Geography Reference
In-Depth Information
site (i.e. at large separation distances), then the elevation can be said to have a low
frequency of spatial variation (a long range).
As noted above, there are many dif erent models that can be i tted to variograms.
h e variogram illustrated above was i tted with a nugget ef ect and a spherical
component. h e nugget ef ect (nugget variance) is given as:
0if
h
=
0
=
Ì
g
()
h
(9.10)
ch
if
>
0
Ó
0
In other words, the modelled semivariance has a value of 0 for a lag of 0, but is equal
to
c
0
for all positive values of the lag. In Figure 9.11, the nugget ef ect is indicated on
the
y
axis of the graph.
h e spherical model, a bounded model (i.e. it reaches a sill) is dei ned as:
Ï
◊
3
c
[1 . 5
h
-
0 . 5
h
] i f
h
£
a
=
Ì
a
a
g
()
h
(9.11)
c
if
h
>
a
Ó
where
c
is called, as noted above, the structured component. In other words, the mod-
elled semivariance is computed using the top line for all lag values up to and including
the range. For lag values larger than the range the modelled semivariance is equal to
c
.
Authorized models may be used in combination where a single model is insui cient to
properly represent the form of the variogram. For example, if the spatial structure is
complex and does not simply increase and level out (as in the example in Figure 9.11)
then models may be combined to take this complexity into account (e.g. a model could
comprise a nugget ef ect and two spherical components, thus there would be two
breaks of slope, rather than just one). Figure 9.12 shows an omnidirectional variogram
of July 2006 precipitation amount in Northern Ireland with a i tted model comprising
600
500
400
300
200
Semivariance
100
195.227 Nug(0) + 320.56 Sph(42428.3)
0
0
10000
20000
30000
40000
50000
60000
Lag (m)
Figure 9.12
Omnidirectional variogram of July 2006 precipitation amount in
Northern Ireland, with fi tted model.
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