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The vast majority of ice-sheet modelling studies rely on simplified representations of the glacial isostatic adjustment (GIA), which, among other limitations, do not account for lateral variations in the lithospheric thickness and upper-mantle viscosity. In studies of the last glacial cycle using 3D GIA models, this has however been shown to have major impacts on the dynamics of marine-based sectors of Antarctica, which are likely to be the greatest contributors to sea-level rise in the coming centuries. This gap in comprehensiveness is explained by the fact that 3D GIA models are computationally expensive, rarely open-source and require a complex coupling scheme. To close this gap between "best" and "tractable" GIA models, we propose FastIsostasy here, a regional GIA model capturing lateral variations in the lithospheric thickness and mantle viscosity. By means of fast Fourier transforms and a hybrid collocation scheme to solve its underlying partial differential equation, FastIsostasy can simulate 100 000 years of high-resolution bedrock displacement in only minutes of single-CPU computation, including the changes in sea-surface height due to mass redistribution. Despite its 2D grid, FastIsostasy parameterises the depth-dependent viscosity and therefore represents the depth dimension to a certain extent. FastIsostasy is benchmarked here against analytical, as well as 1D and 3D numerical solutions, and shows good agreement with them. For a simulation of the last glacial cycle, its mean and maximal error over time and space respectively yield less than 5 % and 16 % compared to a 3D GIA model over the regional solution domain. FastIsostasy is open-source, is documented with many examples and provides a straightforward interface for coupling to an ice-sheet model. The model is benchmarked here based on its implementation in Julia, while a Fortran version is also provided to allow for compatibility with most existing ice-sheet models. The Julia version provides additional features, including a vast library of adaptive time-stepping methods and GPU support. [ABSTRACT FROM AUTHOR]

Determining recent Antarctic ice volume changes from satellite altimeter measurements of ice surface height requires a correction for contemporaneous vertical crustal deformation. This correction must consider two main sources of crustal deformation: (1) ongoing glacial isostatic adjustment (GIA), that is, the deformational, gravitational, and rotational response to Late Pleistocene and Holocene ice and ocean mass changes and (2) modern ice mass change. In this study, we seek to quantify the uncertainties associated with each of these corrections. Corrections of ice surface height changes for correction 1 have generally involved the adoption of global models of GIA defined by some preferred combination of ice history and mantle viscoelastic structure. We have computed the GIA correction generated from a coupled ice sheet–sea level model and a realistic Earth model incorporating three-dimensional viscoelastic structure. Integrating the difference between this correction and those from recent GIA analyses widely adopted in the literature yields an uncertainty in total present-day ice volume change equivalent to approximately 10 % of Antarctic ice mass loss inferred for the period 2010–2020. This reinforces earlier work indicating that ice histories characterized by relatively high excess ice volume at the Last Glacial Maximum may be introducing a significant error in estimates of modern melt rates. Regarding correction 2, a spatially invariant scaling has commonly been used to convert GIA-corrected ice surface height changes obtained from satellite altimetry to ice volume estimates. We adopt modeling results based on a projection of Antarctic ice mass change over the period 2015–2055 to demonstrate a spatial variability in the scaling of up to 10 % across the ice sheet. Furthermore, using these calculations, we find a systematic error of ∼ 3 % in the projected net ice volume change, with most of the difference arising in areas of West Antarctica above mantle zones of low viscosity. [ABSTRACT FROM AUTHOR]

The vast majority of ice-sheet modelling studies rely on simplified representations of the Glacial Isostatic Adjustment (GIA), which, among other limitations, do not account for lateral variations of the lithospheric thickness and upper-mantle viscosity. In studies using 3D GIA models, this has however been shown to have major impacts on the dynamics of marine-based sectors of Antarctica, which are likely to be the greatest contributors to sea-level rise in the coming centuries. This gap in comprehensiveness is explained by the fact that 3D GIA models are computationally expensive, seldomly open-source and require the implementation of an iterative coupling scheme to converge with the history of the ice-sheet model. To close this gap between 'best' and 'tractable' GIA models, we here propose FastIsostasy, a regional GIA model capturing lateral variations of the lithospheric thickness and mantle viscosity. By means of Fast-Fourier transforms and a hybrid collocation scheme to solve its underlying partial differential equation, FastIsostasy can simulate 100,000 years of high-resolution bedrock displacement in only minutes of single-CPU computation, including the changes in sea-surface height due to mass redistribution. Despite its 2D grid, FastIsostasy parametrises the depth-dependent viscosity in a physically meaningful way and therefore represents the depth dimension to a certain extent. FastIsostasy is here benchmarked against analytical, 1D and 3D GIA solutions and shows very good agreement with them. It is fully open-source, documented with many examples and provides a straight-forward interface for coupling to an ice-sheet model. The model is benchmarked here based on its implementation in Julia, while a Fortran version is also provided to allow for compatibility with most existing ice-sheet models. The Julia version provides additional features, including a vast library of time-stepping methods and GPU support. [ABSTRACT FROM AUTHOR]

Determining recent Antarctic ice volume changes from satellite altimeter measurements of ice height requires a correction for contemporaneous vertical crustal deformation. This correction must consider two main sources of crustal deformation: (1) ongoing glacial isostatic adjustment (GIA), that is, the deformational, gravitational and rotational response to late Pleistocene and Holocene ice and ocean mass changes; and (2) modern ice mass flux. In this study, we seek to quantify the uncertainties associated with each of these corrections. Corrections of ice height changes for (1) have generally involved the adoption of global models of GIA defined by some preferred combination of ice history and mantle viscoelastic structure. We have computed the GIA correction generated from a coupled ice sheet – sea level model and a realistic earth model incorporating three-dimensional viscoelastic structure. Integrating the difference between this correction and those from recent GIA analyses widely adopted in the literature yields an uncertainty in total present-day ice volume change equivalent to approximately 10 % of Antarctic ice mass loss inferred for the previous decade. This reinforces earlier work indicating that ice histories characterized by relatively high excess ice volume at the Last Glacial Maximum may be introducing significant error in estimates of modern melt rates. Regarding correction (2), a spatially invariant scaling has commonly been used to convert GIA-corrected ice height changes obtained from satellite altimetry into ice volume estimates. We adopt modeling results based on a projection of Antarctic ice mass flux over the next 40 years to demonstrate a spatial variability in the scaling of up to 10 % across the ice sheet. Furthermore, using these calculations, we find an error in the projected net ice volume change of up to 4.5 mm GMSL equivalent forty years after present, with most of the difference arising in areas of West Antarctica above mantle zones of low viscosity. [ABSTRACT FROM AUTHOR]

Models of glacial isostatic adjustment (GIA) play a central role in the interpretation of various geologic and geodetic data to understand and simulate past and future changes in ice sheets and sea level, and infer rheological properties of the deep Earth. A relatively recent advance has been the development of models that include 3D Earth structure, as opposed to 1D, spherically symmetric structure. However, a major limitation in employing 3D GIA models is their high computational expense. As such, we have developed a method using artificial neural networks (ANNs) and the Tensorflow library to emulate the influence of 3D Earth models with the goal of more affordably constraining the parameter space of these models: specifically the radial (1D) viscosity profile upon which the lateral variations are added. This study provides an initial "proof of concept" assessment of using ANNs to emulate the influence of lateral Earth structure on GIA model output. Our goal is to test whether the fast surrogate model can accurately predict the difference in these outputs (i.e., RSL and uplift rates) for the 3D case relative to the SS case. If so, the surrogate model can be used with a computationally efficient SS (Earth) GIA model to generate output that reproduces output from a 3D (Earth) GIA model. Evaluation of the surrogate model performance for deglacial RSL indicates that it is able to provide useful estimates of this field throughout the parameter space when trained on only ≈ 15 % (≈ 50) of the parameter vectors considered (330 in total). Our results indicate that the ANN:model misfits, while not negligible, are of a scale such that useful predictions of deglacial RSL changes can be made. We applied the surrogate model in a model:data comparison exercise using RSL data distributed along the North American coasts from the Canadian Arctic to the US Gulf coast. We find that the surrogate model is able to successfully reproduce the data:model misfit values such that the region of minimum misfit either overlaps the 3D GIA model results, or is within two increments in the parameter space. The surrogate model can, therefore, be used to accurately explore this aspect of the 3D Earth model parameter space. While the 3D Earth models can outperform the SS Earth models for some regional subsets of the RSL data set, the SS Earth models still produce better fits overall. In summary, this work demonstrates the utility of machine learning in 3D Earth GIA modelling and so future work to expand on this analysis is warranted. [ABSTRACT FROM AUTHOR]

A large ensemble of ice sheet projections to the end of the 21st century have been compiled within community-based initiatives. These ensembles allow for assessment of uncertainties in projections associated with climate forcing and a wide range of parameters governing ice sheet and shelf dynamics, including ice-ocean interactions. Herein, we compute geographically variable sea level 'fingerprints' associated with ∼320 simulations of polar ice sheet projections included in the Ice Sheet Model Intercomparison Project for CMIP6 and ∼180 projections of glacier mass changes from the Glacier Model Intercomparison Project. We find a strong correlation (coefficient > 0.97) between all fingerprints of Greenland Ice Sheet projections when considering a global region outside the near field of the ice sheet. Consistency in the fingerprints for the Antarctic Ice Sheet (AIS) projections is much weaker, though correlation coefficients > 0.80 were found for all projections with global mean sea level (GMSL) greater than 10 cm. The far-field variability in the fingerprints associated with the AIS is due in large part to the sea level change driven by Earth rotation changes. The size and position of the AIS on the south pole makes the rotational component of the sea level fingerprint highly sensitive to the geometry of the ice mass flux, a geometry that becomes more consistent as the GMSL associated with the ice sheet projection increases. Finally, the fingerprints of glacier mass flux show an intermediate level of consistency, with contributions from Antarctic glaciers being the primary driver of decorrelation. [ABSTRACT FROM AUTHOR]

It is generally agreed that the Last Interglacial (LIG; ∼130–115 ka) was a time when global average temperatures and global mean sea level were higher than they are today. However, the exact timing, magnitude and spatial pattern of ice melt is much debated. One difficulty in extracting past global mean sea level from local observations is that their elevations need to be corrected for glacial isostatic adjustment (GIA), which requires knowledge of Earth's internal viscoelastic structure. While this structure is generally assumed to be radially symmetric, evidence from seismology, geodynamics and mineral physics indicates that large lateral variations in viscosity exist within the mantle. In this study, we construct a new model of Earth's internal structure by converting shear wave speed into viscosity using parametrizations from mineral physics experiments and geodynamic constraints on Earth's thermal structure. We use this 3-D Earth structure, which includes both variations in lithospheric thickness and lateral variations in viscosity, to calculate the first 3-D GIA prediction for LIG sea level. We find that the difference between predictions with and without lateral Earth structure can be metres to 10s of metres in the near field of former ice sheets, and up to a few metres in their far field. We demonstrate how forebulge dynamics and continental levering are affected by laterally varying Earth structure, with a particular focus on those sites with prominent LIG sea level records. Results from four 3-D GIA calculations show that accounting for lateral structure can act to increase local sea level by up to ∼1.5 m at the Seychelles and minimally decrease it in Western Australia. We acknowledge that this result is only based on a few simulations, but if robust, this shift brings estimates of global mean sea level from these two sites into closer agreement with each other. We further demonstrate that simulations with a suitable radial viscosity profile can be used to locally approximate the 3-D GIA result, but that these radial profiles cannot be found by simply averaging viscosity below the sea level indicator site. [ABSTRACT FROM AUTHOR]

Sea-level fingerprints define the spatially varying relative sea-level response to changes in grounded ice distribution. These fingerprints are a key component in generating regional sea-level projections. Calculation of these fingerprints is commonly based on the assumption that the isostatic response of the Earth is dominantly elastic on century time scales. While this assumption is accurate for regions underlain my mantle material with viscosity close to that of global average estimates, recent work focusing on the Antarctic region has shown that this assumption can led to significant error when the viscosity departs significantly from typical average values. Here we test this assumption for fingerprints associated with glaciers and ice caps. We compare output from a (1D) elastic Earth model to that of a 3D viscoelastic model which includes low viscosity mantle in three glaciated regions: Alaska, southwestern Canada and the southern Andes (Randolph Glacier Inventory (RGI) regions 1, 2 & 17, respectively). This comparison indicates that the error incurred by ignoring the non-elastic response is generally less than 1 cm over the 21st century but can reach magnitudes of up to several 10s of centimetres in low viscosity areas. This error can have large spatial gradients where crustal uplift in ice covered (or previously ice covered) areas changes into subsidence when moving away from the loading centres to areas peripheral to the mass loss. The existence of these large gradients indicates the need for loading models with high spatial resolution to accurately simulate sea-level fingerprints in these regions. We conclude that sea-level projections for Alaska, southwestern Canada and the southern Andes should not be based on elastic Earth models. [ABSTRACT FROM AUTHOR]