Articles | Volume 14, issue 9
https://doi.org/10.5194/gmd-14-5843-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-14-5843-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
fenics_ice 1.0: a framework for quantifying initialization uncertainty for time-dependent ice sheet models
Conrad P. Koziol
School of GeoSciences, Univ. of Edinburgh, City of Edinburgh, United Kingdom
Joe A. Todd
School of GeoSciences, Univ. of Edinburgh, City of Edinburgh, United Kingdom
School of GeoSciences, Univ. of Edinburgh, City of Edinburgh, United Kingdom
James R. Maddison
School of Mathematics and
Maxwell Institute for Mathematical Sciences, Univ. of Edinburgh, City of Edinburgh, United Kingdom
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Patrick Schmitt, Fabien Maussion, Daniel N. Goldberg, and Philipp Gregor
EGUsphere, https://doi.org/10.5194/egusphere-2025-3401, https://doi.org/10.5194/egusphere-2025-3401, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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To improve large-scale understanding of glaciers, we developed a new data assimilation method that integrates available observations in a dynamically consistent way, while taking their timestamps into account. It is designed to flexibly include new glacier data as it becomes available. We tested the method with idealized experiments and found promising results in terms of accuracy and efficiency, showing strong potential for real-world applications.
Laure Moinat, Florian Franziskakis, Christian Vérard, Daniel N. Goldberg, and Maura Brunetti
EGUsphere, https://doi.org/10.5194/egusphere-2025-2946, https://doi.org/10.5194/egusphere-2025-2946, 2025
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
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We describe a new tool, biogeodyn-MITgcmIS, that consistently reproduces the global-scale dynamics of the ocean, atmosphere, vegetation and ice on multimillennial timescales at low computational cost. Evaluated against observations and state-of-the-art Earth system models, it includes offline coupling to models of vegetation, hydrology and a newly developed global-scale ice sheet. Using arbitrary continental configurations, it enables studies of past and present climates on Earth or exoplanets.
Claire K. Yung, Xylar S. Asay-Davis, Alistair Adcroft, Christopher Y. S. Bull, Jan De Rydt, Michael S. Dinniman, Benjamin K. Galton-Fenzi, Daniel Goldberg, David E. Gwyther, Robert Hallberg, Matthew Harrison, Tore Hattermann, David M. Holland, Denise Holland, Paul R. Holland, James R. Jordan, Nicolas C. Jourdain, Kazuya Kusahara, Gustavo Marques, Pierre Mathiot, Dimitris Menemenlis, Adele K. Morrison, Yoshihiro Nakayama, Olga Sergienko, Robin S. Smith, Alon Stern, Ralph Timmermann, and Qin Zhou
EGUsphere, https://doi.org/10.5194/egusphere-2025-1942, https://doi.org/10.5194/egusphere-2025-1942, 2025
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ISOMIP+ compares 12 ocean models that simulate ice-ocean interactions in a common, idealised, static ice shelf cavity setup, aiming to assess and understand inter-model variability. Models simulate similar basal melt rate patterns, ocean profiles and circulation but differ in ice-ocean boundary layer properties and spatial distributions of melting. Ice-ocean boundary layer representation is a key area for future work, as are realistic-domain ice sheet-ocean model intercomparisons.
Jowan M. Barnes, G. Hilmar Gudmundsson, Daniel N. Goldberg, and Sainan Sun
EGUsphere, https://doi.org/10.5194/egusphere-2025-328, https://doi.org/10.5194/egusphere-2025-328, 2025
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Calving is where ice breaks off the front of glaciers. It has not been included widely in modelling as it is difficult to represent. We use our ice flow model to investigate the effects of calving floating ice shelves in West Antarctica. More calving leads to more ice loss and greater sea level rise, with local differences due to the shape of the bedrock. We find that ocean forcing and calving should be considered equally when trying to improve how models represent the real world.
David T. Bett, Alexander T. Bradley, C. Rosie Williams, Paul R. Holland, Robert J. Arthern, and Daniel N. Goldberg
The Cryosphere, 18, 2653–2675, https://doi.org/10.5194/tc-18-2653-2024, https://doi.org/10.5194/tc-18-2653-2024, 2024
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A new ice–ocean model simulates future ice sheet evolution in the Amundsen Sea sector of Antarctica. Substantial ice retreat is simulated in all scenarios, with some retreat still occurring even with no future ocean melting. The future of small "pinning points" (islands of ice that contact the seabed) is an important control on this retreat. Ocean melting is crucial in causing these features to go afloat, providing the link by which climate change may affect this sector's sea level contribution.
Beatriz Recinos, Daniel Goldberg, James R. Maddison, and Joe Todd
The Cryosphere, 17, 4241–4266, https://doi.org/10.5194/tc-17-4241-2023, https://doi.org/10.5194/tc-17-4241-2023, 2023
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Ice sheet models generate forecasts of ice sheet mass loss, a significant contributor to sea level rise; thus, capturing the complete range of possible projections of mass loss is of critical societal importance. Here we add to data assimilation techniques commonly used in ice sheet modelling (a Bayesian inference approach) and fully characterize calibration uncertainty. We successfully propagate this type of error onto sea level rise projections of three ice streams in West Antarctica.
Helen Ockenden, Robert G. Bingham, Andrew Curtis, and Daniel Goldberg
The Cryosphere, 16, 3867–3887, https://doi.org/10.5194/tc-16-3867-2022, https://doi.org/10.5194/tc-16-3867-2022, 2022
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Hills and valleys hidden under the ice of Thwaites Glacier have an impact on ice flow and future ice loss, but there are not many three-dimensional observations of their location or size. We apply a mathematical theory to new high-resolution observations of the ice surface to predict the bed topography beneath the ice. There is a good correlation with ice-penetrating radar observations. The method may be useful in areas with few direct observations or as a further constraint for other methods.
Alexander Robinson, Daniel Goldberg, and William H. Lipscomb
The Cryosphere, 16, 689–709, https://doi.org/10.5194/tc-16-689-2022, https://doi.org/10.5194/tc-16-689-2022, 2022
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Here we investigate the numerical stability of several commonly used methods in order to determine which of them are capable of resolving the complex physics of the ice flow and are also computationally efficient. We find that the so-called DIVA solver outperforms the others. Its representation of the physics is consistent with more complex methods, while it remains computationally efficient at high resolution.
Jowan M. Barnes, Thiago Dias dos Santos, Daniel Goldberg, G. Hilmar Gudmundsson, Mathieu Morlighem, and Jan De Rydt
The Cryosphere, 15, 1975–2000, https://doi.org/10.5194/tc-15-1975-2021, https://doi.org/10.5194/tc-15-1975-2021, 2021
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Some properties of ice flow models must be initialised using observed data before they can be used to produce reliable predictions of the future. Different models have different ways of doing this, and the process is generally seen as being specific to an individual model. We compare the methods used by three different models and show that they produce similar outputs. We also demonstrate that the outputs from one model can be used in other models without introducing large uncertainties.
Cited articles
Alexanderian, A., Petra, N., Stadler, G., and Ghattas, O.: A-Optimal Design of
Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with
Regularized ℓ_0-Sparsification, SIAM J. Sci. Comp.,
36, A2122–A2148, https://doi.org/10.1137/130933381, 2014. a
Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A.,
Richardson, C., Ring, J., Rognes, M. E., and Wells, G. N.: The FEniCS
Project Version 1.5, Archive of Numerical Software, 3, 9–23, 2015. a
Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., and Wells, G. N.:
Unified Form Language: A Domain-Specific Language for Weak Formulations of
Partial Differential Equations, ACM T. Math. Softw., 40, 1–37,
https://doi.org/10.1145/2566630, 2014. a
Arthern, R. J., Hindmarsh, R. C. A., and Williams, C. R.: Flow speed within the
Antarctic ice sheet and its controls inferred from satellite observations,
J. Geophys. Res.-Earth, 120, 1171–1188,
https://doi.org/10.1002/2014JF003239, 2015. a
Babaniyi, O., Nicholson, R., Villa, U., and Petra, N.: Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty, The Cryosphere, 15, 1731–1750, https://doi.org/10.5194/tc-15-1731-2021, 2021. a
Bui-Thanh, T., Ghattas, O., Martin, J., and Stadler, G.: A
computational framework for infinite-dimensional Bayesian inverse problems.
Part I: The linearized case, with application to global seismic inversion,
arXiv e-prints, arXiv:1308.1313 2013. a, b, c, d
Chen, P.: Hessian Matrix vs. Gauss-Newton Hessian Matrix, SIAM J. Numer. Anal.,
49, 1417–1435, https://doi.org/10.1137/100799988, 2011. a
Cornford, S. L., Martin, D. F., Graves, D. T., Ranken, D. F., Le Brocq, A. M.,
Gladstone, R. M., Payne, A. J., Ng, E. G., and Lipscomb, W. H.: Adaptive
Mesh, Finite Volume Modeling of Marine Ice Sheets, J. Comput. Phys., 232,
529–549, https://doi.org/10.1016/j.jcp.2012.08.037, 2013. a
Cornford, S. L., Martin, D. F., Payne, A. J., Ng, E. G., Le Brocq, A. M., Gladstone, R. M., Edwards, T. L., Shannon, S. R., Agosta, C., van den Broeke, M. R., Hellmer, H. H., Krinner, G., Ligtenberg, S. R. M., Timmermann, R., and Vaughan, D. G.: Century-scale simulations of the response of the West Antarctic Ice Sheet to a warming climate, The Cryosphere, 9, 1579–1600, https://doi.org/10.5194/tc-9-1579-2015, 2015. a, b, c, d
Cornford, S. L., Seroussi, H., Asay-Davis, X. S., Gudmundsson, G. H., Arthern, R., Borstad, C., Christmann, J., Dias dos Santos, T., Feldmann, J., Goldberg, D., Hoffman, M. J., Humbert, A., Kleiner, T., Leguy, G., Lipscomb, W. H., Merino, N., Durand, G., Morlighem, M., Pollard, D., Rückamp, M., Williams, C. R., and Yu, H.: Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+), The Cryosphere, 14, 2283–2301, https://doi.org/10.5194/tc-14-2283-2020, 2020. a
Cuffey, K. and Paterson, W. S. B.: The Physics of Glaciers, Butterworth
Heinemann, Oxford, 4th Edn., 2010. a
Deconto, R. M. and Pollard, D.: Contribution of Antarctica to past and
future sea-level rise, Nature, 531, 591–597, https://doi.org/10.1038/nature17145,
2016. a
Dukowicz, J. K., Price, S. F., and Lipscomp, W. H.: Consistent approximations
and boundary conditions for ice-sheet dynamics from a principle of least
action, J. Glaciol., 56, 480–496, 2010. a
Fürst, J. J., Durand, G., Gillet-Chaulet, F., Merino, N., Tavard, L., Mouginot, J., Gourmelen, N., and Gagliardini, O.: Assimilation of Antarctic velocity observations provides evidence for uncharted pinning points, The Cryosphere, 9, 1427–1443, https://doi.org/10.5194/tc-9-1427-2015, 2015. a
Gagliardini, O., Durand, G., Zwinger, T., Hindmarsh, R. C. A., and Meur, E. L.:
Coupling of ice shelf melting and buttressing is a key process in ice sheet
dynamics, Geophys. Res. Lett., 37, L14501, https://doi.org/10.1029/2010GL043334, 2010. a, b
Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz, C., Zwinger, T., Greve, R., and Vaughan, D. G.: Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model, The Cryosphere, 6, 1561–1576, https://doi.org/10.5194/tc-6-1561-2012, 2012. a
Gladstone, R. M., Lee, V., Rougier, J., Payne, A. J., Hellmer, H.,
Le Brocq, A., Shepherd, A., Edwards, T. L., Gregory, J., and
Cornford, S. L.: Calibrated prediction of Pine Island Glacier retreat
during the 21st and 22nd centuries with a coupled flowline model, Earth
Planet. Sc. Lett., 333, 191–199, https://doi.org/10.1016/j.epsl.2012.04.022,
2012. a
Glen, J. W.: The creep of polycrystalline ice, P. Roy. Soc. Lond. A Mat., 228, 519–538, 1955. a
Goldberg, D. N., Heimbach, P., Joughin, I., and Smith, B.: Committed retreat of Smith, Pope, and Kohler Glaciers over the next 30 years inferred by transient model calibration, The Cryosphere, 9, 2429–2446, https://doi.org/10.5194/tc-9-2429-2015, 2015. a, b
Habermann, M., Truffer, M., and Maxwell, D.: Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland, The Cryosphere, 7, 1679–1692, https://doi.org/10.5194/tc-7-1679-2013, 2013. a
Hernandez, V., Roman, J. E., and Vidal, V.: SLEPc: A scalable and flexible
toolkit for the solution of eigenvalue problems, ACM T. Math. Softw.,
31, 351–362, 2005. a
Higham, N. J.: Functions of Matrices: Theory and Computation, Society for
Industrial and Applied Mathematics, Philadelphia, PA, USA, 2008. a
Hindmarsh, R. C. A. and Payne, A. J.: Time-step limits for stable
solutions of the ice-sheet equation, Ann. Glaciol., 23, 74–85,
https://doi.org/10.1017/S0260305500013288, 1996. a
Isaac, T., Petra, N., Stadler, G., and Ghattas, O.: 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, J. Comput. Phys., 296, 348–368,
https://doi.org/10.1016/j.jcp.2015.04.047, 2015. a, b, c, d, e, f, g, h, i, j, k, l, m, n
Joughin, I., Smith, B., and Holland, D. M.: Sensitivity of 21st Century Sea
Level to Ocean-Induced Thinning of Pine Island Glacier, Antarctica,
Geophys. Res. Lett., 37, L20502, https://doi.org/10.1029/2010GL044819, 2010. a, b
Kalmikov, A. G. and Heimbach, P.: A Hessian-Based Method for Uncertainty
Quantification in Global Ocean State Estimation, SIAM J. Sci.
Comp., 36, S267–S295, https://doi.org/10.1137/130925311, 2014. a, b, c, d
Kaminski, T., Kauker, F., Eicken, H., and Karcher, M.: Exploring the utility of quantitative network design in evaluating Arctic sea ice thickness sampling strategies, The Cryosphere, 9, 1721–1733, https://doi.org/10.5194/tc-9-1721-2015, 2015. a, b
Keuthen, M. and Ulbrich, M.: Moreau–Yosida regularization in shape
optimization with geometric constraints, Comput. Optim.
Appl., 62, 181–216, 2015. a
Khodabakhshi, P., Willcox, K. E., and Gunzburger, M.: A multifidelity method
for a nonlocal diffusion model, Appl. Math. Lett., 121, 107361, https://doi.org/10.1016/j.aml.2021.107361,
2021. a
Larour, E., Rignot, E., Joughin, I., and Aubry, D.: Rheology of the Ronne Ice
Shelf, Antarctica, inferred from satellite radar interferometry data using
an inverse control method, Geophys. Res. Lett., 32, L05503,
https://doi.org/10.1029/2004GL021693, 2005. a
Larour, E., Utke, J., Csatho, B., Schenk, A., Seroussi, H., Morlighem, M., Rignot, E., Schlegel, N., and Khazendar, A.: 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, 2335–2351, https://doi.org/10.5194/tc-8-2335-2014, 2014. a
Logg, A., Mardal, K.-A., and Wells, G.: Automated Solution of Differential
Equations by the Finite Element Method: The FEniCS Book, Springer Publishing
Company, Incorporated, 2012. a
Loose, N., Heimbach, P., Pillar, H., and Nisancioglu, K.: Quantifying
Dynamical Proxy Potential through Oceanic Teleconnections in the
North Atlantic, Earth and Space Science Open Archive,
Earth and Space Science Open
Archive, https://doi.org/10.1002/essoar.10502065.1, 2020. a
MacAyeal, D. R.: Large-scale ice flow over a viscous basal sediment: Theory and
application to Ice Stream B, Antarctica, J. Geophys.
Res.-Sol. Ea., 94, 4071–4087, 1989. a
MacAyeal, D. R.: The basal stress distribution of Ice Stream E, Antarctica,
inferred by control methods, J. Geophys. Res., 97, 595–603,
1992. a
Maddison, J. R., Goldberg, D. N., and Goddard, B. D.: Automated Calculation of
Higher Order Partial Differential Equation Constrained Derivative
Information, SIAM J. Sci. Comp., 41, C417–C445,
https://doi.org/10.1137/18M1209465, 2019. a, b, c
Martin, J., Wilcox, L. C., Burstedde, C., and Ghattas, O.: A Stochastic Newton
MCMC Method for Large-Scale Statistical Inverse Problems with Application to
Seismic Inversion, SIAM J. Sci. Comp., 34, A1460–A1487,
https://doi.org/10.1137/110845598, 2012. a, b
Morales, J. L. and Nocedal, J.: Remark on “Algorithm 778: L-BFGS-B: Fortran
Subroutines for Large-Scale Bound Constrained Optimization”, ACM T.
Math. Softw., 38, 1–4, https://doi.org/10.1145/2049662.2049669, 2011. a
Morlighem, M., Rignot, E., Seroussi, G., Larour, E., Ben Dhia, H., and Aubry,
D.: Spatial patterns of basal drag inferred using control methods from a
full-Stokes and simpler models for Pine Island Glacier, West Antarctica,
Geophys. Res. Lett., 37, L14502, https://doi.org/10.1029/2010GL043853, 2010. a, b, c
Nias, I. J., Cornford, S. L., and Paybe, A. J.: Contrasting the modelled
sensitivity of the Amundsen Sea Embayment ice streams, J. Glaciol.,
62, 552–562, https://doi.org/10.1017/jog.2016.40, 2016. a
Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., Rückamp, M., Saito, F., Souček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM), The Cryosphere, 2, 95–108, https://doi.org/10.5194/tc-2-95-2008, 2008. a, b
Petra, N., Martin, J., Stadler, G., and Ghattas, O.: A Computational Framework
for Infinite-Dimensional Bayesian Inverse Problems, Part II: Stochastic
Newton MCMC with Application to Ice Sheet Flow Inverse Problems, SIAM J. Sci. Comp., 36, A1525–A1555, https://doi.org/10.1137/130934805, 2014. a, b, c
Raymond, M. J. and Gudmundsson, G. H.: Estimating basal properties of ice streams from surface measurements: a non-linear Bayesian inverse approach applied to synthetic data, The Cryosphere, 3, 265–278, https://doi.org/10.5194/tc-3-265-2009, 2009. a
Rignot, E., Mouginot, J., and Scheuchl, B.: MEaSUREs InSAR-Based Antarctica
Ice Velocity Map, Version 2, Boulder, Colorado USA, NASA National Snow and Ice Data Center Distributed Active Archive Center [data set],
https://doi.org/10.5067/D7GK8F5J8M8R,
2017. a
Ritz, C., Edwards, T. L., Durand, G., Payne, A. J., Peyaud, V., and
Hindmarsh, R. C. A.: Potential sea-level rise from Antarctic ice-sheet
instability constrained by observations, Nature, 528, 115–118,
https://doi.org/10.1038/nature16147, 2015. a
Robel, A. A., Seroussi, H., and Roe, G. H.: Marine ice sheet instability
amplifies and skews uncertainty in projections of future sea-level rise,
P. Natl. Acad. Sci. USA, 116, 14887–14892,
https://doi.org/10.1073/pnas.1904822116, 2019. a
Rommelaere, V.: Large-scale rheology of the Ross Ice Shelf, Antarctica,
computed by a control method, J. Glaciol., 24, 694–712, 1997. a
Schoof, C.: A variational approach to ice stream flow, J. Fluid Mech., 556,
227–251, 2006. a
Sergienko, O. V., MacAyeal, D. R., and Thom, J. E.: Reconstruction of snow/firn
thermal diffusivities from observed temperature variation: Application to
iceberg C16, Ross Sea, Antarctica, 2004-07, Ann. Glaciol., 49, 91–95,
2008. a
Shapero, D. R., Badgeley, J. A., Hoffman, A. O., and Joughin, I. R.: icepack: a new glacier flow modeling package in Python, version 1.0, Geosci. Model Dev., 14, 4593–4616, https://doi.org/10.5194/gmd-14-4593-2021, 2021. a
Thacker, W. C.: The role of the Hessian matrix in fitting models to
measurements, J. Geophys. Res., 94, 6177–6196,
https://doi.org/10.1029/JC094iC05p06177, 1989. a
Tierney, L.: Markov Chains for Exploring Posterior Distributions, Ann.
Stat., 22, 1701–1728, https://doi.org/10.1214/aos/1176325750, 1994. a
Todd, J. A., Koziol, C. P., Goldberg, D. N., and Maddison, J. R.: EdiGlacUQ/fenics_ice: fenics_ice (v1.0.1), Zenodo [code], https://doi.org/10.5281/zenodo.5153231, 2021. a
Vieli, A. and Payne, A. J.: Application of control methods for modelling the
flow of Pine Island Glacier, West Antarctica, Ann. Glaciol., 36,
197–204, 2003. a
Villa, U., Petra, N., and Ghattas, O.: hIPPYlib: an Extensible Software
Framework for Large-scale Deterministic and Bayesian Inverse Problems,
J. Open Source Softw., 3, p. 940, https://doi.org/10.21105/joss.00940, 2018. a
Waddington, E., Neumann, T., Koutnik, M., Marshall, H., and Morse, D.:
Inference of accumulation-rate patterns from deep layers in glaciers and ice
sheets, J. Glaciol., 53, 694–712, 2007. a
Zhu, C., Byrd, R. H., Lu, P., and Nocedal, J.: Algorithm 778: L-BFGS-B: Fortran
Subroutines for Large-Scale Bound-Constrained Optimization, ACM T. Math.
Softw., 23, 550–560, https://doi.org/10.1145/279232.279236, 1997. a
Short summary
Sea level change due to the loss of ice sheets presents great risk for coastal communities. Models are used to forecast ice loss, but their evolution depends strongly on properties which are hidden from observation and must be inferred from satellite observations. Common methods for doing so do not allow for quantification of the uncertainty inherent or how it will affect forecasts. We provide a framework for quantifying how this
initialization uncertaintyaffects ice loss forecasts.
Sea level change due to the loss of ice sheets presents great risk for coastal communities....