Background error correlation length-scale estimates and their sampling statistics

WARNING : This is a preprint of an article accepted for publication in QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY ref: Q. J. R. Meteorol. Soc. 134: 497–508 (2008) see the website for final version http://www.interscience.wiley.com/International audienceThis 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