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Publication# Bedrock topography reconstruction of glaciers from surface topography and mass-balance data

Résumé

Three methods based on the three-dimensional shallow ice approximation of glacier flow are devised that infer a glacier's subglacial topography from the observation of its time-evolving surface and mass balance. The quasi-stationary inverse method relying on the apparent surface mass-balance description of the glacier's evolution is first exposed. Second, the transient inverse method that iteratively updates the bedrock topography with the surface topography discrepancy is formulated. Third, a shape optimization algorithm is presented. The aim of the paper is to collect these methods, analyze their differences, and identify what brings the sophistication of shape optimization for reconstructing subglacial topographies. The three methods are compared to the ice thickness estimation method (ITEM) on direct measurements on Gries glacier, Swiss Alps. The paper concludes with a detailed discussion on the sensitivity of the shape optimization method to the model parameters.

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Bilan de matière

Un bilan de matière (parfois simplement bilan matière) est l'application du principe de conservation de la masse à l'analyse d'un système. En analysant soigneusement les flux de matière entrant et sor

Glacier

vignette|Le glacier d'Aletsch (Suisse), le plus grand glacier des Alpes.
vignette|Le glacier Briksdal, en Norvège.
vignette|Front du glacier Hubbard, en Alaska.
Un glacier est une masse de glace plus

Parameter

A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element

Heinz Blatter, Martin Funk, Laurent Michel, Marco Picasso

A shape optimization algorithm is presented that estimates the ice thickness distribution within a three-dimensional, shallow glacier, given a transient surface geometry and a mass-balance distribution. The approach is based on the minimization of the surface topography misfit in the shallow ice approximation by means of a primal-dual procedure. The method's essential novelty is that it uses surface topography and mass-balance data only within the context of a time-dependent problem with evolving surface topography. Moreover, the algorithm is capable of computing some of the model parameters concurrently with the ice thickness distribution. The method is validated on synthetic and real-world data, where the choice of its Tikhonov regularization parameter by means of an L-curve criterion is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

Heinz Blatter, Martin Funk, Laurent Michel, Marco Picasso

We present a shape optimization algorithm to estimate the ice thickness distribution within a two-dimensional, non-sliding mountain glacier, given a transient surface geometry and a mass-balance distribution. The approach is based on the minimization of the surface topography misfit at the end of the glacier's evolution in the shallow ice approximation of ice flow. Neither filtering of the surface topography where its gradient vanishes nor interpolation of the basal shear stress is involved. Novelty of the presented shape optimization algorithm is the use of surface topography and mass-balance only within a time-dependent Lagrangian approach for moving-boundary glaciers. On real-world inspired geometries, it is shown to produce estimations of even better quality in smaller time than the recently proposed steady and transient inverse methods. A sensitivity analysis completes the study and evinces the method's higher susceptibility to perturbations in the surface topography than in surface mass-balance or rate factor.

The question addressed is the determination of a glacier’s subglacial topography, given surface topography and mass-balance data. The input data can be obtained relatively easily for a large number of glaciers. Several methods essentially based on the shallow ice approximation are proposed, some of which are extended to Stokes ice flows. Two gradient-free, iterative methods are first introduced, namely the quasi-stationary inverse method, that relies on the apparent surface mass-balance description of glacier dynamics, and the transient inverse method, consisting in the iterative update of the bedrock topography proportionally to the surface topography misfit at the end of the glacier’s considered evolution. Then, an optimal control algorithm is suggested that calculates the bedrock topography and some model parameters from surface observations through the minimization of a regularized misfit functional by means of a Lagrangian method. Numerical validations, along with sensitivity analyses and applications to real-world data are presented for each method.