Ensemble Size, Balance, and Model-Error Representation in an Ensemble Kalman Filter

Herschel L. Mitchell Direction de la Recherche en Météorologie, Meteorological Service of Canada, Dorval, Quebec, Canada

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P. L. Houtekamer Direction de la Recherche en Météorologie, Meteorological Service of Canada, Dorval, Quebec, Canada

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Gérard Pellerin Centre Météorologique Canadien, Meteorological Service of Canada, Dorval, Quebec, Canada

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Abstract

The ensemble Kalman filter (EnKF) has been proposed for operational atmospheric data assimilation. Some outstanding issues relate to the required ensemble size, the impact of localization methods on balance, and the representation of model error.

To investigate these issues, a sequential EnKF has been used to assimilate simulated radiosonde, satellite thickness, and aircraft reports into a dry, global, primitive-equation model. The model uses the simple forcing and dissipation proposed by Held and Suarez. It has 21 levels in the vertical, includes topography, and uses a 144 × 72 horizontal grid. In total, about 80 000 observations are assimilated per day.

It is found that the use of severe localization in the EnKF causes substantial imbalance in the analyses. As the distance of imposed zero correlation increases to about 3000 km, the amount of imbalance becomes acceptably small.

A series of 14-day data assimilation cycles are performed with different configurations of the EnKF. Included is an experiment in which the model is assumed to be perfect and experiments in which model error is simulated by the addition of an ensemble of approximately balanced model perturbations with a specified statistical structure. The results indicate that the EnKF, with 64 ensemble members, performs well in the present context.

The growth rate of small perturbations in the model is examined and found to be slow compared with the corresponding growth rate in an operational forecast model. This is partly due to a lack of horizontal resolution and partly due to a lack of realistic parameterizations. The growth rates in both models are found to be smaller than the growth rate of differences between forecasts with the operational model and verifying analyses. It is concluded that model-error simulation would be important, if either of these models were to be used with the EnKF for the assimilation of real observations.

Corresponding author address: Dr. Herschel L. Mitchell, Direction de la Recherche en Météorologie, 2121 Route Trans-Canadienne, Dorval, QC H9P 1J3, Canada. Email: Herschel.Mitchell@ec.gc.ca

Abstract

The ensemble Kalman filter (EnKF) has been proposed for operational atmospheric data assimilation. Some outstanding issues relate to the required ensemble size, the impact of localization methods on balance, and the representation of model error.

To investigate these issues, a sequential EnKF has been used to assimilate simulated radiosonde, satellite thickness, and aircraft reports into a dry, global, primitive-equation model. The model uses the simple forcing and dissipation proposed by Held and Suarez. It has 21 levels in the vertical, includes topography, and uses a 144 × 72 horizontal grid. In total, about 80 000 observations are assimilated per day.

It is found that the use of severe localization in the EnKF causes substantial imbalance in the analyses. As the distance of imposed zero correlation increases to about 3000 km, the amount of imbalance becomes acceptably small.

A series of 14-day data assimilation cycles are performed with different configurations of the EnKF. Included is an experiment in which the model is assumed to be perfect and experiments in which model error is simulated by the addition of an ensemble of approximately balanced model perturbations with a specified statistical structure. The results indicate that the EnKF, with 64 ensemble members, performs well in the present context.

The growth rate of small perturbations in the model is examined and found to be slow compared with the corresponding growth rate in an operational forecast model. This is partly due to a lack of horizontal resolution and partly due to a lack of realistic parameterizations. The growth rates in both models are found to be smaller than the growth rate of differences between forecasts with the operational model and verifying analyses. It is concluded that model-error simulation would be important, if either of these models were to be used with the EnKF for the assimilation of real observations.

Corresponding author address: Dr. Herschel L. Mitchell, Direction de la Recherche en Météorologie, 2121 Route Trans-Canadienne, Dorval, QC H9P 1J3, Canada. Email: Herschel.Mitchell@ec.gc.ca

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