Inference of the Bottom Properties in Shallow Ice Approximation Models
Résumé
This study proposes a new inverse method to infer the bottom topography and the friction coe cient in the Shallow Ice Approximation (SIA) models (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
10 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 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
15 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.
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