Articles | Volume 17, issue 23
https://doi.org/10.5194/gmd-17-8535-2024
© Author(s) 2024. 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-17-8535-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
02 Dec 2024
Development and technical paper |
| 02 Dec 2024
| 02 Dec 2024
A fast surrogate model for 3D Earth glacial isostatic adjustment using Tensorflow (v2.8.0) artificial neural networks
Department of Earth Sciences, University of Ottawa, Ottawa, Ontario, Canada
Glenn A. Milne
Department of Earth Sciences, University of Ottawa, Ottawa, Ontario, Canada
Parviz Ajourlou
Department of Earth Sciences, University of Ottawa, Ottawa, Ontario, Canada
Soran Parang
Department of Earth Sciences, University of Ottawa, Ottawa, Ontario, Canada
Lev Tarasov
Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's, Newfoundland, Canada
Konstantin Latychev
SEAKON, Toronto, Canada
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Ryan Love, Lev Tarasov, Heather Andres, Alan Condron, Xu Zhang, and Gerrit Lohmann
EGUsphere, https://doi.org/10.5194/egusphere-2023-2225, https://doi.org/10.5194/egusphere-2023-2225, 2023
Preprint archived
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Freshwater injection into bands across the North Atlantic are a mainstay of climate modelling when investigating topics such as climate change or the role of glacial runoff in the glacial climate system. However, this approach is unrealistic and results in a systematic bias in the climate response to a given flux of freshwater. We evaluate the magnitude of this bias by comparison to two other approaches for introducing freshwater into a coupled climate model setup for glacial conditions.
Ryan Love, Heather J. Andres, Alan Condron, and Lev Tarasov
Clim. Past, 17, 2327–2341, https://doi.org/10.5194/cp-17-2327-2021, https://doi.org/10.5194/cp-17-2327-2021, 2021
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Freshwater, in the form of glacial runoff, is hypothesized to play a critical role in centennial- to millennial-scale climate variability and climate transitions. We track the routing of glaciologically constrained freshwater volumes in glacial ocean simulations. Our simulations capture important generally not well-represented small-scale features (boundary currents, eddies). We show that the dilution of freshwater as it is transported to key climate regions reduces the freshening to 20 %–60 %.
Benoit S. Lecavalier and Lev Tarasov
The Cryosphere, 19, 919–953, https://doi.org/10.5194/tc-19-919-2025, https://doi.org/10.5194/tc-19-919-2025, 2025
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We present the evolution of the Antarctic Ice Sheet (AIS) over the last 200 kyr by means of a history-matching analysis where an updated observational database constrained ~ 10 000 model simulations. During peak glaciation at the Last Glacial Maximum (LGM), the best-fitting sub-ensemble of AIS simulations reached an excess grounded ice volume relative to the present of 9.2 to 26.5 m equivalent sea level relative to the present. The LGM AIS volume can help resolve the LGM missing-ice problem.
Marilena Sophie Geng, Lev Tarasov, and April Sue Dalton
EGUsphere, https://doi.org/10.5194/egusphere-2025-495, https://doi.org/10.5194/egusphere-2025-495, 2025
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We used a fully coupled ice-climate model to simulate the last two glacial inceptions, and compare the ensemble simulated ice sheet evolution to limited geological data. Our results show that Northern Hemisphere ice sheets grew rapidly, sometimes merging in ways not previously assumed and that capturing one glacial inception does not guarantee capturing another. These findings improve our understanding of ice-age dynamics and highlight challenges in predicting past and future climate evolution.
Lev Tarasov, Benoit S. Lecavalier, Kevin Hank, and David Pollard
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2024-175, https://doi.org/10.5194/gmd-2024-175, 2025
Revised manuscript under review for GMD
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We document the glacial system model (GSM), a 3D glaciological ice sheet systems model specifically designed for large ensemble modelling in glacial cycle contexts. The model is distinguished by the breadth of relevant processes represented for this context. This ranges from meltwater surface drainage with proglacial lake formation to state-of-the-art subglacial sediment production/transport/deposition. The other key distinguishing design feature is attention to addressing process uncertainties.
Benoit S. Lecavalier and Lev Tarasov
EGUsphere, https://doi.org/10.5194/egusphere-2024-3268, https://doi.org/10.5194/egusphere-2024-3268, 2024
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To simulate the past evolution of the Antarctic ice sheet (AIS) during past warm and cold periods, a modelling analysis was performed that compared thousands of AIS simulations to a large collection of field observations. As the AIS changes, so does the surface load which leads to crustal deformation, gravitational and sea-level change. The present-day rate of bedrock deformation due to past AIS changes is used with satellite observations to infer AIS changes due to contemporary climate change.
Kevin Hank and Lev Tarasov
Clim. Past, 20, 2499–2524, https://doi.org/10.5194/cp-20-2499-2024, https://doi.org/10.5194/cp-20-2499-2024, 2024
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The ice-rafted debris signature of Heinrich events in marine sedimentary cores is usually attributed to massive ice discharge from the Laurentide Ice Sheet. However, the driving mechanism of this pulsed discharge remains unclear. We compare three previously proposed hypotheses and examine the role of relevant system processes. We find ice stream surge cycling is the most likely mechanism, but its character is sensitive to both the geothermal heat flux and the form of the basal drag law.
Jan Swierczek-Jereczek, Marisa Montoya, Konstantin Latychev, Alexander Robinson, Jorge Alvarez-Solas, and Jerry Mitrovica
Geosci. Model Dev., 17, 5263–5290, https://doi.org/10.5194/gmd-17-5263-2024, https://doi.org/10.5194/gmd-17-5263-2024, 2024
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Ice sheets present a thickness of a few kilometres, leading to a vertical deformation of the crust of up to a kilometre. This process depends on properties of the solid Earth, which can be regionally very different. We propose a model that accounts for this often-ignored heterogeneity and run 100 000 simulation years in minutes. Thus, the evolution of ice sheets is modeled with better accuracy, which is critical for a good mitigation of climate change and, in particular, sea-level rise.
Natasha Valencic, Linda Pan, Konstantin Latychev, Natalya Gomez, Evelyn Powell, and Jerry X. Mitrovica
The Cryosphere, 18, 2969–2978, https://doi.org/10.5194/tc-18-2969-2024, https://doi.org/10.5194/tc-18-2969-2024, 2024
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We quantify the effect of ongoing Antarctic bedrock uplift due to Ice Age or modern ice mass changes on estimates of ice thickness changes obtained from satellite-based ice height measurements. We find that variations in the Ice Age signal introduce an uncertainty in estimates of total Antarctic ice change of up to ~10%. Moreover, the usual assumption that the mapping between modern ice height and thickness changes is uniform systematically underestimates net Antarctic ice volume changes.
Matthew Drew and Lev Tarasov
EGUsphere, https://doi.org/10.5194/egusphere-2024-620, https://doi.org/10.5194/egusphere-2024-620, 2024
Preprint withdrawn
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We model the sediment-ice-climate system over North America for the last 2.58 Myr showing that ice sheets are capable of excavating features the size of the Hudson bay. This work provides a basis for reconstructing past landscapes important to climate modelling efforts, helping us to understand past earth system change.
Brian R. Crow, Lev Tarasov, Michael Schulz, and Matthias Prange
Clim. Past, 20, 281–296, https://doi.org/10.5194/cp-20-281-2024, https://doi.org/10.5194/cp-20-281-2024, 2024
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An abnormally warm period around 400,000 years ago is thought to have resulted in a large melt event for the Greenland Ice Sheet. Using a sequence of climate model simulations connected to an ice model, we estimate a 50 % melt of Greenland compared to today. Importantly, we explore how the exact methodology of connecting the temperatures and precipitation from the climate model to the ice sheet model can influence these results and show that common methods could introduce errors.
Matthew Drew and Lev Tarasov
The Cryosphere, 17, 5391–5415, https://doi.org/10.5194/tc-17-5391-2023, https://doi.org/10.5194/tc-17-5391-2023, 2023
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The interaction of fast-flowing regions of continental ice sheets with their beds governs how quickly they slide and therefore flow. The coupling of fast ice to its bed is controlled by the pressure of meltwater at its base. It is currently poorly understood how the physical details of these hydrologic systems affect ice speedup. Using numerical models we find, surprisingly, that they largely do not, except for the duration of the surge. This suggests that cheap models are sufficient.
Ryan Love, Lev Tarasov, Heather Andres, Alan Condron, Xu Zhang, and Gerrit Lohmann
EGUsphere, https://doi.org/10.5194/egusphere-2023-2225, https://doi.org/10.5194/egusphere-2023-2225, 2023
Preprint archived
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Freshwater injection into bands across the North Atlantic are a mainstay of climate modelling when investigating topics such as climate change or the role of glacial runoff in the glacial climate system. However, this approach is unrealistic and results in a systematic bias in the climate response to a given flux of freshwater. We evaluate the magnitude of this bias by comparison to two other approaches for introducing freshwater into a coupled climate model setup for glacial conditions.
Kevin Hank, Lev Tarasov, and Elisa Mantelli
Geosci. Model Dev., 16, 5627–5652, https://doi.org/10.5194/gmd-16-5627-2023, https://doi.org/10.5194/gmd-16-5627-2023, 2023
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Physically meaningful modeling of geophysical system instabilities is numerically challenging, given the potential effects of purely numerical artifacts. Here we explore the sensitivity of ice stream surge activation to numerical and physical model aspects. We find that surge characteristics exhibit a resolution dependency but converge at higher horizontal grid resolutions and are significantly affected by the incorporation of bed thermal and sub-glacial hydrology models.
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
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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.
Lev Tarasov and Michael Goldstein
EGUsphere, https://doi.org/10.5194/egusphere-2022-1410, https://doi.org/10.5194/egusphere-2022-1410, 2023
Preprint archived
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This overview: 1. Illustrates how current climate and/or ice sheet model-based inferences about the past tend to have little interpretable value about the real world given inadequate accounting of uncertainties. 2. Explains Bayesian inference to a non-statistical community. 3. Sketches out some tractable inferential steps for computationally expensive models in a way that meaningfully accounts for uncertainties. 4. Lays out some steps for the community to move forward.
Lev Tarasov and Michael Goldstein
Clim. Past Discuss., https://doi.org/10.5194/cp-2021-145, https://doi.org/10.5194/cp-2021-145, 2021
Revised manuscript not accepted
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This review: 1. Illustrates how current climate and/or ice sheet model-based inferences about the past tend to have limited interpretable value about the real world given inadequate accounting of uncertainties. 2. Explains Bayesian inference to a non-statistical community. 3. Sketches out tractable Bayesian inference for computationally expensive models in a way that meaningfully accounts for uncertainties. 4. Lays out some steps for the community to move forward.
Ryan Love, Heather J. Andres, Alan Condron, and Lev Tarasov
Clim. Past, 17, 2327–2341, https://doi.org/10.5194/cp-17-2327-2021, https://doi.org/10.5194/cp-17-2327-2021, 2021
Short summary
Short summary
Freshwater, in the form of glacial runoff, is hypothesized to play a critical role in centennial- to millennial-scale climate variability and climate transitions. We track the routing of glaciologically constrained freshwater volumes in glacial ocean simulations. Our simulations capture important generally not well-represented small-scale features (boundary currents, eddies). We show that the dilution of freshwater as it is transported to key climate regions reduces the freshening to 20 %–60 %.
Alan Bartholet, Glenn A. Milne, and Konstantin Latychev
Earth Syst. Dynam., 12, 783–795, https://doi.org/10.5194/esd-12-783-2021, https://doi.org/10.5194/esd-12-783-2021, 2021
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Improving the accuracy of regional sea-level projections is an important aim that will impact estimates of sea-level hazard around the globe. The computation of sea-level fingerprints is a key component of any such projection, and to date these computations have been based on the assumption that elastic deformation accurately describes the solid Earth response on century timescales. We show here that this assumption is inaccurate in some glaciated regions characterized by low mantle viscosity.
Taimaz Bahadory, Lev Tarasov, and Heather Andres
Clim. Past, 17, 397–418, https://doi.org/10.5194/cp-17-397-2021, https://doi.org/10.5194/cp-17-397-2021, 2021
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We present an ensemble of last glacial inception simulations using a fully coupled ice–climate model for the Northern Hemisphere. The ensemble largely captures inferred ice volume changes within proxy uncertainties. Notable features include an ice bridge across Davis Strait and between Greenland and Iceland. Via an equilibrium climate response experiment, we also demonstrate the potential value of fully coupled ice–climate modelling of last glacial inception to constrain future climate change.
Heiko Goelzer, Sophie Nowicki, Anthony Payne, Eric Larour, Helene Seroussi, William H. Lipscomb, Jonathan Gregory, Ayako Abe-Ouchi, Andrew Shepherd, Erika Simon, Cécile Agosta, Patrick Alexander, Andy Aschwanden, Alice Barthel, Reinhard Calov, Christopher Chambers, Youngmin Choi, Joshua Cuzzone, Christophe Dumas, Tamsin Edwards, Denis Felikson, Xavier Fettweis, Nicholas R. Golledge, Ralf Greve, Angelika Humbert, Philippe Huybrechts, Sebastien Le clec'h, Victoria Lee, Gunter Leguy, Chris Little, Daniel P. Lowry, Mathieu Morlighem, Isabel Nias, Aurelien Quiquet, Martin Rückamp, Nicole-Jeanne Schlegel, Donald A. Slater, Robin S. Smith, Fiamma Straneo, Lev Tarasov, Roderik van de Wal, and Michiel van den Broeke
The Cryosphere, 14, 3071–3096, https://doi.org/10.5194/tc-14-3071-2020, https://doi.org/10.5194/tc-14-3071-2020, 2020
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In this paper we use a large ensemble of Greenland ice sheet models forced by six different global climate models to project ice sheet changes and sea-level rise contributions over the 21st century.
The results for two different greenhouse gas concentration scenarios indicate that the Greenland ice sheet will continue to lose mass until 2100, with contributions to sea-level rise of 90 ± 50 mm and 32 ± 17 mm for the high (RCP8.5) and low (RCP2.6) scenario, respectively.
Cited articles
Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X.: TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems, https://www.tensorflow.org/ (last access: January 2022), 2015. a
Afonso, J. C., Salajegheh, F., Szwillus, W., Ebbing, J., and Gaina, C.: A global reference model of the lithosphere and upper mantle from joint inversion and analysis of multiple data sets, Geophys. J. Int., 217, 1602–1628, https://doi.org/10.1093/gji/ggz094, 2019. a, b, c
Auer, L., Boschi, L., Becker, T. W., Nissen-Meyer, T., and Giardini, D.: Savani: A variable resolution whole-mantle model of anisotropic shear velocity variations based on multiple data sets, J. Geophys. Res.-Sol. Ea., 119, 3006–3034, https://doi.org/10.1002/2013jb010773, 2014. a, b
Austermann, J., Mitrovica, J. X., Latychev, K., and Milne, G. A.: Barbados-based estimate of ice volume at Last Glacial Maximum affected by subducted plate, Nat. Geosci., 6, 553–557, https://doi.org/10.1038/ngeo1859, 2013. a
Bagge, M., Klemann, V., Steinberger, B., Latinović, M., and Thomas, M.: Glacial-isostatic adjustment models using geodynamically constrained 3D Earth structures, Geochem. Geophy. Geosy., 22, e2021GC009853, https://doi.org/10.1029/2021GC009853, 2021. a
Baril, A., Garrett, E., Milne, G., Gehrels, W., and Kelley, J.: Postglacial relative sea-level changes in the Gulf of Maine, USA: Database compilation, assessment and modelling, Quaternary Sci. Rev., 306, 108027, https://doi.org/10.1016/j.quascirev.2023.108027, 2023. a, b
Caron, L., Métivier, L., Greff-Lefftz, M., Fleitout, L., and Rouby, H.: Inverting Glacial Isostatic Adjustment signal using Bayesian framework and two linearly relaxing rheologies, Geophys. J. Int., 209, 1126–1147, https://doi.org/10.1093/gji/ggx083, 2017. a, b
Chollet, F.: Deep learning with Python, Simon and Schuster, ISBN 9781617294433, 2021. a
Crawford, O., Al-Attar, D., Tromp, J., Mitrovica, J. X., Austermann, J., and Lau, H. C. P.: Quantifying the sensitivity of post-glacial sea level change to laterally varying viscosity, Geophys. J. Int., 214, 1324–1363, https://doi.org/10.1093/gji/ggy184, 2018. a
Engelhart, S. E. and Horton, B. P.: Holocene sea level database for the Atlantic coast of the United States, Quaternary Sci. Rev., 54, 12–25, https://doi.org/10.1016/j.quascirev.2011.09.013, 2012. a, b, c
Farrell, W. E. and Clark, J. A.: On Postglacial Sea Level, Geophys. J. Roy. Astr. S., 46, 647–667, https://doi.org/10.1111/j.1365-246x.1976.tb01252.x, 1976. a
Gomez, N., Latychev, K., and Pollard, D.: A Coupled Ice Sheet–Sea Level Model Incorporating 3D Earth Structure: Variations in Antarctica during the Last Deglacial Retreat, J. Climate, 31, 4041–4054, https://doi.org/10.1175/jcli-d-17-0352.1, 2018. a
Hijma, M. P., Engelhart, S. E., Törnqvist, T. E., Horton, B. P., Hu, P., and Hill, D. F.: A protocol for a geological sea-level database, in: Handbook of Sea-Level Research, edited by: Shennan, I., Long, A. J., and Horton, B. P., https://doi.org/10.1002/9781118452547.ch34, 2015. a, b
Jospin, L. V., Laga, H., Boussaid, F., Buntine, W., and Bennamoun, M.: Hands-On Bayesian Neural Networks – A Tutorial for Deep Learning Users, IEEE Comput. Intell. M., 17, 29–48, https://doi.org/10.1109/mci.2022.3155327, 2022. a
Karato, S.-i.: Deformation of earth materials, An introduction to the rheology of Solid Earth, 463, ISBN 9780521844048, 2008. a
Kendall, R. A., Mitrovica, J. X., and Milne, G. A.: On post-glacial sea level – II. Numerical formulation and comparative results on spherically symmetric models, Geophys. J. Int., 161, 679–706, https://doi.org/10.1111/j.1365-246x.2005.02553.x, 2005. a
Klemann, V., Ivins, E. R., Martinec, Z., and Wolf, D.: Models of active glacial isostasy roofing warm subduction: Case of the South Patagonian Ice Field, J. Geophys. Res., 112, B09405, https://doi.org/10.1029/2006jb004818, 2007. a
Kuchar, J., Milne, G., and Latychev, K.: The importance of lateral Earth structure for North American glacial isostatic adjustment, Earth Planet. Sc. Lett., 512, 236–245, https://doi.org/10.1016/j.epsl.2019.01.046, 2019. a
Lambeck, K., Rouby, H., Purcell, A., Sun, Y., and Sambridge, M.: Sea level and global ice volumes from the Last Glacial Maximum to the Holocene, P. Natl. Acad. Sci. USA, 111, 15296–15303, https://doi.org/10.1073/pnas.1411762111, 2014. a, b
Lau, H. C. P., Austermann, J., Mitrovica, J. X., Crawford, O., Al‐Attar, D., and Latychev, K.: Inferences of Mantle Viscosity Based on Ice Age Data Sets: The Bias in Radial Viscosity Profiles Due to the Neglect of Laterally Heterogeneous Viscosity Structure, J. Geophys. Res.-Sol. Ea., 123, 7237–7252, https://doi.org/10.1029/2018jb015740, 2018. a
Li, T., Wu, P., Steffen, H., and Wang, H.: In search of laterally heterogeneous viscosity models of glacial isostatic adjustment with the ICE-6G_C global ice history model, Geophys. J. Int., 214, 1191–1205, https://doi.org/10.1093/gji/ggy181, 2018. a, b
Li, T., Wu, P., Wang, H., Steffen, H., Khan, N. S., Engelhart, S. E., Vacchi, M., Shaw, T. A., Peltier, W. R., and Horton, B. P.: Uncertainties of Glacial Isostatic Adjustment Model Predictions in North America Associated With 3D Structure, Geophys. Res. Lett., 47, e2020GL087944, https://doi.org/10.1029/2020gl087944, 2020. a
Li, T., Khan, N. S., Baranskaya, A. V., Shaw, T. A., Peltier, W. R., Stuhne, G. R., Wu, P., and Horton, B. P.: Influence of 3D Earth Structure on Glacial Isostatic Adjustment in the Russian Arctic, J. Geophys. Res.-Sol. Ea., 127, e2021JB023631, https://doi.org/10.1029/2021jb023631, 2022. a, b
Love, R., Milne, G. A., Tarasov, L., Engelhart, S. E., Hijma, M. P., Latychev, K., Horton, B. P., and Törnqvist, T. E.: The contribution of glacial isostatic adjustment to projections of sea‐level change along the Atlantic and Gulf coasts of North America, Earth’s Future, 4, 440–464, https://doi.org/10.1002/2016ef000363, 2016. a, b, c, d, e, f
Love, R., Milne, G. A., Ajourlou, P., Parang, S., Tarasov, L., and Latychev, K.: Supplemental Materials for A Fast Surrogate Model for 3D-Earth Glacial Isostatic Adjustment using Tensorflow (v2.8.0) Artificial Neural Networks, Zenodo [code], https://doi.org/10.5281/zenodo.10045462, 2023a. a
Love, R., Milne, G. A., Ajourlou, P., Parang, S., Tarasov, L., and Latychev, K.: Input Data for A Fast Surrogate Model for 3D-Earth Glacial Isostatic Adjustment using Tensorflow (v2.8.0) Artificial Neural Networks, Zenodo [data set], https://doi.org/10.5281/zenodo.10042047, 2023b. a
Milne, G. A.: Glacial isostatic adjustment, in: Handbook of Sea-Level Research, edited by: Shennan, I., Long, A. J., and Horton, B. P., https://doi.org/10.1002/9781118452547.ch28, 2015. a
Milne, G. A. and Mitrovica, J. X.: Postglacial sea-level change on a rotating Earth, Geophys. J. Int., 133, 1–19, https://doi.org/10.1046/j.1365-246x.1998.1331455.x, 1998. a, b
Mitrovica, J. X. and Milne, G. A.: On post-glacial sea level: I. General theory, Geophys. J. Int., 154, 253–267, https://doi.org/10.1046/j.1365-246x.2003.01942.x, 2003. a, b
Mitrovica, J. X. and Peltier, W. R.: On postglacial geoid subsidence over the equatorial oceans, J. Geophys. Res.-Sol. Ea., 96, 20053–20071, https://doi.org/10.1029/91jb01284, 1991. a
Mitrovica, J. X. and Peltier, W. R.: A comparison of methods for the inversion of viscoelastic relaxation spectra, Geophys. J. Int., 108, 410–414, https://doi.org/10.1111/j.1365-246x.1992.tb04623.x, 1992. a
Mitrovica, J. X., Wahr, J., Matsuyama, I., and Paulson, A.: The rotational stability of an ice-age earth, Geophys. J. Int., 161, 491–506, https://doi.org/10.1111/j.1365-246x.2005.02609.x, 2005. a
Pan, L., Milne, G. A., Latychev, K., Goldberg, S. L., Austermann, J., Hoggard, M. J., and Mitrovica, J. X.: The influence of lateral Earth structure on inferences of global ice volume during the Last Glacial Maximum, Quaternary Sci. Rev., 290, 107644, https://doi.org/10.1016/j.quascirev.2022.107644, 2022. a, b
Paulson, A., Zhong, S., and Wahr, J.: Modelling post-glacial rebound with lateral viscosity variations, Geophys. J. Int., 163, 357–371, https://doi.org/10.1111/j.1365-246x.2005.02645.x, 2005. a
Paulson, A., Zhong, S., and Wahr, J.: Inference of mantle viscosity from GRACE and relative sea level data, Geophys. J. Int., 171, 497–508, https://doi.org/10.1111/j.1365-246x.2007.03556.x, 2007. a
Peltier, W. R.: The impulse response of a Maxwell Earth, Rev. Geophys., 12, 649, https://doi.org/10.1029/rg012i004p00649, 1974. a
Peltier, W. R.: Glacial-Isostatic Adjustment-II. The Inverse Problem, Geophys. J. Roy. Astr. S., 46, 669–705, https://doi.org/10.1111/j.1365-246x.1976.tb01253.x, 1976. a
Peltier, W. R., Argus, D. F., and Drummond, R.: Space geodesy constrains ice age terminal deglaciation: The global ICE6GC (VM5a) model, J. Geophys. Res.-Sol. Ea., 120, 450–487, https://doi.org/10.1002/2014jb011176, 2015. a, b
Powell, E. M., Pan, L., Hoggard, M. J., Latychev, K., Gomez, N., Austermann, J., and Mitrovica, J. X.: The impact of 3-D Earth structure on far-field sea level following interglacial West Antarctic Ice Sheet collapse, Quaternary Sci. Rev., 273, 107256, https://doi.org/10.1016/j.quascirev.2021.107256, 2021. a
Ritsema, J., Deuss, A., van Heijst, H. J., and Woodhouse, J. H.: S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements, Geophys. J. Int., 184, 1223–1236, https://doi.org/10.1111/j.1365-246x.2010.04884.x, 2010. a, b, c
Roy, K. and Peltier, W.: Space-geodetic and water level gauge constraints on continental uplift and tilting over North America: regional convergence of the ICE-6G_C (VM5a/VM6) models, Geophys. J. Int., 210, 1115–1142, https://doi.org/10.1093/gji/ggx156, 2017. a, b, c
Sellevold, R. and Vizcaino, M.: First application of artificial neural networks to estimate 21st century Greenland ice sheet surface melt, Geophys. Res. Lett., 48, e2021GL092449, https://doi.org/10.1029/2021GL092449, 2021. a
Shepherd, A., Ivins, E. R., A, G., Barletta, V. R., Bentley, M. J., Bettadpur, S., Briggs, K. H., Bromwich, D. H., Forsberg, R., Galin, N., Horwath, M., Jacobs, S., Joughin, I., King, M. A., Lenaerts, J. T. M., Li, J., Ligtenberg, S. R. M., Luckman, A., Luthcke, S. B., McMillan, M., Meister, R., Milne, G., Mouginot, J., Muir, A., Nicolas, J. P., Paden, J., Payne, A. J., Pritchard, H., Rignot, E., Rott, H., Sørensen, L. S., Scambos, T. A., Scheuchl, B., Schrama, E. J. O., Smith, B., Sundal, A. V., van Angelen, J. H., van de Berg, W. J., van den Broeke, M. R., Vaughan, D. G., Velicogna, I., Wahr, J., Whitehouse, P. L., Wingham, D. J., Yi, D., Young, D., and Zwally, H. J.: A Reconciled Estimate of Ice-Sheet Mass Balance, Science, 338, 1183–1189, https://doi.org/10.1126/science.1228102, 2012. a
Spada, G.: Glacial Isostatic Adjustment and Contemporary Sea Level Rise: An Overview, 155–187, Springer International Publishing, https://doi.org/10.1007/978-3-319-56490-6_8, 2017. a
Spada, G., Antonioli, A., Cianetti, S., and Giunchi, C.: Glacial isostatic adjustment and relative sea-level changes: the role of lithospheric and upper mantle heterogeneities in a 3-D spherical Earth, Geophys. J. Int., 165, 692–702, https://doi.org/10.1111/j.1365-246x.2006.02969.x, 2006. a, b
Steffen, H. and Kaufmann, G.: Glacial isostatic adjustment of Scandinavia and northwestern Europe and the radial viscosity structure of the Earth’s mantle, Geophys. J. Int., 163, 801–812, https://doi.org/10.1111/j.1365-246x.2005.02740.x, 2005. a, b
Steffen, H., Kaufmann, G., and Wu, P.: Three-dimensional finite-element modeling of the glacial isostatic adjustment in Fennoscandia, Earth Planet. Sc. Lett., 250, 358–375, https://doi.org/10.1016/j.epsl.2006.08.003, 2006. a, b
Steffen, H., Denker, H., and Müller, J.: Glacial isostatic adjustment in Fennoscandia from GRACE data and comparison with geodynamical models, J. Geodyn., 46, 155–164, https://doi.org/10.1016/j.jog.2008.03.002, 2008. a
Tange, O.: GNU Parallel – The Command-Line Power Tool, ;login: The USENIX Magazine, 36, 42–47, http://www.gnu.org/s/parallel (last access: 22 February 2016), 2011. a
Tarasov, L., Dyke, A. S., Neal, R. M., and Peltier, W.: A data-calibrated distribution of deglacial chronologies for the North American ice complex from glaciological modeling, Earth Planet. Sc. Lett., 315–316, 30–40, https://doi.org/10.1016/j.epsl.2011.09.010, 2012. a
TensorFlow Developers: TensorFlow (v2.8.0-rc1), Zenodo [code], https://doi.org/10.5281/zenodo.5898685, 2022. a
Vacchi, M., Engelhart, S. E., Nikitina, D., Ashe, E. L., Peltier, W. R., Roy, K., Kopp, R. E., and Horton, B. P.: Postglacial relative sea-level histories along the eastern Canadian coastline, Quaternary Sci. Rev., 201, 124–146, https://doi.org/10.1016/j.quascirev.2018.09.043, 2018. a, b, c
van Calcar, C. J., van de Wal, R. S. W., Blank, B., de Boer, B., and van der Wal, W.: Simulation of a fully coupled 3D glacial isostatic adjustment – ice sheet model for the Antarctic ice sheet over a glacial cycle, Geosci. Model Dev., 16, 5473–5492, https://doi.org/10.5194/gmd-16-5473-2023, 2023. a
van der Wal, W., Wu, P., Sideris, M. G., and Shum, C.: Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America, J. Geodyn, 46, 144–154, https://doi.org/10.1016/j.jog.2008.03.007, 2008. a
van der Wal, W., Barnhoorn, A., Stocchi, P., Gradmann, S., Wu, P., Drury, M., and Vermeersen, B.: Glacial isostatic adjustment model with composite 3-D Earth rheology for Fennoscandia, Geophys. J. Int., 194, 61–77, https://doi.org/10.1093/gji/ggt099, 2013. a, b, c, d
van der Wal, W., Whitehouse, P. L., and Schrama, E. J.: Effect of GIA models with 3D composite mantle viscosity on GRACE mass balance estimates for Antarctica, Earth Planet. Sc. Lett., 414, 134–143, https://doi.org/10.1016/j.epsl.2015.01.001, 2015. a, b
Wang, H., Wu, P., and van der Wal, W.: Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities, J. Geodyn., 46, 104–117, https://doi.org/10.1016/j.jog.2008.03.003, 2008. a
Wang, H., Jia, L., Steffen, H., Wu, P., Jiang, L., Hsu, H., Xiang, L., Wang, Z., and Hu, B.: Increased water storage in North America and Scandinavia from GRACE gravity data, Nat. Geosci., 6, 38–42, 2013. a
Whitehouse, P., Latychev, K., Milne, G. A., Mitrovica, J. X., and Kendall, R.: Impact of 3-D Earth structure on Fennoscandian glacial isostatic adjustment: Implications for space-geodetic estimates of present-day crustal deformations, Geophys. Res. Lett., 33, L13502, https://doi.org/10.1029/2006gl026568, 2006. a
Whitehouse, P. L.: Glacial isostatic adjustment modelling: historical perspectives, recent advances, and future directions, Earth Surf. Dynam., 6, 401–429, https://doi.org/10.5194/esurf-6-401-2018, 2018. a
Williams, C., Lord, N., Lunt, D., Kennedy-Asser, A., Richards, D., Crucifix, M., Kontula, A., Thorne, M., Valdes, P., Foster, G., and McClymont, E.: The relative role of orbital, CO2 and ice sheet forcing on Pleistocene climate, EGU General Assembly 2023, Vienna, Austria, 24–28 April 2023, EGU23-1048, https://doi.org/10.5194/egusphere-egu23-1048, 2023. a
Wu, P.: Effects of lateral variations in lithospheric thickness and mantle viscosity on glacially induced surface motion in Laurentia, Earth Planet. Sc. Lett., 235, 549–563, https://doi.org/10.1016/j.epsl.2005.04.038, 2005. a
Wu, P. and Peltier, W. R.: Viscous gravitational relaxation, Geophys. J. Int., 70, 435–485, https://doi.org/10.1111/j.1365-246x.1982.tb04976.x, 1982. a
Wu, P., Wang, H., and Steffen, H.: The role of thermal effect on mantle seismic anomalies under Laurentia and Fennoscandia from observations of Glacial Isostatic Adjustment, Geophys. J. Int., 192, 7–17, https://doi.org/10.1093/gji/ggs009, 2013. a
Yousefi, M., Milne, G. A., Love, R., and Tarasov, L.: Glacial isostatic adjustment along the Pacific coast of central North America, Quaternary Sci. Rev., 193, 288–311, https://doi.org/10.1016/j.quascirev.2018.06.017, 2018. a
Yousefi, M., Milne, G. A., and Latychev, K.: Glacial isostatic adjustment of the Pacific Coast of North America: the influence of lateral Earth structure, Geophys. J. Int., 226, 91–113, https://doi.org/10.1093/gji/ggab053, 2021. a, b
Short summary
A relatively recent advance in glacial isostatic adjustment modeling has been the development of models that include 3D Earth structure, as opposed to 1D structure. However, a major limitation is the computational expense. We have developed a method using artificial neural networks to emulate the influence of 3D Earth models to affordably constrain the viscosity parameter space. Our results indicate that the misfits are of a scale such that useful predictions of relative sea level can be made.
A relatively recent advance in glacial isostatic adjustment modeling has been the development of...
