Evaluation of some ground truth designs for satellite estimates of rain rate

In this paper point gauge measurements are analyzed as part of a ground truth design to validate satellite retrieval algorithms at the field-of-view spatial level (typically about 20 km). Even in the ideal case the ground and satellite measurements are fundamentally different, since the gauge can sample continuously in time but at a discrete point, while a satellite samples an area average but a snapshot in time. The design consists of comparing a sequence of pairs of measurements taken from the ground and from space. Since real rain is patchy, that is, its probability distribution has large nonzero contributions at zero rain rate, the following ground truth designs are proposed. Design 1 uses all pairs. Design 2 uses the pairs only when the field-of-view satellite average has rain. Design 3 uses the pairs only when the gauge has rain. For the nonwhite noise random field having a mixed distribution, the authors evaluate each design theoretically by deriving the ensemble mean and the mean-square error of differences between the two systems. It is found that design 3 has serious disadvantage as a ground truth design due to its large design bias. It is also shown that there is a relationship between the mean-square error of design 1 and design 2. These results generalize those presented recently by Ha and North for the Bernoulli white noise random field. The strategy developed in this study is applied to a real rain rate field. For the Global Atmospheric Program (GARP) Atlantic Tropical Experiment (GATE) data, it is found that by combining 50 data pairs (containing rain) of the satellite to the ground site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the system alone. For the less realistic case of a white noise random field, the number of data pairs is about 100. Hence, the use of more realistic fields means that only about half as many pairs are needed to detect a 10% bias.