Ensemble-Based Variational Method with Observation Localization: Difference from LETKF

In the data assimilation with Ensemble Kalman Filter (EnKF), linearity of the observation operator and Gaussianity of the probability distribution function (PDF) are assumed in order to explicitly solve the analysis. To avoid these approximations, it is better to implicitly solve the analysis with the ensemble-based variational method (EnVAR). Although the advantage of EnVAR to make the analysis with the flow-dependent forecast error covariance has been examined in many previous studies, however, the advantage of EnVAR to implicitly solve the analysis has not been clarified. To clarify this advantage, we developed the EnVAR system with observation localization; the formulation of EnVAR is same as that of Local Ensemble Transform Kalman Filter (LETKF) except not assuming linearity of the observation operator and Gaussianity of the PDF. In the single-observation assimilation experiments with the linear observation operator, the EnVAR analysis was completely same as the LETKF analysis at the observation point. However, it was different when it is far from the observation point or the observation operator is non-lenear. In the observation system simulation experiments with the SPEEDY model (Molteni 2003), the root mean square of difference of EnVAR analyses from the true value were smaller than that of LETKF in the same number of ensemble members and the localization radius; therefore, EnVAR has larger advantage than LETKF because linearity of the observation operator and Gaussianity of the PDF are not assumed in the formulation of EnVAR.