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Nonlinear Measurement Function in the Ensemble Kalman Filter

Advances in Atmospheric Sciences 2014年第3期31卷 551-558页

作者： Youmin TANG Jaison AMBANDAN Dake CHEN Environmental Science and Engineering University of Northern BritishColumbiaPrince GeorgeCanadaV2N 4Z9 State Key Laboratory of Satellite Ocean Environment Dynamics Second Institute of OceanographyState Oceanic Administration International Max Planck Research School on Earth System Modelling Max Planck Institute for MeteorologyHamburgGermany 20146

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.

关键词： ensemble Kalman filter measurement function data assimilation.

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