Geoscience Reference
In-Depth Information
for the diagonal neighbors (known as the
bishop
'
s case
). In these formulae,
h
is the cell size,
z
r,c
is the elevation of the central cell, and
z
r+y,c+x
is the
elevation of the neighboring cells. h e cell indices
x
and
y
are obtained from
the matrix
N
. h e gradients are stored in a three-dimensional matrix
grads
,
where
grads(:,:,1)
contains the gradient towards the neighboring cells to
the east,
grads(:,:,2)
contains the gradient towards the neighboring cells
to the south-east, and so on. Negative gradients indicate outl ow from the
central cell towards the relevant neighboring cell. To obtain the surface l ow
between cells, gradients are transformed using the inverse tangent of
grads
divided by 0.5ˀ.
N = [0 -1;-1 -1;-1 0;+1 -1;0 +1;+1 +1;+1 0;-1 +1];
[a b] = size(SRTM);
grads = zeros(a,b,8);
for c = 2 : 2 : 8
grads(:,:,c) = (circshift(SRTM,[N(c,1) N(c,2)]) ...
-SRTM)/sqrt(2*90);
end
for c = 1 : 2 : 7
grads(:,:,c) = (circshift(SRTM,[N(c,1) N(c,2)]) ...
-SRTM)/90;
end
grads = atan(grads)/pi*2;
Since a central cell can have several downslope neighbors, water can l ow
in several directions. h is phenomenon is called
divergent l ow
. Early l ow
accumulation algorithms were based on the single-l ow-direction method
(known as the D8 method, Fig. 7.14), which allows l ow to only one of the cell's
eight neighboring cells. h is method cannot, however, model divergences in
ridge areas and tends to produce parallel l ow lines in some situations. In our
example we illustrate the use of a multiple-l ow-direction method, which
allows l ow from a central cell to multiple neighboring cells. h e proportion
of the total outl ow that is assigned to a neighboring cell is dependent on
the gradient between the central cell and that particular neighboring cell.
Even though multiple-l ow methods produce more realistic results in most
situations, they tend to result in dispersion in valleys, where the l ow should
be more concentrated. A weighting factor
w
is therefore introduced, which
controls the relationship between the outl ows.
