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Using Ensemble Forecasts for Model Validation

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  • 1 Recherche en Prévision Numérique, Atmospheric Environment Service, Dorval, Quebec, Canada
  • | 2 Canadian Meteorological Centre, Atmospheric Environment Service, Dorval, Quebec, Canada
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Abstract

An experimental ensemble forecasting system has been set up in an attempt to simulate all sources of forecast error. Errors in the observations, in the surface fields, and in the forecast model have been simulated. This has been done in different ways for different members of the ensemble. In particular, the N forecasting systems used for the N ensemble members differ in N − 1 aspects.

A model is proposed that writes the systematic component of the forecast error as the sum of the ensemble mean error and a linear combination of the impact of the N − 1 basic modifications to the forecasting system. The N − 1 coefficients of this expansion are the parameters that are to be determined from a comparison with radiosonde observations. For this purpose a merit function is defined that measures the total distance of a set of forecasts, at different days, to the verifying observations. The N − 1 coefficients, which minimize the merit function, are found using a least squares solution. The solution is the best forecasting system that can be obtained at a given truncation using a given set of parametrizations of physical processes and a given set of possibilities for the data assimilation system.

With the above system, several dependent aspects of the forecasting system have been simultaneously validated as a by-product of a daily ensemble forecast. The error bars on the validation results give information on the extent to which changes to the forecasting system are, or are not, confirmed by radiosonde measurements. As an example, results are given for the period 28 March through 17 April 1996.

Corresponding author address: Dr. Peter Houtekamer, Division de Recherche en Prévision Numérique, 2121 route Trans-canadienne, Dorval, PQ H9P 1J3, Canada.

Email: Peter.Houtekamer@ec.gc.ca

Abstract

An experimental ensemble forecasting system has been set up in an attempt to simulate all sources of forecast error. Errors in the observations, in the surface fields, and in the forecast model have been simulated. This has been done in different ways for different members of the ensemble. In particular, the N forecasting systems used for the N ensemble members differ in N − 1 aspects.

A model is proposed that writes the systematic component of the forecast error as the sum of the ensemble mean error and a linear combination of the impact of the N − 1 basic modifications to the forecasting system. The N − 1 coefficients of this expansion are the parameters that are to be determined from a comparison with radiosonde observations. For this purpose a merit function is defined that measures the total distance of a set of forecasts, at different days, to the verifying observations. The N − 1 coefficients, which minimize the merit function, are found using a least squares solution. The solution is the best forecasting system that can be obtained at a given truncation using a given set of parametrizations of physical processes and a given set of possibilities for the data assimilation system.

With the above system, several dependent aspects of the forecasting system have been simultaneously validated as a by-product of a daily ensemble forecast. The error bars on the validation results give information on the extent to which changes to the forecasting system are, or are not, confirmed by radiosonde measurements. As an example, results are given for the period 28 March through 17 April 1996.

Corresponding author address: Dr. Peter Houtekamer, Division de Recherche en Prévision Numérique, 2121 route Trans-canadienne, Dorval, PQ H9P 1J3, Canada.

Email: Peter.Houtekamer@ec.gc.ca

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