大气科学学报2017，Vol.40Issue(2)：158-169,12.DOI:10.13878/j.cnki.dqkxxb.20140510002
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
A study of the sampling error correction localization in a storm-scale ensemble Kalman filter
摘要
Abstract
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.关键词
EnSRF/采样误差/局地化/采样误差订正局/地化Key words
EnSRF/sampling error/localization/sampling error correction localization引用本文复制引用
闵锦忠,黄欣慧,陈耀登,杨春..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[J].大气科学学报,2017,40(2):158-169,12.基金项目
中国气象局武汉暴雨研究所开放基金(IHR2008K01) （IHR2008K01）
2012年江苏省高校研究生创新计划(CXLX12_0494) （CXLX12_0494）
