Agriculture Reference
In-Depth Information
Finally, precision farming aims at a high
spatial resolution
. It should be noted
that instead of the term “resolution”, the denotation “
cell size
” often is used. This
stands for the area, for which the respective farming operations are uniformly
adjusted. Therefore, a low resolution means a large cell size and
vice versa
. The
traditional and still rather common cell size is the individual field. Whilst the sizes
and basic operations of present farm machinery are maintained, about the smallest
cell size that can be realized would be an area that corresponds to the square of the
working width. This approach is derived from the assumption that the basic shape
of a cell would be a square. So if a working width of 20 m for fertilizing and spray-
ing is used, a cell size of 400 m
2
would result. And if fields that are controlled by
small robots become a reality, a high regional resolution based on treating individ-
ual plants or even leaves might become feasible.
Yet these considerations emanate from
technical possibilities
with the respec-
tive farm machinery, provided the control components are available. A better
approach is to base the resolution on the respective soils and crops and to adapt the
technical solutions as well as possible to these.
If theoretically the soil- and crop properties would be completely uniform within
a field, no site-specific treatments would be necessary. And if on the other hand
significant variations would show up within short distances, small cell sizes would
be reasonable. This leads to the question, how - based on variations existing within
fields - proper
cell sizes
can be deduced. Statistical indices of soil- or crop proper-
ties like averages or standard variations are no help in this respect. This is because
intrinsically these indices are independent of location. What is needed are statistical
indices that rely on distances within a field. The semivariance and its graph - the
semivariogram - do this.
2.2
Semivariance and Semivariogram
The geostatistical concept behind semivariances and semivariograms is Matheron's
(
1963
) regionalized variable theory. It states that the differences in the values of a
spatial variable - such as a soil- or crop property - between points in a field depend
on the
distance
between these points. In short, the smaller the distances, the smaller
the differences.
As a logical consequence, the semivariance
v
expresses the dissimilarity of
paired property values as a function of the distances between two sampling points.
The general equation of the semivariance
v
is:
1
2
N
∑
(
)
−
2
v
=
fxhf x
+
()
N
1
Here,
x
and
x + h
stand for the vectors of areal coordinates at two locations in the
field. These locations are separated by the distance
h.
The functions
f
(
x
) and
f
(
x + h
)
together represent thus a pair of soil- or crop properties at these places. N is the
number of location pairs that are involved.
