The Quality of Skill Forecasts for a Low-Order Spectral Model

P. L. Houtekamer Royal Netherlands Meteorological Institute, De Bilt, The Netherlands

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Abstract

A skill forecast gives the probability distribution for the error in the forecast. The purpose of this paper is to develop a skill-forecasting method. The method is applied to a spectral two-layer quasigeostrophic atmospheric model with a triangular truncation at wavenumber 5. The analysis is restricted to internal error growth. It is investigated how observational errors lead to errors in the analysis. It appears that climatological distributions can be used for the errors in the analysis. In the forecast run the evolution of these distributions is computed. For that purpose the tangent-linear equations for the errors are used. Because of this linearization, the results are valid for short-range skill forecasts only. The Lanczos algorithm is used to find the structures that dominate the forecast error. This algorithm is intended to be applicable in a realistic model.

Abstract

A skill forecast gives the probability distribution for the error in the forecast. The purpose of this paper is to develop a skill-forecasting method. The method is applied to a spectral two-layer quasigeostrophic atmospheric model with a triangular truncation at wavenumber 5. The analysis is restricted to internal error growth. It is investigated how observational errors lead to errors in the analysis. It appears that climatological distributions can be used for the errors in the analysis. In the forecast run the evolution of these distributions is computed. For that purpose the tangent-linear equations for the errors are used. Because of this linearization, the results are valid for short-range skill forecasts only. The Lanczos algorithm is used to find the structures that dominate the forecast error. This algorithm is intended to be applicable in a realistic model.

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