Data assimilation in a wave equation: A variational representer approach for the Grenoble tidal model (Q1282377)

We propose a synthesis of both the hydrodynamic and assimilation aspects of the quasi-linearized tidal model developed by the Grenoble tidal group. Starting from the hydrodynamic model, which is represented by a linearized wave equation, we emphasize the different steps taken to lead to the final finite element discrete system of the coupled hydrodynamic and assimilation problem. The assimilation is based on a general inverse method using an \(L_2\) norm-type cost function, weighted by the use of inverse error covariance operators. As an illustration, we propose a realistic application performed on the \(M_2\) tidal elevation problem in the South Atlantic by assimilating tidal gauge data in a solution of the Grenoble model. \(\copyright\) Academic Press.