6.2 Estimation of Model Errors in the Local Ensemble Transform Kalman Filter

Ensemble Kalman Filters (EnKF) have been shown to be more accurate than 3D-Var in data assimilation simulations under the assumption of a perfect model. However, in reality, the forecast model has deficiencies and does not represent the atmospheric behavior precisely due to lack of resolution, approximate parameterizations of subgrid scale physical processes, and numerical dispersion. For assimilation of real observations, into an imperfect model, it is not yet clear whether the EnKF will be competitive or better than the current operational 3D-Var data assimilation systems. Only recently have some EnKF schemes advanced from the perfect model scenario to realworld situations. Houtekamer et al (2005) showed that the quality of EnKF with perturbed observations was comparable to 3D-Var. The Ensemble Square-Root filter (EnSRF) was reported (Whitaker et al 2004) to outperform the NCEP 3D-Var in reconstructing the middle and lower tropospheric analysis in the Northern Hemisphere at T62/L28 resolution. Miyoshi (2005) also showed that EnKF is most advantageous over 3D-Var when the observing network is sparse and also that the advantage diminishes in the presence of model errors. Model errors have a stronger negative influence on the performance of the EnKF than on the 3D-Var because Kalman filtering algorithms rely strongly on the assumption of an unbiased model, an assumption which is not satisfied in practice. Therefore, accounting for systematic errors associated with model deficiencies has become an important issue for all data assimilation systems, and especially for EnKF. The Local Ensemble Transform Kalman Filter (LETKF) (Hunt 2005) is a relatively new data assimilation scheme in the square root EnKF family, and is similar to the Local Ensemble Kalman Filter (Ott et al 2004) but faster. It has been implemented to assimilate simulated observations in the NCEP GFS model (Szunyogh et al. 2005), and recently in the NASA fvGCM