Inference of the Bottom Properties in Shallow Ice Approximation Models

Jerome Monnier (1, 2) , P.-E Des Boscs (1)

1 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
2 IMT - Institut de Mathématiques de Toulouse UMR5219

This study proposes a new inverse method to infer the bottom topography and the friction coefficient in the Shallow Ice Approximation models (lubrication type models for generalized Newtonian fluid flows). The method is based on sub-regime definitions corresponding to different slip ratios; then combinations of explicit field expressions with an elliptic linear-quadratic optimal control problem (solved by variational data 10 assimilation) lead to depth estimations; next the friction field can be deduced. The numerical results performed on realistic multi-regime flows demonstrate the robustness of the method even in presence of uncertain surface measurements and independently of the depth measurement locations (on contrary if inverting a regularized first order transport equation). A method by-product is to make possible the determination of the adequate slope scale of in the shallow flow model. The method can be straightforwardly extended to unsteady flows if time-dependent surface observations (elevation and velocity) are available.

Mots clés: Shallow flow; Shallow Ice Approximation; topography inference; friction; data assimilation; glaciers

Domaines: Optimisation et contrôle [math.OC]; Mécanique des fluides [physics.class-ph]; Glaciologie

Jerome Monnier, P.-E Des Boscs. Inference of the Bottom Properties in Shallow Ice Approximation Models. 2016. ⟨hal-01356778v1⟩