Glacial isostatic adjustment (GIA) has a stabilizing effect on the evolution of the Antarctic ice sheet by reducing the grounding line migration following ice melt. The timescale and strength of this feedback depends on the spatially varying viscosity of the Earth's mantle. Most studies assume a relatively long and laterally homogenous response time of the bedrock. However, the mantle viscosity is spatially variable, with a high mantle viscosity beneath East Antarctica and a low mantle viscosity beneath West Antarctica. For this study, we have developed a new method to couple a 3D GIA model and an ice sheet model to study the interaction between the solid Earth and the Antarctic ice sheet during the last glacial cycle. With this method, the ice sheet model and GIA model exchange ice thickness and bedrock elevation during a fully coupled transient experiment. The feedback effect is taken into account with a high temporal resolution, where the coupling time steps between the ice sheet and GIA model are 5000 years over the glaciation phase and vary between 500 and 1000 years over the deglaciation phase of the last glacial cycle. During each coupling time step, the bedrock elevation is adjusted at every ice sheet model time step, and the deformation is computed for a linearly changing ice load. We applied the method using the ice sheet model ANICE and a 3D GIA finite element model. We used results from a regional seismic model for Antarctica embedded in the global seismic model SMEAN2 to determine the patterns in the mantle viscosity. The results of simulations over the last glacial cycle show that differences in mantle viscosity of an order of magnitude can lead to differences in the grounding line position up to 700gkm and to differences in ice thickness of the order of 2gkm for the present day near the Ross Embayment. These results underline and quantify the importance of including local GIA feedback effects in ice sheet models when simulating the Antarctic ice sheet evolution over the last glacial cycle.

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We present a finite-element model of post-seismic solid Earth deformation built in the software package Abaqus (version 2018). The model is global and spherical, includes self-gravitation and is built for the purpose of calculating post-seismic deformation in the far field (1/4300gkm) of major earthquakes. An earthquake is simulated by prescribing slip on a fault plane in the mesh and the model relaxes under the resulting change in stress. Both linear Maxwell and biviscous (Burgers) rheological models have been implemented and the model can be easily adapted to include different rheological models and lateral variations in Earth structure, a particular advantage over existing models. We benchmark the model against an analytical coseismic solution and an existing open-source post-seismic model code, demonstrating good agreement for all fault geometries tested. Due to the inclusion of self-gravity, the model has the potential for predicting deformation in response to multiple sources of stress change, for example, changing ice thickness in tectonically active regions.

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The Earth’s surface and interior deform due to a changing load of the Antarctic Ice Sheet (AIS) during the last glacial cycle, called Glacial Isostatic Adjustment (GIA). This deformation changes the surface height of the ice sheet and indirectly the groundling line position. These changes in surface height and grounding line position influence the evolution of the AIS and consequently, again the load on the Earth’s surface. As a result, GIA operates as a negative feedback loop and could stabilize the evolution of the AIS. This feedback maybe particularly relevant for relatively low viscosities of the mantle in West Antarctica which lead to a relatively fast response time of the bedrock due to changes in the West Antarctic Ice Sheet loading. Most studies capture this process by ignoring lateral variations in the viscosity of the mantle and the stabilizing GIA feedback loop. Here we present a new method to couple an ice sheet model to a GIA model at a variable timestep in the order of a thousand years. Several experiments have been done using different radial and lateral varying rheologies for simulations of the last glacial cycle. It is shown that the effect of including lateral variations and accounting for the stabilizing GIA feedback is up to 80 kilometers for the grounding line position and 400 meters for the ice thickness. The largest differences are observed close to the grounding line of the Ronne ice shelf and at several locations in East Antarctica. The total ice volume of the AIS increases by 0.5 percent over 5000 years when including the 3D GIA feedback loops in the coupled model. These results quantify the local importance of including GIA feedback effects in ice dynamic models when simulating the Antarctic Ice Sheet evolution over the full glacial cycle. @en

Accurate glacial isostatic adjustment (GIA) models are required for correcting measurements of mass change in Antarctica and for improving knowledge of the sub-surface, especially in areas of large current ice loss such as the Amundsen Sea Embayment (ASE). Regionally, seismic and gravity data suggests lateral differences in viscosity (3D). Furthermore, mantle flow laws allow for a stress-dependent effective viscosity which changes over time (3D-s). In this study we investigate whether models with 3D/3D-s have significant effects on the uplift in the region. We use a finite element model with composite rheology consisting of diffusion and dislocation creep, forced by an ice deglaciation model starting in 1900. We use its uplift predictions as synthetic observations to test the performance of 1D model inversion in the presence of viscosity variations. Stress-dependent rheology results in lower viscosity beneath the load and a more localized uplift pattern. We demonstrate that the background stress from earlier ice load changes can both increase or decrease the influence of stress-induced effective viscosity changes. For the ASE, fitting 1D models to 3D model uplift results in a best fitting model with viscosity that represents the average of a large area, while for 3D-s rheology, local viscosity is more influential. 1D models are statistically indistinguishable from 3D/3D-s viscosity with current GPS stations. However, 3D and 3D-s models should be taken into account when accurate uplift and gravity rate patterns are needed, as uplift can differ up to 45% compared to 1D models in between existing GPS stations.

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Over glacial-interglacial cycles, the evolution of an ice sheet is influenced by Glacial isostatic adjustment (GIA) via two negative feedback loops. Firstly, vertical bedrock deformation due to a changing ice load alters ice-sheet surface elevation. For example, an increasing ice load leads to a lower bedrock elevation that lowers ice-sheet surface elevation. This will increase surface melting of the ice sheet, following an increase of atmospheric temperature at lower elevations. Secondly, bedrock deformation will change the height of the grounding line of the ice sheet. For example, a lowering bedrock height following ice-sheet advance increases the melt due to ocean water that in turn leads to a retreat of the grounding line and a slow-down of ice-sheet advance. GIA is mainly determined by the viscosity of the interior of the solid Earth which is radially and laterally varying. Underneath the Antarctic ice sheet, there are relatively low viscosities in West Antarctica and higher viscosities in East Antarctica, in turn affecting the response time of the above mentioned feedbacks. However, most ice-dynamical models do not consider the lateral variations of the viscosity in the GIA feedback loops when simulating the evolution of the Antarctic ice sheet. The method developed by Gomez et al. (2018) includes the feedback between GIA and ice-sheet evolution and alternates between simulations of the two models where each simulation covers the full time period. We presents a different method to couple ANICE, a 3-D ice-sheet model, to a 3-D GIA finite element model. In this method the model computations alternates between the icesheet and GIA model until convergence of the result occurs at each timestep. We simulate the evolution of the Antarctic ice sheet from 120 000 years ago to the present. The results of the coupled simulation will be discussed and compared to results of the uncoupled ice-sheet model (using an ELRA GIA model) and the method developed by Gomez et al. (2018). @en

Differences in predictions of Glacial Isostatic Adjustment (GIA) for Antarctica persist due to uncertainties in deglacial history and Earth rheology. The Earth models adopted in many GIA studies are defined by parameters that vary in the radial direction only and represent a global average Earth structure (referred to as 1-D Earth models). Oversimplifying the actual Earth structure leads to bias in model predictions in regions where Earth parameters differ significantly from the global average, such as West Antarctica. We investigate the impact of lateral variations in lithospheric thickness on GIA in Antarctica by carrying out two experiments that use different rheological approaches to define 3-D Earth models that include spatial variations in lithospheric thickness. The first experiment defines an elastic lithosphere with spatial variations in thickness inferred from seismic studies.We compare the results from this 3-D model with results derived from a 1-D Earth model that has a uniform lithospheric thickness defined as the average of the 3-D lithospheric thickness. Irrespective of the deglacial history and sublithospheric mantle viscosity, we find higher gradients of present-day uplift rates (i.e. higher amplitude and shorter wavelength) in West Antarctica when using the 3-D models, due to the thinner-than-1-D-average lithosphere prevalent in this region. The second experiment uses seismically inferred temperature as an input to a power-law rheology, thereby allowing the lithosphere to have a viscosity structure. Modelling the lithosphere with a powerlaw rheology results in a behaviour that is equivalent to a thinner lithospheremodel, and it leads to higher amplitude and shorter wavelength deformation compared with the first experiment. We conclude that neglecting spatial variations in lithospheric thickness in GIA models will result in predictions of peak uplift and subsidence that are biased low in West Antarctica. This has important implications for ice-sheet modelling studies as the steeper gradients of uplift predicted from the more realistic 3-D model may promote stability in marine-grounded regions of West Antarctica. Including lateral variations in lithospheric thickness, at least to the level of considering West and East Antarctica separately, is important for capturing shortwavelength deformation and it has the potential to provide a better fit to Global Positioning System observations as well as an improved GIA correction for the Gravity Recovery and Climate Experiment data.

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In the ESA Support to Science Element GOCE+Antarctica, we study the influence of the lithospheric structure on estimates of GIA. From recent geophysical, especially seismological, studies new insights on the deep structure of the Antarctic continents are available. However, the seismological models differ in resolution and do not provide a consistent image of the lithosphere. This is critical in analysing the feedback between the lithosphere and glacial loading or unloading. To reduce such ambiguities, we combine the latest seismological models with gravity gradient data derived from the GOCE satellite mission. The gradients are in particular sensitive to the geometry and density variations of the main lithospheric layers, i.e. ice and sediment thickness, the Moho depth and the temperature and composition of the upper mantle. Initial results indicate that differences exist in the mode of compensation for West and East Antarctica related to different mantle properties. The impact of an improved lithospheric model on GIA modelling is estimated by testing the sensitivity to the new temperature and density distribution and by comparing 1D and 3D viscosity models, especially in areas of low viscosity as in the Amundsen Sea sector. @en