WMOD00547

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

DECEMBER 1981

SILVERMAN, ROGERS AND DAHL

1477

tation experiment. The network sampling variance
component is responsible for < 10% of the total sam-
ple size requirement with a gage density of at least
two per rain cell (an average of four per storm) and
< 27% with a gage density of only one per raincell
(an average of two per storm). Based on the observed
raincell areas and their contribution to the storm's
total rainfall, this corresponds to moderately dense
raingage networks of 45-80 km2 per gage and 90-
160 km2 per gage, respectively. In view of the large
natural variability, there does not appear to be any
advantage in using higher density gage networks.
The main thrust should, for the present, be in the
direction of reducing the natural variability by phys-
ically meaningful stratifications according to predic-
tor variables and covariates. ,It, however, should be
noted that as the efforts to reduce the natural vari-
ability succeed, the importance of network sampling
variance will increase and higher density gage net-
works will be required to attain reasonable sample
sizes in precipitation augmentation experiments.
These results are consistent with the conclusions
of Heimbach and Super (1980) and Olsen and
Woodley (1955) who also assessed the effect of rain-
gage density on the evaluation of simulated precip-
itation enhancement experiments and found that nat-
ural rain variability is the major obstacle in the
determination of a seeding effect. They too stressed
the need for developing covariates and/or predictor
variables to effectively deal with the rain variability
issue.
The large natural variability in convective storm
precipitation volume and the resulting large sample
size requirements to evaluate precipitation augmen-
tation experiments led Huff (1968b) to suggest an
evaluation approach that is based on detecting
changes in the spatial distribution of precipitation
as given by its area-depth relationship. Implicit in
this suggestion, assuming that seeding does, in fact,
cause such changes, is that gage networks of suffi-
cient density to define the area-depth curves of the
experimental storms accurately are used in the pre-
cipitation augmentation experiments. Also implicit
in this suggestion is the assumption that the char-
acteristic parameters of the area-depth curves exhibit
less natural variability with respect to the magnitude
of the changes due to seeding than does mean pre-
cipitation. Eddy (1976) has shown that considerably
higher gage densities are needed to define the struc-
ture of an isohyetal pattern with reasonable accuracy
than are needed to determine total storm precipita-
tion volume. Huffs suggestion is, nevertheless, in-
triguing and, since the overall cost of an experiment
is affected more by the number of seasons it must
run than the number of precipitation gages it em-
ploys, it would be worthwhile to pursue his suggestion
further by examining the statistical properties of
area-depth curve parameters.

i

TABLE 5, Percentage contribution of total sample size to detect
a 25% cha.nge in mean Montana storm precipitation due to sam-
pling variance as a function of gage density (based on both the
median art:a of all rain cells A I, and the median area of the primary
raincells ,<(2)'

Gage density
(km2 fgage) Percentage contribution
by network sampling
GPR Al A2 variance
100 0,9 1.6 0,05
50 1.8 3,2 0,05
10 9,0 16,0 0,5
5 18,0 32,0 1.9
2 45,0 80,0 9,9
I 90,0 160,0 26,9
0,5 180,0 320,0 50,7

An examination of Table 5 reveals other possibil-
ities. Since the values of the coefficient of variation
(log-normal standard deviation for log-normally dis-
tributed variables) for storm area and storm duration
are considerably less than that for storm rainfall vol-
ume, a smaller sample size will be required to detect
an equivalent or even smaller seeding effect if the
evaluation of the experiment were based on these
rain characteristics. Ackerman et al. (1976)6 ob-
tained similar results from an investigation of sample
size requirements for various rain parameters of
METROMEX raincells. Increases in the values of
both parameters have been postulated as a result of
seeding for dynamic effects (Simpson, 1980) which
is thought to induce the merger of neighboring
storms and/or sustain the propagation of the storm
by encouraging the development of additional rain-
cells.

8. Summary

Estimates of precipitation volume from preCIpI-
tation gage networks are subject to a component of
variability that is caused by the random direction of
movement and orientation of the storm and the vari-
ations in storm structure. A computer model of rain-
cell isohyetal patterns has been used to assess quan-
titatively the sampling variance of gage networks.
We have shown that the coefficient of variation in-
creases with decreasing gage density and increasing
precipitation gradient. Contrary to the sampling er-
ror studies of other investigators, it was found that
the mean precipitation remained unbiased as the
gage density decreased but its standard deviation in-
creased.

6 Ackerman, 8., G, L. Achtemeier, H, Appleman, S,A. Chang-
non, F. A., Huff, G, M, Morgan, P. T, Schickedanz, and R, G,
Semonin, 1976: Design of the High Plains Experiment with specific
focus on Phase 2, single cloud experimentation, Illinois State
Water Survey Final Report, Contract 14-06-D-7197 Div, of At-
mos, Water Resour, Management, Bureau of Reclamation, 231
pp.