Geography Reference
In-Depth Information
HaMPbMcPd
(2)
The coefficients
a
,
b
,
c
and
d
are determined at the expense of the coordinates of the square-
defined four vertices.
The determining of slope of each pixel in line l and column
k
is based on elevation values of
neighbouring pixels and the spatial resolution of the model,
E
(distance between pixels). The
slope is calculated using Eq. (3).
2
2
Hlk
(,
1)
Hlk
(,
1)
Hl
(
1, )
k
Hl
(
1, )
k
(3)
2
E
2
E
From the analysis a smooth slope map was produced, using the "Moving Window"
technique with a size of 4,900 m
2
(
i.e.
, 7×7 matrix). For each window was determined a
percentage of soft slope (considered below 4%), and that value was assigned to the central
pixel of the window. After this process, the map was reclassified (Table 1).
Code
Percentage of soft slope
1
More than 80%
2
50% at 80%
3
20% at 50%
4
Less than 20%
Table 1.
Reclassification of the slopes by percentage of soft slopes.
The curvature is defined according to the rate of change of the slope, which is determined
by the partial derivatives of second degree of surface
H
:
2
2
H
H
2
C
H
XY
(4)
A
2
2
As we are working on a discrete space, it is possible to approximate the Laplacian in two
dimensions, using the finite difference method, being the size equal to the unity (one cell):
2
H
Hl
(
1,)
k
Hl
(
1,)
k
Hlk
(,
1)
Hlk
(,
1) 4 (,)
Hlk
(5)
Therefore, the same expression in the matrix form, can be written as follows:
010
141
010
(6)
This matrix 3×3 is called the Laplacian filter, which was used in a spatial convolution
process on the MDT, wherein each central cell of the window was assigned a curvature
value. The negative values indicate concavity (sedimentation basins, valleys, etc.), while
