An adaptive covariance localization method with the LETKF

The forecast error covariance of ensemble Kalman filters (EnKFs) is subject to sampling errors at long distances due to the limited ensemble size, thus it needs empirical localization to reduce them. However, finding an optimal localization function is prohibitive in practice since it would depend on geographical locations, vertical levels, and seasons. Alternatively, Anderson (2007) and Bishop and Hodyss (2009) proposed two approaches to adaptive localization. In this study, another method of adaptive localization is designed particularly efficient with the local ensemble transform Kalman filter (LETKF, Hunt et al. 2007) and tested by numerical experiments using the Lorenz 40-variable and SPEEDY global atmospheric models. The method combines the approaches of Anderson and of Bishop and Hodyss, but it is simplified for computational efficiency. It provides automatic localization in space, time, and inter-variable, though the adaptively estimated localization function itself is subject to sampling errors. Numerical experiments with the Lorenz 40-variable model showed a good performance, although the best analysis accuracy is achieved by well-tuned fixed distance-dependent localization, something feasible in this simple model. Results by the SPEEDY global model indicate significant positive impact from the new adaptive localization method, particularly at lower levels.