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We can write:
In fact:
A measure of accuracy of the estimate given by equation (11.1) is the quantity defined
A
The bar denotes an average over a large series of hG and hG.
From equations (11. I), (11.2) and (II.3), we obtain:
N -
E2 = lim 2(hthf -htho -hrho +%)
N,,N~ i=1 j=l
The measured precipitation depth, ho, can be written as
where h,* is the true precipitation depth at P, and 6 is a random measuring error with
F= 0. (For the sake of simplicity it is assumed that ho has been corrected for systematic
errors such as those due to wind).
Further, it is reasonable to assume that:
The Quantity 62 is the standard error of observations at P.
From equations (II.4), (11.5) and (11.6) we get:
As the homogeneity of S has been assumed, we can write:
(i = 1, ... N).
w-m
Thus the correlation cozff$ent
pB=
"ioj