A variational method for correcting non-systematic errors in numerical weather prediction

A variational method based on previous numerical forecasts is developed to estimate and correct non-systematic component of numerical weather forecast error. In the method, it is assumed that the error is linearly dependent on some combination of the forecast fields, and three types of forecast combination are applied to identifying the forecasting error: 1) the forecasts at the ending time, 2) thecombination of initial fields and the forecasts at the ending time, and 3) the combination of the forecasts at the ending time and the tendency of the forecast. The Single Value Decomposition (SVD) of the covariance matrix between the forecast and forecasting error is used to obtain the inverse mapping from flow space to the error space during the training period. The background covariance matrix is hereby reduced to a simple diagonal matrix. The method is tested with a shallow-water equation model by introducing two different model errors. The results of error correction for 6, 24 and 48 h forecasts show that the method is effective for improving the quality of the forecast when the forecasting error obviously exceeds the analysis error and it is optimal when the third type of forecast combinations is applied.

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