An evolution of the Back and Forth Nudging for geophysical data assimilation: application to Burgers equation and comparisons
Résumé
We study in this article an improvement to the back and forth nudging (BFN) method for geophysical data assimilation. In meteorology or oceanography, the theoretical equations are usually diffusive free, but diffusion is added into the model equations in order to stabilize the numerical integrations and to take into consideration some subscale phenomena. We propose to change the sign of the diffusion in the backward nudging model, which is physically consistent and stabilizes the backward integration. We apply this method to a Burgers equation, study the convergence properties and report the results of numerical experiments. We compare the quality of the estimated initial condition with two other data assimilation techniques that are close from the algorithmic point of view: a variational method, and the quasi-inverse linear method.