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<br />
<br />FIG, 2, A typical output of the sampling variance numerical experiment showing the isohyetal pattern, its generation parameters,
<br />and the results of sampling with the indicated gage networks, Gage densities are 1,4, 11, 25 and 100 mi2 (2,6, lOA, 28,5, 64,7,
<br />and 260,0 km2) gage~l, Scale length (major axis) is 10 mi (16 km).
<br />
<br />the relative magnitudes of sampling and natural
<br />storm variability would probably be similar.
<br />One-hundred different isohyetal patterns were
<br />studied. Their parameters spanned the real-world
<br />range of variation of the input parameters (see Sec-
<br />tion 5), that is E = 1,2,3,4, and 5; G = 0.15,0.6,
<br />1.35, 2.25, and 4.95 (A so = 40, 25, 15, 10, and 5);
<br />and (X offset, Yoffset) = (0.01, 0.01), (0.01, 0.35),
<br />(0.01, 0.75), (0.75, 0.01) (0.35, 0.01), and (0.35,
<br />0.35), with only (X offset, Yoffset) = (0.35, 0.01)
<br />used for E = 4 and 5, and all values of G. The value
<br />of PM was arbitrarily set equal to 3 mm, but it should
<br />be recognized that the results of the study do not
<br />depend on the value assigned to PM since each pre-
<br />cipitation value in the pattern is the same percentage
<br />of PM whatever value PM may have. For each iso-
<br />hyetal pattern simulated, the absolute total amount
<br />of precipitation (RTOTL on Fig. 2) was calculated
<br />by numerical integration. This is the true value
<br />(ground truth) of total raincell precipitation against
<br />which the gage-estimated total rainfall precipitation
<br />values are compared. .
<br />Each model raincell was sampled by gage networks
<br />of five different gage densities, that is 1, 4, 11, 25,
<br />
<br />
<br />and 100 mi2 per gage3 (2.6, 10.4, 28.5, 64.7, and
<br />260.0 km2 per gage). In addition, 15 of the model
<br />raincells [E = 1,2 and 3 for the five values of G and
<br />for (X offset, Yoffset) = (0.35 0.35)] were sampled
<br />by gage networks with gage densities of 0.11 and
<br />0.25 mi2 per gage (0.1 and 1.0 km2 per gage). Each
<br />of the gage networks was configured as a uniformly
<br />spaced, square grid of gages in Cartesian coordinate
<br />space (gage spacing ~X = ~Y). Each gage density
<br />was systematically evaluated by placing the gage
<br />network in 400 equally probable locations with re-
<br />spect to the model raincell such that, for example,
<br />the gage at the origin, XoYo, occupied the following
<br />locations: (xo + i~l)(yo + jM), where i = 0, 1,2, . . . ,
<br />19; j = 0, 1, 2, . . ., 19; and ~l = ~x/20 = ~y/20.
<br />All of the output data from each gage network
<br />were solely determined from the resulting gage
<br />catches. The total raincell precipitation resulting
<br />
<br />3 Gage network characteristics are given in units of miles to
<br />facilitate reference to and comparison with the hydrometeoro-
<br />logical literature and, in particular, well-known gage networks and
<br />watershed areas and their associated gage densities, Metric units
<br />are given along with English units elsewhere,
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