一种基于随机协方差局部化的ETKF数据同化方法  

An ETKF assimilation method based on the random covariance localization

作　　者：陈丽 宋恩彬[2] CHEN Li;SONG En-Bin(School of Science,Civil Aviation Flight University of China,Guanghan 618307,China;School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]中国民用航空飞行学院理学院,广汉618307 [2]四川大学数学学院,成都610064

出　　处：《四川大学学报(自然科学版)》2025年第2期334-339,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(U2066203);中央高校基本业务科研费专项资金资助项目(QJ2023-038);四川省自然科学基金项目(2025ZNSFSC0073)。

摘　　要：数据同化是一组统计方法的集合.在数值模型动态运行过程中,基于数据分布、观测及背景误差,数据同化方法能够融合新观测数据,提高模型对系统瞬时状态的估计精度.当前,数据同化方法已被广泛应用于地球科学等研究领域.集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)是一种常用同化方法.在该方法中,误差的协方差估计很重要,集合数量过少可能在估计误差协方差矩阵时产生伪相关问题,导致滤波发散.协方差局部化方法(Covariance Location,CL)和局部分析(Local Analysis,LA)方法是两种常见的局部化方法,常被用于解决伪相关问题.其中,CL方法不适用于集合变换卡尔曼滤波(Ensemble Transform Kalman Filter,ETKF).近年来,虽有部分研究将变体形式的CL方法成功应用于ETKF数据同化,但计算繁琐.本文提出了随机协方差局部化(Random Covariance Location,RCL)方法,该方法也适用于ETKF同化.本文分析了RCL方法与LA方法在处理误差协方差矩阵、集合变换矩阵等方面的区别,然后将两种方法分别应用于ETKF,生成两种同化算法.本文通过算例对比了各同化算法对不同类型数值模型的同化效果.结果表明,RCL方法同样能解决伪相关问题.另一方面,对不同的模型类型,两种同化算法的同化效果各有特点:对线性平流模型,基于RCL的算法的同化效果略低于基于LA的算法,但鲁棒性更强;对非线性3元Lorenz模型,随观测误差的减小,基于RCL的算法的同化效果优于基于LA的算法,但鲁棒性略有降低.Data assimilation is a set of statistical methods.Based on the data distribution,observations and background errors,a data assimilation method integrates new observational data into the dynamic operation of numerical model and thus improve the estimate accuracy of transient state of system.Nowadays data assimilation methods are utilized in diverse research fields such as earth system science.The ensemble transform Kalman(EnKF)filter is a typical data assimilation method.In EnKF the covariance estimation of errors is crucial.Insufficient number of ensembles can introduce the pseudo-correlation problem into the estimation of error covariance matrix,thus results in the filtering divergence problem.By using the covariance localization(CL)and local analysis(AL)methods,the pseudo-correlation problem can be eliminated,where the CL method is not suitable for the ensemble transform Kalman filter(ETKF).To overcome this problem the approximate CL method is proposed with high computation complexity.In this paper,we introduce the random covariance localization(RCL)method for ETKF.Comparison is done on the error covariance matrix,the ensemble transformation matrix and the performance of the RCL and LA methods.Two assimilation algorithms are constructed by applying the RCL and LA methods to ETKF,respectively.Numerical examples are given to show the performance of two algorithms.It is shown that the former can solve the pseudo-correlation problem.On the other hand,the two algorithms hold their own characteristics for different types of model.In the case of linear advection model,the assimilation performance of the former is slightly lower than that of the latter,but with more strong robustness.In the case of nonlinear Lorenz model of three variables,the assimilation performance of the former is significant better than that of the latter with the decrease of observation errors,but with some loss of robustness.

关 键 词：数据同化 集合变换卡尔曼滤波 协方差局部化 局部分析 

分 类 号：O224[理学—运筹学与控制论]