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Background‐error correlation length‐scale estimates and their sampling statistics
Author(s) -
Pannekoucke O.,
Berre L.,
Desroziers G.
Publication year - 2008
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.212
Subject(s) - standard deviation , scale (ratio) , spatial correlation , statistics , computation , mathematics , sampling (signal processing) , context (archaeology) , correlation , standard error , noise (video) , statistical physics , computer science , algorithm , geography , geometry , artificial intelligence , physics , cartography , archaeology , filter (signal processing) , image (mathematics) , computer vision
This article presents different formulae to estimate correlation length‐scales, and an evaluation of their qualities for practical diagnostic applications. In particular, two new and simple formulae are introduced, which only require the computation of correlation with a single point for a given direction. It is then shown in a 1D heterogeneous context that all formulations lead to similar realistic length‐scale values, and that they represent geographical variations rather well. The estimation of length‐scales within a finite ensemble is also studied. While a positive bias occurs when the ensemble size is too small, the standard deviation of the length‐scale estimation is shown to be the main influence on the estimation error. The spatial structure of sampling noise is then diagnosed, and effects of spatial filtering techniques on the bias and standard deviation are illustrated. Finally, an ensemble of perturbed forecasts from a global NWP model is used, showing a real application example. Copyright © 2008 Royal Meteorological Society