Model error space and data assimilation in the Mediterranean Sea and nested models

In this work, we implemented the GHER hydrodynamic model in the Gulf of Lions (resolution 1/100◦). This model is nested interactively in another model covering the North-Western basin of the Mediterranean Sea (resolution 1/20◦), itself nested in a model covering the whole basin (1/4◦). A data assimilation lter, called the SEEK lter, is used to test in which of those grids observations taken in the Gulf of Lions are best assimilated. Therefore, twin experiments are used: a reference run is considered as the truth, and another run, starting from di erent initial conditions, assimilates pseudo-observations coming from the reference run. It appeared that, in order to best constrain the coastal model, available data should be assimilated in that model. The most e cient setup, however, is to group all the state vectors from the 3 grids into a single vector, so that the 3 domains are coherently modi ed at once during assimilation cycles. Operational forecasting with nested models often only uses so-called passive nesting: no data feedback occurs from the regional models to the global model. A new idea is proposed: to use data assimilation as a substitute for the feedback. Using again twin experiments, it is shown that assimilating outputs from the regional model in the global model, has bene cial impacts for the subsequent forecasts in the regional model. The data assimilation method used in those experiments corrects errors in the models using only some privileged directions in the state space. Furthermore, these directions are selected from a previous model run. This is a weakness of the method when real observations are available. We tried to build new directions of the state space using an ensemble run, this time covering only the Mediterranean basin (without grid nesting). This led to a quantitative characterization of the forecast errors we might expect when various parameters and external forcings are a ected by uncertainties. We looked in detail at both the spatial and temporal evolution of these forecast errors. Finally, using these new directions, we tried to build a statistical model supposed to simulate the hydrodynamical model using only a fraction of the computer resources needed by the latter. To achieve this goal, we tried out linear regressions, arti cial neural networks, nearest-neighbors and regression trees. The inputs of the algorithms were the weights of the EOF decomposition of the ocean state vector and of some atmospheric forcing elds; the weights after some time constituted the outputs. This study constitutes only the rst step towards an innovative statistical model, as in its present form, only a few degrees of freedom are considered and the primitive equation model is still required to build the automatic learning method. We tried forecasting at 2 di erent time horizons: one day and one week. We tried out both cases where only past states were available in the database, or when some future states were available. In the second case, we showed that automatic learning algorithms performed quite well, at both timescales. In the rst case however, satisfying predictions of the future day ocean state could be obtained only with arti cial neural networks (and to a lesser extent regression trees). No usable predictions of the nextweek ocean state could be obtained at all, indicating that a stable relationship between inputs and outputs simply does not exist within our database.