Inference of the Bottom Properties in Shallow Ice Approximation Models

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

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

This study proposes a new inverse method to infer the bottom topography and the friction coecient in the Shallow Ice Approximation (SIA) model (lubrication type models for generalized Newtonian fluid flows). The method is based on the definition of three sub-regimes and an a-priori slip ratio law. Next, explicit calculations provide a first depth estimation for each sub-regime, and this first estimation can be improved by solving an elliptic linear-quadratic optimal control problem (variational assimilation of the surface measurements e.g. by 10 satellite). The friction field is a by-product of the depth inverse method, it can be explicitly deduced. The numerical results performed on multi-regime numerical 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 the regularized depth-averaged mass equation only). Moreover the few derived depth estimations make possible to determine the adequate slope scale in the SIA models. 15

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

Domaines: Optimisation et contrôle [math.OC]; Sciences de l'environnement

Jerome Monnier, P.-E Des Boscs. Inference of the Bottom Properties in Shallow Ice Approximation Models. Inverse Problems, 2017, 33 (11), pp.115001. ⟨hal-01545171v2⟩