## Contribution de N. Martin & J. Monnier & :

*Sensitivity analysis and variational data assimilation for ice flow - Application to the Metz ice-tongue*

*Sensitivity analysis and variational data assimilation for ice flow - Application to the Metz ice-tongue*

*To be confident in the accuracy of the modelling of ice flows requires to confront numerical experiments to actual observations. This type of flows is strongly sensitive to their input parameters and boundary conditions such as rheological parameters or the friction at bottom. Then, using optimal control theory, we build a global 4D-Var algorithm using direct and adjoint model of the variational problem thus providing local sensitivity analysis and data assimilation (see [1]). In order to compute approximation of these flows, one consider the velocitypressure Stokes system described using mixed finite element method. The treatment of the free surface is performed using an Arbitrary Lagrangien Eulerian description with robus elastic deformation and the adjoint method is constructed by algorithmic differentiation of the direct code using Tapenade software (INRIA). We lean on prior developments of the software DassFlow (see [2]). One of the major question for inverse methods in glaciology is to infer the friction coefficient at bottom through data assimilation because it cannot be measured. In other respect, our first results based on real data shows that the rheological exponent and/or the thermal coefficient of the constitutive law (distributed parameter) has the same type of influence (see Figure 1) and can be inferred as well.*

[1] Martin, N. and Monnier, J. : A three fields finite elements solver for viscoplastic free surface flows and variational data assimilation. Submitted.

[2] Data Assimilation for free surface Flow

[1] Martin, N. and Monnier, J. : A three fields finite elements solver for viscoplastic free surface flows and variational data assimilation. Submitted.

[2] Data Assimilation for free surface Flow