Modelling sea-level fingerprints of glaciated regions with low mantle viscosity

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.

A new open-source visco-elastic Earth deformation module implemented in Elmer (v8.4)

We present a new, open source visco-elastic Earth-deformation model, Elmer/Earth. Using the multi-physics Finite Element package Elmer, a model to compute visco-elastic material deformation has been implemented into the existing linear elasticity solver routine. Unlike approaches often implemented in engineering codes, our solver accounts for the restoring force of buoyancy within a system of layers with depth-varying density. It does this by directly integrating the solution of the system rather than by applying stress-jump conditions in the form of Winkler foundations on inter-layer boundaries, as is usually needed when solving the minimisation problem given by the stress-divergence in commercial codes. We benchmarked the new model with results from a commercial Finite Element engineering package (ABAQUS, v2018) and another open-source code that uses visco-elastic Normal Mode theory, TABOO, using a flat-earth setup loaded by a cylindrical disc of 100 km diameter and 100 m height of ice density. Evaluating the differences of predicted surface deformation at the centre of the load and two distinctive distances (100 km and 200 km), average deviations of 7 cm and 2.7 cm of Elmer/Earth results to ABAQUS and TABOO, respectively, were observed. In view of more than 100 cm maximum vertical deformation and the different numerical methods and parameters, these are very encouraging results. Elmer is set up as a highly scalable parallel code and distributed under the (L)GPL license, meaning that large scale computations can be made without any licensing restrictions. Scaling figures presented in this paper show good parallel performance of the new model. Additionally, the high fidelity ice sheet code Elmer/Ice utilises the same source-base of Elmer and thereby the new model opens the way to undertaking high-resolution coupled ice-flow - Earth deformation simulations, which are required for robust projections of future sea-level rise and glacial isostatic adjustment.