WMOD00546

• Project Name: High Plains Cooperative Program
• Title: On the Sampling Variance of Raingage Networks
• Weather Modification - Doc Type: Report

The t.erms in Eq. (2) are presented in the order with which they contribute
to the explanation of the variance of s/i. The multiple correlation
coefficient for this equation is 0.992 such that 98.4 percent of the variance
of six is accounted for by the y'egression equation. The fi rst term in
the equation alone accounts for 80 percent of the variance. Thus, it can be
seen that the data are very well fitted by Eq. (2). The coefficient of
variation is primarily a function of the number of gages per raincell and
secondarily, but importantly, a function of the spatial precipitation gradient.
It should be noted that the coefficient of variation is independent of the
location of the precipitation maximum in the isohyetal pattern.

According to random sampling theory, the standard deviation (and coefficient
of variation) should be inversely proportional to the square root of GPR.
Independent variables involving this term were, therefore, included in the
search for an appropriate regression equation. The term GPRO.5 was not
selected early in the stepwise regression although it alone had a multiple
correlation coefficient of 0.916. However, the first term selected, (G/GPR)0.5,
included this functional relationship and had a multiple correlation coefficient
of 0.978. In fact, the regression equation s/i = 0.8659 (G/GPR)0.5 +
0.2549/GPR fit the data quite WE!ll and had a multiple correlation coefficient
of 0.990. This equation was not selected as the best fit of the data because
it systematically overestimated the values of s/i at very high values
of GPR. Attempts to improve the fit in this range by the inclusion of
additional terms resulted in an equation which predicted negative values of
s/i for some of the high values of GPR.

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