风暴尺度集合卡尔曼滤波中的采样误差订正局地化方法研究

在中尺度WRF-EnSRF系统中最新引入的采样误差订正局地化方法不仅考虑了回归系数偏差,而且计算量较小。该方法基于状态变量和对应观测值的相关系数的分布关系,根据离线蒙特卡洛技术制作的关于集合数和样本相关系数的查找表格确定局地化系数因子,进而订正由集合数选取有限造成的背景误差协方差被低估引起的采样误差。本文利用风暴过程的雷达观测资料做了一系列风暴尺度的资料同化理想试验,探讨了采样误差订正局地化方法在风暴尺度集合卡尔曼滤波同化中的技术特点和同化效果。结果表明:相比于经验局地化方法,采样误差订正局地化方法能够有效地改善集合同化的效果,对距离的敏感度更低,尤其在天气系统发展变化较快的阶段,新方法优势更大。并且,对不同观测变量以及在风暴发展的不同阶段使用不同的局地化方法,所得的结果都存在一定的差异,因此需要根据同化对象合理地选择局地化方法。

A study of the sampling error correction localization in a storm-scale ensemble Kalman filter

An Ensemble Square Root Filter(EnSRF) is a deterministic algorithm without disturbance observations,which was derived from the traditional Ensemble Kalman Filter(EnKF) in order to avoid the sampling errors caused by disturbance observations.An EnSRF uses the flow dependent background error covariance to analyze data,which solves the problem of adjoint models in the variational assimilation.Previous studies have completed the construction of EnSRF systems for storm scale in the Weather Research and Forecasting(WRF) model.However,some problems,such as the sampling error,still exist in the WRF-EnSRF system.Therefore,various other techniques,such as an empirical localization method,should be used to overcome these problems.Since the weight coefficients of the empirical localization method are linear,and are dependent on the local distance radius,they do not reflect the real situation of the state variables and observations.In this study,attempts were made to improve the assimilation effect of a WRF-EnSRF system by utilizing a sampling error correction localization method instead of the empirical localization method.The sampling error correction localization method took into account the biases of regression coefficients,and used less computation.Then,based on the prior distribution information of the correlation coefficient between the state variables and corresponding observations,the method obtained the coefficient factor of the localization through a lookup table,which was related to the ensemble numbers and sample correlation coefficients,and produced by the offline Monte Carlo technique.The sampling error was then corrected,which had resulted from the underestimation of the background error covariance due to the limitation of the selected ensemble numbers.Meanwhile,the weighting coefficient was updated with the assimilation time for each of the observational data assimilations,and reflected the flow dependent feature.This method has been widely used in large-scale models.However,it has also been considered to be applicable,or even more suitable,to small and medium scale weather systems.Therefore,this study attempted to put the method into the WRF-EnSRF,and conducted a series of storm-scale data assimilation tests using Doppler radar observations during storm periods,in order to prove the feasibility of the localization,as well as to explore the technical features and assimilation effects of the sampling error correction localization method in the storm-scale ensemble Kalman filter assimilation.The data in the WRF during a typical super storm which occurred in Del City(central Oklahoma,USA) on May 20,1977,were used in this study.In order to reduce the calculation and avoid the spurious correlation with long distance observations,this study selected reasonable local distance radiuses for the different variables in the assimilation tests.Then,based on the tests with only assimilating radial velocity,it was found that the sampling error correction localization method was able be implemented in the WRF-EnSRF system,and the results achieved the physical analysis field more accurate after adding the assimilation of the radar reflectivity.Since the weighting coefficient of the sampling error correction localization was not dependent on the distance,the assimilation results reduced the sensitivity to the distance.In addition,it was found that there were some differences in the results with different localization methods for the various observed variables and stages of the storm.This is due to the fact that the sampling error correction localization had strong nonlinear characteristics itself,especially for the variables containing water substances.Therefore,the sampling error correction localization achieved better results of the tests in the nonlinear and rapid development stages of the synoptic system or assimilating nonlinear variables,when compared to the empirical localization method.However,in the stable development stage or assimilating linear variables,the empirical method was determined to have more advantages.In summary,according to the results of the tests,it was necessary to reasonably choose the appropriate localization method according to the object of the assimilation.