Geostatistical radar–raingauge merging: A novel method for the quantification of rain estimation accuracy

Abstract Compared to other estimation techniques, one advantage of geostatistical techniques is that they provide an index of the estimation accuracy of the variable of interest with the kriging estimation standard deviation (ESD). In the context of radar–raingauge quantitative precipitation estimation (QPE), we address in this article the question of how the kriging ESD can be transformed into a local spread of error by using the dependency of radar errors to the rain amount analyzed in previous work. The proposed approach is implemented for the most significant rain events observed in 2008 in the Cevennes-Vivarais region, France, by considering both the kriging with external drift (KED) and the ordinary kriging (OK) methods. A two-step procedure is implemented for estimating the rain estimation accuracy: (i) first kriging normalized ESDs are computed by using normalized variograms (sill equal to 1) to account for the observation system configuration and the spatial structure of the variable of interest (rainfall amount, residuals to the drift); (ii) based on the assumption of a linear relationship between the standard deviation and the mean of the variable of interest, a denormalization of the kriging ESDs is performed globally for a given rain event by using a cross-validation procedure. Despite the fact that the KED normalized ESDs are usually greater than the OK ones (due to an additional constraint in the kriging system and a weaker spatial structure of the residuals to the drift), the KED denormalized ESDs are generally smaller the OK ones, a result consistent with the better performance observed for the KED technique. The evolution of the mean and the standard deviation of the rainfall-scaled ESDs over a range of spatial (5–300 km 2 ) and temporal (1–6 h) scales demonstrates that there is clear added value of the radar with respect to the raingauge network for the shortest scales, which are those of interest for flash-flood prediction in the considered region.

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