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

Experiments using the NOAA Finite-Volume Cubed-Sphere Dynamical Core Global Forecasting System (FV3GFS) reveal that the four-dimensional ensemble-variational method (4DEnVAR) outperforms a pure Kalman filter (EnKF) when radiance observations are assimilated. We hypothesize that this is due to differences in vertical localization, which is performed in model space in 4DEnVar and observation space in the EnKF. 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 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. Using the local form of the gain-form ensemble-transform Kalman filter (LGETKF), with special attention paid to computational efficiency, the cost of calculating the analysis increment with model-space localization is increased by approximately a factor of two for a vertical covariance localization length scale of 1.5 scale heights. However, if the localization length scale is increased to 3.0 scale-heights, model-space localization using the LGETKF is slightly less than a factor of two faster than observation-space localization.