Toward variational data assimilation for coupled models : first experiments on a diffusion problem

Nowadays, coupled models are increasingly used in a wide variety of fields including weather forecasting. We consider the problem of adapting existing variational data assimilation methods to this type of application while imposing physical constraints at the interface between the models to be coupled. We propose three data assimilation algorithms to address this problem. The proposed algorithms are distinguished by their choice of cost function and control vector as well as their need to reach convergence of the iterative coupling method (the Schwarz domain decomposition method is used here). The performance of the methods in terms of computational cost and accuracy are compared using a linear 1D diffusion problem.