Agriculture Reference
In-Depth Information
1.0
0.8
only nugget variance
0.6
0.4
0.2
nugget variance
nugget variance
0.0
60
120
180
240
60
120
180
240
60
120
180
240
lag or distance in m
lag or distance in m
lag or distance in m
Fig. 2.4
Semivariances, its semivariograms and pure nugget variance (From suggestions by
Oliver
1999
, altered and redrawn)
The equation resembles the general formula for the standard variance. However,
the basic data for the standard variances are not pairs that are related by distances
and orientation; they just come from a common population and not more. And
because of the
pairs
that are used when calculating the semivariance, the summed
result is halved. This explains the denotations semivariance for the numerical values
and semivariogram for the graphical description.
Most semivariance curves - the semivariograms - are bounded, which means
that they reach an asymptote (Fig.
2.4
). This asymptote is called the
sill variance
.
But unbounded variogram curves also can occur. Note that the semivariograms are
standardized to a sill variance of 1.
The distance at which the sill variance is approached is called the
range
(Fig.
2.5
).
Since this is an asymptotic approach, the range is arbitrarily set to be the distance
needed to get 95 % of the sill variance (Tollner et al.
2002
). All points that are sepa-
rated by distances smaller than the range are spatially correlated. Whenever the
distances are larger than the range, the points are spatially independent. This is very
important: it means that any site-specific operation that is based on squared cells
with sides longer than the range is useless. This is, because with cells of this size it
is not possible any more to detect or catch regional differences of the respective
property. So the control distance that is used for site-specific operations must be
smaller than the range of the semivariogram.
Theoretically, the semivariogram curves start with zero variance and zero
distance. But in reality, this seldom occurs. In practice there always is some
variance already at zero distance. It is called
nugget variance
and represents
variability at distances smaller than the typical sample spacing as well as mea-
surement errors. In rare occasions, there is only nugget variance (Fig
2.4
, right),
which means that any site-specific treatment - at least based on the respective
property - is useless.
