An implementation of the Local Ensemble Kalman Filter in a quasi geostrophic model and comparison with 3D-Var

We perform data assimilation experiments with a widely used quasi-geostrophic channel model and compare the Local Ensemble Kalman Filter (LEKF) with a 3D-Var developed for this model. The LEKF shows a large improvement, especially in correcting the fast growing modes of the analysis errors, with a mean square error equal to about half that of the 3D-Var. The improvement obtained in the analysis is maintained in the forecasts, implying that the system is capable of correcting the initial errors responsible for later forecast error growth. Different configurations of the LEKF are tested and compared. We find that for this system, adding random perturbations after every analysis step is more effective than the standard variance inflation in order to avoid underestimating the background error covariance and the consequent filter divergence. Experiments indicate that optimal results are obtained with a relatively small number of vectors (~30) in the ensemble. The LEKF is characterized by the "localization" of the analysis process over local domains surrounding each gridpoint of the model grid. We find that, when using a fixed number of ensemble vectors, there is an optimal size of the local horizontal domain beyond which the results do not change further.