A viscoelastic solid earth deformation model to Elmer/Ice
In a recent development funded by the University of Tasmania, Hobart, Australia, the linear Elasticity solver in Elmer has been modified to account for Maxwell type of viscoelastic materials. Furthermore, the most simplest implementation of a a viscoelastic solid earth model, neglecting sphericity and self-gravitation has been set up in its weak form. In contrary to for GIA adapted commercial codes, this means that Elmer does not need special treatment of boundaries between layers of different density, which makes the setup of a layered solid earth model much easier and - since Elmer is open source - independent from any license fees that would be imposed by commercial codes. The paper mentioned below itself does not include results from Elmer/Ice, but we would like to utilize this news-feed to point out the possibility to apply the new module, Elmer/Earth, in combination with Elmer/Ice, as the transfer of ice-loads and deformations are easily achieved by the common code-basis Elmer. Imposed by the earlier mentioned simplifications, computations should be confined to regional studies. In future we might think of including missing components to deploy this model on continental scale ice-sheets.
Read more:
Zwinger, T., Nield, G. A., Ruokolainen, J., and King, M. A., 2020. A new open-source viscoelastic solid earth deformation module implemented in Elmer (v8.4), Geosci. Model Dev., 14, 1155–1164, doi:10.5194/gmd-13-1155-2020
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Marine-based sectors of the Antarctic Ice Sheet are increasingly contributing to sea level rise. The basal conditions exert an important control on the ice dynamics and can be propitious to instabilities in the grounding line position. Because the force balance is non-inertial, most ice flow models are now equipped with time-independent inverse methods to constrain the basal conditions from observed surface velocities. However, transient simulations starting from this initial state usually suffer from inconsistencies and are not able to reproduce observed trends. Here, using a synthetic flow line experiment, we assess the performance of an ensemble Kalman filter for the assimilation of transient observations of surface elevation and velocities in a marine ice sheet model. The model solves the shallow shelf equation for the force balance and the continuity equation for ice thickness evolution. The position of the grounding line is determined by the floatation criterion. The filter analysis estimates both the state of the model, represented by the surface elevation, and the basal conditions, with the simultaneous inversion of the basal friction and topography. The idealised experiment reproduces a marine ice sheet that is in the early stage of an unstable retreat. Using observation frequencies and uncertainties consistent with current observing systems, we find that the filter allows the accurate recovery of both the basal friction and topography after few assimilation cycles with relatively small ensemble sizes. In addition it is found that assimilating the surface observations has a positive impact on constraining the evolution of the grounding line during the assimilation window. Using the initialised state to perform century-scale forecast simulations, we show that grounding line retreat rates are in agreement with the reference; however remaining uncertainties in the basal conditions may lead to significant delays in the initiation of the unstable retreat. These results are encouraging for the application to real glacial systems.
The friction coefficient and the base topography of a stationary and a dynamic ice sheet are perturbed in two models for the ice: the full Stokes equations and the shallow shelf approximation. The sensitivity to the perturbations of the velocity and the height at the surface is quantified by solving the adjoint equations of the stress and the height equations providing weights for the perturbed data. The adjoint equations are solved numerically and the sensitivity is computed in several examples in two dimensions. A transfer matrix couples the perturbations at the base with the perturbations at the top. Comparisons are made with analytical solutions to simplified problems. The sensitivity to perturbations depends on their wavelengths and the distance to the grounding line. A perturbation in the topography has a direct effect at the ice surface above it, while a change in the friction coefficient is less visible there.
