Ensemble member generation for sequential data assimilation

Using an ensemble of model forecasts to describe forecast error covariance extends linear sequential data assimilation schemes to nonlinear applications. This approach forms the basis of the Ensemble Kalman Filter and derivative filters such as the Ensemble Square Root Filter. While ensemble data assimilation approaches are commonly reported in the scientific literature, clear guidelines for effective ensemble member generation remain scarce. As the efficiency of the filter is reliant on the accurate determination of forecast error covariance from the ensemble, this paper describes an approach for the systematic determination of random error. Forecast error results from three factors: errors in initial condition, forcing data and model equations. The method outlined in this paper explicitly acknowledges each of these sources in the generation of an ensemble. The initial condition perturbation approach presented optimally spans the dynamic range of the model states and allows an appropriate ensemble size to be determined. The forcing data perturbation approach treats forcing observations differently according to their nature. While error from model physics is not dealt with in detail, discussion of some commonly used approaches and their limitations is provided. The paper concludes with an example application for a synthetic coastal hydrodynamic experiment assimilating sea surface temperature (SST) data, which shows better prediction capability when contrasted with standard approaches in the literature.