Geography Reference
In-Depth Information
Value
High : 172.55
Low : 0.00
Inland water
0
20
40 km
Figure 10.7
Standard deviation of elevation for a 3
¥
3 pixel moving window.
gradient and aspect together is preferred. h ere are several methods for deriving gradi-
ent and one of the most popular is demonstrated here. Given cells labelled as follows:
zzz
zzz
zzz
1
2
3
4
5
6
7
8
9
the gradient can be estimated from (Horn, 1981):
∂
z
x
(
z
+
(2)
z
+
z
)
-
(
z
+
(2)
z
+
z
)
3
6
9
1
4
7
=
(10.1)
∂
8
h
x
∂
z
y
(
z
+
(2)
z
+
z
)
-
(
z
+
(2)
z
+
z
)
3
2
1
9
8
7
=
(10.2)
∂
8
h
x
where
h
x
is the grid spacing in the
x
direction (east-west) and
h
y
is the grid spacing in
the
y
direction (north-south). h e method is illustrated using the following 3 ¥ 3 cell
matrix, which we will assume has a spatial resolution of 10 m (i.e. cells that cover an
area in the real world of 10 ¥ 10 m):
45
44
44
43
42
39
38
32
34
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