## Contribution de Giovanni RUGGIERO:

*Data Assimilation Experiments using the Back and Forth Nudging and NEMO OGCM*

*Data Assimilation Experiments using the Back and Forth Nudging and NEMO OGCM*

*We present Data Assimilation experiments under the OSSE framework using NEMO ocean model and the Back and Forth Nudging (BFN). This algorithm consists of iterating the model forward and backward in time, in a given time window, adding to the model equations a forcing term proportional to the difference between the model state and the observations. The backward integration allows us to estimate an initial condition that produces a trajectory close to the observations at the end of the DA window. This is an important aspect to produce good quality forecasts. In our experiments two sets of observations are used: 1) sea surface height at all grid points and available every day and 2) sea surface height taken at the satellite (Jason-1) track. We compare the BFN results with results obtained using the NEMOVAR system (4D-Var). Also we tested a "hybrid" method which combines the iterative character of the BFN with a correction step similar to that one used in Kalman Filters (KF). In this case, the resulting algorithm can be seen as a Kalman Smoother (KS), as long as we use future observations to estimate the initial condition of the system. Our results show that in the case of experiments using sea surface height observations at all grid points, the BFN converges after 10 iterations and performs better than the 4D-var, when we considered the same computational power for both methods. When we allowed the 4D-var to do a hundred iterations it performed better in the sense of the mean squared error, but with a cost about one hundred times the BFN cost. However, under a more realistic observation network, the performance of the BFN was not as good as the 4D-var. In this case, the hybrid BFN-KF produced results that are comparable with the 4D-var and a KS.*