Information Technology Reference
In-Depth Information
2.2
Generalized Mathematical Models
Urban growth process is effected by many factors, which may change their influential
roles spatially and temporally. The spatial heterogeneity phenomena (heterogeneity in
a spatial context means that the parameters describing the data vary from place to
place) suggests that the search for general laws frequently fail in practice and it is
being replaced by local area analysis like Geographically Weighted Regression
(GWR) and others in the field of spatial statistics. As a consequence, a project-based
local growth modelling is more reasonable for understanding of complex urban growth
process. The spatial extent described below is limited to individual large-scale project.
(3)
L(t)|
t=n
=L
d
(x,y)
Here,
L
d
is the actual area of land development of one project
d
in the whole period
[
t=1
∼
n
].
L
d
in principle should result from traditional top-down socio-economic mod-
els. Here it is assumed to be a known value.
L(t)
is the simulated area of land devel-
opment of same
d
till time
t
.
L(t)
will be calculated from the later section. As an ex-
ample, we only refer to project
d
; the others follow the same procedures.
C
i
(t) = f
i
(L(t))
(4)
Here,
C
i
(t)
is the temporal contribution of factor
i
to
L(t)
at time
t,
which is a func-
tion rather than a subjective parameter. We strongly argue that
C
i
should vary with
L(t). W
i
(t)
in eq. 5 is a relative weight of factor
i (
0
W
i
(t)
1).
C
(
t
)
i
W
(
t
)
=
i
(5)
∑
C
(
t
)
i
i
To some extent,
eq. 4 and 5 indicate a dynamic feedback between
w
i
(t)
and
L(t),
which can be utilized to represent the complex interactions between pattern and proc-
ess. Actually,
L(t)
is to quantify temporal pattern, and the process can be described by
multiple
w
i
(t).
The non-linear iteration function
f
(
L(t))
(
together with
L(t)=g(W
i
(t
))
exhibit the complexity property of the interactions between pattern and process like
'chicken and egg'
. When
f
i
(
L(t))
is constant,
C
i
is becoming universe temporally, which
is treated in most CA applications, however, it can not model the temporal process.
The design of function
f
i
(
L(t))
is a critical point. It needs numerous experimental tests,
which is based on the theoretical understanding of the interaction
"chicken and egg"
.
However, model from the experimental tests with higher temporal resolution are able
to theoretically abstract the hidden temporal rules. The development potential of each
cell
j
at time
t
is defined as:
