Improved basal drag of the West Antarctic Ice Sheet from L-curve analysis of inverse models utilizing subglacial hydrology simulations

Abstract. The West Antarctic Ice Sheet (WAIS) is the focus of current research due to its susceptibility to collapse, which could potentially contribute to rising sea levels. To accurately predict future glacier evolution, precise ice sheet models are essential with regard to suitable approximations of physical behavior to the real system and appropriate input values, as well as computing power. The ice discharge of outlet glaciers into the ocean is one key factor here, primarily caused by basal sliding of ice. Since we cannot directly measure basal properties on a large scale, inverse models can be used to infer the basal drag coefficient by minimizing a cost function that depends on a velocity misfit and a regularization term.

We conduct basal drag inversions and perform L-curve analyses to find the optimal trade-off between the cost function terms, ending up with smooth L-curves. Additionally, the domain L-curve is break down to eight subdomains of the study area in order to reveal how well the inverse method performs in different glaciological settings. It reveals that Pine Island Glacier being the best area and slow-flowing areas such as Roosevelt Island being among the worst in terms of the L-curve behavior for the basal drag inversion. This highlights the importance of performing a subdomain L-curve analysis, whenever an inversion for a larger domain is calculated to discover problematic regions. Comprehensive basal drag inversion experiments allow us to test the dependence of the L-curve and basal drag results on the non-linearity of sliding as well as on the inclusion of subglacial effective pressure in the friction law. The analysis suggest that non-linear friction laws are preferable to linear sliding because of reduced variance of the overall inferred friction coefficient, faster convergence, as well as steeper L-curves leading to a more accurate choice of weight for the regularization term. We show that a Budd-type friction law that incorporates effective pressure from a subglacial hydrology model rather than a simple geometry-based approximation achieves an improved performance in our inverse model. Further comparison reveals that the effective pressure from the hydrology model accounts for a larger part of spatial structure of the basal drag coefficient than the parameterized effective pressure. Allowing the inverted drag coefficient to more precisely reflect actual variations in basal properties. Finally, a comparison of the inferred basal drag across WAIS with observed locations of subglacial lakes reveals a good match, giving us additional confidence in the spatial basal drag structure revealed by the inverse method.