Localization And Sampling Error Correction In WRF-EnSRF

Ensemble square root filter (EnSRF) is a deterministic algorithm without disturbance observation, which derived from the traditional ensemble kalman filter (EnKF), to avoid the sampling error caused by disturbance observation. Ensemble square root filter uses the flow dependent background error covariance to analyze data, sloving the problem of adjoint models in varitional assimilation.But, some problems such as sampling error still exist in ensemble square root filter system, needing other techniques(such as localization, covariance inflation, etc.) to overcome. The paper is trying to change WRF-EnSRF system by using sampling error correction localization. The localization calculated weighting coefficient by using an offline Monte Carlo technique to product a lookup table which is related to the ensemble number and sample correlation coefficient, according to the prior distribution relationship of the correlation coefficient between an observation and a state variable. Finally it can reduce sampling error caused by finite ensemble. We use the algorithm to improve WRF-EnSRF system for a series of storm-scale data assimilation tests of simulated Doppler radar observation, and use the actual Doppler radar data for assimilation tests to verify the practicability of sampling error correction localization. Results are as follows:1) Sampling error correction localization can be implemented in the WRF-EnSRF system, and make the system to get physical analysis field more accurately.2) Weighting coefficient of sampling error correction localization is not dependent on the distance, while the method has low sensitivity to the distance. The weighting coefficient changes along with the time, reflecting flow dependent features.3) In nonlinear and rapid development stage of storm, using sampling error correction localization here has a great advantage.4) The assimilation results of using sampling error correction localization and empirical localization are different, when assimilating reflectivity. Therefore, choosing different localization for observations of different characters can get more reasonable assimilation results.