Analysis Scheme in the Ensemble Kalman Filter

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter . I t i s shown that the obser vations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the obser vations and generate an ensemble of obser vations that then is used in updating the ensemble of model states. T raditionally , this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low . This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.