Performing Model Space Localization for Satellite Radiances in an Ensemble Kalman Filter

Covariance localization is an essential component of ensemble-based data assimilation systems for numerical weather predictions with limited ensemble sizes. For integral observations like the satellite radiances, where the concepts of location or vertical distance are not well defined, vertical localization is not straightforward. Campbell et al. (2010) showed that model space localization was superior to observation space localization for the radiance observations. Experiments using the NCEP Global Forecast System (GFS) also reveal that the four-dimensional ensemble-variational method (4DEnVAR) is better than the ensemble Kalman filter (EnKF) because model space localization is applied in 4DEnVAR while observation space localization is used in EnKF for the radiance observations.

Bishop et al. (2009) proposed the modulated ensembles that are generated from the model-integrated ensemble but implicitly containing localization. Applying the modulated ensemble in an EnKF without localization equivalently performs model space localization in an EnKF. The size of the modulated ensemble is proportional to the number of non-zero eigenvalues of the localization matrix, which makes the modulate ensemble impractical to numerical weather predictions. However, for assimilating the satellite radiances, only vertical localization in model space is needed, thus the size of the modulated ensemble is approximately 10 times more than the model-integrated ensemble. Results from assimilating a single AMSU-A radiance observation in the NCEP GFS confirm that the EnKF using vertically modulated ensemble without localization produce the same vertical increment as the 4DEnVAR using the model-integrated ensemble. Results with assimilating both conventional and radiance observations in the NCEP GFS by the EnKF with the modulated ensemble and 4DEnVAR will be discussed.