RAINOUT RELATIONS ON SAMPLING NETWORKS
915
observational and analytical errors involved in the calculations of
radioactivity at a point, the above assumptions are not completely
correct in some cases. These errors could result in differences that
are greater or less than the true difference in a specific case, but,
after a large number of cases are combined, the resulting average difference should closely approximate the true relation. The 15-storm
averages used in the Illinois study are considered adequate to provide
an approximation of the general magnitude of the point vs. areal dif-
ferences, but a large number of storms must be analyzed before a
highly accurate measurement of these differences can be assured.
Also, it should be realized that the magnitude of the differences between point and areal measurements would be expected to be larger,
on the average, if a central sampling gauge were not used for the point
measurement. The decrease in reliability of a point estimate of the
areal mean as the distance of the single sampling point increases from
the center of the area has been clearly demonstrated by Linsley and
Kohler® with the use of rainfall data from a concentrated network of
gauges.
Gauge 3, located near the center of the network, was used as the
central gauge on the Kaskaskia network (Fig. 1), and areal means were
based on the samples collected at each of the five gauges in the net-
work. This network provides a nearly uniform sampling network, at
least within practical limitations dictated by the existing road systems.
Gauge 11 (Fig. 1) was used as the Single point sample on the Boneyard
network, and the areal means were based on five or six samples col-
lected in each storm on the network. The sampling stations were not
situated as uniformly as on the Kaskaskia network.
The data from the Kaskaskia and the Boneyard networks were
combined to obtain a larger sample in this initial study, and average
sampling errors were calculated. The sampling error was obtained by
dividing the difference between the central gauge and the network
average by the network average and multiplying by 100. An average
error of 23% was obtained for gross beta concentrationin the 15-storm
sample, compared with 22% for deposition and 9% for storm rainfall.
Standard deviations from these mean percentages were 12, 15, and 3%,
respectively, for beta concentration, beta deposition, and storm rain-
fall. From this limited sample, indications are that a single sampling
point in areas of 10 to 12 square miles will indicate the average gross
beta rainout over the area in convective rainstorms with an average
accuracy of 20 to 25%; however, in approximately one-third of the
storms, the sampling error may equal or exceed 35%. Of course, as
pointed out earlier, a much larger sample must be analyzed before the
size of the sampling errors can be established with a high degree of
accuracy.