Inference of the bottom properties in shallow ice approximation models. (22nd September 2017)

• Record Type: Journal Article
• Authors: Monnier, J; des Boscs, P-E
• Is Part Of: Inverse problems. Volume 33:Number 11(2017:Nov.)
• Publication Date: 2017-09-22
• Subjects: shallow flow -- shallow ice approximation -- topography inference -- friction -- data assimilation -- glaciers; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa7b92
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This study proposes a new inverse method to infer the bottom topography and the friction coefficient 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 satellite). The friction field is a by-product of the depth inverse method—it can be explicitly deduced. Numerical results considering multi-regime numerical flows demonstrate the robustness of the method even in the presence of uncertain surface measurements, and independently of the depth measurement locations (the contrary is found, if inverting the regularized depth-averaged mass equation only). Moreover, the few derived depth estimations make it possible to determine the adequate slope scale in the SIA models.