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APPENDIX I
ERRORS DUE TO THE "RANDOM CHARACTER OF RAIN"
When the precipitation depth, h, is measured with a rain gauge, a number of raindrops,
N, with different diameters is caught during a certain time, T.
If we were able to repeat the experiment, it would be expected that we would not find
the same number of drops and the same dropsize distribution. This indefiniteness in both
the number of drops and the size distribution springs from the random nature of the rainproducing
process.
We can write:
where g3 is the average value of the third power of the dropdiameters, and 0 is the area
of the orifice of the rain gauge. If we could repeat the measurement of h many times, we
would get the average value of h, N and E3, denoted by respectively h, fl and E3.
Our problem is to find the random fluctuations of h, N and E3 round their means.
A measure for these functions is the standard deviation a defined by:
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a2(x) = (x - j~)2 = x2 - ~2
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First, we remark that it is reasonable to assume that the random fluctuations of N and
D3 are independent, so we can write for small a (N) and o (E3):
Further, we note that the standard deviation of the mean of P samples of a stochastic
variable is equal to the standard deviation of the variable itself, divided by t/~. SO we can
estimate a(E3) with
This results into:
3 2 1 3 -- I
( E m N
The problem to determine a (N) remains. We, therefore, divide the time interval, T,
into M equal time intervals, where M >> N. If it is assumed that two raindrops never