Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model

The diffusive back-and-forth nudging (DBFN) is an easy-to-implement iterative data assimilation method based on the well-known nudging method. It consists of a sequence of forward and backward model integrations, within a given time window, both of them using a feedback term to the observations. Therefore, in the DBFN, the nudging asymptotic behaviour is translated into an infinite number of iterations within a bounded time domain. In this method, the backward integration is carried out thanks to what is called backward model, which is basically the forward model with reversed time step sign. To maintain numeral stability, the diffusion terms also have their sign reversed, giving a diffusive character to the algorithm. In this article the DBFN performance to control a primitive equation ocean model is investigated. In this kind of model non-resolved scales are modelled by diffusion operators which dissipate energy that cascade from large to small scales. Thus, in this article, the DBFN approximations and their consequences for the data assimilation system set-up are analysed. Our main result is that the DBFN may provide results which are comparable to those produced by a 4Dvar implementation with a much simpler implementation and a shorter CPU time for convergence. The conducted sensitivity tests show that the 4Dvar profits of long assimilation windows to propagate surface information downwards, and that for the DBFN, it is worth using short assimilation windows to reduce the impact of diffusion-induced errors. Moreover, the DBFN is less sensitive to the first guess than the 4Dvar