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6 - Data Assimilation in Glaciology

from Part II - ‘Fluid’ Earth Applications: From the Surface to the Space

Published online by Cambridge University Press:  20 June 2023

By
Mathieu Morlighem  and
Daniel Goldberg
Edited by
Alik Ismail-Zadeh ,
Fabio Castelli ,
Dylan Jones  and
Sabrina Sanchez
Alik Ismail-Zadeh
Affiliation:
Karlsruhe Institute of Technology, Germany
Fabio Castelli
Affiliation:
Università degli Studi, Florence
Dylan Jones
Affiliation:
University of Toronto
Sabrina Sanchez
Affiliation:
Max Planck Institute for Solar System Research, Germany
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Summary

Abstract: Data assimilation has always been a particularly active area of research in glaciology. While many properties at the surface of glaciers and ice sheets can be directly measured from remote sensing or in situ observations (surface velocity, surface elevation, thinning rates, etc.), many important characteristics, such as englacial and basal properties, as well as past climate conditions, remain difficult or impossible to observe. Data assimilation has been used for decades in glaciology in order to infer unknown properties and boundary conditions that have important impact on numerical models and their projections. The basic idea is to use observed properties, in conjunction with ice flow models, to infer these poorly known ice properties or boundary conditions. There is, however, a great deal of variability among approaches. Constraining data can be of a snapshot in time, or can represent evolution over time. The complexity of the flow model can vary, from simple descriptions of lubrication flow or mass continuity to complex, continent-wide Stokes flow models encompassing multiple flow regimes. Methods can be deterministic, where only a best fit is sought, or probabilistic in nature. We present in this chapter some of the most common applications of data assimilation in glaciology, and some of the new directions that are currently being developed.

Keywords

algorithmic differentiationBayesian calibrationdimensional reductionglacier dynamicsice-sheet modellingKalman filterMCMCregularizationsea-level risevariational data assimilation
Type
Chapter
Information
Applications of Data Assimilation and Inverse Problems in the Earth Sciences , pp. 93 - 111
Publisher: Cambridge University Press
Print publication year: 2023

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References

Arthern, R. J. (2015). Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions. Journal of Glaciology, 61(229), 947–62.Google Scholar
Arthern, R. J., and Gudmundsson, G. H. (2010). Initialization of ice-sheet forecasts viewed as an inverse Robin Problem, Journal of Glaciology, 56(197), 527–33.Google Scholar
Ashmore, D. W., Bingham, R. G., Ross, N. et al. (2020). Englacial architecture and age-depth constraints across the West Antarctic ice sheet. Geophysical Research Letters, 47(6), e2019GL086663. https://doi.org/10.1029/2019GL086663.Google Scholar
Babaniyi, O., Nicholson, R., Villa, U., and Petra, N. (2021). Inferring the basal sliding coefficient field for the stokes ice sheet model under rheological uncertainty. The Cryosphere, 15(4), 1731–50.Google Scholar
Barnes, J. M., dos Santos, T. D., Goldberg, D., Gudmundsson, G. H., Morlighem, M., and De Rydt, J. (2021). The transferability of adjoint inversion products between different ice flow models. The Cryosphere, 15(4), 1975–2000. https://doi.org/10.5194/tc-15-1975-2021.Google Scholar
Bell, R. E., et al. (2011). Widespread persistent thickening of the east Antarctic Ice Sheet by freezing from the base. Science, 331(6024), 1592–5. https://doi.org/10.1126/science.1200109.Google Scholar
Blatter, H. (1995). Velocity and stress-fields in grounded glaciers: A simple algorithm for including deviatoric stress gradients. Journal of Glaciology, 41(138), 333–44.Google Scholar
Bodart, J. A., Bingham, R. G., Ashmore, D. et al. (2021). Age-depth stratigraphy of Pine Island Glacier inferred from airborne radar and ice-core chronology. Journal of Geophysical Research: Earth Surface, 126(4), e2020JF005,927.Google Scholar
Borstad, C. P., Rignot, E., Mouginot, J., and Schodlok, M. P. (2013). Creep deformation and buttressing capacity of damaged ice shelves: Theory and application to Larsen C ice shelf. The Cryosphere, 7, 1931–47. https://doi.org/10.5194/tc-7-1931-2013.Google Scholar
Brinkerhoff, D., Aschwanden, A., and Fahnestock, M. (2021). Constraining subglacial processes from surface velocity observations using surrogate-based Bayesian inference. Journal of Glaciology, 67(263), 385–403.CrossRefGoogle Scholar
Bryson, A. E., and Ho, Y.-C. (2018). Applied Optimal Control: Optimization, Estimation, and Control. Boca Raton, FL:CRC Press.Google Scholar
Budd, W. F., and Warner, R. C. (1996). A computer scheme for rapid calculations of balance-flux distributions. Annals of Glaciology, 23, 21–27.Google Scholar
Bui-Thanh, T., Ghattas, O., Martin, J., and Stadler, G.. (2013). A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion. SIAM Journal on Scientific Computing, 35(6). https://doi.org/10.1137/12089586X.Google Scholar
Chandler, D. M., Hubbard, A. L., Hubbard, B., and Nienow, P. (2006). A Monte Carlo error analysis for basal sliding velocity calculations. Journal of Geophysical Research: Earth Surface, 111(F4). https://doi.org/10.1029/2006JF000476.Google Scholar
Chatfield, C. (1995). Model uncertainty, data mining and statistical inference. Journal of the Royal Statistical Society: Series A (Statistics in Society), 158(3), 419–44.Google Scholar
Clarke, G. K. C., Berthier, E., Schoof, C. G., and Jarosch, A. H. (2009). Neural networks applied to estimating subglacial topography and glacier volume. Journal of Climate, 22(8), 2146–60. https://doi.org/10.1175/2008JCLI2572.1.CrossRefGoogle Scholar
Conway, H., Catania, G., Raymond, C. F., Gades, A. M., Scambos, T. A., and Engelhardt, H. (2002). Switch of flow direction in an Antarctic ice stream. Nature, 419(6906), 465–67. https://doi.org/10.1038/nature01081.Google Scholar
Cornford, S. L., et al. (2015). Century-scale simulations of the response of the West Antarctic Ice Sheet to a warming climate. The Cryosphere, 9, 1579–600. https://doi.org/10.5194/tc-9-1579-2015.Google Scholar
Cuffey, K. M., and Paterson, W. S. B. (2010). The Physics of Glaciers, 4th ed. Oxford: Elsevier.Google Scholar
Dansgaard, W., Johnsen, S. J., Møller, J., and Langway, C. C. (1969). One thousand centuries of climatic record from camp century on the Greenland ice sheet. Science, 166(3903), 377–80.Google Scholar
Edwards, T., et al. (2021). Quantifying uncertainties in the land ice contribution to sea level rise this century. Nature, 593. https://doi.org/10.1038/s41586-021-03302-y.CrossRefGoogle Scholar
Evans, S., and Robin, G. d. Q. (1966). Glacier depth-sounding from air. Nature, 210(5039), 883–5. https://doi.org/10.1038/210883a0.Google Scholar
Farinotti, D., Huss, M., Bauder, A., Funk, M., and Truffer, M. (2009). A method to estimate the ice volume and ice-thickness distribution of alpine glaciers. Journal of Glaciology, 55(191), 422–30.Google Scholar
Farinotti, D., et al. (2017). How accurate are estimates of glacier ice thickness? Results from ITMIX, the Ice Thickness Models Intercomparison eXperiment. The Cryosphere, 11(2), 949–70. https://doi.org/10. 5194/tc-11–949–2017.Google Scholar
Farinotti, D., et al. (2021). Results from the Ice Thickness Models Intercomparison eXperiment Phase 2 (ITMIX2). Frontiers in Earth Science, 8, 484. https://doi.org/10.3389/feart.2020.571923.Google Scholar
Fastook, J. L., Brecher, H. H., and Hughes, T. J. (1995). Derived bedrock elevations, strain rates and stresses from measured surface elevations and velocities: Jakobshavns Isbrae, Greenland. Journal of Glaciology, 41(137), 161–73.Google Scholar
Furst, J. J., Durand, G., Gillet-Chaulet, F. et al. (2015). Assimilation of Antarctic velocity observations provides evidence for uncharted pinning points. The Cryosphere, 9, 1427–43. https://doi.org/10.5194/tc-9-1427-2015.CrossRefGoogle Scholar
Fürst, J. J., et al. (2017). Application of a two-step approach for mapping ice thickness to various glacier types on Svalbard. The Cryosphere, 11(5), 2003–32. https://doi.org/10.5194/tc-11-2003-2017.Google Scholar
Fürst, J. J., et al. (2018). The ice-free topography of Svalbard. Geophysical Research Letters, 45(21), 11,760–9. https://doi.org/10.1029/2018GL079734.Google Scholar
Giering, R., Kaminski, T., and Slawig, T. (2005). Generating efficient derivative code with TAF. Future Generation Computer Systems, 21(8), 1345–55. https://doi.org/10.1016/j.future.2004.11.003.Google Scholar
Gilbert, J. C., and Lemaréchal, C. (1989). Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming, 45(1–3), 407–35. https://doi.org/10.1007/BF01589113.Google Scholar
Gillet-Chaulet, F. (2020). Assimilation of surface observations in a transient marine ice sheet model using an ensemble Kalman filter. The Cryosphere, 14, 811–32. https://doi.org/10.5194/tc-14-811-2020.Google Scholar
Gillet-Chaulet, F., Gagliardini, O., Seddik, H. et al. (2012). Greenland Ice Sheet contribution to sea-level rise from a new-generation ice-sheet model. The Cryosphere, 6, 1561–76. https://doi.org/10.5194/tc-6-1561-2012.CrossRefGoogle Scholar
Glen, J. W. (1955). The creep of polycrystalline ice. Proceedings of the Royal Society A, 228(1175), 519–38.Google Scholar
Goldberg, D. N., and Heimbach, P. (2013). Parameter and state estimation with a time-dependent adjoint marine ice sheet model. The Cryosphere, 17, 1659–78.Google Scholar
Goldberg, D. N., Heimbach, P., Joughin, I., and Smith, B. (2015). Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration. The Cryosphere, 9(6), 2429–46. https://doi.org/10.5194/tc-9-2429-2015.Google Scholar
Goldberg, D. N., Narayanan, S. H. K., Hascoet, L., and Utke, J. (2016). An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem. Geoscientific Model Development, 9(5), 1891–904.Google Scholar
Greve, R., and Blatter, H. (2009). Dynamics of Ice Sheets and Glaciers. Berlin: Springer Science & Business Media.Google Scholar
Greve, R., Saito, F., and Abe-Ouchi, A. (2011). Initial results of the SeaRISE numerical experiments with the models SICOPOLIS and IcIES for the Greenland ice sheet. Annals of Glaciology, 52(58), 23–30.Google Scholar
Griewank, A., and Walther, A. (2008). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, vol. 19, 2nd ed. Philadelphia, PA: SIAM Frontiers in Applied Mathematics.Google Scholar
Gudmundsson, G. H. (2003). Transmission of basal variability to a glacier surface. Journal of Geophysical Research: Solid Earth, 108(B5), 1–19. https://doi.org/10.1029/2002JB002107.Google Scholar
Habermann, M., Truffer, M., and Maxwell, D. (2013). Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland. The Cryosphere, 7(6), 1679–92. https://doi.org/10.5194/tc-7-1679-2013.CrossRefGoogle Scholar
Hadamard, J. (1902). Sur les probl`emes aux Dérivées partielles et leur signification physique, Princeton University Bulletin, 13, 49–52.Google Scholar
Hansen, P. C. (2000). The L-curve and its use in the numerical treatment of inverse problems. In Johnston, P., ed., Computational Inverse Problems in Electrocardiology: Advances in Computational Bioengineering. Southampton: WIT Press, pp. 119–42.Google Scholar
Heimbach, P., and Bugnion, V. (2009). Greenland ice-sheet volume sensitivity to basal, surface and initial conditions derived from an adjoint model. Annals of Glaciology, 50(52), 67–80.Google Scholar
Hindmarsh, R. C., Leysinger-Vieli, G. J.-M., and Parrenin, F. (2009). A large-scale numerical model for computing isochrone geometry. Annals of Glaciology, 50(51), 130–40.CrossRefGoogle Scholar
Huss, M., and Farinotti, D. (2012). Distributed ice thickness and volume of all glaciers around the globe. Journal of Geophysical Research: Earth Surface, 117(F4). https://doi.org/10.1029/2012JF002523.Google Scholar
Hutter, K. (1983). Theoretical Glaciology: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets. Dordrecht: D. Reidel Publishing.Google Scholar
Isaac, T., Petra, N., Stadler, G., and Ghattas, O. (2015). Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet. Journal of Computational Physics, 296, 348–38.CrossRefGoogle Scholar
Joughin, I., MacAyeal, D. R., and Tulaczyk, S. (2004). Basal shear stress of the Ross ice streams from control method inversions. Journal of Geophysical Research: Solid Earth, 109(B9), 1–62. https://doi.org/10.1029/2003JB002960.CrossRefGoogle Scholar
Joughin, I., Smith, B. E., and Howat, I. M. (2018). A complete map of Greenland ice velocity derived from satellite data collected over 20 years. Journal of Glaciology, 64(243), 1–11. https://doi.org/10.1017/jog.2017.73.Google Scholar
Jouvet, G. (2023). Inversion of a Stokes glacier flow model emulated by deep learning. Journal of Glaciology, 69(273), 13–26.CrossRefGoogle Scholar
Jouvet, G., Cordonnier, G., Kim, B., Lüthi, M., Vieli, A. and Aschwanden, A. (2022). Deep learning speeds up ice flow modelling by several orders of magnitude. Journal of Glaciology, 68(270), 651–64.Google Scholar
Kalmikov, A. G., and Heimbach, P. (2014). A hessian-based method for uncertainty quantification in global ocean state estimation. SIAM Journal on Scientific Computing, 36(5), S267–S295.Google Scholar
Karlsson, N. B., Bingham, R. G., Rippin, D. M. et al. (2014). Constraining past accumulation in the central Pine Island Glacier basin, West Antarctica, using radio-echo sounding. Journal of Glaciology, 60(221), 553–62.Google Scholar
Kohn, R., and Vogelius, M. (1984). Determining conductivity by boundary measurements. Communications on Pure and Applied Mathematics, 37(3), 289–98. https://doi.org/10.1002/cpa. 3160370302.Google Scholar
Koutnik, M. R., and Waddington, E. D. (2012). Well-posed boundary conditions for limited-domain models of transient ice flow near an ice divide. Journal of Glaciology, 58(211), 1008–20.Google Scholar
Koutnik, M. R., Fudge, T., Conway, H. et al. (2016). Holocene accumulation and ice flow near the West Antarctic ice sheet divide ice core site. Journal of Geophysical Research: Earth Surface, 121(5), 907–924.Google Scholar
Koziol, C. P., Todd, J. A., Goldberg, D. N., and Maddison, J. R. (2021). fenics ice 1.0: A framework for quantifying initialization uncertainty for time-dependent ice sheet models. Geoscientific Model Development, 14, 5843–61. https://doi.org/10.5194/gmd-14-5843-2021.Google Scholar
Krasnopolsky, V. M., and Schiller, H. (2003). Some neural network applications in environmental sciences. Part I: Forward and inverse problems in geophysical remote measurements. Neural Networks, 16(3–4), 321–34.CrossRefGoogle ScholarPubMed
Kyrke-Smith, T. M., Gudmundsson, G. H., and Farrell, P. E. (2017). Can seismic observations of bed conditions on ice streams help constrain parameters in ice flow models? Journal of Geophysical Research: Earth Surface, 122(11), 2269–82.Google Scholar
Larour, E. (2005). Modélisation numérique du comportement des banquises flottantes, validée par imagerie satellitaire, Ph.D. thesis, Ecole Centrale Paris.Google Scholar
Larour, E., Utke, J., Csatho, B. et al. (2014). Inferred basal friction and surface mass balance of the Northeast Greenland Ice Stream using data assimilation of ICESat (Ice Cloud and land Elevation Satellite) surface altimetry and ISSM (Ice Sheet System Model). The Cryosphere, 8(6), 2335–51. https://doi.org/10.5194/tc-8–2335–2014.Google Scholar
Lee, V., Cornford, S. L., and Payne, A. J. (2015). Initialization of an ice-sheet model for present-day Greenland. Annals of Glaciology, 56(70), 129–40. https://doi.org/10.3189/2015AoG70A121.Google Scholar
Leong, W. J., and Horgan, H. J. (2020). DeepBedMap: A deep neural network for resolving the bed topography of Antarctica. The Cryosphere, 14(11), 3687–705. https://doi.org/10.5194/tc-14-3687-2020.Google Scholar
Li, D., Gurnis, M., and Stadler, G. (2017). Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity. Geophysical Journal International, 209(1), 86–105. https://doi.org/10.1093/gji/ggw493.Google Scholar
Logan, L. C., Narayanan, S. H. K., Greve, R., and Heimbach, P. (2020). Sicopolis-ad v1: an open-source adjoint modeling framework for ice sheet simulation enabled by the algorithmic differentiation tool OpenAD. Geoscientific Model Development, 13(4), 1845–64.Google Scholar
Lorenc, A. C. (2003). The potential of the ensemble Kalman filter for NWP: A comparison with 4d-var. Quarterly Journal of the Royal Meteorological Society: A Journal of the Atmospheric Sciences, Applied Meteorology and Physical Oceanography, 129(595), 3183–203.Google Scholar
MacAyeal, D. R. (1989). Large-scale ice flow over a viscous basal sediment: Theory and application to Ice Stream B, Antarctica. Journal of Geophysical Research Atmospheres, 94(B4), 4071–87.Google Scholar
MacAyeal, D. R. (1992a). Irregular oscillations of the West Antarctic ice sheet. Nature, 359(6390), 29–32.Google Scholar
MacAyeal, D. R. (1992b). The basal stress distribution of Ice Stream E, Antarctica, inferred by control methods. Journal of Geophysical Research: Solid Earth, 97(B1), 595–603.Google Scholar
MacAyeal, D. R. (1993). A tutorial on the use of control methods in ice-sheet modelling. Journal of Glaciology, 39(131), 91–8.Google Scholar
MacGregor, J. A. et al. (2015). Radiostratigraphy and age structure of the Greenland Ice Sheet. Journal of Geophysical Research: Earth Surface, 120(2), 212–41. https://doi.org/10.1002/2014JF003215.Google Scholar
Maddison, J. R., Goldberg, D. N., and Goddard, B. D. (2019). Automated calculation of higher order partial differential equation constrained derivative information. SIAM Journal on Scientific Computing, 41(5), C417–C445.Google Scholar
Martin, J., Wilcox, L. C., Burstedde, C., and Ghattas, O. (2012). A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion. SIAM Journal on Scientific Computing, 34(3), A1460–A1487.Google Scholar
Michel, L., Picasso, M., Farinotti, D., Funk, M., and Blatter, H. (2014). Estimating the ice thickness of shallow glaciers from surface topography and mass-balance data with a shape optimization algorithm. Computers & Geosciences, 66, 182–99.Google Scholar
Morlighem, M., Rignot, E., Seroussi, H. et al. (2010). Spatial patterns of basal drag inferred using control methods from a full-Stokes and simpler models for Pine Island Glacier, West Antarctica. Geophysical Research Letters, 37(L14502), 1–6. https://doi.org/10.1029/2010GL043853.Google Scholar
Morlighem, M., Rignot, E., Seroussi, H. et al. (2011). A mass conservation approach for mapping glacier ice thickness. Geophysical Research Letters, 38(L19503), 1–6. https://doi.org/10.1029/2011GL048659.Google Scholar
Morlighem, M., Rignot, E., Mouginot, J. et al. (2013a). High-resolution bed topography mapping of Russell Glacier, Greenland, inferred from Operation IceBridge data. Journal of Glaciology, 59(218), 1015–23. https://doi.org/10.3189/2013JoG12J235.Google Scholar
Morlighem, M., Seroussi, H., Larour, E., and Rignot, E. (2013b). Inversion of basal friction in Antarctica using exact and incomplete adjoints of a higher-order model. Journal of Geophysical Research: Earth Surface, 118(3), 1746–53. https://doi.org/10.1002/jgrf.20125.Google Scholar
Morlighem, M., Rignot, E., Mouginot, J. (2014). Deeply incised submarine glacial valleys beneath the Greenland Ice Sheet. Nature Geoscience, 7(6), 418–22. https://doi.org/10.1038/ngeo2167.Google Scholar
Morlighem, M., et al. (2017). BedMachine v3: Complete bed topography and ocean bathymetry mapping of Greenland from multi-beam echo sounding combined with mass conservation. Geophysical Research Letters, 44(21), 11,051–61. https://doi.org/10.1002/2017GL074954,2017GL074954.Google Scholar
Morlighem, M., et al. (2020). Deep glacial troughs and stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet. Nature Geoscience, 13(2), 132–7. https://doi.org/10.1038/s41561-019-0510-8.Google Scholar
Nias, I. J., Cornford, S. L., and Payne, A. J. (2016). Contrasting the modelled sensitivity of the Amundsen Sea Embayment ice streams. Journal of Glaciology, 62(233), 552–62. https://doi.org/10.1017/jog.2016.40.Google Scholar
Nocedal, J., and Wright, S. (2006). Numerical Optimization. New York: Springer.Google Scholar
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), 1–15. https://doi.org/10.1029/2002JB002329.Google Scholar
Payne, A. J., Vieli, A., Shepherd, A. P., Wingham, D. J., and Rignot, E. (2004). Recent dramatic thinning of largest West Antarctic ice stream triggered by oceans. Geophysical Research Letters, 31(23), 1–4. https://doi.org/10.1029/2004GL021284.Google Scholar
Perego, M., Price, S., and Stadler, G. (2014). Optimal initial conditions for coupling ice sheet models to Earth system models. Journal of Geophysical Research: Earth Surface, 119, 1–24. https://doi.org/10.1002/2014JF003181.Google Scholar
Petra, N., Zhu, H., Stadler, G., Hughes, T. J. R., and Ghattas, O. (2012). An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model. Journal of Glaciology, 58(211), 889–903. https://doi.org/10.3189/2012JoG11J182.Google Scholar
Petra, N., Martin, J., Stadler, G., and Ghattas, O. (2014). A computational framework for infinitedimensional Bayesian inverse problems, Part II: Stochastic Newton MCMC with application to ice sheet flow inverse problems. SIAM Journal on Scientific Computing, 36(4), A1525–A1555. https://doi.org/10.1137/130934805.Google Scholar
Pollard, D., and DeConto, R. M. (2012). A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica. The Cryosphere, 6(5), 953–71. https://doi.org/10.5194/tc-6–953–2012.Google Scholar
Pralong, M. R., and Gudmundsson, G. H. (2011). Bayesian estimation of basal conditions on Rutford Ice Stream, West Antarctica, from surface data. Journal of Glaciology, 57(202), 315–24.Google Scholar
Price, S. F., Payne, A. J., Howat, I. M., and Smith, B. E. (2011). Committed sea-level rise for the next century from Greenland ice sheet dynamics during the past decade. Proceedings of the National Academy of Sciences, USA, 108(22), 8978–83.Google Scholar
Quiquet, A., Dumas, C., Ritz, C., Peyaud, V., and Roche, D. M. (2018). The GRISLI ice sheet model (version 2.0): Calibration and validation for multi-millennial changes of the Antarctic ice sheet. Geoscientific Model Development, 11, 5003–25. https://doi.org/10.5194/gmd-11-5003-2018.Google Scholar
Ranganathan, M., Minchew, B. Meyer, C. R., and Gudmundsson, G. H. (2020). A new approach to inferring basal drag and ice rheology in ice streams, with applications to West Antarctic Ice Streams. Journal of Glaciology, 67(262), 229–42. https://doi.org/10.1017/jog.2020.95.Google Scholar
Rasmussen, L. A. (1988). Bed topography and mass-balance distribution of Columbia Glacier, Alaska, USA, determined from sequential aerial-photography. Journal of Glaciology, 34(117), 208–16.Google Scholar
Raymond, M. J., and Gudmundsson, G. H. (2009). Estimating basal properties of glaciers from surface measurements: a non-linear Bayesian inversion approach. The Cryosphere, 3(1), 181–222.Google Scholar
Rignot, E., and Mouginot, J. (2012). Ice flow in Greenland for the International Polar Year 2008–2009. Geophysical Research Letters, 39(11). https://doi.org/10.1029/2012GL051634.Google Scholar
Rignot, E., Mouginot, J., and Scheuchl, B. (2011). Ice Flow of the Antarctic Ice Sheet. Science, 333(6048), 1427–1430. https://doi.org/10.1126/science.1208336.Google Scholar
Ritz, C., Edwards, T. L. Durand, G. et al. (2015). Potential sea-level rise from Antarctic ice-sheet instability constrained by observations. Nature, 528(7580), 115–18. https://doi.org/10.1038/nature16147.Google Scholar
Rommelaere, V., and MacAyeal, D. R. (1997). Large-scale rheology of the Ross Ice Shelf, Antarctica, computed by a control method. Annals of Glaciology, 24, 43–8.CrossRefGoogle Scholar
Shapero, D., Badgeley, J., Hoffmann, A., and Joughin, I. (2021). icepack: A new glacier flow modeling package in Python, version 1.0. Geoscientific Model Development, 14, 4593–616. https://doi.org/10.5194/gmd-14-4593-2021.Google Scholar
Siegert, M., Ross, N., Corr, H., Kingslake, J., and Hindmarsh, R. (2013). Late Holocene ice-flow reconfiguration in the Weddell Sea sector of West Antarctica. Quaternary Science Reviews, 78, 98–107.Google Scholar
Utke, J., Naumann, U., Fagan, M. (2008). OpenAD/F: A modular open-source tool for automatic differentiation of Fortran codes. ACM Transactions on Mathematical Software, 34(4) 1–36. https://doi.org/10.1145/1377596.1377598.Google Scholar
Waddington, E. D., Neumann, T. A., Koutnik, M. R., Marshall, H.-P., and Morse, D. L. (2007). Inference of accumulation-rate patterns from deep layers in glaciers and ice sheets. Journal of Glaciology, 53(183), 694–712.Google Scholar
Warner, R., and Budd, W. (2000). Derivation of ice thickness and bedrock topography in data-gap regions over Antarctica, Annals of Glaciology, 31, 191–7.Google Scholar
Werder, M. A., Huss, M., Paul, F., Dehecq, A., and Farinotti, D. (2020). A Bayesian ice thickness estimation model for large-scale applications, Journal of Glaciology, 66(255), 137–52. https://doi.org/10.1017/jog. 2019.93.Google Scholar
Wernecke, A., Edwards, T. L., Nias, I. J., Holden, P. B. and Edwards, N. R.. (2020). Spatial probabilistic calibration of a high-resolution Amundsen Sea embayment ice sheet model with satellite altimeter data. The Cryosphere, 14(5), 1459–74.Google Scholar

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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

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