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"distance to minor road" (OR), "distance to major road"(MR), "distance to cen-
ter"(CN), "density of neighbouring new development" (DN), " OR density gradient",
"MR density gradient", "CN density gradient", and "Master planning". So their rela-
tive importance (weight values) could be assigned quantitatively by manual test, fur-
ther improvement can be done by limited number of automatic search like 1000 itera-
tions.
Model accuracy depends on measure approach to comparing simulated and actual
patterns.
[6]
chose four ways to statistically test the degree of historical fit (three r-
squared fits and one modified Lee-Sallee shape index). The last one is a measurement
of spatial fit between the simulated and the actual growth. Supposed that the actual is
denoted by set A, the simulated B; the index is equal to (A ∩ B)/(A∪ B) mathemati-
cally. This simple measure of shape was computed through counting the union and
the intersection of their total areas on a pixel x pixel basis, and then dividing the inter-
section by the union. For a perfect match, the Lee Sallee measure gives a value of 1.0,
and for all others ranging from 0 to 1. Clark reported the practical accuracy of his
model is only 0.3
[6]
. Other measures like fractal and Moran I index are also fre-
quently used for global pattern comparison e.g.
[18]
. In this paper, we use consistency
co-efficient (
CC
) (spatial match between the simulated and the actual) and Lee-Sallee
index (
LI
) for goodness of fit evaluation. Mathematically, CC is equal to (A ∩ B) / A.
As the total number of pixels is set the same for the simulated as the actual, apparently
here
LI=CC/(2-CC).
Following this formula, the Lee-Sallee index of
Zuankou
is com-
puted and listed in table 1. The model accuracy is 55% in
CC
and 39% in
LI
, which is
greater than Clark's
[6]
.
Assisted with SPOT images of 1995, 2000 and IRS images of 1997, we are able to
judge the temporal development pattern of
Zuankou,
compared with other parts of
Wuhan city. In 1993,
Zuankou
was still completely rural and nearly half constructed in
1995. There was not much change from 1997 and 2000. So its temporal growth pattern
is defined as "Quick". The number of iteration is defined as 50 (n=50) as principally
the greater the number is, the finer discriminative capacity the model has, which re-
sults in higher accuracy. Therefore, when c=0.5, c*n=25. As described in equation 15,
the result of simulation is
L
i
(t),
which is different from yearly actual amount
L
i
(y).
We
need a transition from
L
i
(t)
to
L
i
(y).
In simplicity, we just use equal time interval, i.e. a
linear function
:
y = t/7. A
s
t
ranges from 1 to 50 and
y
is from 1 to 7,
L
i
(y)=
Σ
L
i
(t) (t
from
7*(y-1)+1
to
7*y).
A new layer with 7-year urban growth (from 1993 to 2000) is
input into animation software for dynamic exploration. This animation is helpful for
comparing the distinguishing temporal development processes of various projects.
Two models of
Zuankou
in Table 1 have similar model accuracy and also similar
pattern (the CA model is over till the 28
th
step). However, their temporal processes
shown in Figure 2 are quite different. The mode of temporal control is set the same
(c=0.5). Model 1 exhibits a more random process. Model 2 shows a more organized
process. Model 2 is based on the assumption that new development in
Zuankou
first
occurred in the center, then along the major road and finally spread from the center.
The assumption corresponds to a temporal process that is spatially controlled to by
