Observation space localization for assimilation of satellite radiances

Covariance localization is an essential component of any ensemble-based data assimilation system. For integral observations like the satellite radiances, where the concepts of location or vertical distance are not well defined, vertical localization needs better understanding.

The detailed differences between model space and observation space localizations are first examined. Counterintuitive analysis increments from a real radiance observation can be obtained with model space localization when there are negative background-error covariances and a predominately positive forward operator, because model space localization can neglect the negative background-error covariances. An idealized 1D model with an integral observation and known true error covariance is used to compare errors in the sample Kalman gain with model space and observation space localization. Although previous studies have suggested that observation space localization is inferior to model space localization for satellite radiances, the results from the 1D model reveal that observation space localization can have advantages over model space localization when there are negative background-error covariances. Differences between model space and observation space localization disappear as ensemble size, observation error variance and localization scale increase.

A hierarchical ensemble filter is then used to construct the observation-space vertical localization function for the AMSUA radiance observations. The hierarchical ensemble filter does not require the vertical observation location and distances, and it uses few a priori assumptions about the localization function. The estimated vertical localization functions are non-Gaussian and different from the common used Gaussian-like Gaspari and Cohn (GC; Gaspri and Cohn 1994) localization function. The estimated vertical localization functions are superior to the GC localization function in a subsequent assimilation experiment.