WMOD00547

• Title: On the Sampling Variance of Raingage Networks
• Date: 12/12/1981
• Weather Modification - Doc Type: Report

1472

JOURNAL OF APPLIED METEOROLOGY

VOLUME 20

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PRECIPITATION GRADIENT INDEX (G)

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FIG, 3, The percentages of storm area containing 50% of the rainfall volume Aso as a function of precipitation gradient index G,

from each gage network placement was calculated
by the arithmetic method (Linsley et al., 1949) as-
. suming that the precipitation sampled by each gage
was the average value of its grid subarea and sum-
ming all grid subarea precipitation amounts. The
mean and standard deviation of the total raincell
precipitation of each 400 sample set corresponding

TABLE 1. Comparison of some measures of the goodness-of-fit
of the three isohyet models for a representative Montana convec-
tive raincel!. \

Ratio of
calculated Dm
Variance to theoretical Ratio of model
of Dm to computed
Model residuals. (a = 0,05).. rainfall
I J.JI 0.20 0,95
2 1.05 0.20 0,98
3 1.26 0.61 0,73

N N
· u/ = L (ei - e)2/(N - 1) where ei = Yj - Vi and e = L
I I
e;/ N. .
.. Based on the Komolgorov-Smirnov one-sample goodness-of-
fit test where Dm = IFo(x) - s.(x)1 and for which the null hy-
pothesis is rejected if the indicated ratio is greater than 1.

,
to each gage density were calculated and displayed
for each isohyetal pattern. In addition, the percent-
age of completely unsampled cases (misses) and the
maximum density at which the percentage of misses
is still ze~o (critical density) were printed out. A
typical result showing the input and output data is
shown in Fig. 2.

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4. Results

A general examination of the effects of varying
gage density (e.g., Fig. 2) indicates that the sample
mean precipitation amount :i for all gage densities
used in this study is in excellent agreement with the
true precipitation amount R TOTL, that is it is a
statistically unbiased estimate. However, there is ev-
idence that meaningful deviations between :i and
RTOTL are beginning to appear in those cases for
which the precipitation gradients are very steep and
for which the area of the model raincell is very small
compared to the gage density such that the per-
centage of unsampled cases is high (>65%). The
sample standard deviation s increases rapidly with
decreasing gage density in all cases. The variability
is caused primarily by two related factors: 1) the

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