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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The ocean load in glacial isostatic adjustment (GIA) modelling is represented by the so-called sea level equation (SLE). The SLE describes the mass redistribution of water between ice sheets and oceans on a deforming Earth. Despite various teams independently investigating GIA, there has been no systematic intercomparison among the numerical solvers of the SLE through which the methods may be validated. The goal of this paper is to present a series of synthetic examples designed for testing and comparing the numerical implementations of the SLE in GIA modelling. The 10 numerical codes tested combine various temporal and spatial parametrizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parametrize the GIA-related field variables spatially. The surface ice-water load and solid Earth's topography are represented spatially either on an equiangular grid, a Gauss-Legendre or an equiarea grid with icosahedron-shaped spherical pixels. Comparisons aremade in a series of five benchmark examples with an increasing degree of complexity. Due to the complexity of the SLE, there is no analytical solution to it. The accuracy of the numerical implementations is therefore assessed by the differences of the individual solutions with respect to a reference solution. While the benchmark study does not result in GIA predictions for a realistic loading scenario, we establish a set of agreed-upon results that can be extended in the future by including more complex case studies, such as solutions with realistic loading scenarios, the rotational feedback in the linear-momentum equation, and by considering a 3-D viscosity structure of the Earth's mantle. The test computations performed so far show very good agreement between the individual results and their ability to capture the main features of sea-surface variation and the surface vertical displacement. The differences found can often be attributed to the different approximations inherent in the various algorithms. This shows the accuracy that can be expected from different implementations of the SLE, which helps to assess differences noted in the literature between predictions for realistic loading cases.

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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