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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 24, 329-341, 2017
https://doi.org/10.5194/npg-24-329-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
03 Jul 2017
An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter
Guocan Wu1,2 and Xiaogu Zheng3 1College of Global Change and Earth System Science, Beijing Normal University, Beijing, China
2Joint Center for Global Change Studies, Beijing, China
3Key Laboratory of Regional Climate-Environment Research for East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China
Abstract. The ensemble Kalman filter (EnKF) is a widely used ensemble-based assimilation method, which estimates the forecast error covariance matrix using a Monte Carlo approach that involves an ensemble of short-term forecasts. While the accuracy of the forecast error covariance matrix is crucial for achieving accurate forecasts, the estimate given by the EnKF needs to be improved using inflation techniques. Otherwise, the sampling covariance matrix of perturbed forecast states will underestimate the true forecast error covariance matrix because of the limited ensemble size and large model errors, which may eventually result in the divergence of the filter.

In this study, the forecast error covariance inflation factor is estimated using a generalized cross-validation technique. The improved EnKF assimilation scheme is tested on the atmosphere-like Lorenz-96 model with spatially correlated observations, and is shown to reduce the analysis error and increase its sensitivity to the observations.


Citation: Wu, G. and Zheng, X.: An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter, Nonlin. Processes Geophys., 24, 329-341, https://doi.org/10.5194/npg-24-329-2017, 2017.
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Short summary
The accuracy of the assimilation results crucially relies on the estimate accuracy of forecast error covariance matrix in data assimilation. Ensemble Kalman filter estimates the forecast error covariance matrix as the sampling covariance matrix of the ensemble forecast states, which need to be further inflated. The experiment results on the Lorenz-96 model show that the analysis error is reduced and the analysis sensitivity to observations is improved using the proposed inflation technique.
The accuracy of the assimilation results crucially relies on the estimate accuracy of forecast...
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