Empirical Localization of Observations for Ensemble Kalman Filter Data Assimilation in WRF

Localization is essential for good filter performances in atmospheric applications. It is a technique to reduce the sampling error in the statistical relations between observations and model state variables. The empirical localization algorithm described here uses the output from an observing system simulation experiment (OSSE) and constructs localization functions that minimize the root mean square (RMS) difference between the truth and the posterior ensemble mean for state variables. This algorithm can automatically provide an estimate of the localization function and does not require tuning of the localization scale. Moreover, the algorithm can compute an appropriate localization function for any potential observation type and state variable kind.

The empirical localization functions outperformed the best Gaspari and Cohn (GC) function in OSSEs of the dynamical core of the Geophysical Fluid Dynamics Laboratory (GFDL) B-grid model and the Community Atmospheric Model version 5 (CAM5). Here, the empirical localization algorithm is applied to the Weather Research and Forecasting (WRF) model. An OSSE is first conducted in WRF over the CONUS domain with 15-km resolution and 40 vertical levels. From the output of this one-month simulation, the empirical localization function is computed in the horizontal and vertical. The horizontal empirical localization is similar to the best GC localization. However, the vertical empirical localization is broader than the best GC localization and is not a Gaussian-like function with vertical coordinate of the natural logarithm of pressure. The constructed empirical localization functions are applied in an OSSE and a real-observation simulation and compared to results with GC localization. A discussion of the need for different localization in regions with active precipitation is also presented.