Nonlinear Measurement Function in the Ensemble Kalman Filter

作     者：Youmin TANG Jaison AMBANDAN Dake CHEN 

作者机构：Environmental Science and EngineeringUniversity of Northern BritishColumbiaPrince GeorgeCanadaV2N 4Z9 State Key Laboratory of Satellite Ocean Environment DynamicsSecond Institute of OceanographyState Oceanic Administration International Max Planck Research School on Earth System ModellingMax Planck Institute for MeteorologyHamburgGermany 20146 

出 版 物：《Advances in Atmospheric Sciences》 (大气科学进展（英文版）)

年 卷 期：2014年第31卷第3期

页      面：551-558页

核心收录：

学科分类：08[工学] 0816[工学-测绘科学与技术] 0706[理学-大气科学] 0825[工学-航空宇航科学与技术] 

基　　金：supported by research grants from the NSERC (Natural Sciences and Engineering Research Council of Canada) Discovery Program the National Natural Science Foundation of China (Grant Nos.41276029 and 40730843) the National Basic Research Program (Grant No.2007CB816005) 

主　　题：ensemble Kalman filter measurement function data assimilation. 

摘      要：ABSTRACT The optimal Kalman gain was analyzed in a rigorous statistical framework. Emphasis was placed on a comprehensive understanding and interpretation of the current algorithm, especially when the measurement function is nonlinear. It is argued that when the measurement function is nonlinear, the current ensemble Kalman Filter algorithm seems to contain implicit assumptions： the forecast of the measurement function is unbiased or the nonlinear measurement function is linearized. While the forecast of the model state is assumed to be unbiased, the two assumptions are actually equivalent. On the above basis, we present two modified Kalman gain algorithms. Compared to the current Kalman gain algorithm, the modified ones remove the above assumptions, thereby leading to smaller estimated errors. This outcome was confirmed experimentally, in which we used the simple Lorenz 3-component model as the test-bed. It was found that in such a simple nonlinear dynamical system, the modified Kalman gain can perform better than the current one. However, the application of the modified schemes to realistic models involving nonlinear measurement functions needs to be further investigated.