Articles | Volume 17, issue 10
https://doi.org/10.5194/tc-17-4241-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/tc-17-4241-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
06 Oct 2023
Research article |
| 06 Oct 2023
| 06 Oct 2023
A framework for time-dependent ice sheet uncertainty quantification, applied to three West Antarctic ice streams
School of GeoSciences, University of Edinburgh, Edinburgh, UK
Daniel Goldberg
School of GeoSciences, University of Edinburgh, Edinburgh, UK
James R. Maddison
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, UK
Joe Todd
School of GeoSciences, University of Edinburgh, Edinburgh, UK
Related authors
Colin Peter Morice, David I. Berry, Richard C. Cornes, Kathryn Cowtan, Thomas Cropper, Ed Hawkins, John J. Kennedy, Timothy J. Osborn, Nick A. Rayner, Beatriz R. Rivas, Andrew P. Schurer, Michael Taylor, Praveen R. Teleti, Emily J. Wallis, Jonathan Winn, and Elizabeth C. Kent
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-500, https://doi.org/10.5194/essd-2024-500, 2024
Preprint under review for ESSD
Short summary
Short summary
We present a new data set of global gridded surface air temperature change extending back to the 1780s. This is achieved using marine air temperature observations with newly available estimates of diurnal heating biases together with an updated land station database that includes bias adjustments for early thermometer enclosures. These developments allow the data set to extend further into the past than current data sets that use sea surface temperature rather than marine air temperature data.
Beatriz Recinos, Fabien Maussion, Timo Rothenpieler, and Ben Marzeion
The Cryosphere, 13, 2657–2672, https://doi.org/10.5194/tc-13-2657-2019, https://doi.org/10.5194/tc-13-2657-2019, 2019
Short summary
Short summary
We have implemented a frontal ablation parameterization into the Open Global Glacier Model and have shown that inversion methods based on mass conservation systematically underestimate the mass turnover (and therefore the thickness) of tidewater glaciers when neglecting frontal ablation. This underestimation can rise up to 19 % on a regional scale. Not accounting for frontal ablation will have an impact on the estimate of the glaciers’ potential contribution to sea level rise.
Fabien Maussion, Anton Butenko, Nicolas Champollion, Matthias Dusch, Julia Eis, Kévin Fourteau, Philipp Gregor, Alexander H. Jarosch, Johannes Landmann, Felix Oesterle, Beatriz Recinos, Timo Rothenpieler, Anouk Vlug, Christian T. Wild, and Ben Marzeion
Geosci. Model Dev., 12, 909–931, https://doi.org/10.5194/gmd-12-909-2019, https://doi.org/10.5194/gmd-12-909-2019, 2019
Short summary
Short summary
Mountain glaciers are one of the few remaining subsystems of the global climate system for which no globally applicable community-driven model exists. Here we present the Open Global Glacier Model (OGGM; www.oggm.org), developed to provide a modular and open-source numerical model framework for simulating past and future change of any glacier in the world.
Colin Peter Morice, David I. Berry, Richard C. Cornes, Kathryn Cowtan, Thomas Cropper, Ed Hawkins, John J. Kennedy, Timothy J. Osborn, Nick A. Rayner, Beatriz R. Rivas, Andrew P. Schurer, Michael Taylor, Praveen R. Teleti, Emily J. Wallis, Jonathan Winn, and Elizabeth C. Kent
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-500, https://doi.org/10.5194/essd-2024-500, 2024
Preprint under review for ESSD
Short summary
Short summary
We present a new data set of global gridded surface air temperature change extending back to the 1780s. This is achieved using marine air temperature observations with newly available estimates of diurnal heating biases together with an updated land station database that includes bias adjustments for early thermometer enclosures. These developments allow the data set to extend further into the past than current data sets that use sea surface temperature rather than marine air temperature data.
Iain Wheel, Douglas I. Benn, Anna J. Crawford, Joe Todd, and Thomas Zwinger
Geosci. Model Dev., 17, 5759–5777, https://doi.org/10.5194/gmd-17-5759-2024, https://doi.org/10.5194/gmd-17-5759-2024, 2024
Short summary
Short summary
Calving, the detachment of large icebergs from glaciers, is one of the largest uncertainties in future sea level rise projections. This process is poorly understood, and there is an absence of detailed models capable of simulating calving. A new 3D calving model has been developed to better understand calving at glaciers where detailed modelling was previously limited. Importantly, the new model is very flexible. By allowing for unrestricted calving geometries, it can be applied at any location.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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.
Conrad P. Koziol, Joe A. Todd, Daniel N. Goldberg, and James R. Maddison
Geosci. Model Dev., 14, 5843–5861, https://doi.org/10.5194/gmd-14-5843-2021, https://doi.org/10.5194/gmd-14-5843-2021, 2021
Short summary
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.
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
Short summary
Short summary
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.
Stephen L. Cornford, Helene Seroussi, Xylar S. Asay-Davis, G. Hilmar Gudmundsson, Rob Arthern, Chris Borstad, Julia Christmann, Thiago Dias dos Santos, Johannes Feldmann, Daniel Goldberg, Matthew J. Hoffman, Angelika Humbert, Thomas Kleiner, Gunter Leguy, William H. Lipscomb, Nacho Merino, Gaël Durand, Mathieu Morlighem, David Pollard, Martin Rückamp, C. Rosie Williams, and Hongju Yu
The Cryosphere, 14, 2283–2301, https://doi.org/10.5194/tc-14-2283-2020, https://doi.org/10.5194/tc-14-2283-2020, 2020
Short summary
Short summary
We present the results of the third Marine Ice Sheet Intercomparison Project (MISMIP+). MISMIP+ is one in a series of exercises that test numerical models of ice sheet flow in simple situations. This particular exercise concentrates on the response of ice sheet models to the thinning of their floating ice shelves, which is of interest because numerical models are currently used to model the response to contemporary and near-future thinning in Antarctic ice shelves.
Beatriz Recinos, Fabien Maussion, Timo Rothenpieler, and Ben Marzeion
The Cryosphere, 13, 2657–2672, https://doi.org/10.5194/tc-13-2657-2019, https://doi.org/10.5194/tc-13-2657-2019, 2019
Short summary
Short summary
We have implemented a frontal ablation parameterization into the Open Global Glacier Model and have shown that inversion methods based on mass conservation systematically underestimate the mass turnover (and therefore the thickness) of tidewater glaciers when neglecting frontal ablation. This underestimation can rise up to 19 % on a regional scale. Not accounting for frontal ablation will have an impact on the estimate of the glaciers’ potential contribution to sea level rise.
Fabien Maussion, Anton Butenko, Nicolas Champollion, Matthias Dusch, Julia Eis, Kévin Fourteau, Philipp Gregor, Alexander H. Jarosch, Johannes Landmann, Felix Oesterle, Beatriz Recinos, Timo Rothenpieler, Anouk Vlug, Christian T. Wild, and Ben Marzeion
Geosci. Model Dev., 12, 909–931, https://doi.org/10.5194/gmd-12-909-2019, https://doi.org/10.5194/gmd-12-909-2019, 2019
Short summary
Short summary
Mountain glaciers are one of the few remaining subsystems of the global climate system for which no globally applicable community-driven model exists. Here we present the Open Global Glacier Model (OGGM; www.oggm.org), developed to provide a modular and open-source numerical model framework for simulating past and future change of any glacier in the world.
Daniel N. Goldberg, Sri Hari Krishna Narayanan, Laurent Hascoet, and Jean Utke
Geosci. Model Dev., 9, 1891–1904, https://doi.org/10.5194/gmd-9-1891-2016, https://doi.org/10.5194/gmd-9-1891-2016, 2016
Short summary
Short summary
Geophysical adjoint models are powerful tools, allowing sensitivity studies that are not possible otherwise, and enabling optimized fit of models to observing data sets. The complexity involved requires the use of algorithmic differentiation (AD) software, but AD adjoint calculation for ice models can be slow, with prohibitive memory requirements. In this paper, we present a method to improve the performance of ice model adjoint generation, in terms of timing, memory load, and accuracy.
D. N. Goldberg, P. Heimbach, I. Joughin, and B. Smith
The Cryosphere, 9, 2429–2446, https://doi.org/10.5194/tc-9-2429-2015, https://doi.org/10.5194/tc-9-2429-2015, 2015
Short summary
Short summary
We calibrate a time-dependent ice model through optimal fit to transient observations of surface elevation and velocity, a novel procedure in glaciology and in particular for an ice stream with a dynamic grounding line. We show this procedure gives a level of confidence in model projections that cannot be achieved through more commonly used glaciological data assimilation methods. We show that Smith Glacier is in a state of retreat regardless of climatic forcing for the next several decades.
D. N. Goldberg and P. Heimbach
The Cryosphere, 7, 1659–1678, https://doi.org/10.5194/tc-7-1659-2013, https://doi.org/10.5194/tc-7-1659-2013, 2013
Related subject area
Discipline: Ice sheets | Subject: Data Assimilation
Impact of time-dependent data assimilation on ice flow model initialization and projections: a case study of Kjer Glacier, Greenland
DeepBedMap: a deep neural network for resolving the bed topography of Antarctica
Assimilation of surface observations in a transient marine ice sheet model using an ensemble Kalman filter
Youngmin Choi, Helene Seroussi, Mathieu Morlighem, Nicole-Jeanne Schlegel, and Alex Gardner
The Cryosphere, 17, 5499–5517, https://doi.org/10.5194/tc-17-5499-2023, https://doi.org/10.5194/tc-17-5499-2023, 2023
Short summary
Short summary
Ice sheet models are often initialized using snapshot observations of present-day conditions, but this approach has limitations in capturing the transient evolution of the system. To more accurately represent the accelerating changes in glaciers, we employed time-dependent data assimilation. We found that models calibrated with the transient data better capture past trends and more accurately reproduce changes after the calibration period, even with limited observations.
Wei Ji Leong and Huw Joseph Horgan
The Cryosphere, 14, 3687–3705, https://doi.org/10.5194/tc-14-3687-2020, https://doi.org/10.5194/tc-14-3687-2020, 2020
Short summary
Short summary
A machine learning technique similar to the one used to enhance everyday photographs is applied to the problem of getting a better picture of Antarctica's bed – the part which is hidden beneath the ice. By taking hints from what satellites can observe at the ice surface, the novel method learns to generate a rougher bed topography that complements existing approaches, with a result that is able to be used by scientists running fine-scale ice sheet models relevant to predicting future sea levels.
Fabien Gillet-Chaulet
The Cryosphere, 14, 811–832, https://doi.org/10.5194/tc-14-811-2020, https://doi.org/10.5194/tc-14-811-2020, 2020
Short summary
Short summary
Marine-based sectors of the Antarctic Ice Sheet are increasingly contributing to sea-level rise. The basal conditions exert an important control on the ice dynamics. For obvious reasons of inaccessibility, they are an important source of uncertainties in numerical ice flow models used for sea-level projections. Here we assess the performance of an ensemble Kalman filter for the assimilation of transient observations of surface elevation and velocities in a marine ice sheet model.
Cited articles
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
Altena, B., Kääb, A., and Wouters, B.: Correlation dispersion as a measure to better estimate uncertainty in remotely sensed glacier displacements, The Cryosphere, 16, 2285–2300, https://doi.org/10.5194/tc-16-2285-2022, 2022. a, b
Arthern, R. J.: Exploring the use of transformation group priors and the method
of maximum relative entropy for Bayesian glaciological inversions, J.
Glaciol., 61, 947–962, https://doi.org/10.3189/2015JoG15J050, 2015. a
Arthern, R. J., Winebrenner, D. P., and Vaughan, D. G.: Antarctic snow
accumulation mapped using polarization of 4.3-cm wavelength microwave
emission, J. Geophys. Res.-Atmos., 111, D06107,
https://doi.org/10.1029/2004JD005667, 2006. a
Asay-Davis, X. S., Cornford, S. L., Durand, G., Galton-Fenzi, B. K., Gladstone, R. M., Gudmundsson, G. H., Hattermann, T., Holland, D. M., Holland, D., Holland, P. R., Martin, D. F., Mathiot, P., Pattyn, F., and Seroussi, H.: Experimental design for three interrelated marine ice sheet and ocean model intercomparison projects: MISMIP v. 3 (MISMIP+), ISOMIP v. 2 (ISOMIP+) and MISOMIP v. 1 (MISOMIP1), Geosci. Model Dev., 9, 2471–2497, https://doi.org/10.5194/gmd-9-2471-2016, 2016. a, b
Aschwanden, A. and Brinkerhoff, D.: Calibrated Mass Loss Predictions for the
Greenland Ice Sheet, Geophys. Res. Lett., 49, e2022GL099058,
https://doi.org/10.1029/2022GL099058, 2022. a
Aschwanden, A., Bartholomaus, T. C., Brinkerhoff, D. J., and Truffer, M.: Brief communication: A roadmap towards credible projections of ice sheet contribution to sea level, The Cryosphere, 15, 5705–5715, https://doi.org/10.5194/tc-15-5705-2021, 2021. 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
Barnes, J. M. and Gudmundsson, G. H.: The predictive power of ice sheet models and the regional sensitivity of ice loss to basal sliding parameterisations: a case study of Pine Island and Thwaites glaciers, West Antarctica, The Cryosphere, 16, 4291–4304, https://doi.org/10.5194/tc-16-4291-2022, 2022. a, b
Bassis, J.: Quit Worrying About Uncertainty in Sea Level Projections, Eos,
Transactions American Geophysical Union, 102,
https://doi.org/10.1029/2021e210632, 2022. a
Brinkerhoff, D., Aschwanden, A., and Fahnestock, M.: Constraining subglacial
processes from surface velocity observations using surrogate-based Bayesian
inference, J. Glaciol., 67, 385–403, https://doi.org/10.1017/jog.2020.112,
2021. a
Brinkerhoff, D. J.: Variational inference at glacier scale, J. Comput. Phys., 459, 111095, https://doi.org/10.1016/j.jcp.2022.111095, 2022. a
Brondex, J., Gillet-Chaulet, F., and Gagliardini, O.: Sensitivity of centennial mass loss projections of the Amundsen basin to the friction law, The Cryosphere, 13, 177–195, https://doi.org/10.5194/tc-13-177-2019, 2019. a, b
Budd, W. F. and Jenssen, D.: Numerical Modelling of the Large-Scale Basal Water
Flux under the West Antarctic Ice Sheet, in: Dynamics of the West Antarctic
Ice Sheet, edited by: Van der Veen, C. J. and Oerlemans, J., 293–320,
Springer Netherlands, Dordrecht, 1987. a
Budd, W. F., Keage, P. L., and Blundy, N. A.: Empirical Studies of Ice Sliding,
J. Glaciol., 23, 157–170, https://doi.org/10.3189/S0022143000029804, 1979. 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, b
Cuffey, K. and Paterson, W.: The Physics of Glaciers, 4th edn.,
Academic Press, 704 pp., ISBN-10 0-123694-61-2, ISBN-13 978-0-123-69461-4, 2010. a
De Rydt, J., Gudmundsson, G. H., Corr, H. F. J., and Christoffersen, P.: Surface undulations of Antarctic ice streams tightly controlled by bedrock topography, The Cryosphere, 7, 407–417, https://doi.org/10.5194/tc-7-407-2013, 2013. 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
Desroziers, G., Berre, L., Chapnik, B., and Poli, P.: Diagnosis of observation,
background and analysis-error statistics in observation space, Q. J. Roy. Meteor. Soc., 131, 3385–3396,
https://doi.org/10.1256/qj.05.108, 2005. a
Dobrzynski, C.: MMG3D: User Guide, Technical Report RT-0422, INRIA,
https://hal.inria.fr/hal-00681813 (last access: 2 October 2023), 2012. a
Dutrieux, P., De Rydt, J., Jenkins, A., Holland, P., Ha, H., Lee, S., Steig,
E., Ding, Q., Abrahamsen, E., and Schröder, M.: Strong Sensitivity of
Pine Island Ice-Shelf Melting to Climatic Variability, Science, 343,
174–178, https://doi.org/10.1126/science.1244341, 2014. a
Favier, L., Durand, G., Cornford, S. L., Gudmundsson, G. H., Gagliardini, O.,
Gillet-Chaulet, F., Zwinger, T., Payne, A., and Brocq, A. M. L.: Retreat of
Pine Island Glacier controlled by marine ice-sheet instability, Nat.
Clim. Change, 4, 117–121, https://doi.org/10.1038/nclimate2094, 2014. 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
Gardner, A. S., Moholdt, G., Scambos, T., Fahnstock, M., Ligtenberg, S., van den Broeke, M., and Nilsson, J.: Increased West Antarctic and unchanged East Antarctic ice discharge over the last 7 years, The Cryosphere, 12, 521–547, https://doi.org/10.5194/tc-12-521-2018, 2018. a, b, c, d
Geuzaine, C. and Remacle, J.-F.: Gmsh: A 3-D finite element mesh generator with
built-in pre- and post-processing facilities, Int. J.
Numer. Meth. Eng., 79, 1309–1331,
https://doi.org/10.1002/nme.2579, 2009. a
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, b, c
Glen, J. W. and Perutz, M. F.: The creep of polycrystalline ice, P. Roy. Soc. Lond. A,
228, 519–538, https://doi.org/10.1098/rspa.1955.0066, 1955. a, b
Goldberg, D. N.: A variationally derived, depth-integrated approximation to a
higher-order glaciological flow model, J. Glaciol., 57, 157–170,
https://doi.org/10.3189/002214311795306763, 2011. a
Goldberg, D. N. and Heimbach, P.: Parameter and state estimation with a time-dependent adjoint marine ice sheet model, The Cryosphere, 7, 1659–1678, https://doi.org/10.5194/tc-7-1659-2013, 2013. a, b
Gudmundsson, G. H.: Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation, The Cryosphere, 2, 77–93, https://doi.org/10.5194/tc-2-77-2008, 2008. 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
Hansen, P. C.: Analysis of Discrete Ill-Posed Problems by Means of the L-Curve,
SIAM Review, 34, 561–580, https://doi.org/10.1137/1034115, 1992. a
Hansen, P. C.: The L-Curve and Its Use in the Numerical Treatment of Inverse
Problems, WIT Press, 4, 119–142, 2001. a
Hernandez, V., Roman, J. E., and Vidal, V.: SLEPc: A Scalable and Flexible
Toolkit for the Solution of Eigenvalue Problems, ACM Trans. Math. Softw., 31,
351–362, https://doi.org/10.1145/1089014.1089019, 2005. a
Hernandez, V., Roman, J. E., Vidal, V., and Tomás, A.: Krylov-Schur Methods in
SLEPc, Tech. rep., Universidad Politecnica de Valencia, 2007. a
Hock, R., Maussion, F., Marzeion, B., and Nowicki, S.: What is the global
glacier ice volume outside the ice sheets?, J. Glaciol., 69, 204–210,
https://doi.org/10.1017/jog.2023.1, 2023. 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
Jacobs, S. S., Jenkins, A., Giulivi, C. F., and Dutrieux, P.: Stronger ocean
circulation and increased melting under Pine Island Glacier ice shelf, Nat. Geosci., 4, 519–523, https://doi.org/10.1038/ngeo1188, 2011. a
Jay-Allemand, M., Gillet-Chaulet, F., Gagliardini, O., and Nodet, M.: Investigating changes in basal conditions of Variegated Glacier prior to and during its 1982–1983 surge, The Cryosphere, 5, 659–672, https://doi.org/10.5194/tc-5-659-2011, 2011. a, b
Jenkins, A.: A Simple Model of the Ice Shelf-Ocean Boundary Layer and Current,
J. Phys. Oceanogr., 46, 1785–1803,
https://doi.org/10.1175/JPO-D-15-0194.1, 2016. a
Jenkins, A., Shoosmith, D., Dutrieux, P., Jacobs, S., Kim, T. W., Le, S. H.,
Ha, H. K., and Stammerjohn, S.: West Antarctic Ice Sheet retreat in the
Amundsen Sea driven by decadal oceanic variability, Nat. Geosci., 11,
733–738, https://doi.org/10.1038/s41561-018-0207-4, 2018. a
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
Joughin, I., Smith, B. E., and Medley, B.: Marine Ice Sheet Collapse
Potentially Under Way for the Thwaites Glacier Basin, West Antarctica,
Science, 344, 735–738, https://doi.org/10.1126/science.1249055, 2014. a
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
Kazmierczak, E., Sun, S., Coulon, V., and Pattyn, F.: Subglacial hydrology modulates basal sliding response of the Antarctic ice sheet to climate forcing, The Cryosphere, 16, 4537–4552, https://doi.org/10.5194/tc-16-4537-2022, 2022. a
Khazendar, A., Rignot, E., and Larour, E.: Acceleration and spatial rheology of
Larsen C Ice Shelf, Antarctic Peninsula, Geophys. Res. Lett., 38, L09502,
https://doi.org/10.1029/2011GL046775, 2011. a, b
Koziol, C. P., Todd, J. A., Goldberg, D. N., and Maddison, J. R.: fenics_ice 1.0: a framework for quantifying initialization uncertainty for time-dependent ice sheet models, Geosci. Model Dev., 14, 5843–5861, https://doi.org/10.5194/gmd-14-5843-2021, 2021. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u
Lannelongue, L., Grealey, J., and Inouye, M.: Green Algorithms: Quantifying the
Carbon Footprint of Computation, Adv. Sci., 8, 2100707,
https://doi.org/10.1002/advs.202100707, 2021. a
Levermann, A., Winkelmann, R., Albrecht, T., Goelzer, H., Golledge, N. R., Greve, R., Huybrechts, P., Jordan, J., Leguy, G., Martin, D., Morlighem, M., Pattyn, F., Pollard, D., Quiquet, A., Rodehacke, C., Seroussi, H., Sutter, J., Zhang, T., Van Breedam, J., Calov, R., DeConto, R., Dumas, C., Garbe, J., Gudmundsson, G. H., Hoffman, M. J., Humbert, A., Kleiner, T., Lipscomb, W. H., Meinshausen, M., Ng, E., Nowicki, S. M. J., Perego, M., Price, S. F., Saito, F., Schlegel, N.-J., Sun, S., and van de Wal, R. S. W.: Projecting Antarctica's contribution to future sea level rise from basal ice shelf melt using linear response functions of 16 ice sheet models (LARMIP-2), Earth Syst. Dynam., 11, 35–76, https://doi.org/10.5194/esd-11-35-2020, 2020. a
Lilien, D. A., Joughin, I., Smith, B., and Gourmelen, N.: Melt at grounding line controls observed and future retreat of Smith, Pope, and Kohler glaciers, The Cryosphere, 13, 2817–2834, https://doi.org/10.5194/tc-13-2817-2019, 2019. a, b, c
Lindgren, F., Rue, H., and Lindström, J.: An explicit link between Gaussian
fields and Gaussian Markov random fields: the stochastic partial differential
equation approach, J. Roy. Stat. Soc. B, 73, 423–498,
https://doi.org/10.1111/j.1467-9868.2011.00777.x, 2011. a
MacAyeal, D. R.: Large-scale ice flow over a viscous basal sediment: Theory and
application to Ice Stream B, Antarctica, J. Geophys. Res., 94, 4071–4087, 1989. a
MacAyeal, D. R., Bindschadler, R. A., and Scambos, T. A.: Basal friction of ice
stream E, West Antarctica, J. Glaciol., 41, 247–262,
https://doi.org/10.3189/S0022143000016154, 1995. a
Maddison, J. R. and Recinos, B.: EdiGlacUQ/tlm_adjoint: tlm_adjoint (v1.0), Zenodo [code], https://doi.org/10.5281/zenodo.7625841, 2023. 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
Maddison, J. R., Recinos, B., dngoldberg, Koziol, C., and Todd, J.: EdiGlacUQ/fenics_ice: fenics_ice (v1.0.2), Zenodo [code], https://doi.org/10.5281/zenodo.7615309, 2023. a, b
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
Morales, J. L. and Nocedal, J.: Remark on “Algorithm 778: L-BFGS-B: Fortran
Subroutines for Large-Scale Bound Constrained Optimization”, ACM Trans.
Math. Softw., 38, 7, 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, d
Morlighem, M., Rignot, E., Binder, T., Blankenship, D., Drews, R., Eagles, G.,
Eisen, O., Ferraccioli, F., Forsberg, R., Fretwell, P., Goel, V., Greenbaum,
J. S., Gudmundsson, H., Guo, J., Helm, V., Hofstede, C., Howat, I., Humbert,
A., Jokat, W., Karlsson, N. B., Lee, W. S., Matsuoka, K., Millan, R.,
Mouginot, J., Paden, J., Pattyn, F., Roberts, J., Rosier, S., Ruppel, A.,
Seroussi, H., Smith, E. C., Steinhage, D., Sun, B., Broeke, M. R. V. D.,
Ommen, T. D. V., Wessem, M. V., and Young, D. A.: Deep glacial troughs and
stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet,
Nat. Geosci., 13, 132–137, https://doi.org/10.1038/s41561-019-0510-8, 2020. a, b, c, d, e
Mouginot, J., Rignot, E., Scheuchl, B., and Millan, R.: Comprehensive Annual
Ice Sheet Velocity Mapping Using Landsat-8, Sentinel-1, and RADARSAT-2 Data,
Remote Sens., 9, 364, https://doi.org/10.3390/rs9040364, 2017. a, b, c, d
Pattyn, F.: Antarctic subglacial conditions inferred from a hybrid ice
sheet/ice stream model, Earth Planet. Sc. Lett., 295, 451–461,
https://doi.org/10.1016/j.epsl.2010.04.025, 2010. a, b, c, d
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
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. Comput., 36, A1525–A1555, https://doi.org/10.1137/130934805, 2014. a, b, c, d, e, f
Recinos, B.: Output of several experiments with Fenics_ice over Smith, Pope, and Kohler Glaciers, Zenodo [data set], https://doi.org/10.5281/zenodo.7612243, 2023. a
Recinos, B., Goldberg, D., Maddison, J. R., and Todd, J.: bearecinos/smith_glacier: Experiments with Fenics_ice applied to three West Antarctic ice streams (v1.0), Zenodo [code], https://doi.org/10.5281/zenodo.7615259, 2023. a, b
Rignot, E., Mouginot, J., and Scheuchl, B.: Ice Flow of the Antarctic Ice
Sheet, Science, 333, 1427–1430, https://doi.org/10.1126/science.1208336, 2011. a
Rignot, E., Mouginot, J., and Scheuchl, B.: MEaSUREs InSAR-Based Ice Velocity
of the Amundsen Sea Embayment, Antarctica, Version 1,
https://doi.org/10.5067/MEASURES/CRYOSPHERE/nsidc-0545.001, 2014. a, b
Rignot, E., Mouginot, J., and Scheuchl, B.: MEaSUREs InSAR-Based Antarctica Ice
Velocity Map, Version 2, https://doi.org/10.5067/D7GK8F5J8M8R, 2017. a, b, c
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, b
Scheuchl, B., Mouginot, J., Rignot, E., Morlighem, M., and Khazendar, A.:
Grounding line retreat of Pope, Smith, and Kohler Glaciers, West Antarctica,
measured with Sentinel-1a radar interferometry data, Geophys. Res. Lett., 43, 8572–8579, https://doi.org/10.1002/2016GL069287, 2016. a
Schoof, C.: A variational approach to ice stream flow, J. Fluid
Mech., 556, 227–251, https://doi.org/10.1017/S0022112006009591, 2006. a
Seddik, H., Greve, R., Zwinger, T., and Sugiyama, S.: Regional modeling of the Shirase drainage basin, East Antarctica: full Stokes vs. shallow ice dynamics, The Cryosphere, 11, 2213–2229, https://doi.org/10.5194/tc-11-2213-2017, 2017. a, b
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, https://doi.org/10.3189/172756408787814906, 2008. a
Seroussi, H., Nakayama, Y., Larour, E., Menemenlis, D., Morlighem, M., Rignot,
E., and Khazendar, A.: Continued retreat of Thwaites Glacier, West
Antarctica, controlled by bed topography and ocean circulation, Geophys. Res. Lett., 44, 6191–6199, https://doi.org/10.1002/2017GL072910, 2017. 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, b
Still, H., Hulbe, C., Forbes, M., Prior, D. J., Bowman, M. H., Boucinhas, B.,
Craw, L., Kim, D., Lutz, F., Mulvaney, R., and Thomas, R. E.: Tidal
Modulation of a Lateral Shear Margin: Priestley Glacier, Antarctica,
Front. Earth Sci., 10, 828313, https://doi.org/10.3389/feart.2022.828313, 2022.
a, b
Stuart, A. M.: Inverse problems: A Bayesian perspective, Acta Numerica, 19,
451–559, https://doi.org/10.1017/S0962492910000061, 2010. a, b
Tabeart, J. M., Dance, S. L., Lawless, A. S., Migliorini, S., Nichols, N. K.,
Smith, F., and Waller, J. A.: The impact of using reconditioned correlated
observation-error covariance matrices in the Met Office 1D-Var system,
Q. J. Roy. Meteor. Soc., 146, 1372–1390,
https://doi.org/10.1002/qj.3741, 2020. a
Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter
Estimation, Society for Industrial and Applied Mathematics,
https://doi.org/10.1137/1.9780898717921, 2005. 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
Tsai, C.-Y., Forest, C. E., and Pollard, D.: Assessing the contribution of
internal climate variability to anthropogenic changes in ice sheet volume,
Geophys. Res. Lett., 44, 6261–6268,
https://doi.org/10.1002/2017GL073443, 2017. a
Waddington, E. D., Neumann, T. A., Koutnik, M. R., Marshall, H.-P., and Morse,
D. L.: Inference of accumulation-rate patterns from deep layers in glaciers
and ice sheets, J. Glaciol., 53, 694–712,
https://doi.org/10.3189/002214307784409351, 2007. a
Weertman, J.: On the Sliding of Glaciers, J. Glaciol., 3, 33–38,
https://doi.org/10.3189/S0022143000024709, 1957. 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 Trans. Math.
Softw., 23, 550–560, https://doi.org/10.1145/279232.279236, 1997. a
Short summary
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.
Ice sheet models generate forecasts of ice sheet mass loss, a significant contributor to sea...
