Application of Empirical Localization Functions on All-Sky Satellite Radiance Assimilation

To control the sampling errors due to the limited ensemble size, covariance localization has been used in ensemble-based data assimilation. One common method of covariance localization is the uniform application of Gaussian-shaped localization functions for all the model state variables. However, this homogenous localizing method is potentially preventing us from analyzing optimal increments in all-sky satellite radiance assimilation since the covariance structures and effective radius of influence for radiances are highly flow- and situation-dependent. Furthermore, the optimal values of localization functions are hard to find, and require large computational cost to be tuned.

In this study, an application of empirical localization functions (ELFs) for all-sky satellite radiance assimilation is investigated using convective-permitting models with an ensemble Kalman filter. ELFs is a method to find optimal localization functions for a given set of observations and model states using observation system simulation experiments. Here, a boot-strap version of empirical localization functions (BELFs) is proposed to obtain smooth localization functions from non-hydrostatic unbalanced model fields of severe weather events with nonlinear observation operators, which introduce huge representativeness errors. The BELFs method computes optimal localization functions by repeatedly comparing the estimated increments from subsets of (N-1) ensemble members and the differences between (N-1) members’ ensemble mean and the other unselected member. By applying this boot-strap method to variable sky conditions separately, computed BELFs clearly illustrates the cloud-dependency of optimal localizations with vertically wider and horizontally narrower localization radius for higher cloud radiances. Using BELFs shows significantly smaller root mean square error of thermodynamic model state variables than manually tuned localization functions. Since BELFs only require the set of ensemble priors for calculation, the applicability to real-data assimilation is also explored.