Diagnostic and impact studies of a wavelet formulation of background‐error correlations in a global model

Abstract

AbstractA wavelet formulation on the sphere is being considered for modelling heterogeneous background‐error correlations for the Météo‐France global numerical weather prediction (NWP) model. This approach is compared with the operational spectral formulation, which is horizontally homogeneous to a large extent. Diagnostic studies have been conducted to examine geographical variations of three‐dimensional correlations over the whole globe. Results indicate that the contrast between relatively broad horizontal correlations in the Tropics and sharp ones in midlatitudes is well represented by the wavelet formulation. Heterogeneities in vertical correlations are also better captured in the wavelet approach than in the spectral one, with visible changes as functions of e.g. latitude and land/sea contrasts. In addition, wavelet‐based correlation estimates are shown to be partly sensitive to the choice of the calibration period. The impact of the wavelet formulation on the forecast quality has been investigated during a three‐week calibration period, and also during the following three weeks. While the impact of the wavelet formulation is globally positive during the two periods, it tends to be more spectacular during the calibration time interval, as expected. These results indicate that an on‐line calibration should be considered in the future, in order to exploit fully the ability of wavelets to extract correlation heterogeneities from ensemble data. Copyright © 2011 Royal Meteorological Society