Improving Assimilation of Radiance Observations by Implementing Model Space Localization in an Ensemble Kalman Filter

Experiments using the National Oceanic and Atmospheric Administration Finite-Volume Cubed-Sphere Dynamical Core Global Forecasting System (FV3GFS) reveal that the four-dimensional ensemble-variational method (4DEnVAR) performs similarly to an ensemble Kalman filter (EnKF) when no radiance observations are assimilated, but 4DEnVAR is superior to an EnKF when radiance observations are assimilated. The hypothesis for the cause of the differences between 4DEnVAR and EnKF is the difference in vertical localization, since radiance observations are integral observations in the vertical and 4DEnVAR uses model space localization while the EnKF uses observation space localization. A modulation approach, which generates an expanded ensemble from the raw ensemble and eigenvectors of the localization matrix, has been adopted to implement model space localization in the operational National Oceanic and Atmospheric Administration EnKF. As constructed, the expanded ensemble is a square root of the vertically localized background error covariance matrix, so no explicit vertical localization is necessary during the EnKF update. The size of the expanded ensemble is proportional to the rank of the vertical localization matrix-for a vertical localization scale of 1.5 (3.0) scale heights, 12 (7) eigenvectors explain 96% of the variance of the localization matrix, so the expanded ensemble is 12 (7) times larger than the raw ensemble. Results from assimilating only radiance observations in the FV3GFS model confirm that EnKF with model-space vertical localization performs better than observation-space localization, and produces results similar to 4DEnVAR. Moreover, a 960-member ensemble is sufficient to turn off the vertical localization entirely and yields significant improvements comparing to an 80-member ensemble with model space localization.