Filtering properties of wavelets for local background-error correlations

Olivier Pannekoucke (1) , Loïk Berre (1) , Gérald Desroziers (1)

1 CNRM - Centre national de recherches météorologiques

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.

Keywords: assimilation ensemble; background-error covariance; Ensemble Kalman Filter; sampling noise; spherical wavelet; wavelet on the circle

Domains: Sciences of the Universe [physics]; Other

Olivier Pannekoucke, Loïk Berre, Gérald Desroziers. Filtering properties of wavelets for local background-error correlations. Quarterly Journal of the Royal Meteorological Society, 2007, 133 (623), pp.363-379. ⟨10.1002/qj.33⟩. ⟨meteo-00202094⟩