A Robust Gaussian variogram estimator for cartography of hydrological extreme events

Abstract

Kriging is used for spatial interpolation of geophysical and hydrological variables. This technique requires the definition of a mathematical function of spatial correlation known as variogram. Extreme value mapping is critical for the analysis of hydrological problems such as multiple risk and disaster damage valuation. However, the formulation of a variogram is complex and the selection of the variogram model is often crucial in the final representation of extreme values. There is some evidence that a variogram estimator may reduce the negative impact of using data samples with outliers. This is an approach that eliminates the term that takes into consideration the squared differences of empirical values in the calculation of a variogram. Known as Cressie–Hawkins Estimator (CH), it is based on considering a Gaussian distribution for the calculation of the variogram. The CH satisfies the main statistical considerations of normality; however, the formulation of kurtosis is not used to guarantee total normality. The present paper modifies the CH, adding the term corresponding to the fourth statistical moment. The numerical example proposed in the literature to evaluate the efficiency of the CH is reproduced, and it is verified that the new variogram (CH-GLo) decreases further the effect of the extreme values in the cartography. CH-GLo is applied to cartography an extreme storm that happened in August 2014 in the city of Queretaro, Mexico. It is concluded that this new variogram formulation is a suitable alternative for mapping extreme values monitored in real-time in urban areas.