Graphics Programs Reference
In-Depth Information
have less, you should consider computing a maximum likelihood vario-
gram (Pardo-Igúzquiza and Dowd, 1997).
2.
Sampling design
- To get a good estimation at the origin of the variogram
sampling design should include observations over small distances. This
can be done by a nested design (Webster and Oliver, 2001). Other designs
were evaluated by Olea (1984).
3.
Anisotropy
- Until now we have assumed that the structure of spatial cor-
relation is independent from direction. Thus, we have calculated
omni di-
rectional variograms
ignoring the direction of the separation vector
h
. In
a more thorough analysis, the variogram should not only be discretized in
distance but also in direction (directional bins). Plotting
directional var-
iograms
, usually in four directions, we sometimes can observe different
ranges (
geometric anisotropy
), different scales (
zonal anisotropy
), and
different shapes (indicating a trend). The treatment of anisotropy needs
a highly interactive graphical user interface, e.g., VarioWin by Panatier
(1996) which is beyond the scope of this topic.
4.
Number of pairs and the lag interval
- In the calculation of the classical
variogram estimator it is recommended to use more than 30 to 50 pairs
of points per lag interval (Webster and Oliver 2001). This is due to the
sensitivity to outliers. If there are less pairs, the lag interval should be
enlarged. The lag spacing has not necessarily to be uniform, it can be
chosen individually for each distance class. It is also an option to work
with overlapping classes, in this case the
lag width
(
lag tolerance
) has
to be defi ned. On the other hand, increasing the lag width can cause un-
necessary smoothing and detail is lost. Thus, the separation distance and
the lag width have to be chosen with care. Another option is to use a more
robust variogram estimator (Cressie 1993, Deutsch and Journel 1998).
5.
Calculation of separation distance
- If your observations are covering a
large area, let us say more than 1000 km², spherical distances should be
calculated instead of the Pythagorean distances from a plane cartesian
coordinate system.
Kriging
Now we are going to interpolate the observations on a regular grid by
ordi-
nary point kriging
which is the most popular kriging method. Ordinary point
