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Improving the Ensemble Transform Kalman Filter Using a Second-order Taylor Approximation of the Nonlinear Observation Operator : Volume 1, Issue 1 (11/04/2014)

By Wu, G.

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Book Id: WPLBN0004020100
Format Type: PDF Article :
File Size: Pages 40
Reproduction Date: 2015

Title: Improving the Ensemble Transform Kalman Filter Using a Second-order Taylor Approximation of the Nonlinear Observation Operator : Volume 1, Issue 1 (11/04/2014)  
Author: Wu, G.
Volume: Vol. 1, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Zhang, S., Wang, L., Wu, G., Zhang, X., Liang, X., & Zheng, X. (2014). Improving the Ensemble Transform Kalman Filter Using a Second-order Taylor Approximation of the Nonlinear Observation Operator : Volume 1, Issue 1 (11/04/2014). Retrieved from

Description: State Key Laboratory of Remote Sensing Science, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China. The Ensemble Transform Kalman Filter (ETKF) assimilation scheme has recently seen rapid development and wide application. As a specific implementation of the Ensemble Kalman Filter (EnKF), the ETKF is computationally more efficient than the conventional EnKF. However, the current implementation of the ETKF still has some limitations when the observation operator is strongly nonlinear. One problem is that the nonlinear operator and its tangent-linear operator are iteratively calculated in the minimization of a nonlinear objective function similar to 4DVAR, which may be computationally expensive. Another problem is that it uses the tangent-linear approximation of the observation operator to estimate the multiplicative inflation factor of the forecast errors, which may not be sufficiently accurate.

This study seeks a way to avoid these problems. First, we apply the second-order Taylor approximation of the nonlinear observation operator to avoid iteratively calculating the operator and its tangent-linear operator. The related computational cost is also discussed. Second, we propose a scheme to estimate the inflation factor when the observation operator is strongly nonlinear. Experimentation with the Lorenz-96 model shows that using the second-order Taylor approximation of the nonlinear observation operator leads to a reduction of the analysis error compared with the traditional linear approximation. Similarly, the proposed inflation scheme leads to a reduction of the analysis error compared with the procedure using the traditional inflation scheme.

Improving the ensemble transform Kalman filter using a second-order Taylor approximation of the nonlinear observation operator

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