Error analysis for some ground validation designs for satellite observations of precipitation

In this paper point gauges are used in an analysis of hypothetical ground v alidation experiments for satellite-based estimates of precipitation rates. The ground and satellite measurements are fundamentally different since th e gauge can sample continuously in time but at a discrete point, while the satellite samples an area average (typically 20 km across) but a snapshot i n time. The design consists of comparing a sequence of pairs of measurement s taken from the ground and from space. Since real rain has a large nonzero contribution at zero rain rate, the following ground truth designs are pro posed: design 1 uses all pairs, design 2 uses the pairs only when the field -of-view satellite average has rain, and design 3 uses the pairs only when the gauge has rain. The error distribution of each design is derived theore tically for a Bernoulli spatial random field with different horizontal reso lutions. It is found that design 3 cannot be used as a ground-truth design due to its large design bias. The mean-square error is used as an index of accuracy in estimating the ground measurement by satellite measurement. It is shown that there is a relationship between the mean-square error of desi gn 1 and design 2 for the Bernoulli random field. Using this technique, the authors derive the number of satellite overpasses necessary to detect a sa tellite retrieval bias, which is as large as 10% of the natural variability .