Diagnosis and normalization of gridpoint background-error variances induced by a block-diagonal wavelet covariance matrix
Chabot, Vincent ; Berre, Loïk ; Desroziers, Gérald
Année de publication
2017
<span style="color:#800080;"><font face="Times New Roman, serif"><font style="font-size: 12pt" size="3">Abstract</font></font></span></h2><p align="justify"><span style="color:#800080;">A wavelet block-diagonal approach can be used in order to specify 3D background error covariances from ensemble data. In this study, it is first formally demonstrated how resulting variances in grid point space can be expressed and diagnosed from variances of wavelet coefficients of background errors. It is shown in particular that grid point variances can be seen as resulting from the application of scale-dependent spatial filters to wavelet variance fields. In the context of correlation modelling, these formal results can be used for computing normalisation coefficients in an accurate and efficient way, in order to ensure that diagonal elements of the resulting correlation matrix are effectively equal to one. The links between these normalisation coefficients and correlation length scales are illustrated and discussed. The impact of this normalisation approach is also examined in analysis and forecast experiments with the Météo-France ARPEGE 4D-Var system.</span></p>
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