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<br />reality, part of this sampling variance and not a true difference in means in <br /> <br />a statistical sense. In any given situation, the error coul d be in any <br /> <br />di rection and of any magnitude. The empirical relationships do not cover the <br />full spectrum of possibilities. In this paper we have proposed a statistical <br />solution through model simulation studies. <br /> <br />7. Di scussion <br /> <br />The quantitative results of this study of the sampling variance of precipita- <br /> <br />tion gage networks has many pot,ential hydrometeorological applications. <br />Consider, for example, its application in estimating the sample size require- <br /> <br />ments in evaluating precipitation augmentation experiments. The s,ample size <br />requirements for a 50/50 randomized precipitation augmentation experiment may <br />be calculated from the following expression: <br /> <br />N = ~~ZI_a + ZI-B) 2 s2 <br />D2 <br /> <br />(3 ) <br /> <br />where D =ldlogX; normal distribution <br />(1 + d); log-normal distribution <br /> <br />and N is the total sample size, Z is the normal standard deviate, IX is the <br /> <br />probabi 1 i ty of a Type I error, IB is the probabi 1 i ty of a Type I I error, s is <br />the standard deviation (of the log-transformed variable for a log-normal <br />distribution) of the nonseeded sample, x is the mean of the nonseeded <br />sample, and d is the fractional difference in means that it is desired to <br />detect. We first calculate the sample size requirements due to sampling <br />variance alone, Nsv, assumi ng that all the storms are identical but pass <br />over the gage networks in a random manner. Each combination of G and GPR that <br /> <br />17 <br /> <br />/ <br />