Comparison of two kriging interpolation methods applied to spatiotemporal rainfall

Abstract

Summary The variogram structure is an effective tool in order to appraise the rainfall spatial variability. In areas with disperse raingauge network, this paper suggests a 3-D estimation of the variogram, as alternative to the classical 2-D approach for spatiotemporal rainfall analysis. The context deals with the estimation of the spatial variability of maximum intensity of rainfall for a given duration δ . Hence, a 3-coordinate vector (location – rainfall duration – rainfall intensity) is associated to each monitoring location rather than the two coordinate vector, based only on the location in relation to intensity subject to duration. A set of averaging time intervals is taken into account ( δ ranging from 5 min to 2 h). The advantage of the 3-D approach is that it results on a standardized variogram which uniquely characterizes the rainfall event. On the contrary, for the 2-D approach, variograms are subject to intensity duration. The kriging with external drift is performed to make the spatial interpolations and to compute the kriging variance maps. A full comparison of the accuracy of both methods (2-D, 3-D) using cross-validation scheme, shows that the 3-D kriging leads to significantly lower prediction errors than the classical 2-D kriging. It is further suggested to quantify the effect of 3-D and 2-D kriging on the areal rainfall distribution and on the standard deviation of the kriging error SDKE. It is noticed that the 3-D SDKE field displays an empirical distribution which represents a median position among the 2-D distributions corresponding to SDKE ( δ ) fields. On the other hand, results are compared to those obtained through ordinary kriging. In the 3-D approach, cross-validation performances and SDKE maps are found to be less sensitive to the kriging method.