Articles | Volume 19, issue 2
https://doi.org/10.5194/tc-19-645-2025
© Author(s) 2025. 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-19-645-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
07 Feb 2025
Research article |
| 07 Feb 2025
| 07 Feb 2025
Physics-aware machine learning for glacier ice thickness estimation: a case study for Svalbard
Chair of Data Science in Earth Observation, Department of Aerospace and Geodesy, Technical University of Munich, 80333 Munich, Germany
Jonathan Louis Bamber
Chair of Data Science in Earth Observation, Department of Aerospace and Geodesy, Technical University of Munich, 80333 Munich, Germany
Bristol Glaciology Centre, School of Geographical Sciences, University of Bristol, Bristol, BS8 1SS, UK
Xiao Xiang Zhu
Chair of Data Science in Earth Observation, Department of Aerospace and Geodesy, Technical University of Munich, 80333 Munich, Germany
Munich Center for Machine Learning, 80538 Munich, Germany
Related authors
Viola Steidl, Jürgen Kusche, Fupeng Li, and Xiao Xiang Zhu
EGUsphere, https://doi.org/10.5194/egusphere-2026-2312, https://doi.org/10.5194/egusphere-2026-2312, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Terrestrial water storage is an indicator of water availability, but forecasting its changes is difficult as it depends on processes acting at varying spatial and temporal scales. We introduce a hierarchical machine learning model that represents the Earth at two scales, the grid scale and the hydrological basin scale, to forecast global water storage changes up to six months ahead. We identify where model skill fades and which challenges to address to improve its forecasts.
Leyue Tang, Jonathan L. Bamber, Tian Li, and Gang Qiao
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2026-414, https://doi.org/10.5194/essd-2026-414, 2026
Preprint under review for ESSD
Short summary
Short summary
Many Antarctic ice shelves are thinning and retreating, threatening future sea-level rise. Surface damage indicates structural weakening, but long-term records are scarce. We created a multi-decadal surface damage record for nine representative Antarctic ice shelves using satellite imagery and deep learning. The dataset shows that Pine Island, Thwaites and Larsen B have experienced the most significant damage changes since 1999, providing valuable insights into ice shelf stability.
Viola Steidl, Jürgen Kusche, Fupeng Li, and Xiao Xiang Zhu
EGUsphere, https://doi.org/10.5194/egusphere-2026-2312, https://doi.org/10.5194/egusphere-2026-2312, 2026
This preprint is open for discussion and under review for Hydrology and Earth System Sciences (HESS).
Short summary
Short summary
Terrestrial water storage is an indicator of water availability, but forecasting its changes is difficult as it depends on processes acting at varying spatial and temporal scales. We introduce a hierarchical machine learning model that represents the Earth at two scales, the grid scale and the hydrological basin scale, to forecast global water storage changes up to six months ahead. We identify where model skill fades and which challenges to address to improve its forecasts.
Nils Lehmann, Cesar Aybar, Ando Shah, Marcello Passaro, Jonathan L. Bamber, and Xiao Xiang Zhu
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2026-232, https://doi.org/10.5194/essd-2026-232, 2026
Preprint under review for ESSD
Short summary
Short summary
We created a global ocean dataset that brings together satellite measurements, model outputs, and observations into one consistent system. We did this to reduce the time and effort needed to combine different data sources, to improve reproducibility, and enable new analyses. The result makes it easier to study ocean changes, compare methods, and support better understanding of climate processes and extreme events.
Yang Mu, Zhitong Xiong, Yi Wang, Muhammad Shahzad, Franz Essl, Holger Kreft, Mark van Kleunen, and Xiao Xiang Zhu
Earth Syst. Sci. Data, 18, 1379–1403, https://doi.org/10.5194/essd-18-1379-2026, https://doi.org/10.5194/essd-18-1379-2026, 2026
Short summary
Short summary
To better protect our planet's forests, we need to know what trees are where. We created GlobalGeoTree, a massive public dataset linking 6.3 million tree locations worldwide with satellite data. This dataset helps computers learn to identify tree species from space, supporting biodiversity monitoring and climate action. Our baseline model shows this is a promising path to understanding global forests.
Xiao Xiang Zhu, Sining Chen, Fahong Zhang, Yilei Shi, and Yuanyuan Wang
Earth Syst. Sci. Data, 17, 6647–6668, https://doi.org/10.5194/essd-17-6647-2025, https://doi.org/10.5194/essd-17-6647-2025, 2025
Short summary
Short summary
We introduce GlobalBuildingAtlas, a publicly available dataset offering global and complete coverage of building polygons (GBA.Polygon), heights (GBA.Height) and Level of Detail 1 3D models (GBA.LoD1). This is the first open dataset to offer high quality, consistent, and complete building data in 2D and 3D at the individual building level on a global scale. With more than 2.75 billion buildings worldwide, it surpasses the most comprehensive database to date by more than 1 billion buildings.
Gavin A. Schmidt, Kenneth D. Mankoff, Jonathan L. Bamber, Clara Burgard, Dustin Carroll, David M. Chandler, Violaine Coulon, Benjamin J. Davison, Matthew H. England, Paul R. Holland, Nicolas C. Jourdain, Qian Li, Juliana M. Marson, Pierre Mathiot, Clive R. McMahon, Twila A. Moon, Ruth Mottram, Sophie Nowicki, Anna Olivé Abelló, Andrew G. Pauling, Thomas Rackow, and Damien Ringeisen
Geosci. Model Dev., 18, 8333–8361, https://doi.org/10.5194/gmd-18-8333-2025, https://doi.org/10.5194/gmd-18-8333-2025, 2025
Short summary
Short summary
The impact of increasing mass loss from the Greenland and Antarctic ice sheets has not so far been included in historical climate model simulations. This paper describes the protocols and data available for modeling groups to add this anomalous freshwater to their ocean modules to better represent the impacts of these fluxes on ocean circulation, sea ice, salinity and sea level.
Adam Igneczi and Jonathan Louis Bamber
Earth Syst. Sci. Data, 17, 3203–3218, https://doi.org/10.5194/essd-17-3203-2025, https://doi.org/10.5194/essd-17-3203-2025, 2025
Short summary
Short summary
Freshwater from Arctic land ice loss strongly affects the Arctic and North Atlantic oceans. Datasets describing this freshwater discharge have low resolution and do not cover the entire Arctic. We statistically enhanced coarse-resolution climate model data – from approximately 6 km to 250 m – and routed meltwater towards the coastlines to provide high-resolution data covering all Arctic regions. This approach has far fewer computational requirements than running climate models at high resolution.
Zhenghang Yuan, Zhitong Xiong, Lichao Mou, and Xiao Xiang Zhu
Earth Syst. Sci. Data, 17, 1245–1263, https://doi.org/10.5194/essd-17-1245-2025, https://doi.org/10.5194/essd-17-1245-2025, 2025
Short summary
Short summary
ChatEarthNet is an image–text dataset that provides high-quality, detailed natural language descriptions for global-scale satellite data. It consists of 163 488 image-text pairs with captions generated by ChatGPT-3.5 and an additional 10 000 image-text pairs with captions generated by ChatGPT-4V(ision). This dataset has significant potential for training and evaluating vision–language geo-foundation models in remote sensing.
Yifan Tian, Yao Sun, and Xiao Xiang Zhu
Abstr. Int. Cartogr. Assoc., 7, 171, https://doi.org/10.5194/ica-abs-7-171-2024, https://doi.org/10.5194/ica-abs-7-171-2024, 2024
Erik Loebel, Mirko Scheinert, Martin Horwath, Angelika Humbert, Julia Sohn, Konrad Heidler, Charlotte Liebezeit, and Xiao Xiang Zhu
The Cryosphere, 18, 3315–3332, https://doi.org/10.5194/tc-18-3315-2024, https://doi.org/10.5194/tc-18-3315-2024, 2024
Short summary
Short summary
Comprehensive datasets of calving-front changes are essential for studying and modeling outlet glaciers. Current records are limited in temporal resolution due to manual delineation. We use deep learning to automatically delineate calving fronts for 23 glaciers in Greenland. Resulting time series resolve long-term, seasonal, and subseasonal patterns. We discuss the implications of our results and provide the cryosphere community with a data product and an implementation of our processing system.
Weiyan Lin, Jiasong Zhu, Yuansheng Hua, Qingyu Li, Lichao Mou, and Xiao Xiang Zhu
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVIII-1-2024, 371–378, https://doi.org/10.5194/isprs-archives-XLVIII-1-2024-371-2024, https://doi.org/10.5194/isprs-archives-XLVIII-1-2024-371-2024, 2024
Tian Li, Konrad Heidler, Lichao Mou, Ádám Ignéczi, Xiao Xiang Zhu, and Jonathan L. Bamber
Earth Syst. Sci. Data, 16, 919–939, https://doi.org/10.5194/essd-16-919-2024, https://doi.org/10.5194/essd-16-919-2024, 2024
Short summary
Short summary
Our study uses deep learning to produce a new high-resolution calving front dataset for 149 marine-terminating glaciers in Svalbard from 1985 to 2023, containing 124 919 terminus traces. This dataset offers insights into understanding calving mechanisms and can help improve glacier frontal ablation estimates as a component of the integrated mass balance assessment.
Y. Sun, A. Kruspe, L. Meng, Y. Tian, E. J. Hoffmann, S. Auer, and X. X. Zhu
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVIII-1-W2-2023, 225–232, https://doi.org/10.5194/isprs-archives-XLVIII-1-W2-2023-225-2023, https://doi.org/10.5194/isprs-archives-XLVIII-1-W2-2023-225-2023, 2023
J. Zhao, F. Roth, B. Bauer-Marschallinger, W. Wagner, M. Chini, and X. X. Zhu
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., X-1-W1-2023, 911–918, https://doi.org/10.5194/isprs-annals-X-1-W1-2023-911-2023, https://doi.org/10.5194/isprs-annals-X-1-W1-2023-911-2023, 2023
Yao Sun, Stefan Auer, Liqiu Meng, and Xiao Xiang Zhu
Abstr. Int. Cartogr. Assoc., 6, 250, https://doi.org/10.5194/ica-abs-6-250-2023, https://doi.org/10.5194/ica-abs-6-250-2023, 2023
Benoit S. Lecavalier, Lev Tarasov, Greg Balco, Perry Spector, Claus-Dieter Hillenbrand, Christo Buizert, Catherine Ritz, Marion Leduc-Leballeur, Robert Mulvaney, Pippa L. Whitehouse, Michael J. Bentley, and Jonathan Bamber
Earth Syst. Sci. Data, 15, 3573–3596, https://doi.org/10.5194/essd-15-3573-2023, https://doi.org/10.5194/essd-15-3573-2023, 2023
Short summary
Short summary
The Antarctic Ice Sheet Evolution constraint database version 2 (AntICE2) consists of a large variety of observations that constrain the evolution of the Antarctic Ice Sheet over the last glacial cycle. This includes observations of past ice sheet extent, past ice thickness, past relative sea level, borehole temperature profiles, and present-day bedrock displacement rates. The database is intended to improve our understanding of past Antarctic changes and for ice sheet model calibrations.
Alice C. Frémand, Peter Fretwell, Julien A. Bodart, Hamish D. Pritchard, Alan Aitken, Jonathan L. Bamber, Robin Bell, Cesidio Bianchi, Robert G. Bingham, Donald D. Blankenship, Gino Casassa, Ginny Catania, Knut Christianson, Howard Conway, Hugh F. J. Corr, Xiangbin Cui, Detlef Damaske, Volkmar Damm, Reinhard Drews, Graeme Eagles, Olaf Eisen, Hannes Eisermann, Fausto Ferraccioli, Elena Field, René Forsberg, Steven Franke, Shuji Fujita, Yonggyu Gim, Vikram Goel, Siva Prasad Gogineni, Jamin Greenbaum, Benjamin Hills, Richard C. A. Hindmarsh, Andrew O. Hoffman, Per Holmlund, Nicholas Holschuh, John W. Holt, Annika N. Horlings, Angelika Humbert, Robert W. Jacobel, Daniela Jansen, Adrian Jenkins, Wilfried Jokat, Tom Jordan, Edward King, Jack Kohler, William Krabill, Mette Kusk Gillespie, Kirsty Langley, Joohan Lee, German Leitchenkov, Carlton Leuschen, Bruce Luyendyk, Joseph MacGregor, Emma MacKie, Kenichi Matsuoka, Mathieu Morlighem, Jérémie Mouginot, Frank O. Nitsche, Yoshifumi Nogi, Ole A. Nost, John Paden, Frank Pattyn, Sergey V. Popov, Eric Rignot, David M. Rippin, Andrés Rivera, Jason Roberts, Neil Ross, Anotonia Ruppel, Dustin M. Schroeder, Martin J. Siegert, Andrew M. Smith, Daniel Steinhage, Michael Studinger, Bo Sun, Ignazio Tabacco, Kirsty Tinto, Stefano Urbini, David Vaughan, Brian C. Welch, Douglas S. Wilson, Duncan A. Young, and Achille Zirizzotti
Earth Syst. Sci. Data, 15, 2695–2710, https://doi.org/10.5194/essd-15-2695-2023, https://doi.org/10.5194/essd-15-2695-2023, 2023
Short summary
Short summary
This paper presents the release of over 60 years of ice thickness, bed elevation, and surface elevation data acquired over Antarctica by the international community. These data are a crucial component of the Antarctic Bedmap initiative which aims to produce a new map and datasets of Antarctic ice thickness and bed topography for the international glaciology and geophysical community.
Tian Li, Geoffrey J. Dawson, Stephen J. Chuter, and Jonathan L. Bamber
The Cryosphere, 17, 1003–1022, https://doi.org/10.5194/tc-17-1003-2023, https://doi.org/10.5194/tc-17-1003-2023, 2023
Short summary
Short summary
The Totten and Moscow University glaciers in East Antarctica have the potential to make a significant contribution to future sea-level rise. We used a combination of different satellite measurements to show that the grounding lines have been retreating along the fast-flowing ice streams across these two glaciers. We also found two tide-modulated ocean channels that might open new pathways for the warm ocean water to enter the ice shelf cavity.
Jingliang Hu, Rong Liu, Danfeng Hong, Andrés Camero, Jing Yao, Mathias Schneider, Franz Kurz, Karl Segl, and Xiao Xiang Zhu
Earth Syst. Sci. Data, 15, 113–131, https://doi.org/10.5194/essd-15-113-2023, https://doi.org/10.5194/essd-15-113-2023, 2023
Short summary
Short summary
Multimodal data fusion is an intuitive strategy to break the limitation of individual data in Earth observation. Here, we present a multimodal data set, named MDAS, consisting of synthetic aperture radar (SAR), multispectral, hyperspectral, digital surface model (DSM), and geographic information system (GIS) data for the city of Augsburg, Germany, along with baseline models for resolution enhancement, spectral unmixing, and land cover classification, three typical remote sensing applications.
Sam Royston, Rory J. Bingham, and Jonathan L. Bamber
Ocean Sci., 18, 1093–1107, https://doi.org/10.5194/os-18-1093-2022, https://doi.org/10.5194/os-18-1093-2022, 2022
Short summary
Short summary
Decadal sea-level variability masks longer-term changes and increases uncertainty in observed trend and acceleration estimates. We use numerical ocean models to determine the magnitude of decadal variability we might expect in sea-level trends at coastal locations around the world, resulting from natural, internal variability. A proportion of that variability can be replicated from known climate modes, giving a range to add to short- to mid-term projections of regional sea-level trends.
S. Zhao, S. Saha, and X. X. Zhu
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLIII-B3-2022, 1407–1413, https://doi.org/10.5194/isprs-archives-XLIII-B3-2022-1407-2022, https://doi.org/10.5194/isprs-archives-XLIII-B3-2022-1407-2022, 2022
S. Saha, J. Gawlikowski, and X. X. Zhu
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLIII-B3-2022, 423–428, https://doi.org/10.5194/isprs-archives-XLIII-B3-2022-423-2022, https://doi.org/10.5194/isprs-archives-XLIII-B3-2022-423-2022, 2022
K. R. Traoré, A. Camero, and X. X. Zhu
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., V-3-2022, 217–224, https://doi.org/10.5194/isprs-annals-V-3-2022-217-2022, https://doi.org/10.5194/isprs-annals-V-3-2022-217-2022, 2022
T. Beker, H. Ansari, S. Montazeri, Q. Song, and X. X. Zhu
ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., V-3-2022, 85–92, https://doi.org/10.5194/isprs-annals-V-3-2022-85-2022, https://doi.org/10.5194/isprs-annals-V-3-2022-85-2022, 2022
Stephen J. Chuter, Andrew Zammit-Mangion, Jonathan Rougier, Geoffrey Dawson, and Jonathan L. Bamber
The Cryosphere, 16, 1349–1367, https://doi.org/10.5194/tc-16-1349-2022, https://doi.org/10.5194/tc-16-1349-2022, 2022
Short summary
Short summary
We find the Antarctic Peninsula to have a mean mass loss of 19 ± 1.1 Gt yr−1 over the 2003–2019 period, driven predominantly by changes in ice dynamic flow like due to changes in ocean forcing. This long-term record is crucial to ascertaining the region’s present-day contribution to sea level rise, with the understanding of driving processes enabling better future predictions. Our statistical approach enables us to estimate this previously poorly surveyed regions mass balance more accurately.
Tom Mitcham, G. Hilmar Gudmundsson, and Jonathan L. Bamber
The Cryosphere, 16, 883–901, https://doi.org/10.5194/tc-16-883-2022, https://doi.org/10.5194/tc-16-883-2022, 2022
Short summary
Short summary
We modelled the response of the Larsen C Ice Shelf (LCIS) and its tributary glaciers to the calving of the A68 iceberg and validated our results with observations. We found that the impact was limited, confirming that mostly passive ice was calved. Through further calving experiments we quantified the total buttressing provided by the LCIS and found that over 80 % of the buttressing capacity is generated in the first 5 km of the ice shelf downstream of the grounding line.
Tian Li, Geoffrey J. Dawson, Stephen J. Chuter, and Jonathan L. Bamber
Earth Syst. Sci. Data, 14, 535–557, https://doi.org/10.5194/essd-14-535-2022, https://doi.org/10.5194/essd-14-535-2022, 2022
Short summary
Short summary
Accurate knowledge of the Antarctic grounding zone is important for mass balance calculation, ice sheet stability assessment, and ice sheet model projections. Here we present the first ICESat-2-derived high-resolution grounding zone product of the Antarctic Ice Sheet, including three important boundaries. This new data product will provide more comprehensive insights into ice sheet instability, which is valuable for both the cryosphere and sea level science communities.
Fanny Lehmann, Bramha Dutt Vishwakarma, and Jonathan Bamber
Hydrol. Earth Syst. Sci., 26, 35–54, https://doi.org/10.5194/hess-26-35-2022, https://doi.org/10.5194/hess-26-35-2022, 2022
Short summary
Short summary
Many data sources are available to evaluate components of the water cycle (precipitation, evapotranspiration, runoff, and terrestrial water storage). Despite this variety, it remains unclear how different combinations of datasets satisfy the conservation of mass. We conducted the most comprehensive analysis of water budget closure on a global scale to date. Our results can serve as a basis to select appropriate datasets for regional hydrological studies.
Cited articles
Anilkumar, R., Bharti, R., Chutia, D., and Aggarwal, S. P.: Modelling point mass balance for the glaciers of the Central European Alps using machine learning techniques, The Cryosphere, 17, 2811–2828, https://doi.org/10.5194/tc-17-2811-2023, 2023. a
Bolibar, J., Rabatel, A., Gouttevin, I., Galiez, C., Condom, T., and Sauquet, E.: Deep learning applied to glacier evolution modelling, The Cryosphere, 14, 565–584, https://doi.org/10.5194/tc-14-565-2020, 2020. a, b
Bouchayer, C., Aiken, J. M., Thøgersen, K., Renard, F., and Schuler, T. V.: A Machine Learning Framework to Automate the Classification of Surge-Type Glaciers in Svalbard, J. Geophys. Res.-Earth, 127, e2022JF006597, https://doi.org/10.1029/2022JF006597, 2022. a
Cheng, G., Morlighem, M., and Francis, S.: Forward and Inverse Modeling of Ice Sheet Flow Using Physics-Informed Neural Networks: Application to Helheim Glacier, Greenland, Journal of Geophysical Research: Machine Learning and Computation, 1, e2024JH000169, https://doi.org/10.1029/2024JH000169, 2024. a, b
Copernicus: Copernicus DEM GLO-90, Copernicus [data set], https://doi.org/10.5270/ESA-c5d3d65, 2019. a
Farinotti, D., Brinkerhoff, D. J., Clarke, G. K. C., Fürst, J. J., Frey, H., Gantayat, P., Gillet-Chaulet, F., Girard, C., Huss, M., Leclercq, P. W., Linsbauer, A., Machguth, H., Martin, C., Maussion, F., Morlighem, M., Mosbeux, C., Pandit, A., Portmann, A., Rabatel, A., Ramsankaran, R., Reerink, T. J., Sanchez, O., Stentoft, P. A., Singh Kumari, S., van Pelt, W. J. J., Anderson, B., Benham, T., Binder, D., Dowdeswell, J. A., Fischer, A., Helfricht, K., Kutuzov, S., Lavrentiev, I., McNabb, R., Gudmundsson, G. H., Li, H., and Andreassen, L. M.: How accurate are estimates of glacier ice thickness? Results from ITMIX, the Ice Thickness Models Intercomparison eXperiment, The Cryosphere, 11, 949–970, https://doi.org/10.5194/tc-11-949-2017, 2017. a
Glasser, N. F.: Polythermal Glaciers, in: Encyclopedia of Snow, Ice and Glaciers, edited by: Singh, V. P., Singh, P., and Haritashya, U. K., pp. 865–867, Springer Netherlands, Dordrecht, ISBN 978-90-481-2642-2, https://doi.org/10.1007/978-90-481-2642-2_417, 2011. a
GlaThiDa Consortium: Glacier Thickness Database 3.1.0, World Glacier Monitoring Service [data set], https://doi.org/10.5904/wgms-glathida-2020-10, 2020. a
Glen, J. W.: The Creep of Polycrystalline Ice, P. Roy. Soc. Lond. Ser. A-Math., 228, 519–538, https://doi.org/10.1098/rspa.1955.0066, 1955. a
Goodfellow, I., Bengio, Y., and Courville, A.: Deep Learning, MIT Press, https://www.deeplearningbook.org/ (last access: 31 January 2025), 2016. a
Haq, M. A., Azam, M. F., and Vincent, C.: Efficiency of artificial neural networks for glacier ice-thickness estimation: A case study in western Himalaya, India, J. Glaciol., 67, 671–684, https://doi.org/10.1017/jog.2021.19 2021. a
Höhl, A., Obadic, I., Fernández-Torres, M.-Á., Najjar, H., Oliveira, D. A. B., Akata, Z., Dengel, A., and Zhu, X. X.: Opening the Black Box: A systematic review on explainable artificial intelligence in remote sensing, IEEE Geosci. Remote Sens. Mag., 12, 261–304, https://doi.org/10.1109/MGRS.2024.3467001, 2024 a
Hugonnet, R., McNabb, R., Berthier, E., Menounos, B., Nuth, C., Girod, L., Farinotti, D., Huss, M., Dussaillant, I., Brun, F., and Kääb, A.: Accelerated global glacier mass loss in the early twenty-first century, Nature, 592, 726–731, https://doi.org/10.1038/s41586-021-03436-z, 2021. a, b
Iwasaki, Y. and Lai, C.-Y.: One-dimensional ice shelf hardness inversion: Clustering behavior and collocation resampling in physics-informed neural networks, J. Comput. Phys., 492, 112435, https://doi.org/10.1016/j.jcp.2023.112435, 2023. a, b, c, d
Jiskoot, H.: Dynamics of Glaciers, in: Encyclopedia of Snow, Ice and Glaciers, edited by: Singh, V. P., Singh, P., and Haritashya, U. K., Springer Netherlands, Dordrecht, 245–256, ISBN 978-90-481-2642-2, https://doi.org/10.1007/978-90-481-2642-2_127, 2011. a
Jouvet, G.: Inversion of a Stokes glacier flow model emulated by deep learning, J. Glaciol., 69, 13–26, https://doi.org/10.1017/jog.2022.41, 2023. a
Jouvet, G. and Cordonnier, G.: Ice-flow model emulator based on physics-informed deep learning, J. Glaciol., 69, 1941–1955, https://doi.org/10.1017/jog.2023.73, 2023. a
Jouvet, G., Cordonnier, G., Kim, B., Lüthi, M., Vieli, A., and Aschwanden, A.: Deep learning speeds up ice flow modelling by several orders of magnitude, J. Glaciol., 68, 651–664, https://doi.org/10.1017/jog.2021.120, 2022. a
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., and Yang, L.: Physics-informed machine learning, Nat. Rev. Phys., 3, 422–440, https://doi.org/10.1038/s42254-021-00314-5, 2021. a, b
Koch, M., Seehaus, T., Friedl, P., and Braun, M.: Automated Detection of Glacier Surges from Sentinel-1 Surface Velocity Time Series—An Example from Svalbard, Remote Sens., 15, 1545, https://doi.org/10.3390/rs15061545, 2023. a
Kokhlikyan, N., Miglani, V., Martin, M., Wang, E., Alsallakh, B., Reynolds, J., Melnikov, A., Kliushkina, N., Araya, C., Yan, S., and Reblitz-Richardson, O.: Captum: A unified and generic model interpretability library for PyTorch, arXiv [preprint], https://doi.org/10.48550/arXiv.2009.07896, 2020. a
Lagaris, I., Likas, A., and Fotiadis, D.: Artificial neural networks for solving ordinary and partial differential equations, IEEE T. Neur. Netw., 9, 987–1000, https://doi.org/10.1109/72.712178, 1998. a
Leong, W. J. and Horgan, H. J.: DeepBedMap: a deep neural network for resolving the bed topography of Antarctica, The Cryosphere, 14, 3687–3705, https://doi.org/10.5194/tc-14-3687-2020, 2020. a
Lindbäck, K., Kohler, J., Pettersson, R., Nuth, C., Langley, K., Messerli, A., Vallot, D., Matsuoka, K., and Brandt, O.: Subglacial topography, ice thickness, and bathymetry of Kongsfjorden, northwestern Svalbard, Earth Syst. Sci. Data, 10, 1769–1781, https://doi.org/10.5194/essd-10-1769-2018, 2018. a
Lundberg, S. M. and Lee, S.-I.: A Unified Approach to Interpreting Model Predictions, in: Advances in Neural Information Processing Systems 30 (NIPS 2017), edited by: Guyon, I., Luxburg, U. V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R., Curran Associates, Inc., 4765–4774, ISBN 9781510860964, 2017. a
Maussion, F., Butenko, A., Champollion, N., Dusch, M., Eis, J., Fourteau, K., Gregor, P., Jarosch, A. H., Landmann, J., Oesterle, F., Recinos, B., Rothenpieler, T., Vlug, A., Wild, C. T., and Marzeion, B.: The Open Global Glacier Model (OGGM) v1.1, Geosci. Model Dev., 12, 909–931, https://doi.org/10.5194/gmd-12-909-2019, 2019. a
Min, Y., Mukkavilli, S. K., and Bengio, Y.: Predicting ice flow using machine learning, arXiv [preprint], https://doi.org/10.48550/arXiv.1910.08922, 2019. a
Moholdt, G., Maton, J., Majerska, M., and Kohler, J.: Annual coastlines for Svalbard, Norwegian Polar Institute [data set], https://doi.org/10.21334/npolar.2021.21565514, 2021. a
Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Ben Dhia, H., and Aubry, D.: A mass conservation approach for mapping glacier ice thickness, Geophys. Res. Lett., 38, L19503, https://doi.org/10.1029/2011GL048659, 2011. a
Pälli, A., Moore, J. C., and Rolstad, C.: Firn–ice transition-zone features of four polythermal glaciers in Svalbard seen by ground-penetrating radar, Ann. Glaciol., 37, 298–304, https://doi.org/10.3189/172756403781816059, 2003. a
Raissi, M., Perdikaris, P., and Karniadakis, G.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., 378, 686–707, https://doi.org/10.1016/j.jcp.2018.10.045, 2018. a, b
Rathore, P., Lei, W., Frangella, Z., Lu, L., and Udell, M.: Challenges in Training PINNs: A Loss Landscape Perspective, arXiv [preprint], https://doi.org/10.48550/arXiv.2402.01868, 2024. a
RGI Consortium: Randolph Glacier Inventory – A Dataset of Global Glacier Outlines, Version 6, Region 7, National Snow and Ice Data Center [data set], https://doi.org/10.7265/4M1F-GD79, 2017. a
Riel, B., Minchew, B., and Bischoff, T.: Data-Driven Inference of the Mechanics of Slip Along Glacier Beds Using Physics-Informed Neural Networks: Case Study on Rutford Ice Stream, Antarctica, J. Adv. Model. Earth Sy., 13, e2021MS002621, https://doi.org/10.1029/2021MS002621, 2021. a
Rolf, E.: Evaluation Challenges for Geospatial ML, arXiv [preprint], https://doi.org/10.48550/arXiv.2303.18087, 2023. a
Shapley, L. S.: A Value for n-Person Games, in: Contributions to the Theory of Games (AM-28), Volume II, edited by: Kuhn, H. W. and Tucker, A. W., Princeton University Press, 307–318, ISBN 978-1-4008-8197-0, https://doi.org/10.1515/9781400881970-018, 1953. a
Steidl, V.: GlacierPINN: Case Study Svalbard, Zenodo [code and data set], https://doi.org/10.5281/zenodo.13834016, 2024. a
Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., and Ng, R.: Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains, arXiv [preprint], https://doi.org/10.48550/arXiv.2006.10739, 2020. a
Teisberg, T. O., Schroeder, D. M., and MacKie, E. J.: A Machine Learning Approach to Mass-Conserving Ice Thickness Interpolation, in: 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, pp. 8664–8667, IEEE, Brussels, Belgium, https://doi.org/10.1109/IGARSS47720.2021.9555002, 2021. a
van Pelt, W. and Frank, T.: New glacier thickness and bed topography maps for Svalbard, The Cryosphere, 19, 1–17, https://doi.org/10.5194/tc-19-1-2025, 2025. a, b, c, d
Wang, S., Sankaran, S., Wang, H., and Perdikaris, P.: An Expert's Guide to Training Physics-informed Neural Networks, arXiv [preprint], https://doi.org/10.48550/arXiv.2308.08468, 2023. a
Wang, Y., Lai, C.-Y., and Cowen-Breen, C.: Discovering the rheology of Antarctic Ice Shelves via physics-informed deep learning, Research Square [preprint], https://doi.org/10.21203/rs.3.rs-2135795/v1, 2022. a
Welty, E., Zemp, M., Navarro, F., Huss, M., Fürst, J. J., Gärtner-Roer, I., Landmann, J., Machguth, H., Naegeli, K., Andreassen, L. M., Farinotti, D., Li, H., and GlaThiDa Contributors: Worldwide version-controlled database of glacier thickness observations, Earth Syst. Sci. Data, 12, 3039–3055, https://doi.org/10.5194/essd-12-3039-2020, 2020. a
Xu, Q., Shi, Y., Bamber, J., Tuo, Y., Ludwig, R., and Zhu, X. X.: Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology, arXiv [preprint], https://doi.org/10.48550/arXiv.2310.05227, 2023. a, b
Short summary
Glacier ice thickness is difficult to measure directly but is essential for glacier evolution modelling. In this work, we employ a novel approach combining physical knowledge and data-driven machine learning to estimate the ice thickness of multiple glaciers in Spitsbergen, Barentsøya, and Edgeøya in Svalbard. We identify challenges for the physics-aware machine learning model and opportunities for improving the accuracy and physical consistency that would also apply to other geophysical tasks.
Glacier ice thickness is difficult to measure directly but is essential for glacier evolution...
