An Empirical Localization of Surface Observations

To improve the assimilation of surface observations, especially in complex terrain, an empirical localization function for surface observations for an ensemble Kalman filter (EnKF) is constructed using output from an observation system simulation experiment (OSSE) using NCAR's WRF/DART ensemble data assimilation system. The OSSE integrates the WRF model for six days that cover part of IOP5 of the Persistent Cold-Air Pool Study (PCAPS) and assimilates synthetic observations with the EnKF in DART.

The empirical localization is based on the hierarchical ensemble filter. A group of regression coefficients that are the statistical relations between an observation and a state variable are obtained by running a set of ensemble filter assimilations. The empirical localization function is then defined to minimize the sampling error from the set of regression coefficients. The empirical localization function can be computed for any type of observation and any state variable.

Horizontal and vertical empirical localization functions are computed separately for a specific type of surface observation and a state variable kind. The results suggest that different localization functions are needed for different pairs of observation type and state variable kind. The empirical localization is not limited to a Gaussian-like function as in many ensemble filter schemes. The performance of the EnKF and model forecast improvements with the empirical localization functions are further investigated by applying the empirical localization functions in a retrospective and a future simulation. Moreover, the variations of the empirical localization with complex terrain are also explored.