Filtering properties of wavelets for local background-error correlations

Abstract : Background-error covariances can be estimated from an ensemble of forecast differences. The finite size of the ensemble induces a sampling noise in the calculated statistics. It is shown formally that a wavelet diagonal approach amounts to locally averaging the correlations, and its ability to spatially filter this sampling noise is thus investigated experimentally. This is first studied in a simple analytical one-dimensional framework. The capacity of a wavelet diagonal approach to model the scale variations over the domain is illustrated. Moreover, the sampling noise appears to be better filtered than when only using a Schur filter, in particular for small ensembles. The filtering properties are then illustrated for an ensemble of Meteo-France Arpege forecasts. This is done both for the ‘time-averaged correlations', and for the ‘correlations of the day'. It is shown that the wavelets are able to extract some length-scale variations that are related to the meteorological situation.
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Olivier Pannekoucke, Loïk Berre, Gérald Desroziers. Filtering properties of wavelets for local background-error correlations. Quarterly Journal of the Royal Meteorological Society, Wiley, 2007, 133 (623), pp.363-379. ⟨10.1002/qj.33⟩. ⟨meteo-00202094⟩

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