (3.5) i,i x P f(i)−2 i

with f(i) the frequency of the sin/cos used in the basis functions bi, and σx the a-priori root mean square error of the model parameters.

◦ 3. The amplitude of the climate changes is on the order of σx = 0.5 C, following the work of Dahl-Jensen et al.[1999] at Law Dome, where they found using a Monte Carlo scheme that the standard deviation of the reconstructed past temperature was around 0.3◦C.

The inﬂuence of the choice of the matrix P is discussed in Section 3.4.6. The error in the data is represented by the diagonal matrix R whose elements 2 ◦ are σd, with σd = 0.002 C, which reﬂects the precision of our measurements. The least-squares theory shows that the optimum solution to (3.4) is:

T T −1 x1 = PH1 (H1PH1 + R) (d − yo) (3.6)

The same linearization exercise can be performed around θ1 = θ0 + B x1, with the output proﬁle y1, creating a matrix H2. Subsequent solutions take the form [El Akkraoui et al., 2008]:

n n−1 X T T −1 X xj = PHn (HnPHn + R) (d − yn−1 + Hn xj) (3.7) j=1 j=1 57

The history of temperature is recovered using Equation (3.2).

3.2.4 Uncertainty estimation

3.2.4.1 Uncertainty associated with the least-squares optimization

The least-squares optimization provides a new estimate of the covariance of the uncertainty in the model parameters :

ˆ T T −1 P = P − PHn (HnPHn + R) HnP (3.8)

The eigenvectors of Pˆ represent the dimensions least constrained by the data, generally short timescales, which allows us to explore the statistics of the reconstruction. By choosing a stationary prior, we allow a lot of variability to be included in the uncertainty ensemble. In the distant past, all high frequencies are poorly determined. They do not ﬁgure in the optimal least-squares solution, but they are included in the uncertainty ensemble. Our uncertainty estimate is therefore very conservative. The 1-σ error on the reconstruction is given by the square root of the diagonal elements of S = BPBˆ T, but this metric neglects the covariance between the temperature at a certain time, and the temperature a few years before or after. A series of solutions to (3.4) can be created using the eigenvalue decomposition of Pˆ = UDUT, where U is the matrix of eigenvectors, and D the diagonal matrix of the eigenvalues. A solution xm takes the form:

√ xm = x + U D m (3.9) with m a vector of random numbers with zero mean and unit variance, x the optimum √ least-squares solution, and D the element by element square root of the diagonal matrix D. We used a series of xm to explore the position and magnitude of extrema (Figure 3.5). Each one of these solutions was passed through the forward model, and the fit to the data is plotted as the shading in Figure 3.2. The fact that all models can fit the data within the stated error justifies the validity of the linearization around the optimal solution. 58

3.2.4.2 Uncertainty in the timing of the temperature minimum

We explored the smoothing created by both the physical diffusion of heat and our inversion technique by using the same linearization method, but taking piecewise linear T T functions for the bi(t). Each line of the resolution matrix A = PH (HPH + R)H represents the weight given to the temperature at different times in the reconstructed temperature at the speciﬁc time corresponding to that line. Figure 3.3 shows a few examples of this smoothing function. We also explored the position of the temperature minimum for a series of solutions, using Equation (3.9), and the statistics are plotted in Figure 3.5. In addition, the thermal conductivity and accumulation rate have an impact on the timing of the extrema. Decreasing k by 10% results in a shift of the temperature minimum by 58 years. If the mean accumulation was 10% lower, the amplitude of the minima in the reconstruction would increase by 10%, and the temperature minimum would occur 38 years earlier (see Section 3.4.5 for details).

3.2.4.3 Uncertainty associated with the boundary conditions

The initial temperature profile was set to a stationary profile with a realistic seasonal cycle. The real climate is not stationary, and long term climate changes, such as the last ice age, may still have an imprint on the first 300 m of the ice sheet. It is not practical to extend the run time indefinitely. Thus the inversion scheme was run with a suite of initial temperature profiles to include the uncertainty associated with the unknown initial condition. Each optimization with variable initial conditions was used to produce a series of 1000 solutions using Equation (3.9). We used all 6000 solutions to derive the statistics presented in Figure 3.5. The shading in Figure 3.6 represents the number of these solutions to have a given temperature at each point in time. The influence of the bottom boundary condition is negligible (See Section 3.4.2).

3.2.4.4 Uncertainty associated with the model parameters

The thermal conductivity k of the ice is not very well defined, because it depends not only on temperature and density but on the structure of the grains in the ice. We used the Schwerdtfeger formula, which is an upper estimate. Decreasing k by 10% results in 59 a shift of the temperature minimum by 58 years (see Section 3.4.5). The vertical velocity profile is proportional to the mean accumulation rate. In- cluding the variable accumulation record from Banta et al.[2008] for the last 270 years did not affect the borehole temperature profile. However, if the mean accumulation was 10% lower, the amplitude of the minima in the reconstruction would increase by 10%, and the LIA minimum would occur 38 years earlier (see the online supplement). Pre- liminary data from the WAIS-Divide ice core suggest that the mean accumulation rate has not changed by more than 10% over the last 2000 years (Joe McConnell, personal communication, 2012).

3.3 Results and discussion

The temperature measurements show a minimum at 125 m (Figure 3.2; -0.2◦C compared to the 30 m depth value), separating a deeper upward cooling trend from a more shallow upward warming. We interpret this minimum as direct evidence that there was a colder climate at some time in the past, a conclusion that is independent of the model and the inversion. The inversion-based reconstruction of snow surface temperature (Figure 3.4) shows a long term cooling trend from 1000 C.E. to a minimum in seventeenth century. The subsequent warming paused at the beginning of the twentieth century, and accelerated in the last ∼20 years.

3.3.1 Seventeenth century minimum

This temperature reconstruction shows a broad minimum circa 1600 C.E., the timing of which is not constrained very precisely by the data. We estimated the uncertainty in the timing using a distribution of 6000 solutions obtained using Equation 3.9 (Figure 3.5A), and extract meaningful information by comparing long time intervals. Half of the solutions have a minimum between 1420 and 1760 C.E. The temperature in the time period 1400-1800 was 0.52±0.28◦C colder than the last 100 year average. We followed the nomenclature of Mann et al.[2009b] to calculate the temperature difference between the period 950-1250 C.E. (often referred to as the Medieval Warm Period, 60

ï28 ï28 A B =ï29.93°C Cold Interval e0 e =ï29.83°C ï29 0 ï29 =ï29.73°C e0 =ï29.63°C e0 e =ï29.51°C ï30 0 ï30 =ï29.41°C e0 mean 1007ï2007 mean surface temperature °C surface temperature °C ï31 1m error bar ï31

200 400 600 800 1000 1200 1400 1600 1800 2000 1900 1950 2000 time, year C.E. time, year C.E.

Figure 3.4: Surface temperature reconstruction. Colored lines represent the optimal reconstruction for a range of initial conditions. Grey lines represent the 1 σ distribution of 6000 solutions (see section 3.2.4.1). The thick black line is the mean of all reconstructions, and was below the 1000 year average between 1300 and 1800 C.E. This reconstruction shows the smallest amount of change from a constant climate permitted by the data. Borehole temperature-based reconstructions lose resolution of higher frequencies going back in time; therefore, we cannot draw conclusions about the unusual character of the warming of the last 20 years.

MWP) and the period 1400-1700 C.E. (Figure 3.5B). The period 1400-1700 was on average 0.39±0.93◦C colder than 950-1250 C.E. A one tailed student’s t test shows that it was at least 0.33◦C colder at the 99% confidence level. The coldest 200 years, 1500-1700 C.E., were at least 0.43◦C colder than the period 1800-2000 C.E. at the 99% confidence level, with a mean of 0.43◦C and standard deviation of 0.59◦C (Figure 3.5C). This reconstruction is consistent with the temperature estimate based on bubble number density in the WAIS-Divide ice core. Fegyveresi et al.[2011] found that the temperature of WAIS-Divide cooled by 1.7◦C between 0 and 1700 C.E. Water isotopes from the same ice core also show a long term negative trend over the last 2000 years (E. Steig, personal communication). 18 In other Antarctic ice cores, records of water isotopes (δ O and δD of H2O) also support the idea of a long term cooling centered around 1600 C.E. [Bertler et al., 2011]. Talos Dome and Taylor Dome, in the Ross Sea Region of East Antarctica, have persistent negative isotopic values around 1600 C.E. [Stenni et al., 2002]. Dome C has a weaker and longer negative excursion from 1400 to 1700 C.E. However, these records are often difficult to interpret in terms of temperature: changes in the elevation at the site and in the moisture source have dominant effects, and are challenging to constrain 61

timing of the coldest 20 years

200 A 150

100

50 number of solutions 0 1000 1200 1400 1600 1800 time year C.E. Temperature difference Temperature difference [950ï1250] ï [1400ï1700] C.E. [1800ï2000] ï [1500ï1700] C.E. B C 400 400

200 200

0 0 number of solutions ï2 0 2 number of solutions ï1 0 1 2 temperature difference, °C temperature difference, °C

Figure 3.5: A: Timing of the coldest 20 year using statistics made over 6000 solutions with various initial conditions (see text). Half of the solutions have a minimum between 1420 and 1760 C.E.. The most common minimum occurs in 1600 C.E. B: Temperature difference between the average over the time period 950-1250 (Medieval Warm Period), and the average over 1400-1700 (Little Ice Age). The mean of this distribution is 0.39◦C, and the standard deviation 0.93◦C. A one sided student’s t test performed on 6000 solutions conﬁrms that the MWP was at least 0.33◦C warmer than the LIA at WAIS-Divide at the 99% conﬁdence level. C: Temperature difference between the average over the last 200 years, and the coldest period of 1500-1700 C.E. The mean of this distribution is 0.43◦C, and the standard deviation 0.59◦C. 62

[Masson et al., 2000]. In addition, other records have weak trends [South Pole; Mosley- Thompson et al., 1993], or slightly increasing trends [Siple Dome; Mayewski et al., 2004], raising the possibility of considerable spatial heterogeneity of the climate signal within Antarctica. In southern South America, tree ring records have shown a pronounced summer cooling period between 1350 and 1700 C.E. [Neukom et al., 2010], and a later cold event around 1850 C.E., which is consistent with our record. A similar borehole temperature record at GRIP, Greenland, shows two temperature minima in 1550 and 1850 C.E., with respective temperatures 0.34 and 0.49 K relative to the last 1000 year average (-31.82◦C) [Dahl-Jensen et al., 1998]. Green- land Summit has a mean annual temperature and accumulation similar to that of WAIS- Divide, and is a good candidate for inter-hemispheric comparison. Both sites are in the continental interior, and are thought to be representative of their respective regional climate [Kobashi et al., 2010; Steig et al., 2009]. The fact that WAIS-Divide was colder than the last 1000 year average from 1300 to 1800 C.E. supports the idea that the Little Ice Age was not conﬁned to the North Atlantic, and that a decrease in solar activity accompanied by persistent explosive volcanism could be the cause of this event [Miller et al., 2012]. The amplitude of the LIA cooling is half as much at WAIS-Divide as it is at Greenland Summit, suggesting that feedbacks amplifying the radiative forcing may have been stronger in Greenland.

3.3.2 Recent warming

WAIS-Divide has been warming by 0.23±0.08◦C per decade over the last 50 years. This warming rate has accelerated over the last 20 years to an average of 0.80±0.06◦C per decade (Figure 3.6). The Kominko-Slade weather station was fully operational in 2009 and 2010, and the measured annual average air temperature was -28.4◦C in 2009, and -28.5◦C in 2010, in good agreement with our reconstruction (Matthew Lazzara, AMRC, SSEC, UW-Madison). Steig et al.[2009] and O’Donnell et al.[2010] used weather station and satellite data to reconstruct the temperature history of Antarctica over 1957-2006. Steig et al. 63

WAIS Divide Surface Temperature Reconstruction 1 WAIS divide borehole reconstruction cloudïmasked satellite data Steig et al. [2009] climate field reconstruction 0.5 100

ï0.5 Nb of solutions Temperature Change °C ï1 1 1950 1960 1970 1980 1990 2000 Time, year C.E. Average warming rate

800 m = 0.231°C/decade m = 0.804°C/decade 1957ï2007 m = 0.075°C/decade m = 0.058°C/decade 600 1987ï2007 400 200

Nb of Solutions 0 0 0.2 0.4 0.6 0.8 1 1.2 Warming rate, °C/decade

Figure 3.6: Top: Temperature reconstruction over the last 50 years. The shading shows the number of solutions with a specific temperature, based on 6000 solutions (see text). Temperature from cloud masked satellite data and climate field reconstruction [Steig et al., 2009] are independent estimates of the temperature at WAIS-D, and are in good agreement with our reconstruction. Bottom: Histograms of the average warming rate over the periods 1957-2007 and 1987-2007, based on 6000 solutions to the borehole temperature profile. The warming trend has been intensifying. 64

[2009] found an average warming rate of 0.17±0.06◦C for the West Antarctic Continent, and of 0.234±0.09◦C/decade at WAIS-Divide, which is in good agreement with our results. O’Donnell et al.[2010] found weaker trends (0.10 ±0.09◦C/decade for West Antarctica) but also noticed a large increase in the trend at nearby Byrd station from 0.05±0.13◦C/decade over the period 1957-2006 to 0.20±0.36◦C/decade for 1982-2006. These data sets also show that the warming is concentrated in the winter and spring seasons. It is associated with a decrease in sea ice in the Amundsen and Bellingshausen Seas, and an increase in sea ice in the Ross Sea [Parkinson, 2002]. It has been attributed to an increase in warm advection though the Amundsen Sea, associated with a strong teleconnection with the central tropical Paciﬁc Ocean [Schneider et al., 2010; Ding et al., 2011]. The inversion of borehole temperature does not allow us to comment on whether this warming rate is unprecedented, because of the loss of temporal resolution with time (Figure 3.3).

3.4 Sensitivity analysis

3.4.1 Inﬂuence of the initial boundary conditions

The initial temperature profile was set to a stationary profile with a realistic seasonal cycle. The real climate is not stationary, and long-term climate changes, such as the last ice age, may still have an imprint on the first 300 m of the ice sheet. It is not practical to extend the run time indefinitely. Thus the inversion scheme was run with a suite of initial temperature profiles to include the uncertainty associated with the unknown initial condition. Each optimization with variable initial conditions was used to produce a series of 1000 solutions using Equation 3.9. We used all 6000 solutions to derive the statistics presented in the main text.

3.4.2 Inﬂuence of the bottom boundary conditions

The bottom temperature and heat flux affect the steady state temperature profile, and the vertical velocity of the ice. In a thick ice sheet (WAIS is 3450 m deep), and with 65 a large accumulation rate (22 cm/year), the advection of heat from the surface dominates the temperature distribution near the top of the ice sheet. It results that the steady state temperature profile is near isothermal for the first few hundred meters, and the boundary conditions at the bottom of the ice sheet are of limited importance. We ran a series of sensitivity tests to quantify the effect of the bottom boundary on our reconstruction

3.4.2.1 Bottom temperature

The bottom temperature was decreased from -4.68◦C to -5.18◦C. All other parameters, including the temperature history, were kept constant. This resulted in temperature differences smaller than 0.5 mK in the top 300 m of the ice sheet (Figure 3.7).

3.4.2.2 Bottom temperature gradient

The bottom temperature gradient reflects the amount of heat flux at the base of the ice. Preliminary measurements of the deep borehole show that there is a significant amount of heat flux at the bottom of WAIS. It is largely unknown how this flux may have changed in the past, but the fact that the ice is is young and undisturbed throughout most of the depth of the ice sheet suggests that the bottom of WAIS-Divide must have been melting throughout recent history [Fudge et al., 2011]. We established the bottom temperature gradient to reflect the preliminary measurements of borehole temperature in the deep ice core hole. As a sensitivity test, we increased the bottom temperature gradient by 10%. There is no measurable change (less than 0.5 mK ) to the profile in the top 300 m of the ice sheet (Figure 3.7).

3.4.2.3 Bottom depth

Determining the depth of the ice sheet is challenging. It can be done by radar measurements, sonic imaging, or by extrapolating the temperature curve to the pressure melting point. For WAIS-Divide, it is thought to be between 3440 and 3480 m. We tested the inﬂuence on the geometry of our system by changing the depth of the domain from 3500 m to 3400 m. With all other parameters kept constant, it resulted in a temperature increase of 0.4 mK at 300 m, decreasing to zero at the surface. This is insigniﬁcant in relation to the precision of our measurements. 66

50 150 250 0 500 1000 1500 2000 2500 3000 3500 ï29.5 0 best parameters increase T by 0.5°C ï29.6 b ï5 increase the bottom T gradient by 10% ï29.7 make the ice sheet 100m shorter ï10

ï29.8 ï15

ï29.9 ï20 Temperature, °C Temperature, °C ï30 ï25

ï30 ï30.1 ï4 x 10 4 0.5

2 0 0

T difference, °C ï2 ï0.5 T difference, °C 50 150 250 0 500 1000 1500 2000 2500 3000 3500 Depth, m Depth, m

Figure 3.7: Sensitivity to the bottom boundary conditions. 3 tests are presented: 1) increase the bottom temperature by 0.5◦C, 2) increase the bottom temperature gradient by 10%, which corresponds to a larger geothermal heat flux, 3) let the ice sheet thickness be 100 m less. The top 2 panels show the temperature profile, the leftmost one being a zoom over the first 300m where we have data. The bottom panels show the change in the temperature profile obtained by each of these sensitivity tests. The top 1000 m is not noticeably sensitive to changes in the bottom boundary conditions. 67

3.4.3 Inﬂuence of the vertical velocity parameterization

There are a few ways to express the vertical velocity profile. We followed Alley and Koci[1990] and Cuffey et al.[1994] in using a vertical velocity profile corresponding to a constant strain rate. Another popular expression is derived from the analytical model of Lliboutry, as used by Goujon et al.[2003]. These two expressions produce marginally different vertical velocities in the top 300 m: the maximum difference is about 3.5 mm/yr (or 1.8%) at 300 m depth, and it increases to 18 mm/yr at 2800 m depth. It translates to 2 mK difference in the 300 m profile, and a 0.55◦C difference at 2800 m. Getting a realistic parameterization of the vertical velocity is important at depth, but for the top of the ice sheet, our assumption does not affect the conclusions. The uncertainty in the vertical velocity comes mainly from uncertainty in the accumulation rate: the vertical velocity is proportional to the accumulation rate, which is discussed in the next section.

3.4.4 Inﬂuence of the accumulation rate

The model we use has a constant density profile, and only uses the accumulation rate in the calculation of the vertical velocity. Banta et al.[2008] have shown that the accumulation rate is on average 0.22±0.04 mice/yr at WAIS-Divide. We have run a sensitivity test including the variable layer-counting-derived accumulation rate for the last 230 years. It did not affect the temperature profile noticeably, mainly because the mean accumulation rate has not changed significantly. However, if we decrease the accumulation rate to 0.20 m/y, the same temperature anomaly will appear shallower in the ice, and the timing of the extrema will be affected. Decreasing the accumulation rate by 10% creates a temperature difference up to 10 mK at 300 m (third panel of Figure 3.9). It will have an effect on our reconstruction. We performed the same optimization for an accumulation rate of 0.20 m/y and found that the cold minimum was about 10% larger, and its timing offset by 39 years, which fits within the stated error in the main text. Preliminary measurements of layer thickness in the deep ice core WDC06A indicate that the accumulation rate at WAIS-Divide may not have changed by more than 10% over the last 2000 years (Joe McConnell, personal communication). This sensitivity 68

50 150 250 0 500 1000 1500 2000 2500 3000 3500

0.3 0.3 0.2 0.2 m/y m/y 0.1 0.1

vertical velocity, 0 0 vertical velocity, 0 Constant strain rate ï29.6 Lliboutry ï10 ï29.8 ï20

Temperature, °C ï30 Temperature, °C ï30 ï3 x 10 3 1

2 0.5

°C 1 0 T difference,

0 ï0.5 T difference, °C 50 150 250 0 500 1000 1500 2000 2500 3000 3500 Depth, m Depth, m

Figure 3.8: Comparison of the borehole temperature profile obtained from two different vertical velocity parameterizations: 1) constant strain rate [Cuffey et al., 1994], 2) Lliboutry [Goujon et al., 2003]. The top panels show the vertical velocity, the middle panels the temperature profile, and the bottom panels the difference between both temperature profiles. On the left is a zoom over the 300m where we have data. 69 test can be treated as an upper limit to the real variability. A different model with a more sophisticated treatment of the downward motion of the ice could produce a more detailed result.

3.4.5 Inﬂuence of the thermal conductivity of the ice

The thermal conductivity of the ice is difﬁcult to parameterize because it depends not only on density, but also on the type of packing of the snow grains. We used the Schwerdtfeger formula [Cuffey and Paterson, 2010, Chapter 9], which depends on both temperature and density of the snow. It usually gives an upper estimate of the thermal diffusivity of snow. We decreased the thermal conductivity by 10%, and ran the optimization of the temperature again. It resulted in a shift of the timing of the main temperature minimum by 58 years (earlier), but no change in the amplitude of the signal (Figure 3.10). We observed a similar shift when decreasing the initial temperature by 0.1◦C.

3.4.6 Inﬂuence of the basis functions used in the inversion.

3.4.6.1 Inﬂuence of the prior covariance of the model parameters

The shape of the solution is determined in part by the choice of the covariance matrix of the model parameters (denoted by P in the main text). Our assumptions about what constitutes an acceptable solution are manifested in the choice of the matrix P. We made three assumptions:

1. The variability of the climate should not be more than order 0.5◦C. This value was chosen in the range of published changes in climate. Dahl Jensen et al. [1999] found a variability on the order of 0.3◦C using a Monte Carlo inversion of the Law Dome (Antarctica) borehole temperature proﬁle.

2. The low frequencies are favored over the high frequencies: we will favor a long- term climate change over a shorter-lived event of larger amplitude.

3. The prior spectrum is stationary: Every point in time is given the same decorrelation timescale. 70

0.24

0.22 rate, m/y Accumulation 0.2

1750 1800 1850 1900 1950 2000 Time, year C.E. ï29.5 data ï29.6 constant accumulation 0.22 m/y ï29.7 variable accumulation (Banta et al. 2008) accum 0.20 m/y ï29.8 accum 0.24 m/y ï29.9

Temperature, °C ï30

20 Depth, m 0

Temperature ï20

difference, mK 50 100 150 200 250 300 350 Depth, m ï28.5 accum = 0.22 m/y ï29 accum = 0.20 m/y ï29.5 ï30

Temperature, °C ï30.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 time, year C.E.

Figure 3.9: Influence of the accumulation rate. Four scenarios are compared: 1) constant accumulation rate at 0.22 m/yr, 2) variable accumulation rate for the last 230 years according to Banta et al.[2008], 3) constant accumulation rate at 0.20 m/y, 4) constant accumulation rate at 0.24 m/y. The top panels show the accumulation rate history that served as an input. The second panel shows the temperature profile for the first 350 m, with all other inputs unchanged. The third panel shows the difference between scenarios 2, 3, and 4, and scenario 1. The bottom panel shows the reconstruction based on an accumulation rate of 0.20 m/y, with an improved fit to the data, and the initial temperature reconstruction using 0.22 m/y. The reduction in the accumulation rate requires an increase in the amplitude of climate changes, and a shift of the extrema towards earlier times. 71

50 150 250 0 1000 2000 3000 ï29.9 Initial run 0 ï29.95 k decreased by 10%, same T history ï10 ï30 ï20 ï30.05 Temperature, °C Temperature, °C ï30.1 ï30

0.01 0.1

0 0 ï0.1 ï0.01 ï0.2 ï0.02

T difference °C ï0.3 T difference °C ï0.03 ï0.4 50 150 250 0 1000 2000 3000 Depth, m Depth, m ï28.5 Initial run Thermal conductivity decreased by 10% ï29 other initial condition runs

ï29.5

Temperature, °C ï30

ï30.5 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time, year C.E.

Figure 3.10: Sensitivity to a 10% decrease in the thermal conductivity. The top panels show the temperature proﬁles, with the initial run, and the 10% lower k run, using all other parameters equal. On the left is a zoom over the 300m where we have data (black + signs). The middle panels show the difference between these two proﬁles. The bottom panel shows the initial temperature reconstruction used as a boundary condition in blue, the optimal temperature reconstruction for a 10% lower thermal conductivity in dashed red, and optimal solutions for other initial conditions as presented in Figure 3.4 of the main text, to give an idea of the uncertainty in the reconstruction. Lowering the thermal conductivity creates a shift in time, but no change in the amplitude of the extrema 72

There are several ways to weigh the low frequencies. Shen et al [1992] discussed a range of choices for the matrix P. We used the standard inverse-square frequency f −2 spectrum, which translates into choosing

f(i)−2 P = σ2 i,i x P −2 (3.10) i f(i) with f(i) the frequency of the sin/cos used in the basis functions, and σx=0.5C the a- priori root mean square error of the model parameters. This reconstruction is represented by the green curve in Figure 3.11. As a sensitivity test, we also used

(f(i) + f )−2 P = σ2 0 i,i x P −2 (3.11) i(f(i) + f0)

−1 with an offset f0=1/270 yr (red curve in Figure 3.11). This means that the prior spectrum is a little less red, and the higher frequencies have a slightly larger variance.

If we let f0 be too large, the amplitudes of the lowest frequencies become larger than expected, which violates our assumptions. This solution allowed a higher frequency structure, which is reﬂected in the reconstruction by the absence of a bump circa 400 C.E. in the red curve compared to the blue, and the temperature extrema being slightly closer to the present. We also tried a Gaussian spectrum

2 f(i) Pi,i = σxexp − (3.12) f0

−1 with an e-folding scale f0=1/67 yr (blue curve in Figure 3.11). A Gaussian spectrum damps out the high frequencies faster than f−2. In our data, we need enough high frequencies to fit the most recent times. The Gaussian spectrum did not perform as well as the f−2 spectrum. Each spectrum can be converted into a covariance by computing BPBT , which shows the timescales allowed. Figure 3.11 shows the best temperature history found with each one of these prior covariance matrices, along with the misfit with the data, and the prior covariance matrix plotted in the time domain. As the spectrum gets whiter (favoring high frequencies), the covariance between different times diminishes, which 73 will increase our error bars, because we are not able to resolve fast changes in the climate. It should be noted that the prior covariance has a limited effect on the least square optimum, but is a dominant component of the posterior error estimate Pˆ. In other words, the prior spectrum defines our error bars: by choosing a relatively short decorrelation timescale, we allow the temperature to change fast, which will increase the error bars in our reconstruction. We considered that the short decorrelation timescale needed to resolve the recent warming should apply to the whole 2000-year reconstruction. Had we chosen a much larger correlation in the more distant past, the error bars would have been much smaller. The choice we made produces a very conservative error estimation of the Seventeenth century minimum.

3.4.6.2 Inﬂuence of the signal to noise ratio

If the signal to noise ratio is increased, the ﬁt to the data increases, and the amplitude of the extrema also increases. We choose a signal to noise ratio consistent with previous studies, taking care to avoid it being too high and creating spurious extrema.

3.4.6.3 Inﬂuence of the basis functions

We chose to use Fourier Series for a basis functions in order to keep the same baseline assumption of no change with the climate, and no change in the variability in the climate over all time periods. Choosing a stationary prior helps reduce the tendency to over-emphasize the abnormality of the recent warming. As an alternative to Fourier Series, we used piecewise linear functions to describe the space of temperature history, with a time correlation decreasing towards the present (purple curve in Figure 3.11). The matrix P is a little different, which induces a different optimal solution, but it shares the same basic characteristics with the other solutions: a temperature minimum between 1400 and 1800 C.E., and a large increase in temperature over the last 50 years. The variations in the timing of the large minimum reﬂect the uncertainty associated with this timing. 74

Temperature reconstruction ï28 gaussian ï28.5 kï2 with offset kï2 piecewise linear ï29

ï29.5

ï30 Temperature, °C

ï30.5

ï31 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time, year C.E.

modelïdata misfit Prior error covariance matrix 0.01 0.25 2 0.005 0.2 0.15 0 0.1 ï0.005 Temperature, °C 0.05 covariance, in (°C)

ï0.01 0 0 100 200 300 ï1000 ï500 0 500 1000 Depth, m Time, year

Figure 3.11: Influence of the prior covariance and basis functions used in the linearization. The blue line shows the reconstruction using Fourier series, with a Gaussian spectrum. The red line shows the reconstruction using Fourier series, with a quadratic spectrum with an offset. The green line shows the reconstruction for a Fourier decomposition, with simple quadratic spectrum. The purple line shows the optimal solution found using a piecewise linear decomposition with the same signal to noise ratio of 250. The bottom left panel shows the misfit between the temperature profile corresponding to each of these temperature histories, and the data. Note that they do not all fit the data in the same way, but they are all within the stated error. The bottom right panel shows the prior covariance matrix of the modeled temperature as a function of time difference with the reference time at the center. The covariance is stationary, meaning the same for all reference times. The narrower the covariance, the more weight is given to high frequencies, which is reflected in the reconstruction (top): shorter period are supplanted by longer periods. 75

3.4.7 Uncertainty in the measurements

Uncertainties in the measurements are of two types: systematic biases, which affect the accuracy of the absolute value of the temperature measurement, and random noise, which may affect each data point separately. With respect to the borehole temperature problem, we are not as concerned by biases affecting the whole data set uniformly, as we are about errors that can be wrongly interpreted as climate signals. In the following section, we have separated out the uniform biases, and the noise, which affects the reproducibility of one measurement to the next, and which is of a higher concern. The dominant source of uncertainty is the calibration of the thermistor, which has both types of error, and is treated ﬁrst.

3.4.7.1 Uncertainty in the calibration

The thermistor was measured against a secondary standard platinum resistance thermometer (Burns Engineering 12001, with a Hart 1502 readout), in a chilled ethanol bath between 40◦C and 20◦C. The PRT has an expanded uncertainty of 0.006◦C, but we consider that the long-term drift of the probe from the time of NIST calibration may be as much as 0.1◦C (worst case scenario). The repeat uncertainty of this probe in the range -38 to 0◦C is typically 0.003◦C and can be as much as 0.010◦C (manufacturer speciﬁcations). The calibration was done following the Steinhart-Hart equation:

1 = a + a ln(R) + a ln(R)3 (3.13) T 1 2 3 with T the temperature in K, R the resistance in kΩ, and the coefﬁcients −3 −10 −4 −11 a1 = 3.00805×10 ±3.6×10 , a2 = 3.0665027×10 ±5.8×10 and a3 = -5.7055528×10−7±3.14×10−14 The propagation of error in the calibration, supposing that the Steinhart-Hart equation is a near perfect determinant of the temperature behavior of the probe, produces an uncertainty of 2.3 mK in the range of our borehole measurements: -29.4 to -30.8◦C. For this set of measurements, we consider the accuracy of our calibration to be 0.1◦C, and its precision to be 2.3 mK. 76

3.4.7.2 Systematic biases

In addition to systematic bias in the calibration of the probe, several artifacts can bias the measurements. The self heating of the probe can create a positive bias, uh. We ◦ estimated the self heating for a heating rate hr = 1 mW/ C in air, a source current of I = 2 −5 2 5 −3 ◦ 10 µA, and resistance of R = 40 kΩ. It is uh = I ×R/hr = (1e ) ×4e /1e = 0.04 C. We always used the same source current, but the resistance varied by 1.4 kΩ, which includes a potential bias of 1.4 mK over the range of measurements. The self heating was limited by only switching the system ON for a short period of time: in between measurements, the multimeter was turned off, and the probe was allowed to equilibrate with the ambient temperature. The procedure was replicated exactly for every sample, to ensure that the same amount of self heating was introduced into the measurements. Thus self heating bias was likely to be uniform across the data set. The leads may have a certain amount of current leakage. The current leakage is estimated to create a bias ul = 1/a×R/(R+Rl) = 0.6 mK, with a = 0.0611 the probe temperature coefficient, R the thermistor resistance (R≈40 kΩ), and Rl the critical leakage path resistance (Rl ≥ 1GΩ). We used a 1000 ft spool of wire, with 4 wires to limit the uncertainty in the lead wire resistance. We also inspected the wire for any breaks in the shielding, and found that it was in perfect condition. Both the self heating and current leakage effects are accounted for in the calibration. Hysteresis effects were minimized by measuring the temperature after a 20 min equilibration time, and by measuring the temperature both going upwards and downwards. There was no significant difference between upward and downward measurements: the mean difference was 0.95 mK, which is within the stated uncertainty. We used the scanning function of our precision multimeter to verify that the temperature had reached a plateau before starting the measurement integration at each depth. When measuring temperature in an air borehole, we need to consider the possibility of cold air sinking to the bottom of the borehole in winter and biasing our measurements. We measured the temperature during 2 summer Antarctic seasons, and found that the mean difference between the profiles taken in 2008 versus 2009 was 1.6 mK below 100 m (2009 was colder), which is within the stated uncertainty. Therefore, we do not anticipate any cold bias from sinking air. Likewise, we do not expect a warm bias 77 due to thermal disturbance during drilling, which occurred in January 2005, because this disturbance should have decreased with time. Near the surface, solar radiation and wind pumping can have a leading effect on the temperature of the first 10 to 20 m. For that reason, we did not use the first 15 m of the temperature profile in our inversion.

3.4.7.3 Random noise

The temperature resolution of a Kelvin circuit can be calculated as ur = ∆R/(a×R) = 0.1/(0.0611×40000) = 4×10−5 K, with ∆R=100 mΩ the resolution of the readout, a = 0.0611 the probe temperature coefficient, and R the thermistor resistance (R≈40 kΩ). Clearly, this is not a considerable source of uncertainty in our measurement. The most important source of random noise are the electrostatic charges building up near the instrument: On the ice sheet, there is no ground, and the wind can cause a large amount of electrostatic charge to build up on the walls of the nylon tent or on dangling cables. We limited the static buildup by keeping all other electric charges (like the snowmobile) away from the measurement tent, limiting the movements of the electrical wire, and limiting movements of the operator while measuring. We also used 12 V batteries with an inverter to power the multimeter, in order to avoid static buildup from a DC generator. It is difficult to establish how much noise may have been caused by electric charge buildup, but it is reasonable to expect that repeat measurements with several days in between, and from year to year should average out potential errors. High frequency noise was limited by integrating the resistance reading over 5 minutes. Other random processes were taken into account by taking repeat measurements over several days. The standard deviation of repeat measurements in the field was 1.8 mK below 50 m. This number integrates all sources of random noise, and represents the overall reproducibility of our measurements. It is better than the uncertainty in the calibration (2.3 mK), highlighting the fact that the calibration is the dominant source of uncertainty.

3.5 Conclusion

WAIS-Divide was colder than the last 1000 year average from 1300 to 1800 C.E.. This trend is broadly synchronous with the large scale cooling of 1400-1700 C.E. 78 in the Northern Hemisphere, although the details of these records are not in phase. These findings support the hypothesis that solar minima, associated with persistent volcanism, can noticeably cool the planet, but the feedbacks amplifying the radiative forcing may operate differently in each hemisphere. This record also confirms the work of Steig et al.[2009], showing that WAIS- Divide has been warming by 0.23±0.08 ◦C per decade over 1957-2007 C.E. This warming trend has accelerated to 0.8±0.06 ◦C per decade over the last 20 years (1987-2007). It is thought to be associated with a stronger teleconnection with the central tropical Pacific, which induces increased warm advection into the continental interior in winter and spring [Ding et al., 2011], and not with the increase in polar westerlies due to the ozone hole. It is unclear whether this warming is unprecedented, or whether it fits within the natural variability of West Antarctica. Other data that do not have the same type of limitation, such as water isotopes or noble gases from ice cores [Kobashi et al., 2010], will provide additional constraints on this issue. Much remains to be understood about the variability in the West Antarctic climate. Records like this one provide important boundary conditions for climate models in a part of the world with notoriously sparse data coverage.

Appendix 3.A Forward model description

The forward firn and ice model is based on the 1 dimensional heat and ice flow equation, discretized in an explicit finite difference scheme, following Alley and Koci [1990]: ∂T ∂ ∂T ∂T ρc = k − ρc w + Q (3.14) p ∂t ∂t ∂z p ∂z where ρ is the density of firn/ice, k the thermal conductivity, cp the heat capacity, T the temperature, t the time, z the depth, w the downward velocity of the firn/ice, and Q the heat production term, taking into account ice deformation and firn compaction. WAIS-Divide is near the ice flow divide, and the horizontal advection of mass and heat are both negligible. 79

3.A.1 Model parameters

The density of ice, ρ(z), is determined by a quadratic fit to measured bulk density data, following Severinghaus et al.[2010]. Data were collected on meter averages of cores coming from the WDC05A borehole by Todd Sowers [Battle et al., 2011]. The density profile is considered to be in steady state. The accumulation rate was taken as a constant 0.22 mice/yr [Banta et al., 2008]. The year-to-year variability of the accumulation rate is on the order of 0.04 m/yr, and does not result in any significant difference in the temperature reconstruction. A detailed description of the influence of the accumulation rate is presented later in this document. The vertical velocity of the firn or ice w is determined using a constant strain rate, following [Cuffey et al., 1994]. The heat capacity cp, thermal conductivity k and heating term Q are all determined according to the classical equations [Cuffey and Paterson, 2010, Chapter 9 ]. They have a dependance on temperature, and are updated at each time step. The depth of the firn/ice column is 3500 m, and no rock is modeled. We used a depth interval of 1 m for the first 500 m, and 25 m for the deeper section. The model is advanced by an explicit differentiation method, using 200 time steps per year for 2000 years.

3.A.2 Boundary conditions

The model is initialized with a stationary temperature proﬁle corresponding to a constant climate with a seasonal cycle, which is a simpliﬁed average of 3 years of weather station data from WAIS-Divide and Byrd station (AMRC, SSEC, UW-Madison).

Tsea(t) = 10(cos(2πt) + 0.3cos(4πt)) (in K) (3.15)

The seasonal cycle does not change throughout the run, and the annual average temperature is the key evolving parameter. Preliminary measurements of the 3400m deep borehole indicate melting at the bed [Fudge et al., 2011]. We used a constant temperature and temperature gradient at the bed, consistent with those preliminary measurements. The inﬂuence of the bottom boundary condition is detailed in the Section 3.4.2. 80

Acknowledgement This chapter, in full, is a reproduction of the material as it appears in Orsi A., B. Cornuelle and J. Severinghaus, Little Ice Age Cold Interval in West Antarctica: Evidence from Borehole Temperature at the West Antarctic Ice Sheet (WAIS) Divide, Geophys. Res. Let., 2012. The dissertation author was the primary investigator and author of this work. Chapter 4

Analytical Methods

Abstract.

A suite of methods is described to measure nitrogen, argon and krypton isotopes at high precision in gases trapped in ice cores, building on earlier work by Kobashi et al. [2008a] and Severinghaus et al.[2003]. The isotopic values are expressed as a per mil change from a reference, which is modern air taken in La Jolla, California. The stability of the La Jolla air standard over time is evaluated. The first method (hereafter ”copper method”) uses hot copper to remove oxygen, and enables nitrogen and argon isotopes to be measured in the same piece of ice. In air, the precision of this method is 3 per meg for δ15N, and 10 per meg for δ40Ar, and 4.8 and 14 per meg respectively on 100 g, 10 cm long ice samples. The first direct measurement of δKr/N2 is also presented, with a precision of 0.18 per mil in air, and 0.63 per mil with 10 cm ice samples. The second method (hereafter ”getter method”) uses gettered air to make precise measurements of argon and krypton isotopes. We present the first measurement of all the major isotopes of krypton, at masses 78, 80, 82, 83, 84 and 86 in firn air samples using a new MAT-253 mass spectrometer especially designed for this purpose. The precision of these measurements is 20 per meg for δ86/82Kr, 22 per meg for δ86/83Kr, 13 per meg for δ86/84Kr, and 7 per meg for δ40Ar. Separate ice core measurements using a similar method on a MAT-252 mass spectrometer yield a precision of 18 per meg for δ86/82Kr and 10 per meg for δ40Ar. The argon isotopes measured with both methods agree within

81 82

2 per meg.

4.1 Introduction

Polar ice contains air locked in bubbles formed when the snow turns into ice. This air is a unique archive of the ancient atmosphere, but it is not a direct atmospheric sample: in the firn (old snow) layer, gases can unmix by molecular diffusion. The study of inert gases allows us to understand this diffusive process, correct other gases from it, and retrieve the true atmospheric composition. The study of gas diffusion in the firn started with the measurements of nitrogen isotopes [Sowers et al., 1989], and the identification of the two main sources of fractionation: gravitational settling [Craig et al., 1988] and thermal diffusion [Severing- haus et al., 1998]. The separation of these two effects required the use of isotopes from another inert gas, argon, which was initially measured on separate ice samples [Sever- inghaus et al., 2003]. However, the observed decimeter scale variability in ice requires that both isotopes of nitrogen and argon be measured in the same piece of ice [Kobashi et al., 2008a]. Nitrogen isotopes were originally measured at the University of Rhode Island [Sowers et al., 1989], and a similar approach was developed at Scripps Institution of Oceanography and at the Laboratoire des Science du Climat et de l’Environement (LSCE), France [Landais et al., 2004b]. Efforts were made to increase the through- put of the method, using a continuous flow method [Huber et al., 2003; Huber and Leuenberger, 2004], or a semi-automatic extraction [Capron, 2010], but the same precision could not be achieved, because of issues with solubility and automatic valves. We present here in Section 4.3 a method to measure N2 and Ar isotopes at high precision in the same piece of ice, based on the method of Kobashi et al.[2008a], with some improvements. This method also includes the first direct measurements of δKr/N2 in ice cores, to our knowledge. As our understanding of the fractionation in the firn increases, it becomes interesting to measure the isotopes of other noble gases. The isotopes of Kr and Xe can inform us on the thickness of the convective zone, in which convective mixing dominates transport, at the top of the firn [Severinghaus et al., 2010; Kawamura and Severinghaus, 83

2006]. The abundance of Kr and Xe in air is too low to allow for direct measurements, so we must use a large (700g) piece of ice, and concentrate the noble gases by gettering, which removes N2 and other reactive gases [Headly, 2008]. We present in Section 4.4 the ﬁrst measurement of all the stable isotopes of krypton in ﬁrn air, and in Section 4.5 ice core measurements of argon and krypton isotopes, as well as Kr/Ar, Xe/Ar and Ne/Ar, based on the method of Headly[2008].

The isotopic ratios of N2, Ar and Kr are expressed relative to present day air. The extraction and stability of our modern air standard is discussed in Section 4.2. A suite of appendices detailing the step by step procedure for each of the experimental methods discussed is presented at the end of this chapter.

4.2 La Jolla Air standard

The atmospheric composition of isotopes in inert gases is essentially constant on the timescales that we are interested in (>100,000 years). Nitrogen is not strictly inert, but the atmospheric reservoir is so large that even major changes in the nitrogen cycle, or the recent use of nitrogenous fertilizer would not measurably affect the isotopic content of N2 in air [Sowers et al., 1989]. Noble gases (Ne, Ar, Kr, Xe) do not have any major sources and sinks in the ocean-atmosphere system. The small changes in the air abundance of Ne, Ar, Kr and Xe are governed by air-sea gas exchange, which is controlled by mean ocean temperature [Headly and Severinghaus, 2007]. The mean ocean temperature changes during the late Holocene are too small to be noticeable in either isotopic composition or elemental ratios of the noble gases. As the atmospheric mixing time is about one year, these gases are globally uniform and thus serve as a convenient reference for laboratories worldwide. As a result, we use the present day atmosphere as the reference to which we will report changes. The air is extracted from the end of the SIO pier in La Jolla, California. The details of the extraction are given in Sections 4.2.1 and 4.2.2. The stability of the standard is discussed in Section 4.2.4. 84

4.2.1 Pier extraction

Atmospheric air is extracted into 2-L flasks following the method of Headly [2008]. Air is pumped through an aspirated intake, passes through two -100◦C traps, through a neoprene diaphragm pump at 4L/min, and through a 2-L flask. The tubing is made of 1/4 inch synflex R , and the connections made with ultra-torrs R using viton o-rings (Figure 4.1).

Air Air

aspirated PUMP intake 4L/min

-100°C

Figure 4.1: Schematics of the set up to extract La Jolla Air standard.

The flask is flushed for 5 minutes at 4L/min. The pump is then turned off, and the air is allowed to sit still for 5 seconds before the valves of the flask are closed. Details of the protocols are given in Appendix 4.A. The flasks are filled at the end of the pier, on days with a light sea breeze, which minimizes the potential for pollution from the city. We once filled two flasks on a day with easterly wind (i.e. from the city), and got unusual results in all isotopic ratios, both on the MAT-252 and on the Delta- V. The operator sits downwind of the flask while they are flushing. The flasks are also preferably filled in the morning shade, to avoid thermal fractionation due to the radiative heating of the black synflex R tubing. We have not noticed any sign of significant thermal fractionation between flasks. Additionally, we found that we get more reliable results by filling flasks individually, rather than hooking them up in series, even using long synflex R tubes between them. 85

4.2.2 Aliquot extraction

Each 2-L flask can be used to extract up to 10 aliquots. For Ar-N2 samples, the air in the flask is expanded into a series of 3 pre-evacuated volumes: the central volume is 10 cc, and the other two are of comparable size. The use of the three volumes allows us to minimize the small amount of fractionation that might happen during the expansion, which would make the first volume lighter than the last [Severinghaus and Battle, 2006]. The air is expanded for 5 seconds into all three volumes. The flask valve is then closed, and the volumes are allowed to equilibrate for 30 min, after which the central volume is isolated. The first volume is then pumped away, and the central volume extracted following the same procedure as used for ice samples (Section 4.3). This procedure allows us to have a quick extraction of air from the 2-L flask: the volume that it expands into is large enough to allow for bulk motion of air, and avoid fractionation during the valve opening. This quick extraction also minimizes the chance of compromising the 2-L flask with a leak. During the 30 min equilibration of all three volumes, they are placed in thick bubble wrap in order to minimize any temperature difference between them. For the large 80 cc samples used for Kr isotope analyses, the flask is directly expanded into the 80 cc volume, and there is no need to use 3 volumes. Bulk flow of air is apparently strong enough to sweep all fractionated gases into the 80 cc volume, resulting in no net fractionation. The expansion is also limited to 5 seconds. This is long enough to allow bulk flow to cease, but short enough to prevent thermal fractionation in response to the cooling induced by the expansion. The sample is then processed as a sample of ice would be.

4.2.3 Working standard

Due to the labor intensive nature of measuring La Jolla air, we use a working standard, made from a mixture of pure commercially obtained gases in atmospheric proportions. Details about how to fill the standard cans are given in Appendix 4.B.A stainless steel flask, equipped with a 1.4 cc pipette, is filled with enough gas to last through the measurement of the whole data set. This standard is then calibrated against 86

La Jolla air aliquots, regularly through the data set. The sample is measured against the working standard (WSTD), and a delta value is calculated following:

R(sample) δ = − 1 1000 (4.1) 1 R(WSTD)

R refers to the ratio of isotopes, for δ15N, it is mass 29 over mass 28. The La Jolla air standard is measured against the working standard:

R(LJA) δ(LJA) = − 1 1000 (4.2) R(WSTD)

Finally, the isotopic ratio is expressed with respect to La Jolla Air:

R(sample) δ /1000 + 1 δ = − 1 1000 = 1 − 1 1000 (4.3) R(LJA) δ(LJA)/1000 + 1

4.2.4 Stability of the standard

During the year 2010, twelve flasks were filled with La Jolla air, and measured against the working standard ArN2-18 (Figure 4.2). It was a time of method development, and the protocol was not exactly constant. Moreover, we had a lingering problem with the first sample of the day having systematically lower δ40Ar. We found out later that it was due to an incomplete homogenization of the sample before being measured on the mass spectrometer, in combination with the greater temperature stratification of the liquid helium dewar after sitting undisturbed overnight. We measured 118 samples, and rejected those extracted at the beginning of the day, exhibiting low δ40Ar, as well as a few others, when something went wrong during the extraction or the mass spectrometry. A total of 37 samples were rejected. Figure 4.2 shows δ40Ar versus δ15N, with each symbol representing a flask. Rejected samples are highlighted in black crosses. Mass dependent fractionation would align samples on the diagonal of the grid, and thermal fractionation on a slope of 2.75 per meg of δ40Ar for each per meg of δ15N. Table 4.1 40 15 shows the mean and standard deviation of δ Ar, δ N, δAr/N2, and δKr/N2 for each flask, along with the mean and standard deviation of all flasks and all samples. There is 87 no significant offset between flasks, which confirms that the modern atmosphere is an appropriate standard, and that our extraction method is adequate.

Stability of La Jolla Air standard

0.224 0.224 13-Jan 18-Nov 0.208 0.192 18-Nov 13-Jan 0.176 22-Jan 22-Jan 0.208 0.160 9-Feb 9-Feb 0.144 23-Mar 23-Mar 0.128 9-Apr 9-Apr 0.112 20-Apr 0.192 20-Apr 0.096 29-Apr 29-Apr 0.080 Ar, per mil Ar, 19-May per mil Ar, 19-May 0.064 40 1-Jun 40 0.176 1-Jun

δ 0.048 δ 21-Sep 21-Sep 0.032 11-Oct 11-Oct 0.016 "rejected" 0.000 rejected 0.160 1.518 1.526 1.534 1.542 1.550 1.558 1.566 1.574 1.536 1.540 1.544 1.548 1.552 1.556 δ15N, per mil δ15N, per mil

Figure 4.2: Long term stability of the standard. 12 flasks were filled with La Jolla air through the year 2010. Two to 12 samples were processed for each flask, and measured against the working standard ArN2-18.

4.3 Nitrogen and argon isotope measurements

Bubble trapping in a gravitational ﬁeld in the ice is a complex and poorly understood process, and our goal is to measure two pairs of isotopes from the same bubbles in the same piece of ice, so that some of this complexity would cancel out. The two most abundant inert gases in air are N2 (78.084%) and Ar (0.933%). Because we are primarily interested in the difference between δ15N and δ40Ar/4, noise that affects both pairs equally can be eliminated this way. We use about 100 ccSTP of air in order to make a precise measurement of argon isotopes, which corresponds to 80 to 100 g of ice per sample. Argon has stable isotopes of mass 40 (99.6 %), 36 (0.34 %) and 38 (0.06 %). We 40 36 measure mass 40 and 36, and report the ratio RAr= Ar/ Ar, with respect to the same ratio in modern La Jolla air standard RAr,ST :

! R δ40Ar = Ar − 1 1000 (4.4) RAr,ST

We cannot measure 36Ar precisely without removing oxygen from the air because of the 88

Table 4.1: Mean values of La Jolla air flasks against the working standard ArN2-18. The first column labels the time when the first sample was taken out of a flask, the second column the number of samples used to calculate the mean, and subsequent columns the mean and standard deviation of isotopic and elemental ratios, in per mil. The last 3 lines show the mean and standard deviation of the 12 flask-means, the standard deviation of all 81 samples for each ratio calculated, and, for comparison, the raw machine precision (see Section 4.3.4). 40 15 Flask ID nb δ Ar δ N δAr/N2 δKr/N2 mean stdev mean stdev mean stdev mean stdev 18-Nov-09 8 0.1921 0.0082 1.5457 0.0019 3.08 0.06 2.67 0.52 13-Jan-10 7 0.1909 0.0088 1.5476 0.0025 3.11 0.15 3.39 0.72 22-Jan-20 8 0.1957 0.0102 1.5450 0.0034 3.08 0.07 3.07 0.38 9-Feb-10 8 0.1918 0.0118 1.5433 0.0029 3.07 0.10 2.82 0.35 23-Mar-10 5 0.1914 0.0099 1.5439 0.0028 3.04 0.09 3.03 0.45 9-Apr-10 8 0.1861 0.0060 1.5467 0.0049 3.02 0.07 2.42 0.62 20-Apr-10 8 0.1891 0.0090 1.5436 0.0038 3.12 0.20 2.32 0.68 29-Apr-10 11 0.1928 0.0060 1.5451 0.0032 3.07 0.10 2.62 0.30 19-May-10 9 0.1928 0.0080 1.5442 0.0039 3.01 0.29 2.12 0.60 1-Jun-10 5 0.1740 0.0070 1.5390 0.0022 3.03 0.08 2.72 0.27 21-Sep-10 6 0.1869 0.0168 1.5471 0.0058 2.85 0.45 3.50 0.83 11-Oct-10 5 0.1874 0.0060 1.5462 0.0040 3.05 0.20 3.27 0.71 flasks 12 0.1893 0.0056 1.5448 0.0023 3.04 0.07 2.83 0.43 samples 81 0.0096 0.0038 0.17 0.64 raw σ 0.0063 0.0014 0.07 0.35 89 isobaric interference with 18O18O, which also has a mass of 36. The ratio of 18O18O/36Ar in air is 2.6 %, which is significant. We therefore reduce the air to remove oxygen, using hot copper (see Section 4.3.2). Nitrogen has stable isotopes of mass 14 (99.636 %) and 15 (0.364 %), and we measure mass 28 (14N 14N) and mass 29 (14N 15N), and report the ratio 15 14 14 14 RN = N N/ N N in the δ notation with respect to the same ratio in our modern La 15 Jolla air standard RN,ST : δ N = (RN /RN,ST − 1)1000. The reduction of oxygen with hot copper may also cause a reduction of CO2 into CO, which has isotopologues that interfere with N2 at mass 28 and 29. We therefore take care to remove CO2 and other organic molecules with a liquid N2 trap prior to the reduction.

4.3.1 Set up description

The gas extraction set up generally follows the method of Kobashi et al.[2008b] (Figure 4.3). The ice is loaded into a glass vessel and bolted onto the line with a Conﬂat

Pump

2 capillary 9 1 5 6 8 10 4 copper 7 10 11 Torr 1 Torr H2 Trap 2: Trap 3: Liq. N2 Liq. N2 500 C Trap 1: -100 C Ethanol

liq. 4 K Helium

Figure 4.3: Schematics of the set up to measure N2 and Ar isotopes in ice

flange. It is evacuated for 20 min, while the ice is kept at -22◦C by a chilled ethanol bath. The connection to the vacuum pump is then closed, and the sample melted, releasing the air. It is then transferred by cryo-pumping to a dip tube immersed in liquid helium for 25 min, while the vessel is stirred, in order to ensure full degassing of the water. The 90 air passes through a water trap at -100◦C, in order to remove the large amount of water vapor from the air, and to employ water vapor as a carrier gas. The trap is equipped with a capillary to limit the flux of water that is evaporated. Then, the air passes through a ◦ trap of liquid N2 at -196 C to remove CO2 and other contaminants. The sample enters an oven filled with copper wool at 500◦C, in order to remove oxygen. The pressure in the line is kept below 1 Torr, to ensure full O2 removal, and monitored with a 1-Torr

Baratron pressure gauge. Finally, the sample passes through another trap of N2 at - 196◦C, to remove contaminants generated by the oven, and freezes in a stainless steel dip tube immersed in liquid helium at 4 K. When the transfer is ﬁnished, the sample sits in the stainless tube overnight to homogenize at room temperature, and is analyzed on a MAT-252 mass spectrometer the next day (see section 4.3.4). The copper is regenerated ◦ with a stream of pure H2 at 500 C for 3 minutes. The key steps in the extraction, and modiﬁcations from the method of Kobashi et al.[2008b], are highlighted in the next few sections. A detailed set of instructions is provided in Appendix 4.C.

4.3.2 Oxygen removal

Oxygen removal by hot copper is a well established method which dates back to the 19th century and the discovery of air composition by Lord Rayleigh and Ramsay, which earned Sir Ramsay the Nobel prize in chemistry in 1904. Copper removes oxygen at temperatures higher than 500◦C, and it is recommended to use it up to 600◦C[Gibbs et al., 1956]. At 600◦C, the flow rate can be up to 1.83 L/min [Gibbs et al., 1956]. However, if the flow rate is too high for a moment, it compromises the copper, and merely reducing the flow rate will not restore its power [Gibbs et al., 1956]. We used about 2g of copper turnings (Fisher Scientific) spread over 10 to 15 cm in a quartz tube with a 3/8 inch outside diameter, and heated to 500◦C with an inconel wire looped around the tube attached to a variable voltage transformer. The quartz tube had an indent on one end so that the copper turnings would not be sucked into the vacuum pump.

4.3.2.1 Optimisation of the oxygen removal process with hot copper

Kobashi et al.[2008b] heated the copper to 500 ◦C, with a maximum pressure 91 in the line of 500 mT. The flow rate is the limiting factor in the transfer time, and we aim to let it be as high as possible, while still removing all the oxygen. The pressure downstream of the copper was measured with a temperature controlled 1-Torr baratron (Figure 4.3). This baratron was very reliable and did not contribute to any noticeable gas consumption or outgassing. We calibrated the voltage of the inconel oven to temperature by measuring the temperature in the center of the quartz tube, in air, which was free of copper. We also verified that the temperature on the side of the oven, filled with copper, and under vacuum agreed with the calibration curve. The flow rate was controlled by slowly opening a Swagelok 4WT valve with a spherical stem. Swagelok also provides a conical ’regulating’ stem for this valve, but the stem is made of PTFE, which has memory effects due to adsorption. Tests done with a needle valve lead to fractionation (Severinghaus, personal communication, 2010). We tested for the removal of oxygen by measuring the height of the mass 32 peak (16O16O), with a 3x1011Ω resistor, on the sample and standard, after the pressure in both bellows was balanced on the mass spectrometer. We would tolerate up to 300 mV of O2, which would correspond to about 1µV of 18O18O on mass 36. It would take about 15 min to open the regulating valve fully at a line pressure of 500 mT. We found that we could increase the pressure downstream of the oven to 1 Torr while still removing all the oxygen. We could not increase the flow rate further, because our baratron only had a 1-Torr scale, however, it may be possible to do so. Increasing the pressure in the line from 500 mT to 1 T allowed us to reduce the transfer time by 10 min. After 6 months of use, we suddenly had some O2 leakage through the line. An increase in the oven voltage by 20 V (one indent on the variac) fixed the problem. Early tests suggested that the regeneration of the copper would only be needed after 8 to 10 samples had gone through the line, however, we decided to regenerate the copper after every sample in order to make the process as similar as possible for all samples, and to add an extra safety margin to the effectiveness of the hot copper.

4.3.2.2 Tests with Ridox

In an effort to increase the efﬁciency of oxygen removal, we tested a common oxygen scavenger called Ridox. Ridox has the advantage of being usable at room temperature, and its efﬁciency is maximal at 100◦C. We can regenerate it with a low pressure 92

ﬂow of pure H2. A disadvantage was the high surface area of Ridox and its tendency to outgas impurities. Overall, Ridox was neither more reliable nor faster than hot copper, and we decided to keep using hot copper.

4.3.3 Air extraction from ice samples

The extraction broadly follows the methods of Sowers et al.[1989] and Sever- inghaus et al.[2003]. In order to extract air from ice core samples, ice samples are placed into a vessel, along with 2 glass stir bars. The vessel with the ice is placed into a dewar full of ethanol at -23◦C, and bolted to a vacuum line, with a conflat flange and copper gasket. It is then evacuated for 20 min, while the ice is kept frozen by chilled ethanol. The ice is evacuated directly to the pump, on a path that avoids the main gas extraction pathway (in Figure 1, valves 2, 3 and 4 are open, while 5 and 9 are closed), minimizing the deposition of water on the walls of the line. The conflat connections are leak checked using a 10 Torr baratron: upon closing access to the pump (valve 2), the pressure should stabilize in 30 seconds at the saturation vapor pressure of the ice temperature, generally between 200 and 800 mT. Once the flask is evacuated, the connections to the pump (valve 2) and to the 10-Torr baratron (valve 4) are closed, and the ice is melted, releasing the bubble air. The transfer can start when there is a small amount of ice left. The water is stirred, with glass-covered magnetic stir bars, during the transfer, to ensure full degassing.

4.3.3.1 Flask design

Oxygen and argon are especially sensitive to gas loss when the ice gets warmer than -20◦C. In order to make precise measurements of argon isotopes, we want to ensure that the ice would not be warmed up during the pump down time. The pre-existing vessels were made for 10 g of ice [Sowers et al., 1989], and although 100 g of ice can fit in these vessels, the blocks of ice on the top cannot be fully immersed in ethanol and thus risk being warmed up, and losing argon. We designed larger vessels, which would fit in dewars of the next size up, and have a large base (Figure 4.4). The conflat was kept at the same size, to maximize the compatibility with existing hardware. The large base 93 allows for a large surface to exchange gases between the water and the air space, and facilitates full degassing of the water. It is also useful if we were to refreeze the samples: if the water level is too high during freezing, the expansion can break the glass vessel.

Figure 4.4: Vessel design. On the left is the old style, used for whole air measurements using 10 to 25 g of ice, and on the right is the new style.

This new design allows 100g of ice to be contained within the bottom third of the ﬂask, which is the coldest. It also has a larger surface, which facilitates the degassing of the water during the transfer. However, we noticed that the vessel takes up about 70% of the volume of the dewar. As a result, there is relatively little ethanol in the dewar, and a slightly slimmer vessel, which would leave more room for ethanol, would have been better.

4.3.3.2 Evacuation time

The vessels have traditionally been evacuated for 40 min [Severinghaus et al., 2003]. However, we found out that during the evacuation, the pressure would start increasing, after about 10 min (Figure 4.5). This is most likely due to an increase in the chilled ethanol temperature, increasing the water vapor pressure over ice. Temperature measurements showed that the bottom of the dewar, where the ice is located, would stay at -23◦C, but the ethanol near the top of the dewar would warm up to -19◦C after 20 94 min. Most of the air is evacuated after 7 minutes (Figure 4.5), and we estimated that evacuating for 20 min would be sufficient, and would limit the risk of gas loss while the vessel is warming up. This duration still allows for some sublimation of the ice surface, which helps to remove laboratory air contamination [Sowers et al., 1989]. We tested for the difference between evacuating for 20 and 40 min and found no significant difference between replicates: the t-values for a paired t-test on 4 pairs of 40 15 samples were 0.20 for δ Ar, 0.19 for δ N, 0.67 for δAr/N2, and 0.99 for δKr/N2. (The 90% confidence level for 3 degrees of freedom is t=2.35). This data set also shows that there is no sign of argon loss or fractionation during the pumpdown time (Table 4.2).

710 700 690 Closed 2 vessels 680 670 660

pressure, mT 650 640 630 620 0:10:00 0:20:00 0:30:00 0:40:00 pump down me, min

Figure 4.5: Pressure as a function of time during the initial pump down time. Initially, 4 vessels were open. After 20 min, two of the vessels were closed, which is why the pressure drops abruptly. Most of the air is evacuated in the ﬁrst 10 min. For reference, the saturation vapor pressure of ice is 0.773 Torr at -21◦C, and 0.338 Torr at -22◦C, so the increase in pressure between 10 and 40 min corresponds to less that 0.5◦C warming.

4.3.3.3 Melting and stirring

Once the vessel has been evacuated, its valve is closed, and the ice is melted, with the help of warm water. It is important not to let the water be too warm, or the ice will not only melt, but the water vapor pressure will exceed saturation, and condense in the cooler upper parts of the vessel, which might clog it when we start the transfer. Once 95

Table 4.2: Influence of the pumping time on the extraction. The first column shows the identification of the piece of ice, the second column the replicate number, the third column the time the vessel was evacuated prior to the transfer. The following columns show the difference between samples and the mean of all replicates (2 or 4), in per mil. The last two lines show the pooled standard deviation for pairs of ice samples, and the mean difference between the samples evacuated for 20 and 40 min. There is no significant difference between the two. 40 15 Sample replicate pump time(min) δ Ar δ N δAr/N2 δKr/N2 A 1 20 0.0021 -0.0047 -0.2128 -1.4821 A 2 40 -0.0102 -0.0044 -0.2845 -0.0587 A 3 20 0.0012 0.0036 0.1165 1.0158 A 4 40 0.0068 0.0055 0.3809 0.5249 B 1 20 -0.0066 -0.0030 -0.0780 -0.1530 B 2 40 0.0066 0.0030 0.0780 0.1530 C 1 20 -0.0174 -0.0049 0.0392 0.6238 C 2 40 0.0174 0.0049 -0.0392 -0.6238 pooled stdev 0.012 0.003 0.1 0.9 mean difference between 20 and 40 min -0.010 -0.005 -0.068 0.002 most of the ice is melted, the hot water is removed. We took care to leave a small piece of ice in the water at the start of the transfer, to ensure that the water temperature would be uniform, near 0◦C, for all samples. It takes about 15 min with moderate heat to melt 100g of ice, using a warm water bath. Vigorous stirring is necessary in order to degas the water completely. How- ever, splashing can cause clogging. We followed the recommendation of Kobashi et al. [2008b] of using two small magnetic stir bars, and found that a speed of 7.5 on the magnetic stirer was optimal. Improper stiring causes δ15N to be higher than expected, and

δAr/N2 and δKr/N2 to be much lower than expected (Table 4.3).

Table 4.3: Inﬂuence of stirring. The top line shows the results of a sample without stirring. The second line is the mean of 3 other samples, with stirring, from the same depth. 40 15 δ Ar δ N δAr/N2 δKr/N2 no stir bar 1.199 0.371 -3.016 4.350 mean 1.205 0.295 1.472 17.063 96

4.3.4 Mass spectrometry

4.3.4.1 Gas conﬁguration

We use a Finnigan MAT 252 isotope ratio mass spectrometer in dual inlet mode, with a cup conﬁguration allowing us to measure nitrogen and argon isotopes. In addition, we use a peak jumping method to measure the elemental ratios Ar/N2 and Kr/N2. The mole fraction of Ar in dry air is 9.332 mmol /mol [Park et al., 2004]. In order to get good argon isotopic measurements, we use a sample of 100 cc of air, and measure it with an inlet pressure of 200 to 250 mB in the mass spectrometer, which is much higher than the nominal use of 50 mB. We are able to measure the large N2 beam by using smaller resistors (Table 4.4).

Table 4.4: Resistor configuration of the MAT252 for Ar-N2 measurements. channel 1 2 3 4 resistor 3×1011 1×107 3×108 1×109 Argon config 36 40 Nitrogen config 28 29 Ar/N2 config 28 40 Kr/N2 config 86 28

In the following discussion, a ”block” refers to a set of individual sample- standard comparison known as ”cycles”, following peak centering and pressure balancing. We used 4 blocks of 16 cycles for δ40Ar, 3 blocks of 16 cycles for δ15N, and

1 block of 3 cycles for both δAr/N2 and δKr/N2.

4.3.4.2 Source focusing

The MS 252 can be focused either for high sensitivity or high linearity. We are interested in the high linearity focus, because the size of our samples is not always exactly the same as the standard, resulting in pressure imbalance. Both peaks can be found by varying the extraction voltage and recording the beam intensity (Figure 4.6). In some cases, the smaller linearity peak cannot be found. One may be able to recover it by offsetting the beam centering. Once the linearity peak on is found, the extraction voltage should be left in place, and other focus settings adjusted. Detailed instructions 97 are provided in Appendix 4.D.

1900 1700 1500 1300 1100 Linearity peak 900 700 mass40 beam(mV) voltage 500 0 2 4 6 8 10 Extraction voltage, arbitrary units

Figure 4.6: Beam intensity on 40Ar as a function of extraction voltage. The mass spectrometer should be focused on the smaller peak to maximize linearity.

A good linearity focus is associated with a low sensitivity to the pressure imbalance between the standard and sample bellows. It is especially important for argon isotopes, where the pressure imbalance sensitivity can decrease by a factor of 10 from sensitivity to linearity optima. A poor linearity will result in unacceptable precision in argon isotopes, due to a large ( 100 per meg) pressure imbalance correction, that is itself uncertain by about 10%. This is also why this method is probably not suitable for smaller mass spectrometers, such as Delta V or XP, which have poorer linearity [e.g. Kobashi et al., 2008b, p. 4676].

4.3.4.3 Aliquot expansion

When a sample is expanded into the bellows of the mass spectrometer, a portion of the gas is left behind in the sample tube, which might lead to fractionation. We tested for the duration of equilibration, and found that there was no significant difference between 20 and 50 min of equilibration time, and no significant difference whether or not we would use an isothermal water bath (Table 4.5). The most sensitive expansion is the aliquot extraction from the standard can, and the residual of many measurements through 2011 pointed towards a small amount of thermal fractionation, possibly due to 98 the fluctuations of temperature in the room (Figure 4.7). Leaving the can in a water bath would damp these fluctuations. However, we were not able to improve on the precision by using a water bath. Table 4.5: Sensitivity of the reproducibility of standard measurements to the equilibration time. All tests were done with two standard cans in water baths, except for the last two columns (marked with **), which were equilibrated without a water bath. Equilibration time (min) 20 30 40 50 20** 5 sec** Number of samples 6 6 4 6 11 6 δ40Ar std (per meg) 8.1 10 10.1 3.6 6.7 6.4 δ15N std (per meg) 3.8 2.8 5.0 1.1 2.1 3.2

0.0560

0.0480

0.0400

0.0320 δ40Ar 0.0240

0.0160

0.0080 -0.008 -0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 δ15N 20 min 25 min 20 min, no water bath 30 min 40 min thermal line 50 min

Figure 4.7: Sensitivity to the equilibration time. A series of samples of ArN2-19 standard were measured against ArN2-20 standard, with varying equilibration time. The increase in the equilibration time does not improve the precision. The difference between individual samples is similar to a thermal fractionation signature (orange line). Mass-difference dependent fractionation would follow the 1:1 grid points, in the sense of ∆m dependance rather than ∆m/m.

Finally, we tested a radically different approach: a 5 second expansion. Short expansion duration works when the amount of gas moved is much larger than the small amount of gas near the mouth of the valve that may be fractionated by oriﬁce fractionation. This large bulk ﬂow of gas sweeps any fractionated gas into the bellows. It does 99 not leave time for gases to equilibrate, avoiding the sensitivity to changes in the room temperature. We found that a 5 second expansion yielded as good results as a 20 min equilibration, and used that for the ice analysis. It should also be noted that this approach probably only works because our sample comprises about 10 ccSTP, and would probably not work for smaller samples.

4.3.4.4 Quality Control

The MAT-252 has been used exclusively for the measurement of noble gases for at least 5 years, and as a result, it has not been exposed to oxygen for a long time. The testing and measurements have been done over a period of 3 years, using 3 different fila- ments. The absence of oxygen prevents rapid deterioration of the filament. Nonetheless, the high gas pressure probably causes gradual aging, rather than an abrupt break, and we noticed that, as the filament ages, the beam becomes periodically more noisy, exhibiting steps in the voltage of up to 50 mV (Figure 4.8). We monitored the health of the filament by plotting the voltage of every block. These sudden jumps often do not result in any noticeable change in isotope ratios, but they can, if the jump happens between a sample and a standard measurement. We rejected any cycles that would exceed a criterion of 3 standard deviation from the mean of the block, using a standard deviation of 50 per meg for argon isotopes, and 10 per meg for nitrogen isotopes. Overall, very few cycles were rejected. If more than half of the cycles were outside of 3 standard deviations, the whole block was rejected. This only happened twice. The peak jumping methods were run with only 3 cycles, and cycles were rejected if they were outside of 3 per mil from the expected mean. When the problem became persistent, we changed the filament. Another issue was related to the electronics of mass 29 momentarily failing: the voltage on mass 29 would drop for a split second, and come back to normal. This problem is related to the signal processing electronics of Channel 3, and not the physical Faraday cup. It may be associated with poor electrical connection in the channel. In- deed, we have noticed persistent drops in voltage in another channel shortly before it failed entirely. However, this problem was more present when some residual O2 was in the source (up to 300 mV on a 3.1011 resistor), and subsided in the last 2 months of the measurements. The loss of signal on mass 29 would lead to anomalous 29/28 ratios, and 100

Figure 4.8: Example of a time scan showing a step up in beam voltage. This behavior is associated with an aging ﬁlament. 101 cycles were rejected individually, following the 3-σ rule. Overall, the MAT-252 behaved very well. The background was stable and low. The magnet jumped reliably in the right place, and the noise on a time scan would stay below 0.5 mV.

4.3.4.5 Argon isotopes

We measured the isotopes of Ar with mass 36 and 40 simultaneously, against a standard can made with atmospheric proportions of pure N2, Ar and Kr, named ArN2- 20 (see Section 4.2.3). Once the sample is introduced, the pressure in the bellows are balanced to within 50 mV,to minimize the non linearity (pressure imbalance) correction. The machine integrates the signal from the sample for 16 seconds, and the standard for 16 seconds, and interpolates in between standard measurements to calculate the δ values, according to Equation 4.5, where V is the voltage, b the background voltage, SA refers to the sample side, and ST to the standard side.

[V (36,SA) − b(36)]/[V (40,SA) − b(40)] δ = ( − 1)1000 (4.5) [V (36,ST ) − b(36)])/[V (40,ST ) − b(40)]

The mass spectrometer averages out a block of 16 cycles to produce a reported δ value. We chose to use 16 cycles because it is a good compromise between speed and the need to re-adjust the pressure balancing between the bellows every so often. We tested for a range of target voltages (Table 4.6), and found that the standard deviation of a set of 16 cycles was not very sensitive to the target voltage, or the bellow’s pressure. We eventually chose to run the samples at 200 mB, and the corresponding target voltage for that pressure (2400 mV for the second ﬁlament, 5000 mV for the third ﬁlament).

Table 4.6: Sensitivity of the raw machine precision to the target voltage Voltage on mass 40 2604 2554 2440 2347 2323 2116 std of 16 cycles (per meg) 53 53 46 40 48 51

In order to achieve good precision on these sensitive measurements, we chose to run 5 blocks of 16 cycles. However, during method development, we found that the first block was significantly elevated compared to the other four, by 44±15 per meg on average. This discrepancy was not solved by using a short block of 3 cycles prior to 102 the long 16 cycle blocks. The same pattern was also witnessed on nitrogen isotopes. It could be related to a magnet drift at the beginning of the sequence, but we checked that the peak centering was not moving around, and that the peak shape was reasonably flat. In addition, the instrument sits on the argon gas configuration for about 15 min prior to the measurements, during the sample change over, so any short lived drift should have stabilized by the time we start measuring. Argon isotopes were measured at the start of the sequence, and it is possible that the anomalous first cycle may be due to a small amount of fractionation in the capillary when the sample is first introduced, and that this fractionated gas would wash away. However, orifice fractionation usually leads to lower, and not higher values. We eventually decided to reject the first block, and only √ reported the mean of the last 4 blocks, which have a standard error of 50/ 16 ∗ 4 = 6.25 per meg. All samples were run in this mode.

4.3.4.5.1 Pressure imbalance correction The relative ionization efficiency of different isotopes is slightly sensitive to the absolute pressure in the source. As a result, the δ value is slightly sensitive to the difference in pressure between sample and standard. The sensitivity to pressure imbalance is related to the linearity of the machine. The pressure imbalance sensitivity (PIS) was measured at least weekly following the procedure of Severinghaus et al.[2003], and it was very stable through the measurements. For the filament used between July and October 2012, it was 1.7±0.5 per meg per per mil of pressure imbalance. For the filament used in November and December 2012, it was 4.1±0.3 per meg/per mil. The difference can be explained by a different shape and position of the filament, resulting in slight difference in the focus, and hence in the linearity of the machine. In addition to the focus, the pressure imbalance sensitivity is also influenced by the pressure of the sample, which is proportional to the voltage used for balancing the bellows. The PIS increases with increasing pressure (Figure 4.9), thus we can reduce the inlet pressure if the PIS becomes too large. The pressure imbalance is typically on the order of 10 per mil, and the PIS correction can be up to 40 per meg. The error in the correction is on the order of 5 per meg, which is similar to the raw machine precision. As a result, the pressure imbalance 103

Sensitivity of the PIS to total pressure -0.003 -0.0035 -0.004 -0.0045 -0.005 -0.0055 -0.006 per mil/per mil -0.0065 -0.007

Pressure Imbalance Sensitivity, PressureImbalanceSensitivity, -0.0075 -0.008 1000 1500 2000 2500 3000 3500 4000 Target voltage for mass 40 (Ar), mV

Figure 4.9: Sensitivity of the Pressure Imbalance Sensitivity (PIS) to the target voltage for δ40Ar. At high voltage (high inlet pressure), the PIS increases in absolute terms. correction does not signiﬁcantly add to the uncertainty in the measurements.

4.3.4.5.2 Chemical Slope Correction The relative ionization efﬁciency of 36Ar and 40 Ar is also sensitive to ratio of N2/Ar in the source (Figure 4.10). The chemical slope correction was measured for each ﬁlament use according to Severinghaus et al.[2003], and values are given in Table 4.7. δN2/Ar was on the order of 0 to 2 per mil, which translates into a correction of up to 8 per meg, with an uncertainty lower than 6 per meg. The chemical slope correction did not increase the uncertainty in the measurements.

Importantly, research grade N2 was used to perform the chemical slope calibration experiments, rather than the ultrapure N2 as it has been shown that the latter contains up to 150 ppm of Ar [Kobashi et al., 2008b].

40 Table 4.7: Chemical slope of δ Ar as a function of δN2/Ar, in per meg per per mil. Date Aug 2010 Oct 2010 Jan 2011 Sept 2012 Nov 2012 Chemical slope -3.5 -2.2 -2.8 -8.5 -4.9 104

Chemical Slope 9/17/12 11/4/12 Linear(9/17/12) Linear(11/4/12) 0.200 y = -0.005x - 0.0003 -0.300 R² = 0.99451 -0.800 -1.300 d40Ar -1.800 y = -0.0085x + 0.0672 -2.300 R² = 0.99157 -2.800 0 50 100 150 200 250 300 350 dN2/Ar

Figure 4.10: Chemical Slope for Ar and N2 isotope measurements, measured in Septem- ber and November 2012.

4.3.4.6 Nitrogen isotopes

Nitrogen isotopes were measured with 8 second integrations for both mass 28 and 29, with 3 blocks of 16 cycles preceeded by a short block of 2 cycles that was discarded. We found that the first block was sometimes elevated compared to the other two, and solved the problem by adding a -10 mV peak center offset (Figure 4.11). This effect is consistent with a small amount of magnet drift, following the switch to the N2 gas configuration(Figure 4.12). The standard deviation of 16 cycles is about 10 per meg, and the mean of 3 √ cycles has a theoretical standard error of 10/ 16 ∗ 3 = 1.4 per meg. The pressure imbalance sensitivity was difficult to measure because there was not a clear linear relationship between δ15N and the imbalance. When such a relationship was present, it was on the order of 0.1 per meg per per mil. The imbalance being on the order of 10 per mil, the PIS entails a correction of about 1 per meg. However, the uncertainty in repeat aliquots was on the order of 3 per meg, which is larger than what it is for argon isotopes on a per mass unit level. It could be due to thermal fractionation between the standard can and the bellows, since nitrogen isotopes are more sensitive than argon isotopes to temperature gradients, and we limited the equilibration time to 5 seconds to avoid this problem. It is unlikely to be due to orifice fractionation, as argon isotopes should be particularly sensitive to it, being a smaller 105

PIS test with different peak center offsets

y = -0.0016x + 0.1896 1 +10 peak center offset R² = 0.99697 -15 peak center offset Linear regression (+10) 0.5 linear regression (-15) N 15

δ 0 -600 -400 -200 0 200 400 600 800 Raw

-0.5 y = 0.0003x - 0.0423 R² = 0.85155

-1 Pressure imbalance, per mil

Figure 4.11: δ15N as a function of the pressure imbalance for 2 different peak center offsets. The slope of the linear regression reﬂects the pressure imbalance sensitivity. It depends on the peak center offset. If the PIS is unstable, changing the peak center offset might help. atom. It is more likely to be due to non-linear processes in the source such as plasma instabilities. Indeed, we can achieve a better precision in the mass spectrometry using 50 mB of inlet pressure instead of 200 mB used here.

4.3.4.7 Ar/N2 ratio

The measurement of Ar/N2 ratio is done by peak jumping: the magnet has to be moved between the sampling of mass 40 (Ar) and mass 28 (N2). The cup conﬁguration is provided in Table 4.4. The mass spectrometer measures sequentially mass 40 on the sample side (V (40, SA, t1)), mass 40 on the standard side (V (40, ST, t3)), mass 28 on the sample side (V (28, SA, t2)), and mass 28 on the standard side (V (28, ST, t4)). Each measurement is then interpolated to a single time point t, in order to correct for the decrease in sample pressure during the measurement. Background values b are subtracted 106

1 Beam Intensity: 978 2350 0.5 1108 2620

Mass 28 1682 3110 Normalized

beam intensity 1850 4394 0 1950 2000 2050 2100 2150 High Voltage, steps

0.9995 Mass 28 Normalized beam intensity 0.999 2030 2040 2050 2060 2070 2080 High Voltage, steps

0.9995 Mass 29 Normalized beam intensity 0.999 2030 2040 2050 2060 2070 2080 High Voltage, steps

Figure 4.12: Peak shape of mass 28 on the nitrogen gas conﬁguration for a range of absolute beam intensity. The bottom plot shows the peak shape for mass 29. 107

40 14 from each beam intensity V . The value of δ Ar/ N2 is then calculated following:

! [V (40, SA, t) − b(40)]/[V (40, ST, t) − b(40)] δ40Ar/14N = − 1 1000 in per mil 2 [V (28, ST, t) − b(28)]/[V (28, ST, t) − b(28)] (4.6) We measured 4 sets of voltages in order to interpolate to 3 δ values, which takes about 16 minutes.

4.3.4.7.1 Optimization of the method Peak jumping is not a standard method in Isodat, the software driving Thermo mass spectrometers, and we use a script, developed with the help of Hans-Jurgen Schluter, which outputs the raw voltages. The removal 40 14 of the background, interpolation, and calculation of δ Ar/ N2 are all done in Excel. Peak jumping methods are time consuming because of the time it takes to switch the magnet between measurements, and allow the magnet drift to subside. As a result, we cannot reduce the noise by averaging many measurements, and our optimization efforts are focused on saving time, as well as improving the precision of the measurements. The inputs to the script are 1) the gas configuration, 2) the order of the gases, 3) the mass of the gases (i.e. magnet setting), 4) the integration time for each gas. The gas configuration is defined so that we can use the appropriate resistors for each measurement (Table 4.4). The order of the gases is such that the rare gas is gas 1, and the abundant gas is gas 2. Indeed, the script will start by adjusting the pressure between sample and standard on gas 2, as pressure balancing is more effective when performed on the major gas. We used mass 40 (Ar) for gas 1, and mass 28 (N2) for gas 2. In the script, the mass to enter depends on the magnet calibration, and it is useful to check that we are on the right mass by doing a high voltage scan at high precision (2 mV). The masses should be adjusted so that they both require the same high voltage: it allows us to skip peak centering after each movement of the magnet. We used the nominal values of mass 40 and 28.3, with a high voltage of 2025 steps. We found that there was a slight movement of the voltage at the center of the peak from one day to the next, and chose to keep the peak centering routine for Ar/N2 measurements on the 252. However, tests done on a MAT 253 had very stable peak center voltages, and up to 10 min could be saved by skipping the peak centering step on more modern machines. The integration 108

time was set to 8 seconds for both Ar and N2. It could be increased to 16 seconds for measurements on a more sensitive resistor. Overall, the method would last 16 min for 3 δ values. When averaged, the standard deviation of these 3 measurements would yield an approximate estimate of the machine precision.

4.3.4.7.2 Background The background voltage needs to be measured for each magnet setting. We thus created background gas configurations with the same cups active, but with representative magnet settings, and created separate acquisition scripts to measure the background voltages. We measured them at least weekly, and subtracted them from the raw voltages for each measurement, using an Excel spreadsheet. The background did not vary by more than 0.02 mV, which is insignificant. The rationale for making background measurements at realistic magnet settings is that stray ions vary as a function of magnetic field strength.

4.3.4.7.3 Pressure Imbalance Sensitivity We used sequences of 2 blocks instead of 3 for the pressure imbalance sensitivity measurements. The PIS measurement would take about 1hr to be performed, and was measured bi-weekly. The PIS was on the order of 3.5±2.5 per meg per per mil. The imbalance was usually smaller than 10 per mil, which corresponds to a correction of about 35 per meg, smaller than the raw precision of the measurements ( ≈70 per meg). Therefore, the pressure imbalance sensitivity does not contribute to uncertainties in the measurements, and it could be measured more infrequently.

4.3.4.7.4 Precision and outlier rejection The raw standard deviation of 3 cycles was typically about 0.07 per mil, which corresponds to 5.8 per meg per mass unit. The same jumps in the raw voltage shown in Figure 4.8 can cause errors in the estimation of

δAr/N2. We rejected values that were outside of 5-σ = 0.3 per mil from the mean of the other 2. If more than 1 value looked suspect, we rejected those that were outside of the range of all the other measurements: -1 to 5 per mil. We rejected a total of 5 values out of 783.

Gas loss and close off processes introduce variations in δAr/N2 of ice on the 109 order of 0.9 per mil, which is one order of magnitude larger than the machine precision. As a result, we estimated that it was not necessary to improve the resolution of the mass spectrometry. Besides an increase in the number of measurements, an improvement in the precision can be achieved by using a different type (lower mass-resolution) of mass spectrometer, which measures mass 28 and mass 40 simultaneously, instead of resorting to peak jumping. For instance, a Thermo Delta V can measure δAr/N2 with a raw machine precision of 0.044 per mil [Headly and Severinghaus, 2007]. However, these machines have lower accuracy in the isotope measurements, mainly due to poor linearity (see Section 4.3.4.2).

4.3.4.8 Kr/N2 ratio

For the ﬁrst time, we demonstrate the feasibility of direct Kr/N2 measurements in air samples.

−6 4.3.4.8.1 Gas Conﬁguration The Kr/N2 ratio in air is 1.5 10 , however, we cannot measure the most abundant krypton isotope at mass 84 because of interference with 86 −7 (N2)3 forming in the source. We measured the ratio of Kr/N2 = 3.8 10 , at 200 mB, using a 1 107Ω resistor for mass 28, and a 3 1011Ω resistor for mass 86. We had about 2200 mV on mass 28 and 64 mV on mass 86.

4.3.4.8.2 Method The separation of masses between 28 (N2) and 86 (Kr) is so large that we need to measure it by peak jumping, following a method very similar to that for

Ar/N2. The most important difference is that we integrated the 86 beam for 16 seconds, instead of 8 seconds, because the more sensitive resistor is also noisier. Mass 28 was integrated for 8 seconds. We measured the background and the pressure imbalance sensitivity at least weekly. The background was small and stable, and does not contribute to the uncertainty in the measurement. The PIS was on the order of 8 per meg per per mil, and the pressure imbalance correction was generally an order of magnitude smaller than the raw standard deviation of the measurements. We report the average of 3 δ values. 110

4.3.4.8.3 Precision The raw standard deviation of 3 δ values is 0.35 per mil (or 6.1 per meg per mass unit). Kr/N2 can also be measured by separating the sample in 2 pieces, and measuring Ar/N2 in one of them, and Kr/Ar in the other after concentrating the sample by gettering, and then reconstituting the Kr/N2 [Headly and Severinghaus, 2007]. A precision of 0.22 per mil can be achieved by that method using the same amount of gas. If 1 kg of ice is used, a precision of 0.1 per mil can be achieved [Headly and Severinghaus, 2007]. The method we present here is easier, and allows us to measure 4 samples per day instead of just one. If the measurement of δKr/N2 is valued highly, the precision of this method can be improved by increasing the number of cycles measured. We chose to measure just 3 cycles in the interest of time, but a precision of 0.1 per mil may be achieved by measuring 10 blocks of 3 cycles, which would take on the order of 2.5 hr. Using a 1 1012Ω resistor is also likely to improve the signal to noise ratio of the measurements. We were unable to do this because we were interested in measuring δ15N and δ40Ar at the highest precision, and only had 4 working channels on the MAT252.

4.3.5 Ice core measurements of WDC05A

4.3.5.1 WDC05A samples

The WAIS-Divide ice coring site is situated in the center of West Antarctica (79◦S, 112◦W), not far from the Byrd site, where the ﬁrst deep Antarctic ice core was drilled. The climatic conditions at WAIS Divide are very similar to those of central Greenland: a relatively high accumulation rate of 22 cm/yr ice equivalent, and a mean annual temperature of -29◦C. Several shallow cores were drilled in 2005, and we analyzed samples from WDC05A (79◦27.7’S, 112◦07.5’W), a 300m dry-drilled core specif- ically intended for gas measurements. We will later compare our results with samples from the deep core, which is called WDC06A (79◦27.9’S, 112◦06.7’W). The high accumulation at WAIS Divide allows us to investigates changes in climate with a very high temporal resolution. The core was in reasonably good condition, and we expect minimal artifacts from the sampling (e.g. gas loss). The WDC05A core was processed at the National Ice Core Laboratory, in Lake- 111 wood, Colorado in the summer of 2006. Samples were cut for water isotopes, and for gases: CO2, CH4, isotopes of CO2 and CH4, halocarbons, and inert gases. We measured a total of 330 samples from 135 depths, roughly every 2 m, which corresponds to a 10 year resolution.

4.3.5.2 Evaluation of the precision

We evaluated the overall precision of the ice extraction and measurements by making repeat measurements of ice from the same depth [Severinghaus et al., 2003]. We calculated the pooled standard deviation from 2 to 4 replicate samples within the same depth range (Table 4.8). The samples for which the difference between replicates was outside of 4 pooled standard deviation were rejected. If no more than 2 replicate samples were measured, we compared them to nearest-neighbor samples to decide which replicate to reject. Out of the 330 initial samples, 13 were rejected for δ40Ar, 17 15 for δ N, 12 for δAr/N2 and 12 for δKr/N2. Table 4.8: Precision of the copper method. The ﬁrst column designates the method used. ”Can - MS” refers to the expansion of aliquots into the mass spectrometer from two standard cans. ”Can-line” refers to the transfer of aliquots from the standard can through the line. ”LJA” refers to the transfer of La Jolla Air standard through the line, with the same treatment as for the ice. ”ice” refers to the analysis of WDC05A samples. The second column shows the number of samples used to calculate the standard deviation. In the case of the ice, the pooled standard deviation was calculated, and the number of degrees of freedom is shown in the last line. The subsequent columns refer to the standard deviation of each δ measurement, in per meg. 40 15 Method nb δ Ar δ N δAr/N2 δKr/N2 σ σ σ σ raw MS 6.25 1.4 40 202 Can - MS 11 6.7 2.1 57 500 Can - line 25 12 1.2 52 330 LJA 10 10.1 3.0 88 176 ice samples 14.2 4.8 397 631 Degrees of freedom 174 169 174 178 Kobashi LJA 17 14 4 137 Kobashi ice 148 16 4 530

Table 4.8 shows the standard deviation for replicate measurements through different steps of the method. The first line shows the theoretical precision of the mea- 112 surements. The second line (’can-MS’) corresponds to an aliquot expansion into the bellows, from two standard cans, one on each side of the MS. We made a series of tests of the length of equilibration necessary to extract an aliquot from the standard can (see Table 4.5), and the numbers presented here correspond to a 20 min equilibration without a water bath. We later moved to a 5-second equilibration time, but we have fewer samples for that test, and the difference is not significant. The third line (’can - line’) corresponds to repeat measurements of an aliquot from a standard can transferred through the extraction line into a dip tube immersed in liquid helium, and measured on the mass spectrometer. These samples were measured in order to test different parts of the line, and the protocol used for each was not exactly identical, but they give an idea of the noise added by gas handling. Overall, the precision is very similar to that of the previous test, with a simple aliquot expansion, showing that the gas handling does not introduce a large amount of error. The precision for argon isotopes is worse, but the previous value of 6.7 per meg may have been exceptionally low. The fourth line corresponds to the transfer of 10 aliquots of the La Jolla Air standard (LJA) through the line. Although the results are similar to the transfer of working 40 15 standard (’can - line’) for δ Ar, δAr/N2, and δKr/N2, the precision of δ N is a little worse (3 per meg instead of 2). The result of other similar experiments (Table 4.1) also show that δ15N cannot be repeated to better than 3 per meg. It is probably due to some amount of thermal fractionation during gas handling that we were not able to correct. The fifth line shows the pooled standard deviation of WDC05A ice samples, with the numbers of degrees of freedom shown in the line below. The precision of replicates from the same depth interval is notably worse for δAr/N2, which is due to a complex process of expulsion of Ar during the bubble close off, and to selective gas loss of small atoms in the ice [Severinghaus and Battle, 2006]. Nitrogen and argon isotopes have a slightly lower reproducibility than for La Jolla Air, and it is worse for δ15N (4.8 per meg) than for δ40Ar (3.5 per meg per mass unit) in a per-mass unit sense. The 15 15 40 pooled standard deviation of δ Nxs = δ N-δ Ar/4 is 4.2 per meg, showing that part of the noise is mass dependent, and could be caused by inhomogeneous bubble closure. The higher scatter in δ15N may be caused by random thermal fractionation, by a small 113 amount of CO contamination (CO has mass of 28 and 29), or by unknown effects of the high pressure in the MS source. We have found that the sensitivity to pressure imbalance between sample and standard in the mass spectrometer was not very stable for δ15N, and not exactly linear. This effect would be more visible with ice than with a standard can or La Jolla Air samples, since the size of the sample can change by ≈ 30%. Further studies may investigate the sensitivity of the PIS to inlet pressure for δ15N, similarly to what we did for δ40Ar (Figure 4.9). The last two lines in Table 4.8 show the pooled standard deviation obtained by Kobashi et al.[2008b] for their last set of measurements, with LJA standard and GISP-2 ice of similar depths. Our results are slightly better for LJA, showing the effectiveness of the improvements in the extraction method. However, the improvements are less noticeable in the ice. More studies of other ice cores will allow us to improve our understanding of sample-to-sample variability, and identify the limits to the precision of this analytical technique.

4.3.5.3 Gas loss

Small diameter elements, such as O2 and Ar can permeate through the ice lattice and escape from the ice core [Severinghaus and Battle, 2006]. This gas loss is more severe at higher temperature, and we were careful in keeping WAIS-Divide ice below - ◦ 20 C, to limit gas loss. In addition, O2 and Ar are also selectively expelled from closing bubbles in the ﬁrn, which leads to lower δO2/N2 and δAr/N2 than one would expect otherwise [Severinghaus and Battle, 2006].

The large scatter in δAr/N2 measurements indicated that there is a certain amount of gas loss (Table 4.8). However, we do not find any correlation between δAr/N2 and the total air content, or the other isotopic ratios measured (Figure 4.13). This is consistent with the findings of [Kobashi et al., 2008b]. The air content was measured after oxygen removal, and calibrated to a sample of dry La Jolla air, including oxygen. Because of the selective expulsion of oxygen during bubble close off, and due to gas loss, this method is perhaps more accurate than the measurement of all of the air present. Indeed, we do not find any correlation between 2 total air content and δAr/N2 (Figure 4.13A, r =0.05), showing that gas loss is not the 114 dominant signal in the variability in air content. The uncertainty in the total air content is on the order of 2%, or 0.002 cc STP/g. 40 Although some studies have found a correlation between δAr/N2 and δ Ar [Sev- eringhaus et al., 2009], suggesting that gas loss may have a mass dependent component, we find no evidence for that (Figure 4.13B), in accordance with firn air measurements which show no isotopic component to gas permeation [Battle et al., 2011]. Whenever there is an isotopic signal in δ40Ar associated with gas loss, cracks are present in the ice [Severinghaus et al., 2009], suggesting that there are two separate processes in gas loss: one involving cracks, which has a mass dependent component, and one involving permeation, which is purely size dependent. In addition, the lack of correlation between 15 δAr/N2 and δKr/N2 or δ N confirms that neither Kr nor N2 are affected by gas loss, and that gas loss is the dominant signal in δAr/N2. In summary, we found evidence of size dependent gas loss in WDC05A,in keeping with other studies, but it did not correlate with δ40Ar. There are two possible ex- planations for this observation: 1) random variations in δAr/N2 overwhelmed any correlation with δ40Ar, or 2) varying amounts of purely size dependent fractionation overwhelmed an underlying mass-dependent mode of gas loss.

4.3.5.4 Argon isotopic offset

40 Although we do not ﬁnd a correlation of δAr/N2 with δ Ar, it is systematically elevated in the ice, compared to δ15N or δ86Kr. The reason for this offset is unknown. We corrected for it by comparing δ40Ar in the ice between 78 and 100 m with its mean value in ﬁrn air in the lock in zone (Figure 4.14). There is an average offset of 3.7 per meg, which we subtracted uniformly from the whole dataset.

4.3.5.5 Comparison with the getter method

In addition to this set of measurements, we also measured δ40Ar in 600 g samples by gettering the air (See Section 4.5). We compared samples from the same depth interval, measured by both methods,using a paired t-test, and found no signiﬁcant difference between the two sets (p = 0.098, Figure 4.15). 115

0.02 y=ï1.81eï03xï3.95eï05 y=2.15eï03xï3.91eï05 2 2 R =2.08eï01 0.01 R =2.19eï01 0.01

0 0 Ar/4, per mil ccSTP/g ï0.01 40

b ï0.01 Total Air content ï0.02 ï0.1 0 0.1 ï0.1 0 0.1 Ar/N /12, per mil Ar/N /12, per mil b 2 b 2

y=1.85eï02xï6.88eï05 y=5.47eï02x2.83eï06 R2 =2.17eï01 R2 =2.43eï01 0.01 0.02

0 0 /58, per mil 2 N, per mil 15 b ï0.01 ï0.02 Kr/N b ï0.1 0 0.1 ï0.1 0 0.1 Ar/N /12, per mil Ar/N /12, per mil b 2 b 2

Figure 4.13: Correlation of the residuals of δAr/N2 with A) total air content residuals, 40 15 measured after oxygen removal, B) δ Ar residuals, C) δ N residuals and D) δKr/N2 residuals . All the values are given in per mil per mass unit, for individual samples, after removing the mean of replicate samples from the same depth. 116

0.325 δ15N, firn air δ15N, mean, firn air 0.32 δ15N, ice δ15N, mean, ice δ40Ar/4, firn air δ40Ar/4,mean, firn air 0.315 δ40Ar/4, ice δ40Ar/4,mean, ice 0.31

, per mil 0.305 δ

0.3

0.295

0.29 65 70 75 80 85 90 95 100 Depth, m

Figure 4.14: Comparison between firn air data (solid markers) and ice core data (hollow markers), near the firn ice transition. The lines show the average values between 68 and 74 m for the firn, and between 78 and 100 m for the ice. δ15N agrees well between the two, but δ40Ar is elevated by 3.7 per meg in the ice.

0.33 Copper method Getter method 0.32

0.31

0.3 Ar, per mil mass unit 40 b 0.29

100 150 200 250 300 Depth,m

Figure 4.15: Comparison of δ40Ar measurements in WDC05A measured by the Ar- N2 method with oxygen removal (”Copper method”), and by gettered samples (circles). There is no signiﬁcant difference between the two methods (p=0.098). 117

4.3.5.6 Comparison with WDC06A

Nitrogen isotopes were also measured at high resolution on the deep core WDC06A, on whole air samples, with 15 g of ice. There is no signiﬁcant offset between the two data sets (Figure 4.16). Although some of the details are different, many of the features are present in both ice cores, showing that they are a robust climate feature, and not a depositional artifact. Note that some of the features may not align perfectly well with depth, due to slight differences in the small scale variability of snow deposition (e.g. Sastrugi).

0.325 WDC05A 0.32 WDC06A

0.315

0.31

0.305 N, per mil 15

b 0.3

0.295

0.29

80 100 120 140 160 180 200 220 240 260 280 300 Depth, m

Figure 4.16: Comparison of δ15N measurements in WDC05A and nearby WDC06A. The poled standard deviation of the measurements is 0.0048 per mil

4.4 Noble gas measurements in ﬁrn air

Noble gases are valuable tracers of physical processes affecting gases within the firn, because their atmospheric composition remains constant on timescales of 105 years [Sowers et al., 1989; Severinghaus et al., 2003; Headly and Severinghaus, 2007]. The investigation of gas fractionation in the firn started with the study of nitrogen [Sowers et al., 1989] and argon isotopes [Severinghaus et al., 2003] because of their abundance in air. As our knowledge of the sources of fractionation in the firn increases, it is becoming 118 necessary to measure the isotopes of other inert gases in order to separate the different sources of fractionation, and the logical next candidate would be the isotopes of Kr. Krypton was first identified in air by Lord Ramsay in 1898, and its isotopes were identified by mass spectrometry by another Englishman, F.W. Aston in 1920 [Atson, 1920a,b]. They both isolated Kr by letting liquid air evaporate [Ramsay, 1898]. We use a more efficient approach, by concentrating the noble gases using a Zr-Al getter, which selectively removes N2,O2 and other reactive gases from the air, leaving a mixture of noble gases [Headly and Severinghaus, 2007]. The residual gases are measured on a MAT-253 dual inlet mass spectrometer especially built for this purpose. We measure the isotopes of Ar of mass 36, 38 and 40, as well as the isotopes of Kr of mass 78, 80, 82, 83, 84 and 86. In addition, we measure the elemental ratios δKr/Ar, δXe/Ar and δNe/Ar by peak jumping. The detailed experimental protocol and mass spectrometry are presented in the next sections.

4.4.1 Experimental protocol

The samples are initially contained in 2-L glass flasks, equipped with viton o- ring for the La Jolla Air standard, or PTFE o-rings for the firn air samples (see section 4.2 for the flask sampling protocol). The flask is connected to an 80 cc glass volume, which opens into a tube containing Zr/Al getter sheets, to a vacuum pump, and to a sample tube dipped in liquid helium (Figure 4.17). We use a 10-Torr baratron gauge to measure the size of the sample, and a convectron to leak check, and measure any residual pressure. The oven tube is loaded with 30 SAES Zr/Al getter sheets and attached to the line. The flask is also attached to the line, and the set up is evacuated for 20 min. The getter sheets are activated at 100◦C for 10 min. This step can be done during the evacuation. The oven is then put on 900◦C for 10 min. The oven is switched off, and the system checked for leaks for 30 seconds. The oven is switched back on 900◦C. The 80 cc volume valve is then closed and the flask expanded into the 80 cc volume for 5 seconds, the flask valve is then closed. The oven is isolated from the vacuum pump (valve 3 closed on Figure 4.17), and the 80 cc volume expanded into the oven (valve 2 open). The sample is gettered at 900◦C for 30 min (see also Figure 4.18). 119

convec- 10 tron PUMP Torr 4 5 6

3 7

80 cc 2 2 L 1

Zr/Al getter liq. He

Figure 4.17: Experimental set up for the getter method, with air ﬂasks.

In the meantime, a dip tube is pre-cooled in liquid nitrogen, inserted into the liquid helium dewar, connected to the line, and the arm connection evacuated for at least 20 min ( valve 5 and 6 open on Figure 4.17). It is then leak-checked for 30 seconds. When the gettering is finished, the oven is brought down to 300◦C for 5 min, which allows hydrogen to be adsorbed onto the getter material. The pump and convectron are then closed, and the sample allowed to expand on the line. The pressure of the sample is measured with the 10-Torr baratron. The sample is then transferred into the tube dipped into liquid helium for 10 min (valve 7 open), in two increments: the tube is first propped up, and lowered after 2 min, so as to allow a more efficient trapping. When the transfer is finished, the dip tube is closed, and the residual pressure measured with the convectron. The dip tube is then disconnected from the line, lifted off the liquid helium, and allowed to homogenize for 2 hours before being transferred to the mass spectrometer. The typical sample size obtained that way was 0.5 cc STP of noble gases. The same firn air flasks have been used to measure various gas species, and some flasks were significantly depleted by the time of this set of measurements. As a result, we used a 180 cc volume instead of 80 cc, and used 2 getter ovens in parallel to ensure full gettering of the samples. 120

45 40 35 30 25 20

Pressure, mT 15 10 5 0 0 5 10 15 20 25 30 35 40 45 me, min

Figure 4.18: Pressure in the line as a function of time during gettering at 900◦C, for 80 cc STP of dry air. Note that the pressure was not routinely measured during gettering. This analysis was done for demonstration purposes.

4.4.2 Mass Spectrometry

4.4.2.1 Optimisation of the performance of the MAT-253

4.4.2.1.1 Source Focus The software for the MAT-253 can focus the source auto- matically. However, we need to make sure that we are on the linearity maximum, which we find for the extraction around 70%. Note that the sensitivity maximum is found around 50%, which is in the opposite order as it is for the MAT-252. The emission should always be at 1.5 mA. As a first step, the trap and electron energy are left alone, and all other parameters set on 50%. A peak center routine should be run, and then, the extraction should be adjusted to be on the small maximum. The autofocus routine should then be run a few times, on all other parameters. As a last step, the trap and electron energy can be optimized. The pressure imbalance sensitivity is affected by the trap voltage (Kenji Kawamura, personal communication, 2009), and a slightly lower trap voltage can improve the linearity. Once a new focus setting has been found, it needs to be saved, and ”passed to gas configuration”, in order to be effective. It is possible to adjust the focus differently for each gas configuration, but we kept the same focus for all. A pressure imbalance 121 sensitivity should be measured. For δ40Ar, it should be on the order of 1 per meg per per mil of imbalance. A value higher than 8 per meg per per mil is unacceptable. The focus is usually very stable, and it does not need to be adjusted more than once a year.

4.4.2.1.2 Capillaries The crimp on the capillaries linking the bellows to the source need to be balanced between the standard and sample side, so that the two capillaries deliver the same amount of gas for a given bellows pressure. An aliquot of the standard can be introduced into both bellows, and the valves separating the two bellows opened so that the pressure in each bellows is the same. The total pressure should be adjusted to match the pressure that the samples are run at, either by compressing the bellows, or by introducing more gas. The changeover valve can be switched to verify that the voltage seen on either side is the same,within 10 mV. In addition to balanced capillaries, the amount of crimping matters. When we got the machine in 2006, the capillaries were fully opened, which caused a signiﬁcant drift to be present between each cycle in a block (Figure 4.19). We solved this problem by closing the capillaries by about 50%. Note that it is normal to have a drift when the bellows are fully compressed, and the pressure in the bellows drops signiﬁcantly throughout the measurements.

4.4.2.1.3 Beam stability The MAT-253 dedicated to Kr analyses had problems with beam stability from the date of purchase in 2006 (see Figure 4.20 for an example). We tested as many pieces of equipment as we could, taking advantage of the fact that we have another MAT-253, but could not solve the problem ourselves. Eventually, the MAT-253 was shipped back to the factory in Germany, where they found a short circuit in the installation of the magnet, as well as a defective power distribution board. The machine was returned in late 2011. The instability problem was intermittent, and the ﬁrn air data set was analyzed during this period, in 2007. We managed the problem by rejecting cycles which had values outside of 3 expected standard deviations. 122

0 5 10 15 20 25 30 0

ï0.02

Ar ï0.04 40 b ï0.06

ï0.08 0 ï5 ï10 per mil Pressure ï15 Imbalance 0 5 10 15 20 25 30 Cycle number

Figure 4.19: δ40Ar (per mil) measurements in a block of 30 cycles, measured in January 2007. The trend is not related to pressure imbalance (shown at the bottom), but to the capillaries being opened too widely, which causes progressive fractionation of the remaining gas in a Rayleigh distillation.

4.4.2.2 Sample handling

After extraction into a dip tube, the samples are allowed to homogenize for 2 hours before being measured on the mass spectrometer [Headly, 2008]. The tube is connected to the mass spectrometer via an ultra-torr R , and the connection is evacuated for at least 20 min. The bellows are evacuated for at least 5 min. An aliquot is then taken from the standard can for 3 min, and expanded into the standard bellows for another 3 min. Simultaneously, the sample is expanded into the sample bellows for 3 min. A typical sample would expand to 15 mB. The bellows are then closed, and their volume adjusted so that the pressure is around 35 mB. The sequence can then start. Once the sequence is running, the next sample can be attached to the line, and the connections to the inlet pumped out for the duration of the sequence, which is about 5 hr.

4.4.2.3 Standard

The standard to which isotopic ratios are referred to is modern air, measured in La Jolla, California (See Section 4.2). We use a high pressure working standard can made with atmospheric proportions of pure commercially obtained Ar, Ne, Kr and 123

4984

4980 Intensity, mV Intensity,

4976

4972

100 200 300 400 Time, sec

Figure 4.20: Scan of intensity vs time for argon 40, highlighing problems with beam stability. These events were typical of the problems experienced until the machine was ﬁxed in the factory in 2011. 124

Xe. La Jolla Air is measured with the same process as the ﬁrn air samples, and these measurements are used to normalize to the working standard (Equation 4.3).

4.4.2.4 Argon isotopes

The stable isotopes of Ar are present at mass 36, 38 and 40. We can measure all three, but the precision of mass 38 is too low to provide interesting information, and we report δ40Ar as:

! [V (40,SA) − b(40)]/[V (36,SA) − b(36)] δ40Ar = − 1 1000 (4.7) [V (40,ST ) − b(40)]/[V (36,ST ) − b(36)] where V represents the voltage on a specific mass, and either on the sample side (SA) or the standard side (ST), and b the background value. Similarly to Section 4.3.4, the raw values are corrected for pressure imbalance. The pressure imbalance sensitivity was measured bi-weekly, and was between 0.5 and 1.1 per meg per per mil of imbalance. We ran 3 blocks of 16 cycles, which led to a raw machine precision of 5.6 per meg. The standard deviation of repeat LJA samples was around 10 per meg. The pooled standard deviation of 22 firn air flasks run in duplicates was 7 per meg.

4.4.2.5 Krypton isotopes

The MAT-253 has the ability to measure mass 78, 80, 82, 83, 84 and 86 simultaneously. The abundance of 78Kr is too low to make this measurement useful, and mass 80 is compromised by a 40Ar dimer. As a result, we measured δ86/82Kr, δ86/83Kr, and δ86/84Kr. The fractionation of Kr is almost purely mass dependent (Figure 4.21), and we combined all four masses into a single uncertainty weighted value called δ∗Kr as follows: δ86/82Kr δ86/83Kr δ86/84Kr + + σ2 σ2 σ2 ∗ 86/82 86/83 86/84 δ Kr = 2 2 2 (4.8) 4/σ86/82 + 3/σ86/83 + 2/σ86/84

With σi the standard deviation of repeat standard measurements for the pair i (Table 4.9). Each δ is also weighted by the mass difference ∆m, due to the fact that the gravitational 125 signal scales with ∆m.

Kr isotopes with respect to the mass diﬀerence. 86/82 86/84 and 86/83 are ploed. 1.4

1.2

0.8

0.6 Kr, per mil δ 0.4

0.2

0 0 1 2 3 4 5 mass diﬀerence

Figure 4.21: Krypton isotopes in ﬁrn air in the lock-in zone at WAIS-Divide. Each symbol represents a different sample. For each sample we plotted δ86/82Kr (∆m=4), δ86/83Kr (∆m=3) and δ86/84Kr (∆m=2). The line shows the gravitational slope.

The raw δ are corrected for pressure imbalance. The pressure imbalance sensitivity was measured bi-weekly, and was stable at 0.6 per meg per mer mil for δ86/82Kr, 0.01 per meg per per mil for δ86/83Kr and 1 per meg per per mil for δ86/84Kr. We measured 5 blocks of 16 cycles, for an overall precision of 4.6 per meg per mass unit (Table 4.9).

4.4.3 Elemental ratios

We measured δKr/Ar, δXe/Ar and δNe/Ar by peak jumping, similarly to what was described in Section 4.3.4.7. The target masses were adjusted precisely, so that the peak center routine could be skipped after switching masses. We did keep the peak center routine for δNe/Ar, because the magnet jump was less precise. For each mass, we created a background gas conﬁguration, and measured the background for each sample. 126

Table 4.9: Precision of krypton isotopes, in per meg. The first line shows the mass difference. The second line shows the raw standard deviation of a block of 16 cycles. The next line shows standard error on the mean of 5 blocks of 16 cycles. The next line shows the standard deviation of 7 samples taken from the same flask of La Jolla Air (LJA) standard. The next line shows the standard deviation of 17 LJA samples taken from 3 different flasks. The last line shows the pooled standard deviation of the measurement of 22 flasks in duplicates. δ86/82Kr δ86/83Kr δ86/84Kr δ∗Kr ∆m 4 3 2 1 std of 16 cycles 110 111 84 raw ms σ 12 12 9 σ, LJA ,1 flask (7) 17 15 14 4.5 σ, LJA ,3 flasks (17) 21 37 13 6.4 pstd samples 20 22 13 4.6

For each elemental ratio, we measured 1 block of 5 cycles. The pressure imbalance was measured bi-weekly, and it was on the order of 7 per meg per per mil for δNe/Ar, and negligible for δKr/Ar and δXe/Ar. The precision of each measurement is detailed in Table 4.10. Table 4.10: Precision of elemental ratios, in per mil. The first line shows the mass difference. The second line shows the raw standard deviation of a block of 5 cycles. The next line shows the standard deviation of 6 samples taken from the same flask of La Jolla Air (LJA) standard. The next line shows the standard deviation of 16 LJA samples taken from 3 different flasks. The last line shows the pooled standard deviation of the measurement of 22 flasks in duplicates. δKr/Ar δXe/Ar δNe/Ar ∆m 50 108 14 std of 5 cycles 0.049 0.17 0.19 LJA ,1 flask (6) 0.18 0.28 0.26 LJA ,3 flasks (16) 0.16 0.42 0.55 pstd samples 0.07 0.16 0.67

4.5 Noble gas measurements in ice cores

This section presents a method to measure δ40Ar, δ86/82Kr, δ Kr/Ar, δXe/Ar and δNe/Ar in ice core samples, following the method of Headly[2008]. 127

4.5.1 Sample preparation

The sample preparation is divided in two steps: ﬁrst, the air is extracted from the ice, and transferred into a tube dipped in liquid helium. The air is then gettered and transferred into another tube, which will be measured on the mass spectrometer. It takes about 6 hours to prepare a sample, and the hardware availability is such that only one sample can be measured in a day. The experimental protocol follows Headly[2008], and is detailed in Appendix 4.E.

4.5.1.1 Ice extraction

This method requires large 750g pieces of ice, because large samples of air are needed to get a precise measurement of δ86/82Kr. The outside 5mm of the ice are shaved off, and the ice is loaded into a cold 1-L stainless steel vessel, along with a glass coated stir bar. The vessel is closed in the freezer, and brought to the lab where it is placed into a dewar of ethanol at -23◦C. It is connected to the vacuum line, which contains a water trap with glass beads, a pump, and another cold trap between the fore-vacuum pump and the turbo: the large amount of water vapor that passes through the line could otherwise condense in the fore-vacuum pump and damage it (Figure 4.22). The vessel is evacuated for 40 min, leak checked and closed. The cold ethanol is replaced by warm water, and the ice melted. A dip tube is then inserted into liquid helium, connected to the line, and the connection evacuated for 10 min, and leak checked. A dewar of ethanol is cooled with liquid nitrogen to -100◦C, and inserted on the beaded trap. The pump is then closed, and the air from the vessel transferred into the tube for 60 min. Once the pressure in the line starts decreasing, the hot water is replaced by a magnetic stirrer, and the water stirred vigorously until the end of the transfer.

4.5.1.2 Gettering

The gettering process is very similar to the one used for air samples (Section 4.4). The dip tube is connected to a 80 cc STP volume, and the getter oven, previously 128

10-torr Step1: ice extraction Baratron gage

Ice sample -100°C Turbo N Stir bar 2 rough Hot Water PUMP He 4 K PUMP Magnetic stirer Water trap Ethanol and N2

Step 2: gettering valve glass volume 80 cc ultratorr connection

Sample oven Zr/Al 10-torr 900°C getter Baratron gage

PUMP He 4 K

Figure 4.22: Experimental setup for the extraction of noble gases

ﬁlled with 30 sheets of Zr/Al getter. The getter oven is preconditionned at 100◦C for 10 min, then at 900◦C for 10 min. The system is leak checked. Then the pump is closed, and the tube opened for 10 min, while the oven is at 900◦C. The tube is then closed, and the air present gettered for another 10 min. The oven is brought down to 300◦C for 5 min, after which the gettered sample is transferred to the dip tube for 10 min. The process is repeated for the air remaining in the tube, which is transferred in the same dip tube. This two step transfer using a large expansion volume near the oven ensures that all the air is gettered [Kawamura, 2000]. A detailed set of instruction is given in Appendix 4.E. Once the transfer is ﬁnished the sample is allowed to equilibrate for 2 hours before being measured on the MAT-252 mass spectrometer. 129

4.5.2 Mass spectrometry

Due to stability problems with the MAT-253, we decided to use the MAT-252 for the analysis of ice samples. This mass spectrometer measures δ40/36Ar, δ86/82Kr, δKr/Ar, δXe/Ar and δNe/Ar. The mass spectrometry generally follows what has been outlined in the previous sections. For each sample, an aliquot of the standard gas equilibrates for 10 min before being expanded into the bellows. The sample equilibrates for another 10 min after expansion. The Kr isotope method is run with 5 blocks of 25 cycles each. The Ar isotope method is run with 4 blocks of 16 cycles. The elemental ratio methods are run with 1 block of 5 cycles each. Pressure balancing is done at the start of each bloc.

4.5.2.1 Background

A new background is taken at the start of each sample, in each gas conﬁguration. The background value is subtracted from the beam intensity by the mass spectrometer software. The background variation is less than 0.10mV. It affects the delta values by less than 0.2 per meg. The variation in the background is therefore not affecting the precision of our measurements signiﬁcantly.

4.5.2.2 Pressure imbalance sensitivity

The pressure imbalance sensitivity (PIS) is the sensitivity of the measurements to an imbalance in the pressure between the standard and the sample side. It is measured in (per meg in delta value)/(per mil of pressure imbalance). The 252 is very linear and the PIS is low, on the order of 0.2 per meg/per mil. Pressure balancing results in about 0-20 per mil of pressure imbalance for typical samples (Tables 4.11). An aliquot of the standard upon expansion gave 13 mB, and we adjusted the sample size so that its pressure would be between 10 and 15 mB, ensuring a small pressure imbalance correction. If we were to suppose that the variations of the pressure imbalance sensitivity are due to our inability to measure it correctly, we can use the standard deviation of all PIS measurements as a measure of our error in estimating the PIS. This approach gives 130

Table 4.11: Pressure Imbalance Sensitivity (PIS) for δ40Ar, δ86Kr, and elemental ratios in per meg per per mil. δ40Ar δ86Kr δKr/Ar δXe/Ar δNe/Ar date PIS r PIS r PIS PIS PIS Aug-09 -0.531 -0.876 -0.481 -0.974 1.4 2.5 -3.9 Oct-09 -0.540 -0.944 -0.086 -0.990 Feb-10 -0.252 -0.988 Apr-10 -0.481 -0.974 -0.254 -0.995 Jun-10 -0.383 -0.998 -0.200 -0.999 1.3 0.4 4.1 an upper bound to the error associated with the PIS correction, as the PIS is actually changing on the time scale of months in the machine. This error in the estimation of the pressure imbalance results in an uncertainty of about 1.6 per meg on δ40Ar and δ86Kr, 1.1 per meg on δKr/Ar, of 44 per meg on δXe/Ar, and 0.25 per mil on δNe/Ar. These errors are on the order of 1/10 of the gas handling error (Table 4.13), so they are not signiﬁcant.

4.5.2.3 Chemical slope

The chemical slope (CS) is a correction accounting for the variability in ionization efﬁciency of Kr isotopes depending on the relative abundance of Kr and Ar. It is calculated as the slope of the regression between δAr/Kr and δ86Kr (Figure 4.23)

86 86 δ KrCS−corrected = δ KrPIS−corrected − CS δAr/Krmeasured (4.9)

The chemical slope is a stable value, and was measured at the beginning and the end of the experiment. I used the mean value between these 2 measurements to correct the entire data set. The uncertainty on the CS is about 0.1 per meg/per mil. δKr/Ar is typically on the order of 30 per mil. The uncertainty in the CS correction can create an offset of up to 3 per meg on δ86Kr, which is less than half of the uncertainty associated with gas handling. 131

Chemical Slope -0.020 -0.021 -0.022 y = -2E-05x - 0.0195 -0.023 Kr R² = 0.89237 86

δ -0.024 -0.025 -0.026 -0.027 50.00 100.00 150.00 200.00 250.00 300.00 350.00 δAr/Kr

Figure 4.23: Chemical slope measurements for krypton isotopes. In this case, the slope is 0.2 per meg per per mil.

4.5.3 WDC05A samples

WDC05A was drilled in January 2005, and was sampled at the National Ice Core Laboratory in July 2005. The core quality is generally good: there were no visible fractures, except for one heavily fractured piece (most likely from drilling) at 145m. Be- cause the core was dry drilled, however, large pressure gradients must have existed near the cutter tips due to the lack of borehole pressure compensation. These gradients may have caused momentary micro-cracking and gas loss. I measured the samples between April 15, 2009 and June 10, 2010. Each sample is 30 to 40cm long and 750g in size. Duplicates were cut along the side of the core. Occasionally, one sample would be too small, and I would need to cut a piece of the whole width of the core to adjust for the difference (about 100g out of 700g). It would also happen that the sample would have a diagonal break, and that the 2 samples were not strictly equivalent. In one instance, at 184m, we have 2 samples from neighboring depths rather than duplicates on the same depth. There are bubble free layers in almost every sample, and those are not believed to affect our measurements.

4.5.3.1 La Jolla Air calibration

58 samples of La Jolla Air, out of 7 ﬂasks were taken throughout the experiment (Table 4.12). There is no clear difference between ﬂasks, which shows that we do not expect a drift in the standard over the duration of the experiment (Figures 4.24 and 4.25). 132

Table 4.12: Mean La Jolla air values used to normalize the results run against the working standard can. δ40Ar δ86Kr δKr/Ar δXe/Ar δNe/Ar mean -1.811 1.361 15.277 -24.160 153.535 std 0.014 0.022 0.097 0.504 0.438

δ40Ar La Jolla Air -1.77 0 1 2 3 4 5 6 7 8 12-Aug-09 -1.78 15-Oct-09 -1.79 3-Dec-09 -1.8 22-Feb-10

Ar -1.81 5-Mar 40 δ -1.82 25-Mar

-1.83 29-Apr

-1.84 18-May

-1.85 14-Jun nb of sample in the ﬂask

Figure 4.24: Argon isotope measurements. The colors correspond to different ﬂasks. The good agreement between ﬂask shows that the working standard did not drift.

δ86Kr La Jolla Air 1.440 12-Aug-09 1.420 15-Oct-09 1.400 3-Dec-09

Kr 1.380 22-Feb-10 86 1.360 δ 1.340 5-Mar 1.320 25-Mar 1.300 29-Apr 0 2 4 6 8 18-May nb of sample in th flask 14-Jun

Figure 4.25: Krypton isotope measurements. The colors correspond to different ﬂasks. The good agreement between ﬂask shows that the working standard did not drift. 133

4.5.3.2 Evaluation of the precision

We measured a total of 73 samples of ice, including 35 pairs. The precision of the ice measurements is as good as the La Jolla air measurement for δ40Ar and δ86Kr (Table 4.13), which shows that the ice extraction technique is adequate, and that long pieces (30 to 40 cm) of ice from the same depth have the same isotopic content. The elemental ratios have more scatter in the ice because of gas loss, which is especially true for δNe/Ar. Table 4.13: Precision of the Kr-Ar method: the ﬁrst line represent the standard deviation of 10 measurements of 2 working standard cans, in per mil. The second line shows the standard devation of 58 La Jolla air measurements, and the last line the pooled standard deviation of 73 samples from 38 depths. δ40Ar δ86Kr δKr/Ar δXe/Ar δNe/Ar Standard 0.009 0.023 0.086 0.373 0.713 LJA 0.014 0.022 0.097 0.504 0.438 Ice 0.010 0.018 0.179 0.545 40.25

4.5.3.3 Fractured ice

Overall, the ice was in excellent condition. However, at 145 m, there was a heavily fractured piece, which we did not include in the data set. The results from this piece are given in Table 4.14. The isotopic ratios are elevated, and δNe/Ar is very negative, which is compatible with preferential loss of the light isotopes, and small atoms from the cracks. Table 4.14: Comparison between a fractured piece, and neighboring samples. The last line is the standard deviation of neighboring samples, which shows the along-core variability. δ40Ar δ86Kr δKr/Ar δXe/Ar δNe/Ar broken 1.253 1.137 23.07 38.27 -712.0 reference 1.249 1.214 16.939 31.831 -279.0 stdev 0.029 0.009 0.572 1.166 38.0 134

Appendix 4.A Protocol for extracting La Jolla Air

4.A.1 In the laboratory

• Take the two traps out of the drying oven. • Fill a dewar with liquid nitrogen. • Take the ethanol dewar out of the freezer, and prepare the cold trap by slowly adding liquid nitrogen to it. The temperature of the ethanol should be -80 to - 100◦C. If it is too cold, it will start freezing xenon at -110◦C. The dewar should only be half full, because of the volume displacement of the traps, and because of the splashing when we move the cart. It can take up to 20 min to get the ethanol to temperature. If the ethanol becomes very thick and milky, but the temperature does not go down, it probably has too much water in it, and the ethanol should be discarded and replaced. Ethanol is considered hazardous material, and should be discarded properly. • When the temperature gets to -100◦C, put both traps in the ethanol and add a little bit of liquid nitrogen so that it freezes over and it will not splash during the trip to the pier. • Make sure that you have all the ultra-torr R s. Screw them all the way in, or they will come apart during transport. • Make sure you have the right number of pieces of synﬂex R tubing. • Take the pier key, the extension power cord, a timer and a temperature couple. • Take something to secure the ﬂask in the cart. such as a concave piece of foam.

4.A.2 At the pier

There is a power outlet at the end of the pier, in the middle. Its preferable to go there in the morning, when the buildings provide shade. Otherwise, bring an umbrella to keep the apparatus in the shade. Look at the wind direction and arrange for the operator to be downwind from the intake during sampling. Put everything together and verify the cold trap temperature (Figure 4.26). • Open the valves of the ﬂask • Plug in both pumps 135

Air Air

aspirated PUMP intake 4L/min

-100°C

Figure 4.26: Schematics of the set up to extract La Jolla Air standard.

• Verify that the flow rate is at its maximum • Allow the flask to be flushed for 10 min • Unplug the pumps, and wait 5 seconds. • Close the valves on the flask, as fast as possible • Take everything down • Screw in all ultra-torrs R , or they will come apart during the travel back to the lab.

4.A.3 Take down

• When back in the lab, label the ﬂask with the date of sampling. • Take the traps out of the ethanol, let them drip dry and put them in the drying oven. Beware that ethanol is ﬂammable, be sure to let it fully evaporate before putting the traps in the oven. • Bring the ethanol back into the chest freezer. • Return the pier key to the key locker 136

Appendix 4.B Protocol for ﬁlling working standard cans

4.B.1 Ar-N2 standard

4.B.1.1 Preparation

• The standard can should be leak checked and evacuated overnight. • Gather a 100-Torr baratron, and a Paroscientiﬁc 500 psia gauge, or equivalent. • Bring the argon and nitrogen cylinder in the rigth place.

4.B.1.2 Addition of argon

The ﬁrst step is to calculate how much argon to add. The dry atmosphere contains 78.084% of N2, and 9.332 mmol/mol of Ar [Park et al., 2004]. A number previously used is 48.34 Torr. The cylinder of argon should be connected to the line with a piece of synﬂex R tubing, with a valve. The pressure is measured with a 100-torr baratron gauge (Figure 4.27)

PUMP

2 Ar 1 100 Torr 3 5 4 ST can

Figure 4.27: Setup for adding Ar to an Ar-N2 standard

• Flush the regulator on the Ar cylinder. • Attach everything. While you are attaching the last element, let a ﬂow of Ar go through, so that you minimize the amount of air and water vapor in the line. • Open (1), (2), (3), then close (1), and pump the Ar out. Repeat once. 137

• Close (1). Open (2), (3), (4) and evacuate for at least 1 hr. to make sure its really clean. • Leak check. • When it is all evacuated, with pump closed and convectron closed, open (2), (3), (4), and slowly open (1) to dial in the desired pressure. Close (1). • Close (4), (3), (2).

4.B.1.3 Addition of nitrogen

4.B.1.3.1 Set up Flush the regulator of the N2 cylinder, to get fresh gas into it. Con- nect the cylinder with a valve (1) and a synflex R tube to the Paroscientific 500 vacuum gauge and the standard can (Figure 4.28). The pressure will get above atmospheric pressure in this part of the line, and it is best not to expose the baratron gauges to it. Tape the ultra-torrs R , to ensure that they will not pop out. Before connecting the last piece of equipment, allow a small flow of N2 through the system, to flush it.

PUMP

10 2 Torr N2 1

P 3 5 gauge 4 ST can

Figure 4.28: Setup for adding N2 to an Ar-N2 standard

4.B.1.3.2 Operation • Open the outer can valve (3) • Open the cylinder valve, adjust the regulator to several psig or the desired pressure.

• Close convectron gauge, and vacuum pump, ﬂush the line with N2 (open valve to

the line (1)). You can open a valve to the room if you wish, to allow N2 to bleed into the room, in order to ﬂush the synﬂex R more rapidly, without taxing the pump 138

too much. It is important to make sure the synflex R and regulator are well flushed so that water vapor does not get into the standard can. • Close valve to the line (1), and evacuate the line (open (2) slowly, check the flow with the 10 Torr gauge: make sure it stays around a few Torr, no more, so that the pump is not overtaxed.)

• Repeat: ﬂush with N2, then evacuate. • When baratron is on 0, close the valve to the pump (2).

• On the regulator, dial in the desired pressure of N2 you want to add to the can (for example: 50 psig) • Open the line valve (1), then slowly open the standard can valve (4), and you will hear a hissing sound of gas rushing into the can. Wait until the needle of the manometer is steady (ﬂow has stopped), or until you read the desired pressure on the Paroscientiﬁc readout. Remember that the pressure you will read is the total

pressure, sum of Ar and N2, in absolute pressure (psia), not gauge pressure (psig). Note: 50 psig is 64.7 psia in La Jolla. If you allow the gas in too quickly, it will cool and give a false reading on the pressure gauge. Generally, let the whole gas transfer process take about 5 min. • Close the can valves (4) then (3), close valve (1). • Be careful when you take off the can: the pressure will make a pop sound.

• Close the N2 cylinder. • Let the standard can homogenize and equilibrate overnight.

4.B.1.4 Correct the Ar/N2 ratio by adding Ar

Calculate how much Ar you need to add:

X = [Ar(ST )] ∗ δAr/N2/1000 ∗ 1200 (4.10)

where [Ar(ST )] is the initial amount of Ar in the can, in Torr, δAr/N2 is the measured La Jolla air versus your standard can, and 1200 is the ratio of volume between the ﬂask+aliquot and the aliquot. If you need to add more than 1000 Torr, you will have to add it in multiple 1000 Torr increments. 139

The set up is similar to Figure 4.27, but with the 1000 Torr gauge. • open the Ar cylinder, and let a steady flow of Ar flush the synflex R line. • Connect a valve to the synflex R (valve 1), then the standard can (with a tee), to the extraction rack, and flush again with Ar before plugging in the 1000 Torr baratron (This baratron takes a special readout, one of the dual channel readouts). • Attach the 1000-Torr baratron, • Close valve 1, open valve 2 to the pump to evacuate the air, open the pump, then open valve 3 (outer valve of the ST can). • Let it pump out for 1 hour. • Leak check. • Close pump, close valve 2 • Dial in desired pressure with valve 1. • If you overshoot, open the pump briefly • Close valve 3, open valve 4 • Disconnect everything • Let the standard flask homogenize and equilibrate overnight in horizontal position.

4.B.2 Ar-Kr-Xe standard

4.B.2.1 Handling of Kr and Xr tanks

The tanks for pure Kr and Xe should be rigged with a 4H valve. These gases are so expensive that we cannot afford to use a regulator, which is wasteful. The aliquot between the tank valve and the 4H valve is full of pure gas. It is at high pressure. Evacuate the volume between the tank valve and the 4H valve with great care: open the 4H valve very slowly, so as not to damage the turbo. Evacuate for 20 min.

4.B.2.2 Setup

You will need the pre-evacuated standard can (evacuate for 24hr), a 10 Torr and a 1000 Torr baratron, and a port for your standard tank (Figure 4.29). Be sure to support the baratrons. 140

PUMP

10 2 Torr Ar 1

3 5 1000 Kr 4 Torr ST can

Figure 4.29: Setup for building a Ar-Kr-Xe standard

4.B.2.3 Calculations

You need to decide the total pressure of the ﬂask, P t. One aliquot is 1.3 cc, and a dip tube is 10 cc. 1aliquot is 1/1200 of the volume of the can. If you want to match 1 atm in a 10 cc dip tube, you will need to have 1atm*10 cc/1.3 cc for total pressure in your can. You need to decide the ratios rk = Kr/Ar and rx = Xe/Ar. For air, Ar = 0.933%, Kr = 1.14 10−6, Xe = 0.87 10−6, So rk = 1.22.10−3 and rx = 9.315.10−4 Then calculate: rx P (Xe) = P t (4.11) (1 + rx + rk)

(rx + rk) P (Xe + Kr) = P t (4.12) (1 + rx + rk)

4.B.2.4 Operation

• Hook up the least abundant gas ﬁrst (Xe). • Evacuate the connections, including the volume between the tank valve and valve 1 for 20 min. • Leak check. • Close valve 1. Introduce an aliquot of gas by opening the tank valve. Close the tank valve immediately. • Open valve ST can valves 3 and 4. Verify that convectron is at baseline pressure. • Close pump. (2). 141

• Open valve 1 slowly until you reach the desired pressure P(Xe). • Close valve 3 and 4. • Hook up the next gas (Kr). • Evacuate the connection for 20 min (1,3,4 closed, 2 open). Leak check. • Close pump, open valve 1 slowly until you reach the desired pressure P(Xe+Kr). • Close valve 3 and 4. • Repeat for Ar, until you reach Pt. After you are done, let the can equilibrate for 24hr before using it.

4.B.2.5 Notes

• If you overshoot, you can bleed the gas out to the pump. • Xe is a very sticky gas, it will take a long time to pump it out. Be sure to evacuate the line for a couple hours after making the standard before running samples: there will be some residual xenon in there for a while. • After running La Jolla Air or other standards, you may have to adjust the amount of gas in the ST can. For that, use the fact that the aliquot is 1/1200 of the volume, and add gas by closing the outer ST valve with a measured pressure of gas in the aliquot volume, then opening the inner ST valve, and allowing the content to homogenize for several hours. 142

Appendix 4.C Protocol for extraction of Ar and N2 in ice samples: Copper method

4.C.1 Preparation of the method

4.C.1.1 Chest freezer

You need to have a clean chest freezer for your own use in the lab. Inquire about what is in it, and get it defrosted. In the chest freezer, you will need 4 dewars of Ethanol for each of the vessels, plus 1 for the water trap. You also need space for 4 flasks, and the cooler. You need a pair of tweezers to lower the ice down, and 4 pairs of small stir bars for each of the samples. The stir bars should stay in the freezer when not in use. You need a lid for all of the dewars, and collars for 4 flasks, that match the size of the dewars. They are made of some sturdy plastic, but alternatively, cardboard covered with duct tape can work. You need yellow caps for all the flasks.

4.C.1.2 Getting the ﬂasks ready

Each flask has to be thoroughly cleaned before the experiment: • Rinse it with deionized water, clean with glassware soap and rinse thoroughly. • Dry the flasks with house pressured air, and put them in the oven, overnight if possible, 30 min at the minimum. • Let them cool down outside for 30 min, • Put them in the freezer with a yellow cap on, if possible overnight. • If time is running out, and you need to cool the flasks down, cool them with liquid nitrogen, and once they are cold, let them sit in the freezer for 30 min, allowing them to homogenize the temperature.

4.C.2 The night before

• Put clean dry vessels and stir bars (2 per vessel) in the freezer overnight to chill. Cover with yellow lid to keep dry. 143

• Make sure ethanol dewars are in freezer at least several hours to chill to -25◦C, covered to prevent evaporation. • Evacuate dip tubes

4.C.3 In the freezer

• Before you go down, open all valves on the line to pump it all, and switch on the oven. • Take the key, and bags that you will use in the cooler. The cooler should be filled with eutectic packs, and sit in the chest freezer in the lab while not in use. • Label the bags you will need. It leaves time for the ink to dry. • Cut the ice, making sure that replicates cover the same depths: cut lengthwise first. • You want 100 g (90-120 g window) • Shave off 1cm if possible, at least 2 mm. • Cut into small pieces that fit into the flask vessel (3cmx3x8cm), check with the vessel in the freezer. Note that some of our vessels have a thinner neck, so dont make it too tight. • Weigh your sample and record the weight • Put in Ziplock bag to bring up in cooler. Label the bags with bottom depth and weight. • Dont lose the orientation of the piece of ice left over. Make sure that there is an arrow on it, and put it the right way in the original bag.

4.C.4 In the lab

1. Make labels for the samples, and stick them somewhere near the line. 2. Take a water trap with capillary out of the oven to cool for the end of the day. 3. Place 1 vessel in ethanol dewar, using a cardboard collar to suspend it, within the freezer. 4. Place 2 cold stir bars 5. Place ice pieces in vessels using pre-chilled stainless steel tongs, try not to drop them. 144

Pump

2 capillary 9 1 5 6 8 10 4 copper 7 10 11 Torr 1 Torr H2 Trap 2: Trap 3: Liq. N2 Liq. N2 500 C Trap 1: -100 C Ethanol

liq. 4 K Helium

Figure 4.30: Set up for the Ar-N2 method

6. Keep ice pieces as low as possible in flask to minimize warming from above. 7. Carry the dewar with vessel to extraction line. Select the right label, and put it on the port. 8. Place copper gaskets on vessel seat, lift vessel out of ethanol, and finger-tighten bolts on flange. 9. Make sure the flange is ”mated” properly to the vacuum line, and not crooked. 10. Tighten bolts gradually and evenly in the usual mechanic’s star pattern, using two 7/16” box wrenches (across, 2 bolts clockwise, repeat). Typically 25 strokes are needed, each about a quarter-turn. Do not over-tighten bolts; just ”snug”. Mini- mize the amount of time the vessel is out of the ethanol. Copper gaskets may be used about 2 times 11. Once you are done with bolting the flask, adjust the jack to cover the flask fully with ethanol. Verify that there is enough ethanol in the dewar, otherwise, add some with the reserve dewar in the freezer. 12. Close off the main line (valve 5 and 9), open the valve to the back way to the pump (valve 2), open the flask valve (1), and slowly open the pump valve (3) to get the fore-vacuum convectron reading up to 3 to 5 Torr. 13. Proceed to the next flask. 14. When all the flasks are bolted and open, slowly open the valve to the pump (3), all 145

the way. 15. When the 10-Torr baratron says 1 Torr (or when turbo is at full speed, whichever comes first), start the timer for 20 min. 16. After 10 min, note the reading from baratron (red): It should be around the vapor pressure over ice at -25◦C: between 0.1 and 0.7 Torr. If it is much higher, check the temperature of the ethanol, if not, there might be a leak: check the flanges one by one. Ethanol must not be colder than -30◦C or sublimation will be too slow. Ideal temperatures are between -25 and -20◦C. 17. Check for leaks by closing pump and seeing if pressure plateaus at vapor pressure over ice. 18. Make the slush for the first trap: Take the (small blue) dewar filled with ethanol out of the freezer, and slowly add liquid nitrogen, stirring often. Stop when the consistency is very thick, and the temperature -110◦C. If you cannot get below -100, there is too much water in the ethanol, and you need to recycle it and use some fresh, new ethanol. 19. When 20 min is up, • check the vapor pressure over the flasks: close valve 2, read the pressure on the 10-Torr baratron, and note it in the notebook. Open valve 2 again • Close all vessels • Close valves to the pump, 2 and 3, and baratron (valve 4). 20. Remove ethanol bath of the first sample and allow to drip dry for 30 sec. 21. Melt ice with lukewarm water if desired, take out the warm water when there is still a little bit of ice left. Make sure sample never goes above room temperature (water will condense on valve if this happens, potentially blocking the valve). It is best to leave a small amount of ice at the start of the transfer, so that the water is always near 0◦C during the transfer. 22. Precool the dip tube in liquid nitrogen, and insert it into liquid helium, close valve 8 (to the line), open the valve to the pump (9), and the arm valve (10). Set the timer on 10 min. 23. When 10 min is up, insert the liquid nitrogen dewar on the trap, and leak check with then 1-Torr baratron. It passes the leak check if the pressure does not go up 146

more than 1e-4 Torr in 30 seconds. 24. Open valve (8) to the rest of the line. 25. Leak check for 30 seconds. 26. Add the other liquid nitrogen trap, and the slush. Check the temperature of the water trap, it should be between -85 and -110◦C. Cool it with liquid nitrogen if necessary. 27. When everything is ready, take out the warm water bath, and start the stirrer on 7-8 (vigorous, but without splashing more than 2/3 of the way up the ﬂask). 28. Close the pump (valve 9). 29. On the octopus, make sure that back line (to vacuum) and baratron (valve 2 and 4) are closed. Let the main line valve (5) open, close valve (6), open the vessel valve (1). 30. Open the dip tube valve (11). 31. Start 24 min transfer

32. Open slowly valve 6 to dial in P ¡ 1 Torr to ensure complete burning of O2. Note the time when the valve is fully open. 33. After 5 min have elapsed, lower the tube, and reset the timer. Top off the dewars, check the temperature in the 100◦C traps. After 12 min, lower the tube all the way, and check the traps again. 34. When 10 min are left, remove the ethanol dewar from the next sample, and start warming it with lukewarm water. 35. At the end of the 20 min transfer, stop stirrer. 36. Close the vessel valve (1). 37. Close dip tube. 38. Take out the dip tube. 39. Record in the notebook the residual pressure. (should be 0 to 0.2 mT) 40. Open the valve to the pump (9). 41. Wait a few seconds for the baratron to read 0, and close valve (8), to the oven and the rest of the line. 42. Take the dewar out of trap 3. ◦ 43. Regenerate the copper wool with H2 gas at 500 C: allow H2 to ﬂow between 100 147

and 500 mTorr for 3 min, and pump the water away for 5 min. • Take a copper line and hook it up to the line via 1/4 ultra-torr R . • Close all unncecessary parts of the line. • Take one aliquot out of the tank: close the little valve out, open the main tank valve, dial in some pressure, and open the little valve all the way. • Dial between 100 and 500 mTorr for 3 min.

• Make sure that you are indeed ﬂowing H2: check that your aliquot is not empty. • Evacuate the water produced for 5 min. 44. Insert next dip tube, evacuate the arm valve: (8) is closed, open (10). Set the timer to 5 min. 45. Check the temperature of the water trap, add liquid nitrogen if necessary, to reach -100◦C.

4.C.5 Clean up

It can be done during the next transfer. • Make sure the sample valve is shut, or you risk venting. • Unbolt vessel from line in a spare moment (after starting next sample). • Weigh vessel and record weight. Calculate ice mass by subtracting vessel and stirrer tare. • Empty out the water through a sieve to retrieve the stir bar. • Inspect the stir bars for cracks. • Rinse vessel and stir bars in deionized water and dry in oven, then store in freezer with yellow cap covering opening. After re-generating, replace the water trap: • Close valves (5), (6), (7), take out the trap • Replace it with another trap. • Let the old trap warm up and drain the water, then quickly blow it out with house air before putting it into the oven. • Evacuate the trap using the back side: keep (1) and (4) closed, open (2) and (3) slowly, so as not to overpower the turbo. 148

• Evacuate dip tubes for the next day • Put vessels and stir bars into the freezer

4.C.6 Mass spectrometry

15 40 Let the dip tubes homogenize overnight and measure δ N, δ Ar, δKr/N2 and

δAr/N2 on the MAT-252. • Evacuate the inlet with fore-vacuum. When the fore-vacuum gauge is below 1e-3, switch to high vacuum. When the ion gauge is at its base pressure ( 7e-7), bring both bellows to 100% • Close valves to the bellows • Take an aliquot out of the standard for 3 seconds, then close the inside valve. • Expand the aliquot into the bellows for 5 seconds, then close inlet valves • Expand the sample into the bellows for 5 seconds, then close inlet valves • Set the pressure in each bellows to 230 mB (200-250 range is ﬁne) • Start the sequence • Hook up the next sample. If there is none, hook up the other standard can. 40 15 We run 5 blocks of δ Ar, 3 blocks of δ N, 3 cycles of δAr/N2, and 3 cycles of

δKr/N2, which takes about 3 hr. 149

Appendix 4.D Notes on Focusing the MAT-252

This section contains instructions on how to focus the MAT-252 properly. Put an aliquot of ST gas in the MS. One bellows is enough. Adjust the bellows pressure to the usual measurement pressure, and set the gas conﬁguration to the major gas. Put the cursor on the major isotope (28 for N2, 40 for Ar).

4.D.1 Settings that should be left alone

On the right of the panel are settings that we do not touch: The emission is set at the maximum, so that we get a total intensity of 1.5 mA. If the beam was to become unstable, the extraction could be lowered slightly. The trap voltage is set at 20 V. It has been this way since Jeff installed the MS. In the manual, it is recommended to use 50 V, but we have had good success with 20 V, and changing it to 50 V did not increase the performance. The Electron Energy is set at 60V. It has been this way since Jeff installed the MS. In the manual, the recommended range depends on the type of focus: For sensitivity focusing, the recommended range is 50 to 60 V For linearity focusing (what we want), the recommended range is 80-90 V Roger Husted (Thermo) recommends using 85 V, and 50 V for the trap. However, we have always had it on 60 V, and had great linearity. I tried to change it to 80 V, and saw no improvement on the focus, but the trap emission decreased a lot. So, for our MS, it is probably better to keep the Electron Energy at 60 V. The trap emission should be between 1/3 and 2/3 of the total emission The total emission should be 1.5 mA, so the trap emission should be between 0.5 and 1mA. If it is larger than 1, it means that you are on a sensitivity peak, and the linearity is very bad, the MS should be focused very often (daily). It is a bit unstable this way. If it is lower than 0.5 mA, it means that the source is dirty. Try cleaning the source. (All this is said in the manual).

4.D.2 Settings that should be adjusted

On the left of the panel, There are the adjustable knobs. The screws are for the coarse settings, and the 10-turn potentiometers for the ﬁne tuning. 150

1. Put all potentiometers in their middle position (5.0)

2. Put all the screws in their middle position

3. Adjust the screws, from top to bottom, starting with the Extraction, to maximize the intensity.

4. Adjust the 10-turn potentiometers

(a) Extraction: There should be 2 peaks for the Extraction: a small peak around 5, and a larger peak around 8. In order to maximize the linearity, we need to be on the small peak. If you cannot ﬁnd the small peak, try to adjust the coarse setting a little. If you still can’t ﬁnd it, adjust the Beam Centering, and then, go back to the Extraction. I have noticed that moving the Beam Centering may cause the linearity peak to disappear. (b) Focus1: adjust it to maximize the intensity. The peak is rather narrow. (c) Focus 2: adjust it to maximize the intensity. The peak is wider than the previous one, and neither of these is very sensitive to a change in the Extraction or Beam Centering focus. (d) Beam Centering: adjust it to maximize the intensity. It is a rather large broad maximum. Try to be in the middle of it.

5. Go back and adjust the extraction again (with the knob), to be on the smaller linearity peak. If the peak has suddenly disapeared, you can try to move the Beam centering a bit, and see if you recover the peak.

6. Look at the linearity in the raw ratio: In the method, it is called rR. Run 2 cycles, imbalance the pressure, then run 2 cycles again. Do that 3 times. You can let the method running, and imbalance the SA bellows while it is evaluating the ST bellows (Figure 4.31). Note that the rR applies to the sample. If you want rR for the standard, you have to calculate it from δ and the sample rR.

In a good linearity focus, the value should change by less 0.002 over a wide range of pressure. If it changes a lot, say from 0.94 to 0.98, then the linearity is not good enough. This is a quick way to evaluate the linearity, without running a formal PIS. When you get a good focus, run the PIS properly to verify that everything is running smoothly. 151

Figure 4.31: Screenshot of the Ar method, highlighting where to ﬁnd the rR indicative of the pressure imbalance.

Each filament produces a different voltage for a given bellows pressure. Over the life of the filament, the voltage will drop. After you have finished focusing, verify the voltage for the pressure that you nominally run your samples at, and adjust the Pressure Adjust target voltage in each method if necessary. It is not impossible that with a new filament, your target voltage might double. Run the PIS and background frequently shortly after venting the MS, especially after a filament change. It may vary substantially in the first week. 152

Appendix 4.E Protocol for the measurement of noble gases in ice samples

10-torr Step1: ice extraction Baratron gage

Ice sample -100°C Turbo N Stir bar 2 rough Hot Water PUMP He 4 K PUMP Magnetic stirer Water trap Ethanol and N2

Step 2: gettering valve glass volume 80 cc ultratorr connection

Sample oven Zr/Al 10-torr 900°C getter Baratron gage

PUMP He 4 K

Figure 4.32: Experimental setup for the extraction of noble gases

4.E.1 The day before

• Make sure that the 2 water traps needed are drying in the oven: one long beaded one, and one medium with no capillaries. • Put 2 dewars of ethanol to cool down in the freezer: a blue short one, and a blue long one. Top them off if there is not enough in it. You can verify the level when you introduce the trap in it. • Make sure there is enough ethanol in the big stainless steel dewar for the ice vessel. • Pump out 2 dip tubes. 153

4.E.2 Before going down to the freezer

• take both water traps out of the oven and let them cool down (until you can manip- ulate them with bare hands, about 3 min) • Set up the line: place 2 wooden stands on each side of large jack (where ice vessel will be placed), attach ultra-torr R connections (w/ ﬂexible piece) to line, which will be used to connect vessel to line. • Connect water trap to line. Use a long water trap with beads. • Fill up the liquid nitrogen dewar • Bring down the big vessel, screws, 2 wrenches (1/2 in), copper gasket, stir bar, and plastic cap to protect the end of the tube on the lid.

4.E.3 In the freezer:

• Shave off the outer few mm of the surface of the sample with the band saw. The ceramic knife is very useful for that. At the end, dust the ice with a brush. For ice that has been sitting in a freezer for many years, especially on parts that were the outside of the core, we should shave off a whole cm. • Weigh the sample (after shaving off the surface); should be > 600g • Write down the sample weight and depth • Carefully place sample in stainless steel extraction vessel, using large kimwipe. • Use tongs to place a large stir bar into the extraction vessel (place it horizontally, on the bottom of the vessel. If placed at the top, it risks falling during melting and breaking.) • Make sure that the rim of the extraction vessel is clean and dry on both ends (use brush and kimwipe). • Remove large copper o-ring from plastic bag using large kimwipe (use scissors to cut bag open) • Place large copper o-ring onto extraction vessel, and then place cover onto vessel, making sure that o-ring is properly ﬁtting into place. • Make sure the cover has the right orientation. • Gather screws and bolts 154

• Hand tighten 4 screws evenly around the vessel (i.e. 12, 6, 3, and 9, in a clock) • Then hand tighten the other screws (in star pattern). To help yourself, put the 4 ﬁrst screws upside down, and then do the middle ones, then the left ones, then the right ones ( right of the upside down one).

4.E.4 Sample preparation for the line

• Before bringing the ice up, prepare the -100◦C slush for the fore-vacuum water trap: Take the small blue dewar of ethanol from the freezer and slowly add liquid nitrogen while sitting to reach a thick honey consistency. Wear eye protection. Insert the water trap in the dewar. • Close valve to the turbo and connect fore-vacuum water trap in between the turbo and fore-vacuum pump. This water trap is a U shape with no capillaries. Put the larger side (that delivers the air on the top) on the upstream side. Dont forget to open the valve to the turbo again. • Before removing vessel from freezer, place large bucket of ethanol on large jack near the vacuum line (between the 2 wooden stands) • Remove extraction vessel from freezer (walk fast) and place on wooden stands, balancing it over the ethanol • Connect extraction vessel to vacuum line using the ultra-torr R connections already set-up, dry up the frost on the edge with kimwipe. • Raise ethanol as high as possible

4.E.5 Pumping out ambient air

• Open a valve from trap to pump slowly, open the other one, • Slowly open vessel valve. Keep fore-vacuum under 200 Torr. When 3 lights are off, turn off the turbo, then keep opening the valve slowly. When the pressure is clearly decreasing, turn the turbo back on. • Once turbo is up to full speed, start 40 minute timer (starting 40 minutes of pumping) • Record vapor pressure over ice at 5 minutes (e.g. 0.592 Torr) 155

• Record vapor pressure over ice at the end of the 40 minute pump-down . Verify on the chart that it corresponds to a reasonable temperature (between -21 and -23◦C) • Close valve to extraction vessel • Close valve to water trap

4.E.6 Preparing the vacuum line for transfer

• Precool a dip tube in liquid nitrogen, place it in liquid He (propped up so that it can be lowered 3 times), attach to vacuum line, and open valve to line • Open valve from water trap to the line (keep valve to line between water trap and extraction vessel closed so all air has to pass through water trap) • Raise a tall dewar (the same type as the one used to precool dip tubes) around the water trap and fill with liquid nitrogen (this speeds up pump down and leak check) • Pump down this volume (the connection to the dip tube in liquid He and the water trap and assoc. connections) for 20 minutes • In the meantime, fill the tupperware bowl to just below the brim with warm water, and heat this water in the microwave for 20 minutes • While water is heating, make up the water trap: take ethanol in tall dewar out of the freezer, and mix with liquid nitrogen until temperature is around -100◦C • Make sure dewar around ”water trap” is filled with liquid nitrogen • Leak check the vacuum line (connection to the dip tube in liquid He and water trap) after 20 min of pumping • Keeping the liquid nitrogen around the ”water trap”, close valve to convectron, close valve left of the trap, and open valve to extraction vessel to leak check the extraction vessel. Make sure the path is through the water trap. • Once baratron pressure is 0.001 Torr, open convectron to leak check: Leave the pump closed for 3 min and see that the pressure stabilizes for more than 30 sec (1.2 mTorr is an ok value to get). • Note on leak checking the seal: If there are cracks in the ice, the pressure will slowly increase, even in the absence of leak. Clathrate ice outgases continuously, it gives higher value than bubbly ice. • Close valve to extraction vessel after leak check , 156

• Close both valves to the water trap and evacuate the convectron, until it reads 5e-4. • Close convectron, close valve right of the water trap, and open the left one: the water should evacuate backwards, so that when you put the -100◦C trap, it doesnt freeze the small opening shut. (≈10 min) • Remove liquid nitrogen dewar from water trap and place another tall dewar full of warm water around water trap - this allows the water and gases trapped in the trap to be pumped away. • As the trap is pumping down, remove hot water from microwave and pour into bucket • Once the pressure in the line is stable at 0.050 Torr ( 5 min), replace hot water dewar with the dewar of ethanol at -100◦C • Allow pressure to decrease down to 0.001 Torr

4.E.7 Extraction and transfer

• Verify that pathway through the trap is right (ﬁrst valve closed, second one open). • Open valve to extraction vessel • Allow pressure to decrease down to 0.001 Torr • Close valve to pump (between front line and pump) • Open valve to dip tube in liquid He • Start 60 minute timer • Remove large ethanol dewar surrounding extraction vessel and put it back into the freezer • Place bucket of hot water on jack under extraction vessel and raise it until only the very bottom of the extraction vessel is touching the hot water ( 2 mm of vessel in water) (record time on the timer at this point) • Note: When warming, the pressure should increase on the baratron. If not, no worries, it needs to melt a little bit: maybe a very small piece of ice was the only thing touching the bottom. This is a critical step: we do not want too much pressure in the vessel, otherwise, the gas will dissolve in liquid water. If its too slow, then it would take forever. • Pressure on baratron should be about 2 Torr or so during melting 157

• Once pressure decreases to 1 Torr and is relatively stable raise hot water a few cm ( about 5 min into melting) • Check temperature of water trap - add liquid nitrogen if needed - repeat this throughout 60 minute transfer • When pressure falls to 0.050 Torr, remove hot water bucket (record time on timer) • Place large stirrer on jack under extraction vessel • Turn stirrer to maximum (record time on timer) • When baratron reads 0.010 Torr, lower tube by 1 step (record time on timer) • When baratron reads 0.005 Torr, lower tube by 1 more step (record time on timer) • When baratron reads 0.001 Torr, lower tube all the way (record time on timer). • Note: The baratron may stop at 0.003 Torr, which is the residual when you have a lot of ice. Leave the tube fully immersed in liquid He for at least 10 min. • After 60 minutes, close valve to dip tube • Switch the stirrer off. Open convectron and record residual pressure (typically 2 E-3 Torr)

• Note: CO2 is outgassing from the water as it warms, and will look like a leak. This is why you do not want to stir during leak check. You can test for the presence

of H2 or He from the difference between baratron reading and convectron: if the convectron reads twice or more as much as the baratron, you probably essentially have helium, which does not get trapped in liquid He. • Close valve between line and dip tube, make sure tube is labeled, and remove dip tube from liquid helium • Close valve between line and water trap • Close valve to extraction vessel • Remove water trap and extraction vessel • Let water trap melt, pour out the water, then place it in oven • Remove all screws from the extraction vessel. Use a small screwdriver to remove o-ring: do not touch the inside of the vessel. From the indent on the outside, insert the screwdriver to lodge it in the copper and push upwards, to eject the o-ring. Make sure not to risk any indentation of the seal of the vessel. • Use tongs or kimwipe to remove stir bar from vessel. Let it dry, then put it in the 158

freezer. • Dump water remaining in extraction vessel into the sink • Place extraction vessel upside down (but tilted so that inside can ventilate) on ”team towels” overnight • Place top of extraction vessel with vacuum side facing up on team towel (with another team towel covering it) • Both parts of extraction vessel dry out overnight.

4.E.8 Gettering

• Use 80 cc volume, the getter tube and the sample tube • Make sure that the volume is well attached. If it is not properly aligned with the ultra-torr R , it can cause a leak. • Insert 30 getter sheets in the tube, and connect it to the line using a shield of aluminum foil to protect the rest of the line from the heat. • When everything is connected, close convectron valve and open valve to the pump • Switch the oven on 100◦C for 10 min. • Close volume valve, switch oven on 900◦C for 10 min. • Switch the oven off, allow it to cool down (2 min), open the volume valve and the convectron. Leak check the system. • Switch the oven on 900◦C. • Close valve to the line, open volume valve, open sample tube valve. Getter at 900◦C for 10 min. • Pre-cool a dip tube in liquid nitrogen, insert it in He tank and connect it to the line. Close convectron, evacuate the arm. • After 10 min, close the tube valve. Getter for 10 min more. ◦ • Switch the oven on 300 C for 5 min. (note: this step gets rid of H2 produced by gettering) • In the meantime, leack check the dip tube • Turn off the oven, close the pump and convectron, open the valve to the line, record the pressure on the 10 Torr baratron. • Open tube valve. Transfer for 10 min. After 2 min, lower the tube, lower all the 159

way after 2 more min. • Close tube valve, check for residual. Write it into the notebook. It should be close to zero. • Close the valve from getter to the line • Switch the oven on 900◦C. open the dip tube valve. (volume is open). • Getter for 20 min. • Write a tag for the sample • Switch the oven on 300◦C for 5 min. • Shut down oven, close convectron and pump, open valve to the line. • Record the pressure on the notebook • Open tube valve, transfer for 10 min, lower at 8 and 6 min. • Close the tube valve, check for residual (should be close to zero) • Close arm valve, take tube out, verify that it has a tag. • Close valve from getter to the line, open the pump • Close volume valve and sample tube valve. • Break the vacuum, and take out the getter tube, discard the sheets

4.E.9 At the end of the day

• make sure all traps are in the oven • make sure dewars of ethanol are in the freezer. Top them off if needed. • Do not forget the fore-vacuum water trap. Make sure the fore-vacuum valve is open • Evacuate dip tubes for the next day. Chapter 5

Constraints on the recent warming in West Antarctica

Abstract

The instrumental record of temperature in Antarctica started in 1957, and is now complemented by satellite measurements which started in the 1980s. This record is short and discontinuous, and it has been difficult to establish a warming rate precisely. We present here a temperature reconstruction at the West Antarctic Ice Sheet (WAIS) Divide for the last hundred years, based on a joint inversion of both borehole temperature measurements and the noble gas isotopic composition of the firn and ice. Bore- hole temperature measurements provide information on the absolute temperature and long term changes, while isotopes of N2, Ar and Kr record fast changes in temperature, making them an independent measure of decadal temperature tends. This reconstruction confirms that West Antarctica has been warming for the last 50 years by at least 0.2◦C/decade, and gives a broader temporal context to this trend.

5.1 Introduction

Our global climate is presently in a warming phase, and this trend is expected to continue for decades to come, due to the increase in greenhouse gases in the atmosphere

160 161

[IPCC, 2007]. The polar regions are expected to warm more than the global average, which will trigger mass loss from the ice sheets and rising sea level, and will impact most of the human population. During the Eemian, 125 thousand years ago, the temperature in high-elevation Greenland was 8±4◦C warmer than the last 1000 year average [NEEM community members, 2013], which is not unlike what climate models project for the end of this century [IPCC, 2007]. The sea level was 6 to 8 m higher than today’s; yet less than half of this could have come from Greenland [NEEM community members, 2013], which implies that the remainder had to come from Antarctica. This conclusion calls into question the stability of the West Antarctic Ice Sheet to global warming. West Antarctica is a very remote part of the world, and there are few direct temperature observations beyond the last 20 years, and virtually none before 1957. The lack of data makes it difficult to estimate the significance of recent trends, and it complicates the calibration of paleoclimate proxies. We present here a temperature reconstruction of the last 50 years based on the combination of borehole temperature and inert gas isotope data from firn air, taken at the WAIS-Divide site. This reconstruction allows us to quantify the recent warming trend, which gives highly complementary information to the instrumental record, and allows us to state with confidence that West Antarctica is warming.

5.1.1 Site location

WAIS-Divide is located 30 km east of the ice divide at the center of West Antarc- tica (79◦S, 112◦W). It is also 100 miles away from the historical Byrd Station (80◦S, 120◦W), where the only weather station of the interior of West Antarctica dating back to 1957 is located. The West Antarctic Ice Sheet covers a deep oceanic trench, and it is grounded at a depth up to 1.7 km below sea level. As a result, the elevation of the WAIS-Divide site is only 1766 m above sea level. Unlike the East Antarctic plateau, which sits 3000 m above sea level, the lower elevation of West Antarctica allows for more marine air mass intrusions to the center of the sub-continent. As a consequence, West Antarctica has a much more dynamic climate, is generally warmer, and has a higher accumulation rate than East Antarctica. WAIS-Divide has a mean annual temperature of -30◦C, and a mean 162 accumulation rate of 0.22 m/yr in ice equivalent [Banta et al., 2008]. The geography of West Antarctica also makes it susceptible to melting under ice shelves driven by the warm upper ocean, and this is the leading cause of current mass loss [Jacobs et al., 2011].

Figure 5.1: The color shadings show the correlation between the annual mean temperatures at Byrd and the annual mean temperatures at every other grid point in Antarc- tica. The correlations are computed using ERA-Interim 2-meter temperature time series from 1979 to 2011. The star symbol denotes the location of Byrd Station/AWS. The ﬁlled black circles denote the locations of permanent research stations with long-term temperature records [Bromwich et al., 2012]. 163

There is a large amount of spatial coherence in the climate of West Antarctica, as we can see in modern satellite observations (Figure 5.1[Nicolas and Bromwich, 2011; Bromwich et al., 2012]). WAIS-Divide is situated at the center of West Antarctica, and is thought to be representative of the sub-continent as a whole (Figure 5.1). In particular, the weather stations at Byrd and WAIS-Divide capture very similar climate variability (Figure 5.2), and we will compare temperature reconstructions under the assumption that the two sites record the same climate signal.

ï10 Byrd WAISïD ï20

ï30

Temperature, °C ï40

ï50

2006 2006.5 2007 2007.5 2008 2008.5 2009 Time, year

Figure 5.2: Weather station data from Byrd and WAIS-Divide, situated 180 km from each other. Both stations have very similar temperature variability. Data courtesy of Matthew Lazzara (AMRC, SSEC, UW-Madison).

5.1.2 Variability in the atmospheric circulation and teleconnections with the central tropical Paciﬁc

The dominant source of inter-annual variability in West Antarctic climate is due to the displacement of the Amundsen Sea low pressure system (ASL) [Nicolas and Bromwich, 2011]. When the ASL is shifted westwards towards the Ross Sea, air mass trajectories come straight through Marie Byrd Land, bringing warm moist air to West Antarctica. When the ALS is shifted eastwards towards the Bellingshausen Sea, West Antarctica is sheltered from incoming storm activity, and is generally colder and drier [Nicolas and Bromwich, 2011]. 164

The position of the ASL is in part controlled by a Rossby wave train originating in the central tropical Pacific [Ding et al., 2011; Schneider et al., 2010]: warm SST in the central tropical Pacific triggers anomalous convection, which starts a wave train locking the ASL towards the Ross sea, thus bringing anomalous warm moist air to West Antarctica. This teleconnection is especially strong in the Southern Hemisphere winter [Ding et al., 2011], and is one of the reasons why ENSO events can be recorded in West Antarctic ice cores [Schneider and Steig, 2008]. As a result, temperature reconstructions in West Antarctica can inform us on the climate history of the tropical Pacific, and deepen our understanding of atmospheric teleconnections.

5.1.3 Evidence for widespread warming in West Antarctica

Antarctica is surrounded by persistent westerly winds that act as a barrier, which prevents warm air masses from penetrating into the interior, especially in East Antarc- tica. It was long thought that the acceleration of the westerlies, in part due to the ozone hole, would in effect shelter Antarctica from global warming [Thompson and Solomon, 2002]. The Antarctic Peninsula, on the other hand, has been warming significantly over the past few decades, which has led to the dramatic loss of ice shelves [e.g. Scambos et al., 2000]. Whether West Antarctica would follow the eastern part of the continent or the Peninsula has been a long standing debate, due to the severe lack of data. The first attempt at reconstructing West Antarctic temperature since 1957 was presented by Steig et al.[2009], and showed a significant warming trend, especially in winter and spring. This study was, however, challenged by skeptics, and several other temperature reconstructions have been published since then [e.g. O’Donnell et al., 2010; Kuttel¨ et al., 2012; Bromwich et al., 2012], which all showed a warming trend, albeit with different amplitudes. We present here independent temperature reconstructions, based on ice core paleo-climate proxies at WAIS-Divide, which can establish a baseline of climate variability and precisely quantify the amount of warming that West Antarctica has experienced in recent decades. Section 5.2 details the different methods that can be used to reconstruct paleo-temperature, and Section 5.3 presents the results and compares them to existing surface temperature reconstructions. 165

5.2 Paleo-temperature measurements

5.2.1 Borehole temperature

Heat diffuses through the snow and ice rather slowly. Many years after the snow has fallen, it retains a trace of the temperature held upon deposition, both due to slow diffusion and rapid downwards advection from snow accumulation. We can measure the temperature of the ice in a hole left over from an ice core expedition, and re-construct the surface temperature history at the site (see Chapter3). The biggest advantage of borehole temperature is that it provides an absolute temperature measurement, and is not a proxy that needs to be calibrated. However, the diffusive process causes the time resolution of the signal to decrease as we go back in time (Figure 5.3 and 5.4), and borehole temperature measurements are only useful to measure long-term changes. Another drawback is that borehole temperature only measures the surface temperature, and not the free troposphere temperature, which may be more climatically relevant. In polar regions, near-surface radiative inversions can be very strong, especially in the winter [e.g. Tomasi et al., 2011]. We measured the borehole temperature in a 300 m hole at WAIS-Divide (Figure 5.5, see also Chapter3). The direct comparison of the data with a modeled stationary temperature proﬁle shows that there is a signiﬁcant warming trend captured in the top 100 m of the ice (Figure 5.5). We reconstructed the temperature history using an iterative least squares inverse method (Chapter3 and Orsi et al.[2012]).

5.2.2 Inert gas isotopes

The molecular diffusion of inert gas isotopes in air in polar firn allows isotopes to separate under gravitation and temperature gradients [e.g. Severinghaus et al., 1998, see also Chapter2]. We measured isotopes of nitrogen, argon and krypton in air from the firn at WAIS-Divide (Figure 5.6), following the laboratory method outlined in Chapter 4. We used a 1-D model of gas diffusion and advection in the firn to quantify the sources of fractionation. The governing equation for the mixing ratio x of a trace gas in 166

Age distribution 20

30 12

40 10 50 8 60 6 Depth, m 70 4 80 Age Distribution, %

90 2

100 0 1950 1960 1970 1980 1990 2000 time, year A.D

Figure 5.3: Age distribution of a 2-year, 1◦C pulse as a function of depth and time in the borehole temperature proﬁle. The resolution of recovered fast changes decreases rapidly with time, due to the fundamental fact that diffusion destroys information.

6 1931 1951 4 1971 1991 2003 2 2007 age distribution, % 0 15 25 50 100 200 300 Depth, m

Figure 5.4: Age distribution of a temperature pulse in the ice, for selected times. The resolution decreases rapidly with time. 167

ï29.4

ï29.6

ï29.8 Temperature, °C ï30

50 100 150 200 250 300 Depth, m

Figure 5.5: WAIS-Divide measured borehole temperature proﬁle (+). The accuracy of the measurement is better than 0.1◦C, and the precision is 2.3 mK, which is smaller than the size of the symbols. The grey lines represent stationary temperature proﬁles, computed for mean annual temperatures of -30.03 to -29.73◦C. The slight deviations in the top 30 m are due to the annual cycle of temperature, and the strain heating as the snow is compressed into ice.

0 15 b N 40 10 b Ar/4 * b Kr 20

40 Depth, m 50

70 Lock In Zone 80 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 b, per mil

Figure 5.6: Inert gas isotopic measurements in the WAIS-Divide ﬁrn air. δ15N data are from Battle et al.[2011], and the rest from this study. 168 the open ﬁrn is [Kawamura et al., 2006; Severinghaus et al., 2010]:

∂ ∂ ∂x ∆m g dT ∂x ∂x fC (x) = fC D ( − x + Ω x) + D − C fw (5.1) a ∂t ∂z a m ∂z RT dz e ∂z a a ∂z where f is the open porosity, Ca is the concentration of whole air, determined by the hydrostatic balance, t is the time, z is the depth, Dm is the molecular diffusivity, ∆m the mass difference, g the gravitational constant, R the ideal gas constant, T the temperature,

Ω the thermal diffusion sensitivity, De is the eddy diffusivity, and wa the vertical velocity of the air, which depends on the rate of snow accumulation. The coordinate system is ﬁxed at the snow surfaace (z = 0), and the z is positive downwards, following the model of Rommelaere et al.[1997]. The porosity f(z) is determined by the measured density proﬁle: f(z) =

1 − ρ(z)/ρice. The molecular and the eddy diffusivities, Dm and De, need to be param- 15 eterized at each site, using observations of CO2, δ N and halocarbons [Buizert et al.,

2012]. The eddy diffusivity, De, represents the convective mixing due to wind pumping in the ﬁrst few meters of the ﬁrn. It is parameterized as an exponential decrease with depth [Kawamura et al., 2006; Severinghaus et al., 2010]:

z De = De(0) exp(− ) (5.2) hcz

The surface value De(0) and the scale height hcz can be determined by a fit to the the δ86Kr profile, taking advantage of the fact that krypton isotopes are not very sensitive to thermal fractionation (Figure 5.7). We find an optimal solution for De(0) = −5 2 1.2 10 m /s, and hcz = 5 m. For comparison, Battle et al.[2011] found De(0) = −5 2 1.6 10 m /s, and hcz = 1.4 m, but they did not have the advantage of the krypton data, and nitrogen isotope data are also affected by thermal fractionation due to the recent warming.

We used the measured proﬁles of CO2 and CH4, for which we know the recent atmospheric history, to reconstruct the molecular diffusivity proﬁle with depth, using a linearized least squares inversion, as outlined in Buizert et al.[2012] (Figure 5.8). Once the model has been calibrated, we can use the fractionation of inert gas 169

0 with 5 m convective zone no convective zone 20 data

40 depth, m

Lock In Zone 80 0 0.2 0.4 0.6 0.8 1 1.2 1.4 d86/82Kr, per mil

Figure 5.7: Calibration of De in the convective zone with krypton isotopes. The dashed curve shows the model result without any convective zone, the solid line shows the −5 2 model output with a 5 meter convective zone, and De(0) = 1.2 10 m /s.

0 0 Model Data 20 20

40 40 Depth, m 60 60

80 80 300 320 340 360 380 1200 1400 1600 1800 CO , ppm CH , ppb 2 4

Figure 5.8: Model validation: the diffusivity profile was tuned so that the gas diffusion model, forced with a known atmospheric history of both CO2 and CH4 (line), would fit the firn air data (circles). 170 isotopes to infer the temperature gradient in the firn, and reconstruct the temperature history. The temperature diffusion process is precisely reproducible in the laboratory and the calculation of temperature differences is straightforward [Grachev and Sever- inghaus, 2003a,b]. Measurements of δ15N and δ40Ar in the firn are an independent source of information on firn temperature gradients. However, they do not provide an absolute temperature measurement. In the ice, the vertical profile of temperature contin- ues to diffuse, but the diffusion of gases stops when the gas get occluded in the ice, at the lock-in depth. As a result, δ15N and δ40Ar in the ice core can provide additional, higher frequency information to a temperature reconstruction based on borehole temperature. Inert gas isotopes, like borehole temperature, measure the ground surface temperature, and thus are also influenced by surface temperature inversions.

5.2.3 Water isotopes

The stable isotopes of precipitation, described commonly by δ18O and δD, fractionate during phase changes, and this fractionation depends on temperature. The isotopic composition of precipitation is a complex function of the temperature of the evap- orative source region, the path the moist air followed, and the temperature at the precipitation site [Dansgaard, 1964]. The variability in snow δ18O and δD in polar regions is thought to be primarily caused by condensation temperature or cloud temperature, which is closely related to the temperature at the ice core site [Jouzel et al., 1997]. Wa- ter isotopes record temperature during every precipitation event, and can be measured at very high resolution, including sub-annual events. In addition, it is not affected by temperature inversions. The main drawback of water isotopes is that the calibration of this proxy is not straightforward: it depends on each site, and it is difficult to find a valid calibration for all timescales [e.g. Cuffey and Clow, 1997; Jouzel et al., 1997]. At WAIS-Divide, water isotopes appear to be temporally correlated with temperature [Steig et al., 2013], but they are also influenced by sea ice extent [Kuttel¨ et al., 2012]. 171

5.3 Results

5.3.1 Temperature reconstruction

We reconstructed the ground surface temperature history from borehole temperature data and inert gas isotopes (δ15N, δ40Ar and δ86/82Kr), using the linearized least-squares inversion method presented in Chapter2. The temperature reconstruction, along with water isotope data is shown in Figure 5.9.

ï28 18 b O Temperature reconstruction ï29

ï30

Temperature, °C ï31

ï32 1800 1850 1900 1950 2000 time, year C.E.

Figure 5.9: Surface temperature reconstruction, with error bars shown by the dashed line, and the WDC05A δ18O record for comparison.

The constraints provided by the borehole temperature data are much stronger than that of δ15N, and the reconstruction of both data sets together resembles strongly the borehole temperature reconstruction (blue line in Figure 5.9 and 5.10). Figure 5.10 shows the δ15N and temperature profiles for each of the surface temperature histories shown on Figure 5.9. The borehole temperature reconstruction (blue line in Figure 5.9 and 5.10) over- estimates the amount of thermal fractionation in the open firn (20 to 60 m, Figure 5.11), by about 3.1 per meg. For comparison, the analytical uncertainty on δ15N is 2 per meg (Chapter4). This observation is reminiscent of firn air studies at other sites, where we have witnessed a cold bias in the expression of the seasonal cycle [Severinghaus et al., 2001]. This cold bias consists of a mean annual δ15N value at depth that is lower than 172

0 0

10 10

20 20

30 30

40 40 depth, m 50 50

60 60 18 b O 70 model 70 data 80 80 0 0.2 0 0.05 ï30 ï29.5 ï29 15 15 b N , per mil b N thermal, per mil Temperature, °C

Figure 5.10: Data and model output for a) nitrogen isotope profile b) thermal component of nitrogen isotopes, c) temperature profile. The model was run with the best fit solution (blue), and the δ18O record (green). 173 expected from a stationary climate. We also find a similar cold bias in the NEEM firn, in North Greenland (78◦N, 51◦W), where we measured both the borehole temperature profile and inert gas isotopes precisely. This cold bias may be caused by an increased downward advection of cold air during the winter, where cold dense air sits above warmer, less dense air, although this mechanism has yet to be quantified precisely.

0.02 15N mismatch LIZ b therm 0.015 20ï60 m mean 0.01

0.005

0 mismatch, per mil ï0.005 therm N 15

b ï0.01

ï0.015 0 20 40 60 80 Depth, m

15 Figure 5.11: Data-model mismatch of the thermal component δ Ntherm (data - model). The precision of the measurements is 2 per meg, and it is illustrated in the error bars in the data. The model-data mismatch is smaller than 15 per meg. In the diffusive zone, the data are lower than the model by about 3.1 per meg, which is illustrated in the thick blue line. The deeper part of the ﬁrn is the Lock-In Zone (LIZ), which records older air, and may be affected by close off fractionation, and should be interpreted with caution.

Overall, the inert gas isotope data conﬁrm the warming trend of the last 50 years identiﬁed in the borehole temperature record in Chapter3. It is also consistent with water isotope data at the same site, showing that this signal must be affecting the free troposphere, and not just the inversion layer. 174

5.3.2 Comparison with reconstructions based on satellite and weather station data at WAIS-Divide

The very first weather stations of the Antarctic continent were deployed during the International Geophysical Year of 1957. Most of them were on the coast, and there was only one station in West Antarctica: Byrd station (80◦S, 119◦W), about 100 miles away from WAIS-Divide. Fortunately, there is a large spatial covariance in the center of West Antarctica, and Byrd is well correlated with WAIS-Divide (Figure 5.2). The satellite era has dramatically improved the availability of temperature data from the Antarctic, starting in 1978. The surface temperature can be measured with a infrared radiometer, such as Temperature Humidity Infrared Radiometer (THIR) or the Advanced Very High Resolution Radiometer (AVHRR), onboard NOAA’s Polar- orbiting Operational Environmental Satellites. These radiometers can only measure clear sky temperature, and the accuracy of the temperature estimate depends on the accuracy of the cloud masking: in Antarctica, the albedo of the ground is not much different from the albedo of a cloud, which makes the process challenging [e.g. Comiso, 2000]. Several studies have used the spatial covariance of temperature from satellite data to extend and fill in the weather station records, and produce a temperature history covering the whole Antarctic continent from 1957 to the present [Monaghan et al., 2008; Steig et al., 2009; O’Donnell et al., 2010]. The data presented in this chapter are an independent estimate of temperature from the data sets used in these reconstructions, which allows us to test the accuracies of these reconstruction. The only weather station present in West Antarctica since 1957 is at Byrd station (80◦S, 119◦W), and all the reconstructions are based on this data set. However, there were significant data gaps, which leave room for interpretation [Bromwich et al., 2012]. Steig et al.[2009] (hereafter S09) and O’Donnell et al.[2010] (hereafter O10) used covariance maps based on satellite data to fill in the gaps, with slightly different methods. The O10 reconstruction has notably less variability, and produces a smaller trend at WAIS-Divide than S09 (Figure 5.12). We used these input histories to produce a inert gas isotope and a borehole temperature profile, and compared those to the data (Figure 5.12). The top 10 m are affected 175

ï26

ï28

ï30

ï32 Temperature, °C ï34 1950 1960 1970 1980 1990 2000 2010 Time, year A.D

0.02

, per mil 0.01 therm

N 0 15 b 80 70 60 50 40 30 20 10 0 Depth, m ï29 data Orsi 2012, WAIS Steig 2009, WAIS ï29.5 O Donnell 2010, WAIS Küttel 2012, Byrd Bromwich 2012, Byrd

Temperature, °C ï30

300 200 100 50 20 Depth, m logïscale

Figure 5.12: Comparison of several published temperature reconstructions of the last 50 years at WAIS-Divide and Byrd station. WAIS-Divide and Byrd are well correlated, and the Byrd station records have been adjusted by a constant to reproduce WAIS-Divide conditions. The top panel shows the temperature histories. The bottom two panels show the model output when it is forced by said histories. The middle panel shows the fractionation of δ15N due to thermal diffusion. The bottom panel shows the borehole temperature proﬁle, on log depth-scale, so as to emphasize the upper section. 176

0.06 10 Borehole data Orsi 2012, WAIS 8 Steig 2009, WAIS 0.04 O Donnell 2010, WAIS 6 Küttel 2012, Byrd Bromwich 2012, Byrd 0.02 4

T gradient, K/m 2 T gradient, mK/m 0 0

10 20 30 40 60 80 100 120 140 Depth, m Depth, m

Figure 5.13: Comparison of several published temperature reconstructions of the last 50 years at WAIS-Divide or at Byrd station. This figure shows the temperature gradients in the ice, produced by the temperature diffusion model, with various input temperature histories. by the seasonal cycle and should be interpreted with caution (Figure 5.14). The interannual variations are noticeable up to 100 m (Figure 5.15). The inert gas isotope profile does not show a significant difference between the various scenarios. The borehole temperature profile agrees better with S09. The temperature reconstructions were published as anomaly maps, and we transposed them into a temperature history by adding an absolute value, which ensures that the mean temperature for the last 50 years was identical to that of the best solution found in Chapter3. It is possible however to adjust this parameter, and shift the whole profile up and down. It is perhaps more objective to examine the temperature gradient in the ice, which we computed as positive upwards, so that a positive value means a warming trend with time (Figure 5.13). O10 has a more constant temperature gradient, showing a gradual increase in temperature rather than a small trend, which accelerated in the last 20 years. S09 has the right temperature gradient up until 35 m, where it is smaller than what can be seen in the data. Kuttel¨ et al.[2012] (hereafter K12) adjusted the gaps in the Byrd station record after 1998 by weighing nearby weather stations, rather than using thermal infrared data, and found a larger amount of warming in the last 10 years. We translated their Byrd 177

ï29.4 data Dec 1st ï29.5 Jan 1st Feb 1st ï29.6

ï29.7 Temperature, °C ï29.8

ï29.9 10 15 20 25 30 Depth, m

Figure 5.14: Seasonal variability of the borehole temperature proﬁle. The model results for for Dec 2007, Jan 2008 and Feb 2008 are shown for the S09 temperature history. Uncertainties on the date do not affect the proﬁle below 10 m.

ï29.2 data Jan 2006 ï29.4 Jan 2007 Jan 2008 ï29.6 Jan 2009 Jan 2010 Jan 2011 ï29.8 Temperature, °C ï30

ï30.2 10 20 30 40 50 60 70 80 90 100 Depth, m

Figure 5.15: Influence of interannual variability on the borehole temperature profile. Each line shows the temperature profile in January of 2006 to 2010, with the Bromwich et al.[2012] temperature history. 178 record to WAIS-Divide by adjusting the mean value for the last 50 years (Figure 5.2). However, the comparison with our data shows that the warming rate is perhaps too high over the last few decades (Figure 5.13). Bromwich et al.[2012] (hereafter B12) have taken the task of going back through the entirety of the Byrd weather station records, and corrected several calibration issues. Their record is a near perfect fit to the top 30 m (Figure 5.13), but the warming rate is a little bit higher in the 40-80 m range, where both K12 and S09 performed very well. One should note that both K12 and B12 were intended for the Byrd station, and that there might be some real differences in the climate between Byrd and WAIS-Divide, which would explain why Byrd would have started warming earlier. It is possible to speculate that Byrd’s position on the flank of the ice sheet, rather than on the divide, makes it more susceptible to the effects of changes in the katabatic wind frequency.

5.3.3 Is it normal?

18 This recent warming trend has been associated with sustained high δ O of H2O values in all of the West Antarctic ITASE cores [Kuttel¨ et al., 2012]. ITASE was a traversing expedition, which recovered 90 m cores across West Antarctica, between 2000 and 2002 (Figure 5.16). By averaging data from all of these cores, we can recover the part of the signal that is spatially coherent. We compared the δ18O of West Antarctic precipitation averaged over the last 15 years (1991-2005) to other 15-year periods, and found that it is likely (p<0.33) that the last 15 years are more elevated than any 15-year period since 1800, with the possible exception of the 1940’s (Figure 5.17)[Steig et al., 2013]. Look- ing further back using the WAIS-Divide deep ice core, the last decade corresponds to a 2σ event [Steig et al., 2013], and is not unprecedented.

5.4 Conclusion

Results from two independent data sets, borehole temperature and inert gas isotopic measurements, conﬁrm that West Antarctica has been warming by at least 0.23◦C per decade over the last 50 years, and that this trend has accelerated to 0.8◦C per decade 179

Figure 5.16: Location map of the ITASE cores, courtesy of the NSIDC. 180

0.66 0.33 Probability 0 1800 1850 1900 1950 2000

O, per mil ï1 18 b ice core stack ï2 annual mean 10ïyear mean ï3 1800 1850 1900 1950 2000 Time, year C.E.

Figure 5.17: Top: Probability that the δ18O of West Antarctic precipitation averaged over the last 15 years (1991-2005) was greater than any other fifteen year period of the last 200 years. Calculation is based on statistics of the fifteen ITASE ice core records and the WAIS-Divide ice core [Steig et al., 2013]. Bottom: δ18O of West Antarctic precipitation, Stack of 15 ITASE cores, with mean removed. 181 since 1990. This finding provides a benchmark upon which to calibrate reanalyses. The comparison of this record with the updated Byrd station profile indicates that Byrd may have started warming earlier than WAIS-Divide. This trend is linked to the observed warming of the central tropical Pacific through atmospheric teleconnections, especially in the winter [Ding et al., 2011]. The comparison with water isotope data from a stack of ice cores in the area suggests that this trend is anomalous in the context of the last 200 years, but not unprecedented. Chapter 6

Surface temperature reconstruction using inert gas isotopes

Abstract

WAIS-Divide has experienced a long-term cooling trend from 950 to 1850 A.D., similar to the trend observed at Greenland Summit. This is consistent with a global cooling during the “Little Ice Age” period, when the solar forcing decreased by 0.9 to 1.5 W/m2. We present data that are consistent with the mechanism of Meehl et al. [2008] whereby an increase in solar radiation strengthens the Walker cell, which triggers planetary Rossby waves, which in turn affect the circulation in the Amundsen sea. Superimposed on this long-term trend are a series of centennial scale warming events, notably between 1315-1395 A.D., 1596-1626 A.D., and 1847-1875 A.D, with a warming rate of 0.24, 0.32 and 0.84◦C/decade respectively. This suggests that the current rate of warming at WAIS-Divide, of 0.23◦C/decade for the last 50 years. is not unprecedented.

6.1 Introduction

The Northern Hemisphere experienced a widespread cooling from about 1400 to 1850 A.D., often referred to as the “Little Ice Age” (hereafter LIA) [Moberg et al.,

182 183

2005]. The LIA cooling was associated with a time of lower solar irradiance and increased persistent volcanism [Mann et al., 2009a]. The Maunder minimum (1645-1715 A.D.) is thought to have had lower Total Solar Irradiance (TSI) of -0.9 to -1.5W/m2 compared to the 1985 minimum [Gray et al., 2010]. The response of the climate to such a weak change in the forcing is difficult to measure because of the large amplitude of interannual variability. The temperature reconstructions of the Northern Hemisphere [e.g. Mann et al., 1998; Moberg et al., 2005] attempt to average out the regional variability and reconstruct a time series that would highlight global trends. In the Southern Hemi- sphere, there is still a dire lack of temperature reconstructions, and the proxy coverage under-samples important regions. This lack of data prevents us from reconstructing a true global temperature time series. One of these missing regions is West Antarctica. The climate of West Antarctica is much more dynamic than that of East Antarc- tica, because the relatively low elevation of West Antarctica allows marine air masses to penetrate into the continent interior, bringing with them heavy precipitation and warmer temperatures [Nicolas and Bromwich, 2011]. As a result, West Antarctica is strongly connected to the climate of the South Pacific [Ding et al., 2011], and is sensitive to El- Nino˜ Southern Oscillation [Mayewski et al., 2009; Fogt et al., 2011]. We present here a temperature reconstruction from WAIS-Divide (79◦28’ S, 112◦05’ W, 1766 m a.s.l.), situated near the flow divide at the center of West Antarctica. This reconstruction builds on the published borehole temperature record (see Chapter3), and includes nitrogen and argon isotopic measurements in air bubbles in the

WAIS-Divide ice core WDC05A. Inert gases like N2 and Ar have a constant isotopic composition in the air, and fractionate in the ﬁrn in response to gravity (heavy isotopes fall down faster), and temperature gradients (heavy isotopes are concentrated on the cold side). Once corrected from gravitational fractionation, we can integrate the temperature signal to produce a surface temperature history with decadal resolution. We show here for the ﬁrst time the dual inversion of both borehole temperature and inert gas isotopes to produce the most accurate reconstruction of the past 1000 years’ temperature at a polar site. 184

6.2 Analysis of the raw data

6.2.1 Nitrogen and Argon isotope data in the WDC05A ice core

The concentration and isotopic composition of inert gases in the atmosphere is constant, and the ice core data reflect the isotopic fractionation happening in the firn (see Chapter2). The two major sources of fractionation are gravitational and thermal fractionation. The gravitational fractionation allows us to reconstruct the firn depth with time, which provides constraints on the snow accumulation history, and determines the age of the gases in the ice core. It is also useful to help constrain mass balance estimates of the ice sheets from satellite altimetry. Thermal fractionation allows us to reconstruct the temperature history at the site. Other sources of fractionation of inert gas isotopes in the firn and ice include gas loss and disequilibrium fractionation.The raw data are first corrected from these effects, and then the data are combined to isolate the gravitational and thermal component (Section 6.2.3).

6.2.1.1 Gas loss

Oxygen and argon are systematically depleted in ice cores. At WAIS-Divide, 15 the mean δ N value is 0.306 , which would correspond to δAr/N2 of 3.67 if all of the signal was due to gravitationalh fractionation. However, we measured an averageh of

δAr/N2 = 1.58 in the ice core. The first reason for the depletion of argon with respect to nitrogen is theh expulsion of elements smaller than 3.6 A˚ during the bubble close off process [Severinghaus and Battle, 2006]. Indeed, the firn profile shows a strong enrichment of δAr/N2 with depth in the Lock-In-Zone (LIZ), and the ice is largely depleted in δAr/N2 (Figure 6.1). The expulsion of oxygen and argon is a purely size dependent process, and is not affecting the isotopes [Severinghaus and Battle, 2006; Battle et al., 2011]. A second cause of argon depletion is gas loss during storage. The first mechanism for gas loss is the loss of small elements by hydrogen bond-breaking [Bender et al., 1995; Ikeda-Fukazawa et al., 2005; Battle et al., 2011]. Again, oxygen and argon are preferentially lost. This is a size-dependent mechanism, which is very sensitive 185

6 raw LIZ Ice gravitationally corrected 4

2 , per mil 2 0 Ar/N b ï2

ï4 0 20 40 60 80 100 Depth, m

Figure 6.1: δ Ar/N2, in the WAIS-Divide firn (line), and in the ice core (triangles). The raw data, and the data corrected from gravitational correction are shown. In the lock- in zone (LIZ), δ Ar/N2 becomes enriched in firn air, due to the selecting expulsion of argon during bubble close off. As a result, closed bubbles, and hence ice samples have a negative δ Ar/N2. to temperature: the probability of hydrogen bond breaking is higher at higher temper- ◦ ature. Storage at temperature higher than -20 C causes severe gas loss of O2, as has been witnessed during the summer 2009 season at NEEM (Kenji Kawamura, personal communication, 2010). The WAIS-Divide ice core was kept below -20◦C in the field with the help of active cooling. It was transported below -20◦C and stored below -23◦C, in order to minimize this component of gas loss. The second gas loss mechanism is the expulsion of gas through micro-cracks, due to the fact that the air bubbles are over-pressured with respect to the surface air pressure [Bender, 2002]. This mechanism causes a preferential loss of lighter elements, and causes a depletion in light isotopes. It is especially prevalent with heavily fractured ice or in the brittle zone [Severinghaus et al., 2009]. We dealt with ice of excellent quality, but the WDC05A core was dry-drilled, without any fluid to compensate for the hydrostatic pressure, and it is still possible to have a small amount of mass dependent gas loss. By comparing data from the lock-in zone and from the top of the ice core, we are able to evaluate the presence of any artifacts in the ice data. δAr/N2 is significantly 186 depleted in the ice (Figure 6.1), which is principally due to size-dependent gas loss. The gas loss fractionation is a first order contribution to the variability in δAr/N2, and we do not intend to use the data for anything other than evaluating gas loss. δ40Ar is enriched in the ice by 3.7 per meg, compared to the Lock-In Zone.

This depletion is not correlated with δAr/N2. As a result, we corrected the ice data by subtracting 3.7 per meg uniformly through the data set (Figure 6.2).

15 15 b N LIZ mean 0.32 b N firn 40 40 b Ar/4 firn b Ar/4 LIZ mean 15 15 0.315 b N ice b N 78ï100m mean 40 40 b Ar/4 ice b Ar/4 78ï100m mean 0.31

0.305 , per mil b 0.3

0.295

0.29

0.285 65 70 75 80 85 90 95 100 Depth, m

Figure 6.2: Comparison between firn air data (solid markers) and ice core data (hollow markers), near the firn ice transition. The lines show the average values between 68 and 74 m for the firn, and between 78 and 100 m for the ice. δ15N agrees well between the two, but δ40Ar is elevated by 3.7 per meg in the ice.

15 86 δ N, δ N, and δKr/N2 are not offset, and we do not need to make any corrections.

6.2.1.2 Disequilibrium

Slowly diffusing gases do not get to complete isotopic equilibrium when they reach the lock in zone. As a result, the isotopic enrichment in the ice is lower than what is predicted by theory. The disequilibrium can be quantified by running the gas diffusion 187 model in steady state. Figure 6.3 shows the isotope data in the firn, and a steady state model run, without any temperature variations. We find that δ∗Kr is depleted by 8.9 per meg, and δ40Ar is depleted by 1.7 per meg with respect to δ15N, for a firn lock in depth of 66.5 m.

0 55 15 b N 40 b Ar/4 60 20 * b Kr 65 40 70 Depth, m Depth, m

60 75 Lock In Zone 80 80 0 0.1 0.2 0.3 0.26 0.28 0.3 b, per mil b, per mil

Figure 6.3: Evidence for disequilibrium fractionation in the WAIS-Divide ﬁrn. The symbols show the ﬁrn air data, and the solid lines the steady state model, without any thermal fractionation.

The variations of the disequilibrium with changing lock-in depth are very small, on the order of 0.09 per meg per m for δ∗Kr, which allows us to correct the data uniformly with time, regardless of small changes in the lock-in depth.

6.2.2 Source of the scatter in the data

We measured δ15N and δ40Ar on 100 g, 10 cm ice samples in the WDC05A ice core. We found a large amount of sample-to-sample variability, which was essentially mass dependent (i.e. would be seen with the same amplitude in δ15N and δ40Ar/4, Figure 6.4). In order to evaluate the heterogeneity of bubble trapping, we measured 3 cm long samples consecutively on a 30 cm piece of ice, and looked at the sample to sample variability (Figure 6.4 bottom). The difference between consecutive samples can be up to 20 per meg, and it is largely co-varying between δ15N and δ40Ar. The scatter of 188

0.32

0.31

0.3 , per mil b 0.29 80 85 90 95 100 105 110 115 120 Depth, m

0.32

0.31 15 b N 40 0.3 b Ar/4 , per mil b 0.29

84 84.05 84.1 84.15 84.2 84.25 Depth, m

Figure 6.4: Subset of the N2 and Ar isotope data showing the scatter between individual samples. In the top plot, the hollow symbols are individual samples, and the solid symbols with a line shows the mean of samples from the same depth. The bottom plot shows a series of measurements made consecutively, with 3 cm samples (hollow symbols), or 10 cm samples (solid symbols). In both cases, δ15N (green) and δ40Ar/4 (blue) covary, which indicated that this scatter is due to mass dependent fractionation, likely caused by heterogeneous bubble trapping. 189

10 cm samples is smaller, on the order of 10 per meg. This evidence suggests that the layering of the ﬁrn causes the lock-in depth (LID) to vary between samples (10 per meg correspond to a 2 m change in the LID). The high frequency variations of the LID are not well understood, and we can consider them as a random process. We averaged out samples in a 5 m running window (±2.5 m), in order to limit this high frequency noise, and retrieve the mean thermal and gravitational fractionation (Figure 6.5). The rest of this chapter will use the 5 m running mean data.

0.34 individual replicate mean 0.33 running mean, 5 m 0.32

0.31 N, per mil 15 b 0.3

0.29

100 150 200 250 300 Depth, m

Figure 6.5: Nitrogen isotope data. The individual data are shown with green symbols. The mean of replicate samples from the same depth is shown in the dashed blue line. The 5 m running mean is shown in the solid red line. The 5 m running mean averages out at least 6 samples, which reduces the scatter due to inhomogeneous bubble trapping. We use the 5 m running mean in the rest of this chapter.

6.2.3 Separation of gravitational and thermal component

Once they have been corrected for gas loss and disequilibrium, the δ15N and δ40Ar data can be expressed as the sum of thermal and gravitational fractionation:

 15 δ N = δg + Ω15∆T (6.1) 40 δ Ar = 4δg + Ω40∆T 190

gZ with δg = (6.2) RT δg represents the gravitational fractionation, at equilibrium, for 1 mass unit difference between isotopes. It is a function of the gravitational constant g = 9.81m2/s , R = 8.314J/K/mol the ideal gas constant, T the temperature, and Z the diffusive col- 15 40 umn height. Ω15 and Ω40 represent the thermal diffusion sensitivity of δ N and δ Ar respectively, and ∆T is the temperature difference between the top and bottom of the diffusive column height. It would be straightforward to solve Equation 6.1 for δg and ∆T , independently at each level:  15 40  δ N − δ Ar/4 ∆T =  Ω15 − Ω40/4 (6.3) 40 15  Ω15 δ Ar − Ω40 δ N δg = 4 Ω15 − Ω40 However, this approach has a tendency to create ﬂuctuations in the δg that are unlikely to be realistic (Figure 6.6). Instead, we used a least-squares technique to take into account the uncertainty in the data. We want to solve:

 15    δ N(z1)   δg(z1)   1 Ω15    δ15N(z )     δg(z )   2     2   .     .   .   1 Ω   .    =  15    (6.4)  40      δ Ar(z1)  1 Ω40/4  ∆T (z1)        40      δ Ar(z2)   ∆T (z2)  .     .  . 1 Ω40/4 .

We note the data vector d = [δ15N; δ40Ar], G the matrix above, and m = [δg; ∆T ], so that Equation 6.4 can be written as:

d = G m (6.5) 191

0.33 15 40 b N b Ar/4 15 40 b N fit b Ar/4 fit 0.32

0.31 , per mil b

0.3

0.29 2 direct solution leastïsquares solution 1

0 T, °C 6

ï1

ï2

40 0.33 b Ar/4 direct solution leastïsquares solution 0.32 0.31 0.3 g, per mil b 0.29 0.28

0.27 100 150 200 250 300 Depth, m

Figure 6.6: Separation of gravitational and thermal fractionation. The data is shown on the top plot, along with the ﬁt to the data. The gravitational and thermal fractionation are shown with (+) symbols for the direct calculation, following Equation 6.3, and with a blue line for the least squares solution. 192

The inversion of Equation 6.5 is given by (see Chapter2 for details):

m = PGT(GPGT + R)−1d (6.6)

We note that P is the square matrix representing the a-priori covariance of uncertainty in the model parameters m, and R the covariance of uncertainty in the residual r = d − Gm. (Details about this technique are give in Chapter2). P allows us to control the smoothness of the solution. We considered the elements of δg to be uncorrelated, and with an a-priori root mean square error of σg = 0.0048 , which corresponds to the standard deviation of δg using Equation 6.3. We used an a-priorih root mean square error ◦ of σ∆T = 0.73 C for ∆T , and enforced time smoothing by adding a cross covariance, decreasing exponentially with a length-scale of τ=10 m, which corresponds to about 3 data points, or 50 years. The sensitivity of the results to the choice of τ is shown in Figure 6.7. R was scaled so that we have a signal to noise ratio (snr) of 1000. The solution is shown in Figure 6.6.

1 direct solution o = 1 m o = 10 0

T, °C o = 20 6 o = 40 ï1 o = 60

ï2 100 150 200 250 300 Depth

Figure 6.7: Sensitivity of the ∆T calculation to τ. The (+) symbols show the direct calculation, using Equation 6.3, the lines show the least squares solution for different values of τ, the a-priori covariance of ∆T with depth.

The 1-σ uncertainty can be estimated by the square root of the diagonal elements 193 of Pˆ (dashed lines in Figure 6.6):

Pˆ = P − PGT(GPGT + R)−1GP (6.7)

We ﬁnd that the 1-σ uncertainty on δg is 0.0016 , and it is 0.13◦C for ∆T , when we average over all the data points. It is better than theh pooled standard deviation of δg and ∆T derived from individual samples using Equation 6.1, which is 0.0061 for δg and 0.57◦C for ∆T . h The gravitational fractionation δg is analyzed in Section 6.3, and the thermal fractionation in Section 6.4.

6.3 Firn thickness and ∆age

The gravitational fractionation of inert gases allows us to reconstruct the past thickness of the ﬁrn, with certin simplifying assumptions [Sowers et al., 1992]. It is essential to the determination of ∆age, the age difference between the ice and gases occluded in it. It also has an application for satellite altimetry: Altimeters measure the thickness of the ice sheet, but a knowledge of the thickness of the ﬁrn layer is needed to convert this altitude measurement into a mass balance estimate [e.g. Helsen et al., 2008].

6.3.1 Firn thickness and diffusive column height

δg allows us to calculate the thickness of the diffusive column, ZD [Sowers et al., 1992]: g Z δg = D (6.8) RT

The diffusive column height ZD is actually slightly smaller than the ﬁrn thickness Zfirn:

Zfirn = Zc + ZD + ZLIZ .

The convective zone thickness Zc is determined by the strength of wind pumping at the surface, which entails bulk motion of the air, and prevents unmixing by molecular diffusion. It is also inﬂuenced by macro-cracks [Severinghaus et al., 2010]. At WAIS-

Divide, Zc ∼ 5 m (see Chapter5), and there is no evidence for deep cracks being present 194 at the surface at the WAIS-Divide site. The thickness of the convective zone is unlikely to vary by more than 1 or 2 m. The interface between the diffusive zone and the lock in zone is called the lock-in depth (hereafter LID). Below the LID, gases are still able to move and diffuse horizontally, but there is little vertical movement of the air, gravitational and thermal fractionation stop, and the air starts aging at the same rate as the surrounding ice. The precise mechanisms controlling the LID are still uncertain. Once a layer of ﬁrn reaches a certain density threshold, it becomes impermeable and effectively locks-in all the lower density layers below it. As a result, the LID is extremely sensitive to the layering of the ﬁrn. In cold, low accumulation sites like Vostok and Dome Fuji, the snow sits at the surface for a long time, and its properties homogenize, creating little layering. As a result,

ZLIZ is generally small. On the other hand, high accumulation sites like GISP2 have a thicker ZLIZ , and lower ZD. WAIS-Divide, like other high accumulation sites has a thick ZLIZ ≈12 m (see Chapter5).

Diffusive column height 66

65 64

63 , m D

Z 62

59 100 150 200 250 300 Depth, m

Figure 6.8: Diffusive column height, calculated from the WDC05A ice core.

15 40 We calculated ZD from δ N and δ Ar in the WAIS-Divide ice core WDC05A (Figure 6.8), using a constant temperature T = −30◦C in Equation 6.8. 195

6.3.2 Modeling the lock-in depth

6.3.2.1 Lock-in depth parameterization

The time variations of the lock-in depth can be predicted by a firn densification model, although no model has yet successfully treated the effects of layering. The current generation of densification models take the surface temperature and accumulation histories as input, and output the density profile with depth. The LID can be parameterized as a function of bulk density as follows:

The porosity is defined as P = 1 − ρ/ρice, with ρ the density, and ρice the ice density. It represents the amount of air space in a volume of firn. The effective porosity at close-off, when the bubbles are fully sealed, is related to the deep firn temperature T by the parameterization of Martinerie et al.[1994]:

−4 3 −1 V c = 6.95.10 Ts(K) − 0.042 (cm .g ) (6.9)

1 1 = Vc + (6.10) ρc ρice The distinction between open and closed porosity is described following the Barnola parameterization [Goujon et al., 2003]:

−7.6 Ptotal Pclosed = 0.37Ptotal (6.11) Pc with ρ ρc Ptotal = 1 − and Pc = 1 − = ρcVc (6.12) ρice ρice

Pc represents the mean close off porosity of bubbles in mature ice, and it is reached when the closed porosity is 37% of total porosity. For the WAIS-Divide modern ◦ 3 3 ﬁrn, with T =-30 C, we ﬁnd Vc = 0.127 m /kg, ρc = 0.8206 kg/m and Pc = 0.1041. The 3 lock-in depth is at 66.5 m, which corresponds to a bulk density of ρLID=0.8155 kg/m ,

PLID=0.1097. Finally, the ratio of closed to total porosity at the Lock-In Depth is

γ = Pc,LID/PLID=0.249. It should be noted that all the porosities given here are bulk porosities, not local ones. By tracking the density and closed porosity, we are able to reconstruct the LID 196 history with time.

6.3.2.2 Variability in the diffusive column height

The scatter between neighboring ice samples of 3 cm height can be up to 20 per meg (Figure, 6.4), and it reduces to 10 per meg for 10 cm ice samples. If the sample to sample variability is attributable to heterogeneity in the lock-in depth, it would correspond to 4 to 2 m changes in the lock-in depth, for samples that are just a few cm apart.

0.9

0.8 3

0.7

0.6 raw data

Density, kg/m 1m average Goujon 0.5 H&L Arthern 0.4 0 20 40 60 80 100 Depth, m

Figure 6.9: Density profile in the WDC06A ice core [Breton, 2010]. The black line shows the 1 m average density. The 3 colored profiles refer to density profiles for the Goujon et al.[2003] model, the Herron and Langway[1980] model, and the [Arthern et al., 2010] model, with appropriate parameters to have the right density in the lock-in zone. The horizontal lines show the depth of the density threshold 0.82 kg/m3 for the density and the bulk density. Because of strong horizontal layering in local density, the meaning of a density threshold for vertical gas transport depends on the resolution of the density profile.

There is ample evidence that neither the density nor the open porosity of the firn are homogeneous [Horhold¨ et al., 2011; Breton, 2010]. The application of the closed porosity threshold to the small scale density or the bulk density would result in vastly different estimates of the LID (Figure 6.9). For instance, the density threshold of 0.82 is reached for the first time at 50.4 m, but corresponds to 67.5 m for the bulk density. As 197 a result, we must take care to apply Equations 6.9- 6.12 to the bulk (1 m) density. This bulk parameterization will inevitably miss the real high-frequency variations in the LID found in the data (see also Figure 6.11). For this reason, we chose a slightly different approach than the classical use of Equation 6.11 in the context of a densification model to predict ∆age over time. Instead, we adopted the measured inert gas isotope estimate of the LID for this purpose.

6.3.2.3 Densiﬁcation model description

Densification models are generally designed to model the bulk density profile, which depends strongly on temperature and accumulation. They take the temperature and accumulation histories as inputs, and output the density profile as a function of time. From the density profiles, we can derive the lock-in, and close-off depths using Equations 6.9-6.11. We can also track layers, find the age of the ice at the lock-in depth, and derive the gas-age-ice-age difference ∆age [Goujon et al., 2003]. We use the transient densification model of Goujon et al.[2003] (hereafter G03). The densification scheme is separated in two stages: The first stage is dominated by grain boundary sliding [Alley, 1987]. The second stage uses a hot-isostatic power law creep, that was initially used for hot pressure sintering of ceramics and metals [Arzt, 1982; Arzt et al., 1983]. The densification model is also coupled to a heat diffusion model, and thus includes the effect of temperature changes in the densification process. We also introduced the densification equation of Herron and Langway[1980] and Arthern et al.[2010] into the Goujon model framework. Herron and Langway[1980] use empirical relationships between temperature, accumulation and the densification rate. This model is meant to be used for steady-state conditions, and we use it here as an illustrative example of slightly different densification physics. We will refer to this model as the HL model. The densification rate follows the equation: Dρ = c(ρ − ρ) (6.13) Dt ice Dρ where ρ is the snow/firn density,ρice is the ice density, Dt represent the total deriva- tive with respect to time, and c the rate parameter which depends on accumulation and temperature. 198

The parameters for each densiﬁcation stage are as follows:

˙ 10160 3 co = 11(b/ρw)exp(− RT ) for ρ < 550Kg/m (6.14) q ˙ 21400 3 c1 = 575 b/ρwexp(− RT ) for ρ > 550Kg/m (6.15)

˙ b is the mass accumulation rate, ρw the density of water, R the gas constant, and T the temperature in K.

[Arthern et al., 2010] (hereafter A10) follows the same equation for the densi- ﬁcation rate (Equation 6.13), but uses a more sophisticated dependency on temperature that takes into account the large seasonal temperature gradients at the top of the ﬁrn.

Here T is the temperature, and Tav the annual average temperature.

c = 0.07(bg˙ )exp(− 60,000 + 42,400 ) for ρ < 550Kg/m3 (6.16) o RT RTav c = 0.03(bg˙ )exp(− 60,000 + 42,400 ) for ρ > 550Kg/m3 (6.17) 1 RT RTav

6.3.2.4 Inputs to the densiﬁcation model

We calculated the time history of accumulation rate at WAIS-Divide by scaling mean annual layer thickness of WDC05Q (0-90 m), WDC05A (0-300 m), and WDC06A (124-577 m). First the annual layer thickness λ is scaled with density to provide a water equivalent layer thickness λw = λ/ρ, using the high resolution density data from WDC06A [Breton, 2010]. Second, the layer thickness is corrected for ice ﬂow thinning, using the equation of Nye[1963]:

H λ = λ (6.18) 0 w H − z

λ0 is the accumulation rate in water equivalent, H is the thickness of the ice sheet (3460 m), and z the depth. There is an excellent correlation between the accumulation rate derived from each of the three cores (Figure 6.10), and calculating the mean allows us to eliminate small scale noise caused by sastrugi. The temperature input was set to match the inversion of the ∆T signal from inert gas isotopes (See Section 6.4). 199

0.3

/yr 0.25

w.e. 0.2 m

Accumulation 0.15 0.1 1000 1200 1400 1600 1800 2000 Time, year A.D. 0.4 WDC06A WDC05A WDC05Q mean 0.3 /yr w.e.

m 0.2 Accumulation 0.1 1800 1805 1810 1815 1820 1825 1830 1835 1840 time, year A.D.

Figure 6.10: Accumulation rate at WAIS-Divide, derived from annual layer counting from 3 cores. The top plot shows a 5-year average for the last 1000 years, the bottom plot shows annual data for a subset of time. The dashed line shows the average accumulation for all 3 cores. 200

6.3.2.5 Results

Each densification model was tuned to produce the right density profile under current conditions (Figure 6.9), using an adjustable constant temperature offset. Partic- ular attention was paid to the lock in zone: If the lock-in density is reached at the wrong depth, it would incorrectly predict past lock-in depth and ∆age. To bring modeled and observed LID together, we added a -3◦C offset to the temperature of the G03 model. We had already observed in Chapter2 that the G03 model tends to densify too fast in this temperature range, letting it reach the lock-in depth too early. We also added a -3◦C offset to the A10 model, and -1.5◦C to HL. These offsets were used during the calculation of ∆age over time. In the first set of experiments, the lock-in depth was defined as the first depth when the ratio of closed to total porosity reaches 0.07. Each of the models was run with a) both temperature and accumulation forcing, b) accumulation forcing, but constant temperature, c) temperature forcing but constant accumulation. The lock-in depth and ∆age are shown in Figure 6.11. The variations in the LID are similar for G03 and HL, and they are mostly due to the variations in the accumulation rate. A10 is much less sensitive to accumulation. All of the models share the same temperature diffusion scheme, and have a similar weak response to the temperature forcing. The gas-age-ice-age difference ∆age is very similar for all models. It is especially interesting to see that for the accumulation-only forcing, A10 has a similar ∆age to G03 and HL even though it has a near constant lock-in depth. It shows that the age is controlled by the advection of layers down, rather than the change in the lock-in depth. The temperature-only forcing shows relatively little response. This observation allows us to decouple the temperature and gravitational fractionation: small changes in the temperature history will affect neither the LID nor ∆age significantly. The G03 model is able to reproduce the trend in the LID as seen by the data, but fails to reproduce the magnitude of the variability. It could be because the LID variability is due to small scale heterogeneity in bubble trapping, or due to missing physics in the model. However, we know what the real LID is from nitrogen and argon isotope data, and we can use this knowledge to prescribe the LID to the data in the model. We use

Equation 6.8 to calculate the diffusive column height Zd and add a constant convec- 201

With temperature and accumulation forcing 70 220

200 65 Goujon age, yr 180 6 H&L

Lock in depth Arthern 60 160 100 150 200 250 100 150 200 250 depth depth With accumulation forcing only 70 220

200 65

age, yr 180 6 Lock in depth 60 160 100 150 200 250 100 150 200 250 depth depth With temperature forcing only 70 210

200 65

age, yr 190 6 Lock in depth 60 180 100 150 200 250 100 150 200 250 depth depth

Figure 6.11: Densiﬁcation model outputs for the lock-in depth (left panels), and ∆age (right panels), for 3 scenarios: both temperature and accumulation forcing (top), only the accumulation forcing (middle), and only the temperature forcing (bottom). The grey line shows the lock-in depth derived from the data. 202

tive zone of Zc=5 m to obtain the LID at each data point. The LID is interpolated in between data points, and prescribed at each model time step. Figure 6.12 shows the result of a second set of experiments with a prescribed LID, for a) both temperature and accumulation forcing, b) accumulation forcing only, c) temperature forcing only.

With temperature and accumulation forcing

3 220 A B 0.81

0.8 200 Goujon age, yr

6 H&L 0.79 Arthern LI density, kg/m 180 100 150 200 250 100 150 200 250 depth depth With accumulation forcing only

3 220 C D 0.81

0.8 200 age, yr 6 0.79

LI density, kg/m 180 100 150 200 250 100 150 200 250 depth depth With temperature forcing only

3 220 E F 0.81

0.8 200 age, yr 6 0.79

LI density, kg/m 180 100 150 200 250 100 150 200 250 depth depth

Figure 6.12: Densiﬁcation model outputs, when the LID is set by δg measurements. The left panels show the bulk density at the LID, and the right panels show ∆age, for 3 scenarios: both temperature and accumulation forcing (top), only the accumulation forcing (middle), and only the temperature forcing (bottom).

The left panels of Figure 6.12 show the lock-in density. It can vary between 0.79 and 0.81 kg/m3. This is a reasonable range, and it highlights that the bulk density may not be the appropriate parameter to deﬁne the LID. Despite their disagreements 203 regarding the lock-in density, all models produce very similar ∆age for each experiment. It shows that knowing the LID is a strong constraint on ∆age, and that the variability in ∆age is mainly due to accumulation changes, which are very well constrained by ice core data. ∆age varies by less than 5 years between the three scenarios. We adopt the output of the G03 model with both temperature and accumulation forcing and a prescribed LID as the estimate of ∆age for the temperature inversion.

6.3.3 Gas age calculations

For the reconstructions performed here, we use the output of the G03 model with both temperature and accumulation forcing, and a prescribed LID, to estimate the ice age at the LID. The gas age at the lock-in depth is determined using the ﬁrn gas diffusion model (see Chapter5). We ran a pulse of 1 arbitrary unit for 1 year, and look at the evolution of the concentration with time at selected depths (Figure 6.13). We ﬁnd a mean age of 15.5 years at 66.5 m. The distribution is not gaussian, and the width of the age distribution is best described by the spectral width ∆ [Battle et al., 2011]:

1 Z ∞ ∆2(z) = (t − m(z))2 P (z, t)dt (6.19) 2 0 where P (z, t) is the age distribution at depth z, t is the time, z the depth and m(z) the mean of the distribution. The spectral width at the LID is ∆ = 4.5 years. The scatter in the data between samples from neighboring depths is related to changes in the LID. We can therefore use the scatter in the isotope data to give an upper bound of the error in the lock in depth, which is directly proportional to an error in ∆age. The root mean square error in the estimation of δg by equation 6.3 is 4.8 per meg, which corresponds to 0.86 m, or 4 years. For the least squares estimate of δg, it is even smaller. The maximum sample to sample difference is about 10 per meg, which corresponds to 2 m or 9.4 years. The maximum difference between the densiﬁcation model scenarios is also under 10 years. As a result, we consider that our error in the estimation of the gas age is under 10 years. 204

67.71 m 63 m 0.01 69.34 m 64 m 71.03 m 65 m 72.81 m 0.005 66 m 74.77 m 67 m 76.89 m Age distribution 0 0 20 40 60 80 100 Time, years

60 Mean age 40 8

20 6

Mean age, years 0 4 Spectral width 2 64 66 68 70 72 74 76 spectral width, years Depth, m

Figure 6.13: Top: Age distribution of gases in the WAIS-Divide ﬁrn, at selected depth horizon. Bottom: mean age and spectral width as a function of depth, in the lock-in zone. 205

6.4 Temperature reconstruction

6.4.1 Analysis of the temperature difference ∆T

The temperature difference between the top and bottom of the ﬁrn, ∆T , is negative for most of the past millennium, which is evidence for a long-term cooling trend (Figure 6.14). The cooling trend is interrupted between 1325 and 1405 A.D., when there is a strong warming of 0.7◦C which begins and end abruptly. This feature is supported by 8 data points, and is coincident with a relative increase in accumulation (Figure 6.14). The long-term cooling trend comes to an end in 1850, after which ∆T remains positive, except for a brief interruption around 1940, supported by 2 data points. The recent temperature increase is not accompanied by an increase in accumulation.

1000 1200 1400 1600 1800 Wolf Spörer Maunder Dalton

0.26 /yr ice 0.24 rate, m 1 0.22 accumulation

0 T, °C 6 ï1

1000 1200 1400 1600 1800 Time, year A.D.

Figure 6.14: Top: accumulation rate at WAIS-Divide, in meters of ice per year, 50-year average. Bottom: Firn temperature gradient, ∆T , in ◦C. Individual samples are shown in grey (+) signs, and the interpolation in blue. The solar minima are highlighted on the very top. the horizontal lines show the mean of each record.

6.4.2 Dual inversion of ∆T firn and borehole temperature

The ∆T signal can be integrated to produce a surface temperature history. We use the temperature diffusion model and the inverse method detailed in Chapter2. We run the inversion both for ∆T and for the borehole temperature proﬁle simultaneously. 206

The two types of information are complementary: the borehole temperature profile fixes the absolute value of temperature and the long-term trend, while ∆T resolves decadal scale changes. In addition, we add a parameter allowing for an offset in the ∆T time series: a small bias in ∆T can cause a spurious trend that would make it incompatible with the borehole temperature profile. The inverse problem is formulated following:

d − y0 = Hx + r (6.20)

where d is the data vector, y0 the forward model output for our initial assumption, H the linearized and discretized version of the forward model, x the discretized temperature history, and r the residual. Generally speaking, we use bold lower case letters for vector, and bold upper case letters for matrices. We ran the forward model for 2000 years, and discretized the functional space of surface temperature history with Fourier series, with periods ranging from 4000 years to 5 years. Our initial assumption for the temperature history, T0, is the result of the borehole temperature inversion found in Chapter3.

The matrix H = [H1 h2] contains the Fourier components H1, and one additional vector h2 representing a potential offset of the ∆T data. The inversion of Equation 6.20 is given by (see Chapter2 for details):

n n−1 X T T −1 X xj = PHn (HnPHn + R) (d − yn−1 + Hn xj) (6.21) j=1 j=1

where j refers to each iteration, n refers to the current iteration, Hn is the lin- th earized and discretized version of the forward model for the n iteration, yn−1 the model output of the previous iteration, around which the model is linearized, P is the inverse of the penalty weighting for model structure, which provides regularization, and R is the inverse of the penalty weighting for model-data misﬁt (residuals) r. P allows us to control the smoothness of the temperature history. We assumed the Fourier components to be uncorrelated and used a prior variance proportional to the 207

square of their period τi: 2 2 τi P (i, i) = σx P 2 (6.22) i τi ◦ 2 We chose σx = 2 C. R is a diagonal matrix whose elements are σd. For the borehole ◦ temperature, we used σd1 = 0.02 C, which corresponds to a signal to noise ratio of 100.

For ∆T , we used σd2 = 20σd1, reflecting the fact that, in case of disagreement, we want to fit the borehole temperature profile at the expense of ∆T . The uncertainty of the temperature reconstruction can be estimated by calculating Pˆ, the new estimate of the covariance of the uncertainty in the model parameters:

ˆ T T −1 P = P − PHn (HnPHn + R) HnP (6.23)

The 1-σ error on the reconstruction is given by the square root of the diagonal elements of S = BPBˆ T, where B is the discretization and linearization of the functional space of temperature history. A temperature history T can be written as T = T0 + Bx, with T0 the initial history around which the linearization is done, and x as above (Equa- tion 6.20). The solution and the fit to the data are shown in Figure 6.15. We find that we need to use an offset of -0.35◦C for ∆T , which corresponds to an error of 1.6 per meg per mass unit, on either δ15N or δ40Ar/4, which is within the estimated uncertainty (4.8 per meg for δ15N and 3.6 per meg for δ40Ar/4). There is a slight disagreement between the two data sets around 1900 A.D., where the increase in ∆T is smaller than what is dictated by the borehole temperature profile. In this instance, we favor the match to the borehole temperature profile, and we are able to find a solution which satisfies both data sets within their respective uncertainties. It is possible that this discrepancy arises from the fact that we have neglected gas diffusion when analyzing the temperature signal. When the change is abrupt, gas diffusion will decrease the magnitude of the temperature fractionation signal recorded in δ15N and δ40Ar, and ∆T derived from inert gas isotopes will appear lower than the true ∆T in the ice. 208

1000 1200 1400 1600 1800 2000 ï27 Borehole reconstruction ï28 Full reconstruction

ï29

Surface ï30

temperature, °C ï31

ï322

0 T, °C 6 ï1

ï2 1000 1200 1400 1600 1800 2000 Time, year A.D. ï29.95 ï29.6 ï30 ï29.8 ï30.05

Temperature, °C ï30 ï30.1 300 250 200 150 100 50 40 30 20 Depth, m

Figure 6.15: Top: Surface temperature reconstruction, from the borehole temperature data (dark blue), and from the dual inversion of borehole temperature and ∆T (teal). The dashed line shows the uncertainty estimation in the reconstruction. Middle: ∆T data (+), and forward model output for the temperature history shown above (line). Bottom: Borehole temperature data. The right panel is on a different scale for the top 50 m. The line shows the forward model output corresponding to the full temperature reconstruction. The uncertainty in the data is on the order of 2 mK, and up to 10 mK for the top 20 m, which is smaller than the (+) symbols. 209

6.4.3 Description of the surface temperature record

The snow surface temperature at WAIS-Divide appears to follow a long-term decreasing trend, from the start of this record in 950 A.D. to 1846 A.D., after which it starts warming abruptly (Figures 6.15 and 6.16). This trend is punctuated by several fast increases in temperature, notably between 1315 and 1395 A.D. where the temperature increases by 1.87◦C, or 0.24◦C/decade, and between 1596 and 1626 A.D., where the temperature increased by 0.96◦C, or 0.32◦C/decade. Between 1847 and 1875 A.D., the temperature increased by 2.3◦C, which corresponds to 0.84◦C/decade over a 30 year period. These observations show that the current warming rate of 0.23◦C/decade over the last 50 years is not unprecedented (see Chapters3 and5).

1000 1200 1400 1600 1800 2000 26 Na 24 22 Na, ppb 20 18 b O, WDC05A ï33.2 18 b O, WDC06A ï33.4 ï33.6 ï33.8 ï34 ï34.2 mil per 18O, Temperature b ï29 ï30 Surface 0.26 ï31 /yr

temperature, °C

0.24 ice m Accumulation 0.22 Accumulation

1000 1200 1400 1600 1800 2000 time, year A.D. (WDC06Aï6 timescale)

Figure 6.16: Comparison of the WAIS-Divide temperature reconstruction with other climate indicators. Sodium (Na) is a sea ice proxy (data from WDC06A, courtesy of John Edwards, DRI, Reno, NV). δ18O is a classic temperature proxy(data from two cores, WDC05A and WDC06A, courtesy of Eric Steig, UW, Seattle, WA and James White, INSTAAR, Boulder, CO). The surface temperature is from this work. The accumulation rate is calculated from the layer counting timescale (TJ Fudge et al., in review). 210

The first two rapid warming events of 1315-1395 A.D. and 1596-1626 A.D. were accompanied by a increase in accumulation (Figure 6.16). However, this is not the case for the more recent event of 1847-1875 A.D.. The leading mode of interannual climate variability in West Antarctica at present is due to the oscillation of the Amundsen Sea Low pressure system (hereafter ASL) between the Ross Sea and the Bellingshausen Sea [Nicolas and Bromwich, 2011]. When the ASL is located predominantly towards the Ross Sea, air masses can flow directly from the Amundsen Sea towards the center of WAIS, bringing both warm air and heavy precipitation. When the ASL is located towards the Bellingshausen Sea, the center of West Antarctica is sheltered from storms, and precipitation diminishes. The close association of warming with increased precipitation suggests that the cause of these warming events is related to the movement of the ASL towards the Ross Sea. The position of the ASL is influenced by the propagation of planetary Rossby waves from the central Tropical Pacific [Ding et al., 2011], and these events may be connected to anomalous heating in the central tropical Pacific, and associated changes in the Walker circulation. The warming of the last 200 years is not associated with an increase in accumulation, which suggests that it may be caused by radiative forcing rather than dynamical connections to the tropics (Figure 6.16). Water isotopes (δ18O) share the same long-term trend with the temperature record, but events on a 100-year timescales are distinct (Figure 6.16). Water isotopes in West Antarctica are also very sensitive to the sea ice extent: when there is less sea ice, the contribution of heavy local moisture increases, and δ18O increase [Kuttel¨ et al., 2012]. The amount of sodium reaching the site is linked to the sea ice because frost flowers formed on the winter sea ice are an important source of sodium aerosols in Antarctica. A greater sea ice extent, longer seasonal duration of sea ice, or increased winds can increase the sodium concentration in the ice core. Some of the variations in δ18O are correlated with variations in sodium, but not all, and over the whole record, the correlation is not significant, showing that the relationship between δ18O and climate variables is complex. 211

6.5 Discussion

6.5.1 Comparison with Northern Hemisphere records

1000 1200 1400 1600 1800 2000

2 1365.5 0 1365 TSI 1364.5 20 2 TSI, W/m 0 ï0.2 ï0.4 40

T, °C ï0.6 Flux, kg/km

ï28 NH temperature anomaly 4 60 ï29 WAIS ï30 80 ï31 Volcanic SO

Temperature, °C ï32 GISPï2 100 1000 1200 1400 1600 1800 2000 Time in year A.D.

Figure 6.17: Comparison of the Surface temperature reconstruction with Northern Hemisphere records. The top plot shows the Total Solar irradiance [Delaygue and Bard, 2010]. The grey shading in the background highlightss solar minima. The brown lines show bipolar volcanic events, with the sulfate ﬂux for each (Sigl et al., in review). The second line shows the Northern Hemisphere surface temperature anomaly, 30-year average, from Moberg et al.[2005]. The blue line shows the temperature reconstruction from this work, and the last line the temperature reconstruction at GISP2 in Greenland following the same methodology [Kobashi et al., 2008a].

The climate of the Northern Hemisphere exhibits a warm period around 950- 1250, followed by a long-term cooling trend until the 1800s, and a warming towards the present (Moberg et al.[2005], and Figure 6.17). The succession of the “Medieval Warm Period” with the “Little Ice Age” (hereafter LIA) is correlated with solar forcing [Mann et al., 2009a]. In particular, the LIA is concurrent with deep solar minima, and persistent explosive volcanism (Figure 6.17). The clearest evidence for a cold period around 1400-1800 A.D. comes from the North Atlantic region of the world, and there 212 is still some debate about whether the Southern Hemisphere experienced cooling, and whether the magnitude of the cooling was similar [e.g. Duncan et al., 2010]. If the LIA was a response to solar forcing, we would expect hemispheric synchroneity, although the feedback amplifying the forcing may not operate in the same way in each hemishphere. We compare the temperature of the last 1000 years between GISP2 in central Greenland (72◦N, 38◦W, 3200 m.a.s.l.) and WAIS-Divide, in West Antarctica (Figure 6.17). Both WAIS-D and GISP2 have similar mean annual temperature and similar accumulation at present, which allows for a meaningful inter-hemispheric comparison. WAIS-D and GISP2 both experienced a long-term cooling trend from 1000 to 1750 A.D. GISP2 started warming first, and the warming was gradual, whereas WAIS-D warmed abruptly, in the 1850s. The amplitude of the LIA minimum at GISP2 is −1.36◦C compared to the last 1000 year average, while it is −1.01◦C for WAIS-Divide, or 36% larger in Greenland than in West Antarctica. It has been suggested that persistent volcanic events combined with the ice-albedo feedback may produce a cooling signal that per- sists beyond the initial volcanic aerosol shortwave radiative forcing [Miller et al., 2012]. The ice albedo feedback may operate very differently in Antarctica than in Greenland: the Antarctic land is already mostly ice covered, and the sea ice extent is largely controlled by atmospheric and oceanic circulation. As a result, this feedback may be less efficient in the Southern Hemisphere, which would explain the smaller amplitude of the temperature response in Antarctica compared to Greenland. The timing is also not exactly the same: central Greenland leads Antarctica in the recovery from the LIA, but this discrepancy may be an expression of natural variability at the regional scale, due to the well known effect of the North Atlantic Oscillation in GISP2 temperature [Kobashi et al., 2011]. The persistence of the LIA into the 1850s at WAIS-Divide is consistent with the maximum extent of glacial moraines in New Zealand [Schaefer et al., 2009]. The multi- decadal fluctuations between both records are uncorrelated, which shows that global signals are superimposed onto large regional variability. This natural variability obscures the common signal, and complicates the establishment of clear causal mechanisms. However, the general presence of a millennial cooling trend in both polar regions indicates that there may be a sensitivity to small changes in radiative forcing. It pro- 213 vides us with an opportunity to estimate the climate sensitivity, if we would have temperature records from all the representative places on the planet. This work is the first step towards quantitative temperature estimations in Antarctica, at decadal to millennial timescales.

6.5.2 Solar Forcing

The Sun is the source of energy for the climate system. The Total Solar Irradi- ance (TSI) is on average 1366 W/m2 over the observed period of the last few decades, and the solar power available to the Earth System, is on average 239 W/m2, using an albedo of 0.3 [Gray et al., 2010]. The variability in the Sun’s energy manifests itself by changing numbers of sunspots, which are related to convection cells on the Sun’s surface: the more sunspots, the more active the Sun is. It is also expressed in the amount of galactic cosmic rays reaching the Earth. Sunspots numbers have been monitored since Galileo’s time in the 1600s, and these observations have shown the presence of an 11 year solar cycle. The broadband amplitude of the 11 year solar cycle is about 0.17 W/m2, so 0.07% of the total [Gray et al., 2010]. One caveat of the sunspot record is that it is impossible to quantify how low the TSI goes during minima, and there is evidence that the sunspot number is a function of an unknown background state [Gray et al., 2010]. TSI can also be reconstructed, albeit with less certainty, using the cosmogenic isotope reconstruction from tree rings and ice cores: 10Be, 36Cl and 14C are produced in the atmosphere by galactic cosmic rays, and during solar maxima, the magnetic field of the solar wind deflects the flux of cosmic rays, leading to a reduction of cosmogenic nuclide production [Bard et al., 2000].The cosmogenic isotopes provide a measure of the solar magnetic field, but the relationship between it and TSI is not obvious [Steinhilber et al., 2009; Delaygue and Bard, 2010]. As a result, there is still some debate about the absolute amplitude of the variations in TSI at the centennial and longer timescales, although it is essential for the determination of the climate sensitivity. The study of climatic variations correlated with the 11-year solar cycle (here after SC) established key feedback mechanisms that could amplify the very weak forcing (0.17 W/m2 [Gray et al., 2010]). The first feedback involves solar absorption at the surface. It is especially preva- 214 lent in the Pacific Ocean, where surface warming in the Tropical Pacific enhances evaporation from the ocean, and strengthens the Walker cell, which maintains the subsidence region cloud free, and allows for solar radiation to reach a larger surface area [Meehl et al., 2008]. The increased evaporation also increases the trade winds, which cause more upwelling, and a cooling of the Tropical East Pacific, similarly to La Nina.˜ In addition, this mechanism allows for a broadening of the Hadley cell, and a poleward movement of the subtropical jet and the Ferrel cell. The stronger Walker cell also triggers planetary Rossby waves in the winter hemisphere, which reduce precipitation in the Northwest United States [van Loon et al., 2007]. The second feedback involves variations of the UV part of the solar spectrum, which varies by 7% in a solar cycle, and its relationship to ozone in the stratosphere. The ozone concentration in the mid-stratosphere increases by about 4% from solar minimum to solar maximum, which causes differential warming in the stratosphere and influences the polar vortex circulation. During a solar maximum, the polar vortex is weaker and warmer on the positive phase of the QBO, but stronger and colder on the negative phase of the QBO [Gray et al., 2010]. Both of these feedbacks can act in concert to contribute to a poleward movement of the subtropical jet [Meehl et al., 2009]. These observations have a bearing on centennial scale solar variability: Indeed, Mann et al.[2009a] compared the (warm) period 950-1250 to the (cold) period 1400- 1700, and found a similar La Nina˜ like cooling in the Tropical Pacific. The climate of West Antarctica is very sensitive to planetary wave propagation from deep convection in the central Tropical Pacific [Ding et al., 2011]. As a result, we might expect that during a solar maximum, the same phenomenon described by van Loon et al.[2007] as an increase in sea level pressure in the Northwest Pacific would also cause an increase in sea level pressure in the Southwest Pacific during its winter, which would bias the Amundsen Sea Low towards the Ross Sea, and cause warming and heavy precipitation in West Antarctica. Conversely, low solar activity would result in cooling and lower precipitation in West Antarctica. The temperature reconstruction at WAIS-Divide is consistent with this mechanism (Figure 6.16), especially between 1630 and 1850 A.D., which include the Maunder (1645-1715 A.D.) and Dalton (1790-1830 A.D.) sunspot minima, where there was a strong cooling associated with low accumulation. 215

6.6 Conclusion

We reconstructed the temperature at WAIS-Divide for the last 1000 years using a novel combination of gas and borehole observations. We found a long-term cooling trend from 950 A.D. to 1850 A.D. which ended abruptly, with a strong warming of 2.3◦C over a 30 year period, from 1847 to 1875A.D.. There were two other strong warming events, between 1315 and 1395 A.D. and between 1596 and 1626 A.D., with a warming rate of 0.24◦C/decade and 0.32◦C/decade respectively. This record shows that the current rate of warming at WAIS-Divide, of 0.23◦C/decade for the last 50 years is not unprecedented. The long-term cooling trend is similar to that at GISP2 in Central Greenland, with a 25% lower amplitude. This trend is correlated with a decrease in solar radiation and increase in explosive volcanism. The period 1630-1850 A.D. was characterized by a cooling trend accompanied by lower accumulation. This observation is consistent with the mechanism of amplification of the solar forcing, which involves the Walker circulation in the Tropical Pacific, and teleconnections to high latitudes in the Pacific via Rossby wave trains [Meehl et al., 2008; van Loon et al., 2007]. There is, however, a large amount of regional natural variability which obscures the global trend, and it is necessary to have climate records in all parts of the world to reconstruct the global temperature field. This is the first absolute temperature record of West Antarctica. Many more are needed before we can quantitatively separate regional and global trends. The accurate estimation of the sensitivity of the climate to radiative forcing depends on this type of effort, and it is a key parameter in our ability to predict the amplitude of future climate changes.

Acknowledgement This chapter is being prepared for publication in a yet to be determined journal, as: Orsi, A. J., and J. P. Severinghaus, Temperature reconstruction for the last thousand years at the West Antarctic Ice Sheet Divide using inert gas isotopes. The dissertation author was the primary investigator and author of this work. Chapter 7

On bubble-free layers in the WAIS-Divide ice core

Abstract

Melt layers in ice cores can compromise the integrity of the gas record of past atmospheres, by dissolving soluble gases, leading to anomalously high concentrations in extracted air, or by altering gas transport in the ﬁrn, which affects the gas chronology. There is a very large number of easily visible 1 mm thick bubble-free layers in the WAIS- Divide ice core, on average four per year. We show that these layers are not melt layers, and do not cause artifacts or discontinuities in the gas chronology. Instead, these layers are likely to be formed by condensation of water vapor on wind crusts at the surface, during episodes of sub-surface temperature inversions, which opens the possibility that they might be used to evaluate the strength of temperature inversions at the site.

7.1 Introduction

Ice cores are a unique archive of ancient air. The air contained in ice cores has been filtered through the firn layer on top of the ice sheet. The term firn refers to re- crystalized old snow. It is a porous medium where air moves essentially by molecular diffusion [Schwander et al., 1988]. If there is an impermeable layer in the firn, perhaps

216 217 caused by refrozen snowmelt, it is likely to impede gas transport, and create a discontinuity in the gas chronology [Trudinger et al., 1997]. The presence of melt water can also affect the gas composition: soluble gases like carbon dioxide, methane, nitrous ox- ide, krypton and xenon can dissolve in the liquid water before it freezes, and induce very high concentrations of these elements in the ice core [Ahn et al., 2008; NEEM community members, 2013]. The WAIS Divide ice core is expected to provide the most precise gas record for the last 60,000 years. Indeed, the WAIS-Divide site is located in Antarctica (79◦S, 112◦W), where dust ﬂuxes are minimal, and in-situ production of greenhouse gases is much smaller than in Greenland. It is also in a high accumulation region, which allows for a small gas-age-ice-age difference (∼500 years at the last glacial maximum), and a small uncertainty in the gas chronology, including during Termination 1, unlike existing East Antarctic deep ice cores like Dome C or Vostok. Upon physical inspection of the core, we noticed a very large number of bubble- free layers, about 1 mm in thickness, at the rate of about 15 per m, or four per year. It is important for the accuracy of the gas record to know whether these layers were caused by melt, in which case they would compromise the soluble gas record, and whether they affected gas diffusion through the ﬁrn, in which case they would complicate the gas chronology.

7.2 Analysis of bubble-free layers

7.2.1 Description

Bubble-free layers are clear layers, about 1-2 mm in thickness, without any bubbles, which lets the light shine through easily (Figure 7.1). Their position is recorded manually during the visual stratigraphy inspection of the core at the National Ice Core Laboratory. They can only be detected in the ﬁrst 600 m of the core: the bubbles disappear in the deeper part of the core, due to the formation of air hydrates under high hydrostatic pressure, making the ice perfectly clear, and the bubble-free layers indistin- guishible from the rest of the ice. These bubble-free layers are present very regularly throughout the core, at a rate 218

Figure 7.1: A pair of bubble-free layers in the WDC05A core. The layers are 1 mm thick. Black in this image represents clear ice, and bubbles appear white. Photo courtesy of John Fegyveresi. of 4.3±2 layers per year. They are visible in all seasons, with a higher occurrence in the late summer (Figure 7.2).

7.2.2 Are bubble-free layers caused by ice melt?

Melt layers in ice cores typically appear bubble-free [e.g. Das and Alley, 2008]. They are a few mm to 1 cm thick, clear layers, with bubbly ice above and below (Figure 7.3). During a melt event, liquid water percolates through the snow until it ﬁnds a hard crust, on which it spreads laterally and refreezes [Das and Alley, 2005]. There were 62 melt events recorded in the ﬁrst 614 m of the Siple Dome ice core, also in West Antarctica, which corresponds to once every 200 years [Das and Alley, 2008]. Siple Dome is at a much lower elevation (621 m) than WAIS Divide, and is also warmer (-24.9◦C). However, it is possible to have melt events at WAIS Divide. Krypton and xenon are very soluble gases. When melt water is present, they dissolve from the air into the liquid water. As a result, melt-layers have a very high Kr/Ar and Xe/Ar ratio [Headly, 2008]. Melt layer samples from Dye 3 in Greenland range from 23 to 63 for δKr/Ar, and 46 to 170 for δXe/Ar. Non-melted ice from Dye 3, in contrast, hadh δKr/Ar values of 11.00±0.49h , and δXe/Ar of 22.58±1.16 , where the uncertainty is the pooled standard deviationh of replicate samples [Headlyh, 2008] (Figure 7.4). These values are consistent with gravitational fractionation inferred from δ40Ar from the same samples. 219

4 layer per year 2

number of bubble free 0 500 1000 1500 2000 time in years A.D. 40

20 % per year

0 amount of BF layers 0 Summer 0.25 Fall 0.5 Winter 0.75 Spring 1 position relative to an annual layer

Figure 7.2: Top: Number of bubble-free layers per year, 20 year average, as a function of time. The tapering down towards the present may be an artifact: these layers are harder to detect in snow than in ice. Bottom: Seasonality of the bubble-free layers. They are present in all seasons, but occur more often in summer and fall. 220

Figure 7.3: Melt layers from the NEEM ice core, in North Greenland, at 44.3 m. This melt event is dated tot 1888 A.D.. Photo courtesy of Kaitlin Keegan.

200 Dye 3 melt Dye 3 control 150 WAIS control WAIS bubble free

100

gravitational fractionation Xe/Ar, per mil b 50

0 0 10 20 30 40 50 60 70 bKr/Ar, per mil

Figure 7.4: Melt layer identiﬁcation. When δKr/Ar (x-axis) and δXe/Ar are high, they indicate the presence of melt, as can be seen in Dye-3 melt layer samples (solid dia- monds) [Headly, 2008]. WAIS Divide bubble-free layers (crosses) do not have anomalously high δKr/Ar and δXe/Ar, which shows that they are not melt layers. The box shows the range of values found in the WDC05A ice core. 221

We tested for the presence of melt water in bubble-free layers by cutting three to ﬁve bubble-free layers per sample with a band saw, each slab being ∼5 mm thick, and measured δKr/Ar and δXe/Ar, using the getter method outlined in Chapter4. We measured two bubble-free samples and three control pieces, consisting of the same number of slabs of bubbly ice, from neighboring ice (Table 7.1). The ice was from the WDC05A ice core, between 114 and 147 m deep.

Table 7.1: Analysis of bubble-free layers in the WDC05A ice core. The bottom 2 lines show the mean and standard deviation of all WDC05A samples. type δ40Ar δ86Kr δKr/Ar δXe/Ar δNe/Ar δXe/Kr bubble-free 1.26 1.156 21.90 37.16 -72.32 14.94 layers 1.204 0.880 15.50 28.8 -50.59 13.14 1.218 1.131 17.22 31.92 -36.37 14.45 Control 1.199 1.078 17.32 30.89 -94.79 13.34 1.203 1.126 16.25 30.50 -71.02 14.02 mean all WDC05A 1.220 1.182 16.64 31.10 -303.25 14.22 σ all WDC05A 0.024 0.033 0.91 1.35 139.28 0.64

The ﬁrst bubble-free sample is slightly elevated in Kr and Xe: when compared to the standard deviation of all ice core measurements taken together, σ, δKr/Ar is 5.4 σ from the control samples, and δXe/Ar is 4.5 σ higher than control samples (Table 7.1). However, we have used very thin samples, which can be subject to the loss of argon through cut bubbles and permeation [Severinghaus and Battle, 2006]. Indeed, δ40Ar is elevated by 54 per meg in the ﬁrst sample (Table 7.1), and this is not expected of melt, but is characteristic of gas loss [Severinghaus et al., 2003]. We can compute δ Xe/Kr, which is independent of Ar:

δXe/Ar ! 1000 + 1 δXe/Kr = δKr/Ar − 1 × 1000 (7.1) 1000 + 1 We ﬁnd that for Dye 3 melt layers, δXe/Kr is between 22 and 99 , and control samples are between 7 and 19 . Our two bubble-free samples have δXe/Krh at 14.94 and 13.14 which is within theh range of WDC05A samples (between 11.36 and 15.7 ), and lowerh than what is found in melt layers (Table 7.1). h We thus conclude that the 1 mm bubble-free layers in the WAIS-Divide ice core are unlikely to be caused by melt. 222

7.2.3 Do bubble-free layers impede gas ﬂow?

When they are in the firn, bubble-free layers are likely to have lower porosity than the surrounding firn. We were actually unable to find ice lenses in 2 m snow pits dug in 2008, 2009 or 2010, but we found evidence for numerous hard “crusts”. However, these layers definitely had some granularity (Figure 7.5 C). There is evidence from porosity measurement in firn cores that even melt layers have some open porosity, and that gases can diffuse through [Keegan and Albert, 2012]. What is more, these crusts typically have a limited spatial extent, on the order of 3 m by 10 m, and they can be broken by what looks like thermal cracks, through which gases can flow (Figure 7.5 B). Although there are numerous crusts in the WAIS-Divide firn, there is no evidence of any discontinuity or impedance in gas diffusion (see Chapter6 and Battle et al.

[2011]). This observation is conﬁrmed by the studies of CO2 in the WAIS-Divide ice core which show no sensitivity to the presence of a bubble-free layer in a sample [Ahn et al., 2009]. We conclude from these observations that the presence of bubble-free layers does not compromise the integrity of the gas record.

7.3 Discussion

We have shown that the bubble-free layers are not caused by melt. We suggest that they are connected to the hard crusts seen from time to time on the surface at WAIS-Divide. These crusts are highly reﬂective, and resemble the glazed areas of East Antarctica [Frezzotti et al., 2002, ; Lou Albershardt, pers. comm.]. Gow[1964] suggested that the glazed areas around South Pole are the product of multi-year exposure of the snow surface, which allows the wind to polish them repeatedly. Once these crusts are hard, they are even less likely to retain wind blown snow, which may amplify the wind polishing. Indeed, most of the reported glazed areas are associated with very strong katabatic winds. Additionally, glazed areas in the Megadunes region of East Antarctica were associated with very porous hoar underneath, suggesting that water vapor transport from 223

Hard crust that footsteps do not perforate

B C cracks through hard crusts 4 mm

2 cm

crust

Figure 7.5: Hard surfaces (”crusts”) seen at WAIS-Divide. These crusts are hard enough that the weight of a person does not puncture through. They can be laced by cracks, reminiscent of thermal cracks (B). The thickness of these crusts can be up to 5 mm thick (C). They are common, but their horizontal extent is limited. 224 the lower layer to the bottom of the glazed area had contributed to its hardening [Albert et al., 2004; Frezzotti et al., 2002; Fujii and Kusunoki, 1982]. There is little water vapor in the cold air at Megadunes, but the long exposure allows for hoar to slowly form below the glazed areas, which eases the vapor transport, causing a positive feedback [Albert et al., 2004]. The trapping of heat from solar shortwave radiation beneath this semi-transparent glaze also may hasted sumblimation. The accumulation at WAIS-Divide is on the order of 0.22 m/year, which corresponds to close to a meter of snow per year [Banta et al., 2008]. The surface does not get a long multi-year exposure, and the fact that there are several layers per year indicates that the bubble-free layers at WAIS-Divide are not caused by a long and slow process. However, WAIS-Divide receives frequent storms, with strong winds that may be involved in polishing the surface. In addition, WAIS-Divide has a mean annual temperature of -29◦C, and a seasonal cycle amplitude of about 10◦C[Orsi et al., 2012]. There is a lot more water vapor available for transport than at the Megadunes sites (- 50◦C). The vapor transport chieﬂy depends on the near surface temperature gradient. The prevalence of these layers in late summer, when the surface is cooler than the ﬁrn, suggests that subsurface temperature inversions can cause the water vapor in the subsurface layer to condense on the surface crust, creating a tight compaction of grains that leads to bubble-free layers. If this mechanism is correct, it suggests that we may be able to use the frequency and thickness of bubble-free layers as a proxy for the occurence of surface temperature inversions. The logical next step is direct observation of the relationship between both below- and above-surface temperature gradients, and crust formation (John Fegyveresi, in prep.)

7.4 Conclusion

The WAIS-Divide ice core is covered with bubble-free layers of about 1 mm in thickness. There are about 4±2 layers per year with a slight preference for late summer / early fall. These layers are not caused by melt, and do not impede gas ﬂow in the ﬁrn. In this respect, they do not interfere with the gas record. They are likely caused by the 225 succession of strong wind events with calm days when a surface temperature inversion can develop, increasing the metamorphism of surface snow, where water vapor from the sub-surface condenses on a surface crust, making it dense and bubble-free. These layers may be used to learn about surface temperature inversions, once a clear mechanism of formation has been developed.

Acknowledgement This chapter is being prepared for publication in the Journal of Glaciology, as: Orsi, A. J., J. Fegyveresi and J. P. Severinghaus, On bubble-free layers in the WAIS Divide ice core. The dissertation author was the primary investigator and author of this work. Chapter 8

Conclusion and perspectives

We presented the ﬁrst 1000-year temperature reconstruction of West Antarctica. This reconstruction improves our understanding of the global climate. In particular, the inclusion of this previously unrepresented region in global paleoclimate data sets will shed new light on the geographical patterns and mechanisms of climate change during the late Holocene.

8.1 Borehole temperature

We made precise measurements of borehole temperature at the WAIS-Divide site (79◦S, 112◦W), using an inexpensive setup especially designed for this project (Chapter 3). The borehole temperature record establishes the long term temperature trend at the site. It shows that WAIS Divide was colder than the last 1000 year average from 1300 to 1800 A.D. The temperature in the time period 1400-1800 was 0.52±0.28◦C colder than the last 100-year average. It also proves that West Antarctica has been warming signiﬁcantly over the past 50 years, by 0.23±0.08◦C per decade over the period 1957- 2007 A.D. This warming trend has accelerated to 0.8±0.06◦C per decade over the period 1987-2007. This temperature record puts an end to the speculation that Antarctica might not follow the global warming trend. It is especially valuable to have such a record in a place where there are virtually no direct temperature observations. Borehole temperature measurements are relatively cheap and easy to make. This work shows that the drilling community should take every opportunity to make bore-

226 227 hole temperature measurements after drilling a core. These measurements are especially suitable for estimating recent warming trends. Since the original WAIS-Divide measurements, the temperature logger has travelled to NEEM in North Greenland, and to Dome Fuji in East Antarctica. A similar instrument built on the same model was sent to Dron- ing Maud Land, Antarctica in 2012. These new measurements will greatly improve the estimate of the warming rate in polar regions.

8.2 Inert gas isotope measurements

The time resolution of temperature reconstruction from borehole data decreases rapidly with age; as a result, we are unable to compare the recent trend with older events. We complemented the borehole temperature measurements with inert gas isotope measurements, which record the temperature difference between the top and bottom of the ﬁrn and therefore provide an estimate of decadal to centennial temperature changes. We measured isotopes of nitrogen, argon and krypton in the ﬁrn and in the ice at WAIS- Divide (Chapter4). We improved on the technique to measure these isotopes, which allows us to detect events of smaller amplitude. Future improvements might make it feasible to extend this technique to East Antarctica, where the signal is even smaller. The main limitation of this measurement comes from the need for an accurate gravitational correction. We found that it is imper- ative to measure long ice samples, averaging over the small scale heterogeneity in pore closure due to layering. Another improvement might come from the mass spectrometry of nitrogen isotopes at high pressure. Investigations of the linearity of the measurements at high pressure could improve the analytical precision.

8.3 Inverse method

We presented in Chapter2 a new inverse technique to reconstruct temperature from inert gas isotopic measurements, based on generalized least-squares. This method improves upon existing work by making an explicit hypothesis regarding the shape of the solution for an under-determined problem (Chapter3). It allows us to reconstruct 228 the time evolution of abrupt climate change (Chapter2). It also allows us to calculate error bars explicitly and objectively. Finally, with this method we have been able for the first time to invert a series of different data sets together, which has been applied to the determination of the gas diffusivity profile in the firn (Chapter5 and Buizert et al. [2012]), and to the dual inversion of borehole temperature and noble gas data (Chapter 6). This method is versatile, and it can be used on a variety of paleoclimate proxy inversions.

8.4 Surface temperature reconstruction

The dual inversion of inert gas and borehole temperature data shows that WAIS- Divide cooled from 950 to 1850 A.D., and that this cooling trend ended abruptly by a 2.3◦C warming in 30 years. This trend was interrupted by two warming events, between 1315 and 1395 A.D. and between 1596 and 1626 A.D., with a warming rate of 0.24◦C/decade and 0.32◦C/decade. This record shows that the current rate of warming at WAIS-Divide, of 0.23◦C/decade for the last 50 years, is not unprecedented. The long- term cooling trend is similar to that at GISP2 in Central Greenland, with a 25% lower amplitude. This trend is correlated with a decrease in solar radiation and increase in explosive volcanism. The period 1630-1850 A.D. was characterized by a cooling trend accompanied by lower accumulation. This observation is consistent with the mechanism of amplification of the solar forcing which involves the Walker circulation in the Tropical Pacific, and teleconnections to high latitudes in the Pacific via Rossby wave trains [Meehl et al., 2008; van Loon et al., 2007]. This temperature reconstruction is a new Southern Hemisphere temperature record that can be used to benchmark climate models for simulations of the last millennium. It will improve southern hemispheric mean temperature proxy reconstructions. It will allow us to improve our understanding of the variability in the atmospheric circulation in the Pacific Ocean through teleconnections between tropical and high latitudes. 229

8.5 Bubble-free layers

We showed in Chapter7 that the numerous bubble-free layers seen in the WAIS divide ice core are not caused by melt, and provided an alternative hypothesis for their formation, involving the succession of a wind event with a quiet time when a surface temperature inversion can develop. This hypothesis opens up the possibility of using bubble-free layers as a proxy for surface temperature inversions. Surface temperature inversions can be up to 20◦C in amplitude, and 200 m thick in Antarctica [Tomasi et al., 2011], and there is no information on their variability on interannual or longer timescales. The surface temperature reconstruction presented here is located inside the boundary layer, and knowing about changes in the strength of the inversion would be helpful.

8.6 Perspectives

There is a strong need for more well calibrated temperature records in Antarctica for the late Holocene. We presented here a method for reconstructing the surface temperature at decadal scale. This method can be used in several other places in Antarctica, although the analytical precision will limit its applicability in low accumulation sites of East Antarctica. The combination of this temperature record with precise measurements of all water isotopes (δ18O, δD, 17O) will help shed some light on the relationship between temperature and water isotopes [Kuttel¨ et al., 2012]. This endeavor will be helped by generating data from more sites with both an independent temperature record and the full suite of water isotopes. The variability in the climate of West Antarctica is connected to that of the Trop- ical Paciﬁc through planetary Rossby wave propagation, and the detailed analysis of this record will help us understand the variations in position and intensity of deep convection in the Tropical Paciﬁc. References

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