Error analysis of rain gauge and satellite estimates using a high-density gauge data set for West Africa

Gauge data from two West African networks, a dense network of 920 stations for 1998 and a long-term network of 211 stations, are used to estimate the errors of satellite products. The satellite error is determined by subracting the rain gauge estimation error from the satellite vs. gauge difference, as the rain gauge error cannot be neglected, particularly for regions with low gauge density. An existing expression for the sampling error of the rain gauge arithmetic mean is re-derived for application to an arbritrary spatial interpolation scheme. This expression is used to estimate the sampling error of the inverse-distance interpolation scheme used to create the area-averaged rain gauge estimates used for validation of satellite products using these networks in two prior companion studies. The high-density network is used for sub-sampling investigations to verify the sampling error formula for typical gauge densities of only few gauges per 2.5 degree grid box found in both our long-term network and the global rain gauge data set used in the Global Precipitation Climatology Project (GPCP). Through this work, we can put error bars on the satellite vs. gauge comparisons of the companion studies, a key aspect for interpreting the results.