Agriculture Reference
In-Depth Information
2.3
Cell Sizes
Knowing that the cell squares should have side lengths between zero and the range
alone is not sufficient. Very small cells result in high costs, and rather large cells can
impair the precision. And since the number of cells that must be dealt with qua-
druples with each halving of cell-side length, more precise information about the
size that should be used is desirable. This information can be derived from the semi-
variance (Fig.
2.5
).
An interesting approach for this was developed by Russo and Bresler (
1981
) as well
as by Han et al. (
1994
). It is based on the notion that as the semivariance is an indicator
of
dissimilarity
of a site-specific soil- or crop property,
vice versa
the complement
function to the semivariance provides information of
similarity
or
relatednes
s. For
normalized situations, the semivariance plus its complement function for all respective
distances or lags add up to one (1). Therefore, the complement function is the vertical
mirror image of the semivariance (Fig.
2.5
). It can be shown that for the pairs involved,
this complement function of the semivariance is a well known statistical function - the
covariance (Davis
1973
; Gringarten and Deutsch
2001
). In contrast to this: the sill of
the semivariogram is the standard variance, which in this case stands for zero correla-
tion. Therefore, the semivariance is standard variance minus covariance.
The area under the curve of the complement function to the semivariance can be
regarded as an accumulation of all relatedness or similarity of the respective
sill = standard variance
1.0
0.8
beyond range, data are
independent of distance
0.6
0.4
0.2
40
80
120
160
range
distance or lag in m
1.0
0.8
rectangle of same area as shaded integral
0.6
0.4
0.2
distance or lag in m
0.0
0
160
upper limit of cell size
Fig. 2.5
Semivariance, its complement function and the upper limit of cell size
