An augmented Lagrangian algorithm for recovery of ice thickness in unidirectional flow using the Shallow Ice Approximation

TL;DR

This paper introduces an augmented Lagrangian method to simultaneously recover ice thickness and basal slip from surface measurements using the shallow ice approximation, improving inverse modeling in glaciology.

Contribution

It presents a novel combined approach for inferring ice thickness and basal slip from surface data, leveraging an augmented Lagrangian algorithm within the shallow ice approximation framework.

Findings

Method successfully recovers parameters in test cases

Potential applicability to 2D ice flow modeling

Enhances inverse problem solutions in glaciology

Abstract

A key parameter in ice flow modelling is basal slipping at the ice-bed interface as it can have a large effect on the resultant ice thickness. Unfortunately, its contribution to surface observations can be hard to distinguish from that of bed undulations. Therefore, inferring the ice thickness from surface measurements is an interesting and non-trivial inverse problem. This paper presents a method for recovering dually the ice thickness and the basal slip using only surface elevation and speed measurements. The unidirectional shallow ice approximation is first implemented to model steady state ice flow for given bedrock and basal slip profiles. This surface is then taken as synthetic observed data. An augmented Lagrangian algorithm is then used to find the diffusion coefficient which gives the best fit to observations. Combining this recovered diffusion with observed surface velocity, a simple Newton's method is used to recover both the ice thickness and basal slip. The method was successful in each test case and this implies that it should be possible to recover both of these parameters in two-dimensional cases also.