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Reconstructing spatially variable mass balances from past ice extents by inverse modeling

  • VJERAN VIŠNJEVIĆ (a1), FRÉDÉRIC HERMAN (a1) and YURY PODLADCHIKOV (a2)

Abstract

With the conclusion of the Last Glacial Maximum (LGM), about 20 000 years ago, ended the most recent long-lasting cold phase in Earth history. This last glacial advance left a strong observable imprint on the landscape, such as moraines, trimlines and other glacial geomorphic features. These features reflect the extent of former glaciers and ice caps, which in turn provides information on past temperature and precipitation conditions. Here we present an inverse approach to reconstruct the equilibrium line altitudes (E) from observed ice extents. The ice-flow model is developed solving the mass conservation equation using the shallow ice approximation and implemented using Graphical Processing Units (GPUs). We present the theoretical basis of the inversion method, which relies on a Tikhonov regularization, and demonstrate its ability to constrain spatial variations in mass balance with idealized and real glaciers.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Correspondence: Vjeran Višnjević <vjeran.visnjevic@unil.ch>

References

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Anderson, RS, Molnar, P and Kessler, MA (2006) Features of glacial valley profiles simply explained. J. Geophys. Res.: Earth Surf., 111, 459 doi: 10.1029/2005JF000344)
Barrell, DJA (2011) Quaternary glaciers of New Zealand. Dev. Quat. Sci., 15, 10471064, Elsevier
Barrows, TT, Juggins, S, De Deckker, P, Calvo, E and Pelejero, C (2007) Long-term sea surface temperature and climate change in the Australian-New Zealand region. Paleoceanography, 22, 149
Becker, P, Seguinot, J, Jouvet, G and Funk, M (2016) Last Glacial Maximum precipitation pattern in the Alps inferred from glacier modelling. Geogr. Helv., 71(3), 173187
Blanckenburg, von F and Willenbring, JK (2014) Cosmogenic nuclides: dates and rates of Earth-surface change. Elements, 10, 341346
Braithwaite, RJ (1995) Positive degree-day factors for ablation on the Greenland ice sheet studied by energy-balance modelling. J. Glaciol., 41(137), 153160
Brædstrup, CF, Damsgaard, A and Egholm, DL (2014) Ice-sheet modelling accelerated by graphics cards. Comput. Geosci., 72, 210220
Budd, WE, Keage, PL and Blundy, NA (1979) Empirical studies of ice sliding. J. Glaciol., 23(89), 157170
Cohen, D, Gillet-Chaulet, F, Haeberli, W, Machguth, H and Fischer, UH (2017) Numerical reconstructions of the fl w and basal conditions of the rhine glacier, european central alps, at the last glacial maximum. Cryosphere Discuss., 2017, 142
Cuffey, KM and Paterson, WSB (2010) The physics of glaciers. Academic Press, Amsterdam
Denton, GH, Anderson, RF and Toggweiler, JR (2010) The Last Glacial Termination. Science, 328(5986), 16521656
Eaves, SR, Mackintosh, AN and Anderson, BM (2016) The Last Glacial Maximum in the central North Island, New Zealand: palaeoclimate inferences from glacier modelling. Clim. Past, 12, 943960
Egholm, DL, Knudsen, MF, Clark, CD and Lesemann, JE (2011) Modeling the flow of glaciers in steep terrains: The integrated second-order shallow ice approximation (iSOSIA). J. Geophys. Res.: Earth Surf., 116, F2
Fletcher, R (2013) Practical methods of optimization. John Wiley & Sons, Chichester.
Golledge, NR and 10 others (2012) Last Glacial Maximum climate in New Zealand inferred from a modelled Southern Alps icefield. Quat. Sci. Rev., 46, 3045
Gosse, JC and Phillips, FM (2001) Terrestrial in situ cosmogenic nuclides: theory and application. Quat. Sci. Rev., 20(14), 14751560
Hajdas, I (2009) Applications of radiocarbon dating method. Radiocarbon, 51(1), 7990
Hansen, PC (1998) REGULARIZATION TOOLS: a Matlab package for analysis and solution of discrete ill-posed problems. Numer. Algorithms., 6, 135
Henderson, RD and Thompson, SM (1999) Extreme rainfalls in the Southern Alps of New Zealand. J. Hydrol. (New Zealand), 38(2), 309–33
Herbert, TD and 5 others (2016) Late Miocene global cooling and the rise of modern ecosystems. Nat. Geosci., 9, 843847
Hindmarsh, RC and Payne, AJ (1996) Time-step limits for stable solutions of the ice-sheet equation. Ann. Glaciol., 23, 7485
Hutter, K (1983) Theoretical glaciology. Kluwer, Dordrecht, Holland
Jarosch, AH, Schoof, CG and Anslow, FS (2013) Restoring mass conservation to shallow ice-flow models over complex terrain. Cryosphere, 7(1), 229240
Jarvis, A, Reuter, HI, Nelson, A and Guevara, E (2008) Hole-filled SRTM for the globe Version 4. available from the CGIAR-CSI SRTM 90 m Database (http://srtm.csi.cgiar.org)
Jouvet, G, Picasso, M, Rappaz, J and Blatter, H (2008) A new algorithm to simulate the dynamics of a glacier: theory and applications. J. Glaciol., 54(188), 801811
Jouvet, G, Rappaz, J, Bueler, E and Blatter, H (2011) Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy- minimization approach. J. Glaciol., 57(202), 345354
Jouvet, G and Bueler, E (2012) Steady, shallow ice sheets as obstacle problems: well-posedness and finite element approximation. SIAM. J. Appl. Math., 72(4), 12921314
Kessler, MA, Anderson, RS and Stock, GM (2006) Modeling topographic and climatic control of east-west asymmetry in Sierra Nevada glacier length during the Last Glacial Maximum. J. Geophys. Res.: Earth Surf., 111, 532
Kirchner, N and 8 others (2016) Shallow ice approximation, second order shallow ice approximation, and full Stokes models: a discussion of their roles in palaeo-ice sheet modelling and development. Quat. Sci. Rev., 147, 136147
Laabs, BJ and Carson, EC (2005) Glacial geology of the southern Uinta Mountains. Uinta Mountain Geology, 33, 235253
Lisiecki, LE and Raymo, ME (2005) A Pliocene-Pleistocene stack of 57 globally distributed benthic δ18O records. Paleoceanography, 20(1), PA1003. https://doi.org/10.1029/2004PA001071
Luetscher, M and 8 others (2015) North atlantic storm track changes during the last glacial maximum recorded by alpine speleothems. Nat. Commun., 6, 6344
Mahaffy, MW (1976) A three-dimensional numerical model of ice sheets: tests on the Barnes Ice Cap, Northwest Territories. J. Geophys. Res., 81(6), 10591066
Mayo, LR (1984) Glacier mass balance and runoff research in the USA. Geografiska Annaler: Series A, Physical Geography, 66(3), 215227
McGlone, MS, Turney, C and Wilmshurst, JM (2010) Divergent trends in land and ocean temperature in the Southern Ocean over the past 18000 years. Nature, 3(9), 622626
Meier, MF (1962) Proposed definitions for glacier mass budget terms. J. Glaciol., 4(33), 252263
Mey, J and 7 others (2016) Glacial isostatic uplift of the European Alps. Nat. Commun., 7, 19, https://doi.org/10.1038/ncomms13382
Micikevicius, P (2009) 3D finite difference computation on GPUs using CUDA. Proceedings of 2nd workshop on general purpose processing on graphics processing units
Newnham, RM, Lowe, DJ and Green, JD (1989) Palynology, vegetation and climate of the Waikato lowlands, North Island, New Zealand, since c. 18000 years ago. Journal of the Royal Society of New Zealand, 19, 127150
NVIDIA, (2017) CUDA C Programming Guide Nvidia Corporation, 8.0 edition
Oerlemans, J (1992) Climate sensitivity of glaciers in southern Norway: application of an energy-balance model to Nigardsbreen, Hellstugubreen and Alfotbreen. J. Glaciol., 38(129), 223232
Oerlemans, J (1997) Climate sensitivity of Franz Josef Glacier, New Zealand, as revealed by numerical modeling. Arct. Alp. Res., 29, 233239
Oerlemans, J (2001) Glaciers and climate change. CRC Press, Lisse
Oerlemans, J (2008) Minimal Glacier Models, Igitur, Utrecht University, 192
Pattyn, F (2003) A new three-dimensional higher-order thermomechanical ice sheet model: basic sensitivity, ice stream development, and ice flow across subglacial lakes. Journal of Geophysical Research: Solid Earth, 108(B8), 115
Pellicciotti, F and 5 others (2005) An enhanced temperature-index glacier melt model including the shortwave radiation balance: development and testing for Haut Glacier d'Arolla, Switzerland. J. Glaciol., 51(175), 573587
Penck, A (1905) Glacial features in the surface of the Alps. J. Geol., 13(1), 119
Peyron, O and 7 others (1998) Climatic reconstruction in Europe for 18,000 yr bp from pollen data. Quat. Res., 49(2), 183196
Plummer, MA and Phillips, FM (2003) A 2-D numerical model of snow/ice energy balance and ice flow for paleoclimatic interpretation of glacial geomorphic features. Quat. Sci. Rev., 22(14), 13891406
Poplavskii, KN, Podladchikov, YY and Stephenson, RA (2001) Two-dimensional inverse modeling of sedimentary basin subsidence. Journal of Geophysical Research: Solid Earth, 106(B4), 66576671
Press, WH (2007) Numerical recipes 3rd edition: the art of scientific computing. Cambridge university press, New York
Rhodes, EJ (2011) Optically stimulated luminescence dating of sediments over the past 200000 years. Annu. Rev. Earth. Planet. Sci., 39, 461488
Rojas, M and 8 others (2009) The Southern Westerlies during the last glacial maximum in PMIP2 simulations. Clim. Dyn., 32(4), 525548
Rowan, AV, Brocklehurst, SH, Schultz, DM, Plummer, MA, Anderson, LS and Glasser, NF (2014) Late quaternary glacier sensitivity to temperature and precipitation distribution in the Southern Alps of New Zealand. J. Geophys. Res.: Earth Surf., 119(5), 10641081
Seltzer, AM, Stute, M, Morgenstern, U, Stewart, MK and Schaefer, JM (2015) Mean annual temperature in New Zealand during the last glacial maximum derived from dissolved noble gases in groundwater. J. Geophys. Res.: Earth Surf., 431, 206216
Seguinot, J and 5 others (2018) Modelling last glacial cycle ice dynamics in the alps. Cryosphere Discuss., 2018, 130
Suggate, RP (1990) Late pliocene and quaternary glaciations of New Zealand. Quat. Sci. Rev., 9, 175197
Tikhonov, AN (1963) The regularization of ill-posed problems. Dok 1. Akad. Nau. SSR., 153, 4952
Wang, Y, Liang, Q, Kesserwani, G and Hall, JW (2011) A positivity-preserving zero-inertia model for flood simulation. Comput. Fluids, 46(1), 505511
Whitehouse, IE (1988) Geomorphology of the central Southern Alps, New Zealand: the interaction of plate collision and atmospheric circulation. Z. Geomorphol. NF, 69, 105116
Zachos, J, Pagani, M, Sloan, L, Thomas, E and Billups, K (2001) Trends, rhythms, and aberrations in global climate 65 Ma to present. Science, 292, 686693
Zhang, Y and Xu, X (2011) Inverse source problem for a fractional diffusion equation. Inverse. Probl., 27(3), 035010

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