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Filtering properties of wavelets for local background‐error correlations
Author(s) -
Pannekoucke Olivier,
Berre Loïk,
Desroziers Gerald
Publication year - 2007
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.33
Subject(s) - wavelet , diagonal , noise (video) , filter (signal processing) , sampling (signal processing) , mathematics , scale (ratio) , statistics , statistical physics , algorithm , computer science , artificial intelligence , physics , geography , geometry , cartography , image (mathematics) , computer vision
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 Météo‐France Arpège 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. Copyright © 2007 Royal Meteorological Society