Mesh sensitivity to friction law and sub-shelf melting
Computer models are necessary for understanding and predicting marine ice sheet behaviour. However, there is uncertainty over implementation of physical processes at the ice base, both for grounded and floating glacial ice. Here we implement several sliding relations in a marine ice sheet flow-line model accounting for all stress components and demonstrate that model resolution requirements are strongly dependent on both the choice of basal sliding relation and the spatial distribution of ice shelf basal melting.
Sliding relations that reduce the magnitude of the step change in basal drag from grounded ice to floating ice (where basal drag is set to zero) show reduced dependence on resolution compared to a commonly used relation, in which basal drag is purely a power law function of basal ice velocity. Sliding relations in which basal drag goes smoothly to zero as the grounding line is approached from inland (due to a physically motivated incorporation of effective pressure at the bed) provide further reduction in resolution dependence.
A similar issue is found with the imposition of basal melt under the floating part of the ice shelf: melt parameterisations that reduce the abruptness of change in basal melting from grounded ice (where basal melt is set to zero) to floating ice provide improved convergence with resolution compared to parameterisations in which high melt occurs adjacent to the grounding line.
Thus physical processes, such as sub-glacial outflow (which could cause high melt near the grounding line), impact on capability to simulate marine ice sheets. If there exists an abrupt change across the grounding line in either basal drag or basal melting, then high resolution will be required to solve the problem. However, the plausible combination of a physical dependency of basal drag on effective pressure, and the possibility of low ice shelf basal melt rates next to the grounding line, may mean that some marine ice sheet systems can be reliably simulated at a coarser resolution than currently thought necessary.
More information: Gladstone, R.M., R.C. Warner, B.K. Galton-Fenzi, O. Gagliardini, T. Zwinger and R. Greve, 2017. Marine ice sheet model performance depends on basal sliding physics and sub-shelf melting, The Cryosphere, 11, 319-329, doi:10.5194/tc-11-319-2017.
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We present a comparison of the numerics and simulation results for two "full" Stokes ice sheet models, FELIX-S (Leng et al. 2012) and Elmer/Ice (Gagliardini et al. 2013). The models are applied to the Marine Ice Sheet Model Intercomparison Project for plan view models (MISMIP3d). For the diagnostic experiment (P75D) the two models give similar results ( < 2 % difference with respect to along-flow velocities) when using identical geometries and computational meshes, which we interpret as an indication of inherent consistencies and similarities between the two models. For the standard (Stnd), P75S, and P75R prognostic experiments, we find that FELIX-S (Elmer/Ice) grounding lines are relatively more retreated (advanced), results that are consistent with minor differences observed in the diagnostic experiment results and that we show to be due to different choices in the implementation of basal boundary conditions in the two models. While we are not able to argue for the relative favorability of either implementation, we do show that these differences decrease with increasing horizontal (i.e., both along- and across-flow) grid resolution and that grounding-line positions for FELIX-S and Elmer/Ice converge to within the estimated truncation error for Elmer/Ice. Stokes model solutions are often treated as an accuracy metric in model intercomparison experiments, but computational cost may not always allow for the use of model resolution within the regime of asymptotic convergence. In this case, we propose that an alternative estimate for the uncertainty in the grounding-line position is the span of grounding-line positions predicted by multiple Stokes models.
Surface mass balance data from the regional climate model HIRHAM5 was used to force a transient Elmer/Ice as well as a lower order model (BISICLES) simulation of Austfonna ice cap (Svalbard) from pre-surge stage at 1995 to December 2011. Basal sliding distributions at the bounding dates were inferred from satellite data and different types of temporal changes between these limiting states (step functions, linear evolution) were tested. Beyond 2011, the authors tried to deduce the evolution of the basal friction coefficients from the two inverted states, finding that the 2012 surge is a result of basal processes that are yet not represented in the model. The picture shows the inverted surface velocities for Elmer/Ice (left) and BISICLES (right) and their difference (middle).
