Tests of different flavours of EnKF on a simple model

The Met Office is currently developing an ensemble-based data-assimilation system for use in numerical weather prediction (NWP). In an effort to inform those developments, a simple model has been used to compare a number of different flavours of ensemble Kalman filter (EnKF). As in many previous studies, deterministic (square-root) filters are seen to perform better than stochastic (perturbed-observations) filters. Two previously proposed methods for mitigating the effects of perturbing the observations were tested. These modified stochastic filters improved performance, but were still worse than the deterministic filters. Very little difference was seen between the performance of the various deterministic filters tested. The typical approach to localization in the Local Ensemble Transform Kalman Filter (LETKF) is based solely on the distance between each observation and the model point being updated. It takes no account of the inter-observation distance and we argue that this is incorrect. However, the difference between covariance localization and observation localization is only relevant when the assimilation is not weak and hence it did not affect performance in these tests. If a hybrid covariance matrix is used to update the ‘deterministic’ forecast around which the ensemble is centred, then using the same covariance matrix when updating the perturbations is seen to be beneficial in a stochastic filter. This is not the case in the square-root filter, due to restrictions imposed by its formulation. Tests with a nonlinear observation operator indicate better behaviour when observations are assimilated simultaneously rather than sequentially. An ensemble of variational minimizations has some advantages in this situation. These results, along with other considerations, have led the Met Office to develop a 4-dimensional ensemble-variational (4D-En-Var) system for data assimilation and ensemble generation.