A Scale-Dependent Quality Index of Areal Rainfall Prediction

Eddy Yates Laboratoire d’étude des Transferts en Hydrologie et Environnement, Grenoble, France

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Jean-Dominique Creutin Laboratoire d’étude des Transferts en Hydrologie et Environnement, Grenoble, France

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Sandrine Anquetin Laboratoire d’étude des Transferts en Hydrologie et Environnement, Grenoble, France

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Jacques Rivoirard Centre de Géostatistique, Ecole des Mines de Paris, Fontainebleau, France

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Abstract

Many performance indexes have been proposed to assess the quality of predicted rainfall fields. Each new index is generally tested on schematic cases or on case studies. A quality index of predicted rainfall fields is proposed based on the evolution versus scale of the correlation between observed and predicted areal rainfalls, for different scales of integrating surfaces. The authors examine this quality index with both an analytical and a numerical approach. The geostatistical structure of the rainfall field is assumed known. The index generally shows a fast increase around a scale, which is called “critical scale.”

The effect on this index of a bad localization of the predicted field is to change the critical scale, and there is a simple link between the shift and this critical scale. This link depends on the short-range structure of the rainfall field for small shifts.

The effect of having a reference known only by point measures and interpolation is a decrease of the index. An even repartition of the rain gauges improves the index. The critical scale for a perfectly localized simulation corresponds to a surface containing one rain gauge. If the simulation is badly localized, the index cannot see the bad localization if the shift is smaller than the distance between two rain gauges.

Corresponding author address: Eddy Yates, Laboratoire d’étude des Transferts en Hydrologie et Environnement, BP 53, 38 041 Grenoble CEDEX 09, France. Email: eddy-yates@yahoo.fr

Abstract

Many performance indexes have been proposed to assess the quality of predicted rainfall fields. Each new index is generally tested on schematic cases or on case studies. A quality index of predicted rainfall fields is proposed based on the evolution versus scale of the correlation between observed and predicted areal rainfalls, for different scales of integrating surfaces. The authors examine this quality index with both an analytical and a numerical approach. The geostatistical structure of the rainfall field is assumed known. The index generally shows a fast increase around a scale, which is called “critical scale.”

The effect on this index of a bad localization of the predicted field is to change the critical scale, and there is a simple link between the shift and this critical scale. This link depends on the short-range structure of the rainfall field for small shifts.

The effect of having a reference known only by point measures and interpolation is a decrease of the index. An even repartition of the rain gauges improves the index. The critical scale for a perfectly localized simulation corresponds to a surface containing one rain gauge. If the simulation is badly localized, the index cannot see the bad localization if the shift is smaller than the distance between two rain gauges.

Corresponding author address: Eddy Yates, Laboratoire d’étude des Transferts en Hydrologie et Environnement, BP 53, 38 041 Grenoble CEDEX 09, France. Email: eddy-yates@yahoo.fr

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