Advances in Atmospheric Sciences

, Volume 31, Issue 3, pp 551–558 | Cite as

Nonlinear measurement function in the ensemble Kalman filter

  • Youmin TangEmail author
  • Jaison Ambandan
  • Dake Chen


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.

Key words

ensemble Kalman filter measurement function data assimilation 


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Copyright information

© Chinese National Committee for International Association of Meteorology and Atmospheric Sciences, Institute of Atmospheric Physics, Science Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Environmental Science and EngineeringUniversity of Northern BritishColumbiaCanada
  2. 2.State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of OceanographyState Oceanic AdministrationHangzhouChina
  3. 3.International Max Planck Research School on Earth System ModellingMax Planck Institute for MeteorologyHamburgGermany

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