Relationship between point rainfall, average sampled rainfall and ground truth at the event scale in the Sahel

Geostatistical techniques are used to quantify the reference mean areal rainfall (ground truth) from sparse raingaugenetworks. Based on the EPSAT-Niger event cumulative rainfall, a linear relationship between the ground truth considered as the mean area rainfall estimated from the densely available raingauge network and the area rainfall estimated from sparse network are derived. Also, a linear relationship between the ground truth and point rainfall is established. As it was reported experimentally by some authors, the slope of these relationships is less than one. Based on the geostatistical framework, the slope and the ordinate at the origin can be estimated as a function of the spatial structure of the rainfall process. It is shown that the slope is smaller than one. For the special case of one gauge inside a fixed area or a Field Of View (FOV), an areal reduction factor is derived. It has a limit value which depends only on the size of the area and the spatial structure of the rainfall process. The relative variance error of estimating the FOV cumulative rainfall from point rainfall is also given.