Editorial Type:
Article
Article Type:
Research Article

Model Error Representation in an Operational Ensemble Kalman Filter

P. L. Houtekamer Meteorological Research Division, Dorval, Québec, Canada

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Herschel L. Mitchell Meteorological Research Division, Dorval, Québec, Canada

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Xingxiu Deng Canadian Meteorological Centre, Dorval, Québec, Canada

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Print Publication:
01 Jul 2009
DOI:
https://doi.org/10.1175/2008MWR2737.1
Page(s):
2126–2143
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Abstract

Since 12 January 2005, an ensemble Kalman filter (EnKF) has been used operationally at the Meteorological Service of Canada to provide the initial conditions for the medium-range forecasts of the ensemble prediction system. One issue in EnKF development is how to best account for model error.

It is shown that in a perfect-model environment, without any model error or model error simulation, the EnKF spread remains representative of the ensemble mean error with respect to a truth integration. Consequently, the EnKF can be used to quantify the impact of the various error sources in a data-assimilation cycle on the quality of the ensemble mean.

Using real rather than simulated observations, but still not simulating model error in any manner, the rms ensemble spread is found to be too small by approximately a factor of 2. It is then attempted to account for model error by using various combinations of the following four different approaches: (i) additive isotropic model error perturbations; (ii) different versions of the model for different ensemble members; (iii) stochastic perturbations to physical tendencies; and (iv) stochastic kinetic energy backscatter.

The addition of isotropic model error perturbations is found to have the biggest impact. The identification of model error sources could lead to a more realistic, likely anisotropic, parameterization. Using different versions of the model has a small but clearly positive impact and consequently both (i) and (ii) are used in the operational EnKF. The use of approaches (iii) and (iv) did not lead to further improvements.

Corresponding author address: P. L. Houtekamer, Meteorological Research Division, 2121 Route Trans-Canadienne, Dorval, QC H9P 1J3, Canada. Email: peter.houtekamer@ec.gc.ca

Abstract

Since 12 January 2005, an ensemble Kalman filter (EnKF) has been used operationally at the Meteorological Service of Canada to provide the initial conditions for the medium-range forecasts of the ensemble prediction system. One issue in EnKF development is how to best account for model error.

It is shown that in a perfect-model environment, without any model error or model error simulation, the EnKF spread remains representative of the ensemble mean error with respect to a truth integration. Consequently, the EnKF can be used to quantify the impact of the various error sources in a data-assimilation cycle on the quality of the ensemble mean.

Using real rather than simulated observations, but still not simulating model error in any manner, the rms ensemble spread is found to be too small by approximately a factor of 2. It is then attempted to account for model error by using various combinations of the following four different approaches: (i) additive isotropic model error perturbations; (ii) different versions of the model for different ensemble members; (iii) stochastic perturbations to physical tendencies; and (iv) stochastic kinetic energy backscatter.

The addition of isotropic model error perturbations is found to have the biggest impact. The identification of model error sources could lead to a more realistic, likely anisotropic, parameterization. Using different versions of the model has a small but clearly positive impact and consequently both (i) and (ii) are used in the operational EnKF. The use of approaches (iii) and (iv) did not lead to further improvements.

Corresponding author address: P. L. Houtekamer, Meteorological Research Division, 2121 Route Trans-Canadienne, Dorval, QC H9P 1J3, Canada. Email: peter.houtekamer@ec.gc.ca

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