Comparison Between Observation Space Localization and Model Space Localization in a Four-Dimensional Ensemble-Variational System

Due to a limited number of ensemble members, localization is used in the ensemble Kalman filter (EnKF) to remove artifact correlations between distant points. Localization can be applied for correlations between model variables, called model space localization, or for correlations between model variables and observations, called observation space localization. Like EnKF, the ensemble variational method (EnVAR) also uses ensemble forecast but in the variational context. Since EnVAR is established with a cost function in the model space, a natural choice for localization in EnVAR is model space localization. By some modifications this study shows that observation space localization can also implemented in EnVAR. Furthermore, when observation space localization is applied, the Jacobian of observation operator and its adjoint can be replaced by their finite-difference approximations using the observation operator. This enables EnVAR to assimilate observations that are difficult to develop the Jacobian for their observation operators like tropical cyclone positions and intensities.

To compare model space localization and observation space localization in EnVAR, a four-dimensional EnVAR system (NHM-4DEnVAR) was developed using the Japan Meteorological Agency limited-area operational model NHM. An EnKF system based on the local ensemble transform Kalman filter method was run in parallel to provide forecast perturbations for NHM-4DEnVAR. Real observation experiments were carried out for the August in 2014 over a domain covering entire Japan. Verification shows that in general EnVAR using observation space localization outperformed EnVAR using model space localization. This may result from the adaptive vertical localization to be used in case of observation space localization. However, at the levels above 500 hPa EnVAR with model space localization was better in predicting temperature and humidity.