Some statistical problems inherent in measuring precipitation

A formula permitting calculation of the mean-square error of the mean value of a random variable due to periodic sampling is derived and applied to estimating the sampling error for satellite observation of the mean rainfall during the GARP Atlantic Tropical Experiment (GATE). The effects of both spatial resolution and frequency of observation on the sampling error are summarized in graphs. It is found that four observations per day are sufficient to determine the monthly mean rainfall over an area of 2.5 deg square (280km x 280km) to within a standard deviation of 5 percent of its mean value; two samples per day would yield an error with a standard deviation slightly less than 10 percent of the mean. A satellite instrument with less frequent sampling may produce significantly greater error in the estimate of monthly mean rainfall.