The interplay between zero-rainfall and multifractal estimates of the extremes: a weighed analysis
Résumé
In the framework of the universal multifractals the scaling variability and the extremes of the rain are quantified with the help of three parameters. The multifractal analysis basically consists in estimating different statistical moments at various scales. Of course the numerous zeros of high resolution rainfall data, which by the way are either real or artificial (i.e. due to quantification effects or sensor dynamic limitations), dont influence the extremes. Nevertheless, for many reasons they influence the multifractal estimates and so the quantification of extremes. In this paper we suggest to investigate this influence. The estimates obtained with the help of this standard technique are compared to that obtained with the help of a new technique that is based on the use of weighted moments instead of the usual ones. The weight attributed to a pixel (or time step) at a larger scale depends on the percentage of zero values of the corresponding smaller scale pixels. In particular this would concentrate the rain over its support, i.e. the area where is estimated as non-zero. Both techniques are tested on two data sets corresponding to a heavy rainfall event in the south of France: the rainfall outputs of the Meso-NH model (Meteo-France/CNRM and Laboratoire dAérologie, Toulouse, France) and radar data. Both data sets exhibited the same multifractal qualitative behavior with the standard analysis but with rather significant quantitative differences. The weighed analysis yielded to the same quantitative estimates for both data sets, furthermore on a wider range of scale. Finally, the standard and the weighed analysis are applied to synthetic multifractal fields, which have been thresholded in order to reproduce the numerous zero values.