Empirically-based modeling of spatial sampling uncertainties associated with rainfall measurements by rain gauges

In the quantitative evaluation of radar-rainfall products (maps), rain gauge data are generally used as a good approximation of the true ground rainfall. However, rain gauges provide accurate measurements for a specific location, while radar estimates represent areal averages. Because these sampling discrepancies could introduce noise into the comparisons between these two sensors, they need to be accounted for. In this study, the spatial sampling error is defined as the ratio between the measurements by a single rain gauge and the true areal rainfall, defined as the value obtained by averaging the measurements by an adequate number of gauges within a pixel. Using a non-parametric scheme, the authors characterize its full statistical distribution for several spatial (4, 16 and 36 km2) and temporal (15 min and hourly) scales. To accomplish this task, a large dataset (more than six years) of rain gauge measurements obtained through a highly dense rain gauge network deployed in the Brue catchment in southwest England is used. The authors show that the standard deviation of the spatial sampling error decreases with increasing rainfall intensity and accumulation time and increases with increasing pixel size. Additionally, the authors show how the Laplace distribution could be used to model the distribution of spatial sampling errors for the spatial and temporal scales considered in this study.