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5. SPATIAL VARIABILITY WITHIN A PRECIPITATION FIELD
From our own experiences we know that the spatial distribution of precipitation can
be highly irregular. The meteorological processes responsible for this variability were
reviewed this morning by Schmidt (1976).
To illustrate the possible differences over a short distance, the spatial distribution of
the daily precipitation amounts is shown in Figure 3, as measured on May 24, 1972, with
a dense network installed in Salland, a district in the eastern part of the Netherlands, in
1970-1972. This was done within the framework of a hydrological research programme
(Santing et al., 1974).
In this figure the same precipitation field is drawn as "seen" by the (less denser)
national rain gauge network of the Royal Netherlands Meteorological Institute.
This example shows that, over distances of 1 kilometre, differences of 20 mm/day can
occur.
Generally, these differences within areas such as Salland are not systematic. For most
of the practical applications, areas in the Netherlands of, say, 1000 krn2 can largely be
considered to be climatologically homogeneous and isotrope.
It will be pointed out in the next section that a convenient quantity to describe the
statistical spatial structure of a precipitation field is the correlation coefficient, p, defined
by:
in which the bars indicate an average over a long time series; hi and hk are the precipitation
depth measured at the ith and kth station, while oi and ok are the standard deviations
(of time series) of these stations.
If the distance between the two stations is denoted by rik, it is to be expected that
pik decreases with increasing rik, if a homogeneous and isotrope area is considered.
It has been found (see e.g. St01 (1972) and De Bruin, (1975) that the "correlation
function", p(r), can be (more or less) satisfactorily described by:
which relationship can be written for r