Nonlinear Measurement Function in the Ensemble Kalman Filter

• Published in: Advances in atmospheric sciences Vol. 31; no. 3; pp. 551 - 558
• Main Authors: Tang, Youmin, Ambandan, Jaison, Chen, Dake
• Format: Journal Article
• Language: English
• Published: Heidelberg Science Press 01.05.2014; Springer Nature B.V; Environmental Science and Engineering, University of Northern British, Columbia, Prince George, Canada, V2N 4Z9; State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012%Environmental Science and Engineering, University of Northern British, Columbia, Prince George, Canada, V2N 4Z9; International Max Planck Research School on Earth System Modelling, Max Planck Institute for Meteorology,Hamburg, Germany 20146%State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012
• Subjects: Algorithms; Atmospheric Sciences; Dynamical systems; Earth and Environmental Science; Earth Sciences; Equivalence; Gain; Geophysics/Geodesy; Kalman; Kalman filters; Mathematical models; Meteorology; Nonlinearity; Optimization; 卡尔曼滤波算法; 增益算法; 测量功能; 组件模型; 统计分析; 集合; 非线性动力系统; measurement function; data assimilation; ensemble Kalman filter
• ISSN: 0256-1530; 1861-9533
• DOI: 10.1007/s00376-013-3117-9

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.