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1 Introduction
An understanding of urban development processes is crucial in urban development
planning and sustainable growth management. The urban development process
involves many actors and types of behaviour and various policies, resulting in spatial
and temporal complexity. The nonlinear dynamics inherent in these growth processes
opens up the possibility for `emergencies' (sudden changes) that are difficult or impos-
sible to predict. Owing to the hidden complexity of reality, our science has become less
orientated to prediction and more an aid to understanding in order to structure debate
(Batty and Torrens, 2001). Orjan (1999) argued that without a proper understanding of
the recent past we are in no position to comprehend
ö
let alone predict
ö
emerging
patterns and processes. Couclelis (1997) first put forward the idea of a spatial under-
standing support system (SUSS). Horita (2000) reported a new SUSS for representing
community disputes. Limited by existing sciences and techniques, understanding-
oriented modelling is orientated more to practicability than to prediction. To achieve a
reasonable understanding we need reliable information sources and models. Successful
models should have a strong interpretive element and an interactive environment to
simulate `what-if' scenarios. Consequently, they require an innovative simulation approach.
Understanding spatial and temporal processes of urban
growth: cellular automata modelling
Jianquan Cheng
Department of Urban and Regional Planning and Geo-information Management, International
Institute for Geo-Information Science and Earth Observation, Hengelosestraat 99, PO Box 6,
7500 AA Enschede, The Netherlands and School of Urban Studies, Wuhan University,
430072 Wuhan, Hubei, People's Republic of China; e-mail: jianquan@itc.nl
Ian Masser
Department of Urban and Regional Planning and Geo-information Management, International
Institute for Geo-Information Science and Earth Observation, Hengelosestraat 99, PO Box 6,
7500 AA Enschede, The Netherlands; e-mail: masser@itc.nl
Received 2 August 2002; in revised form 12 March 2003
Environment and Planning B: Planning and Design 2004, volume 31, pages 167 ^ 194
Abstract. An understanding of the dynamic process of urban growth is a prerequisite to the prediction
of land-cover change and the support of urban development planning and sustainable growth manage-
ment. The spatial and temporal complexity inherent in urban growth requires the development of a
new simulation approach, which should be process-oriented and have a strong interpretive element.
In this paper the authors present an innovative methodology for understanding spatial processes and
their temporal dynamics on two interrelated scales
ö
the municipality and project scale
ö
by means of
a multistage framework and a dynamic weighting concept. The multistage framework is aimed at
modelling local spatial processes and global temporal dynamics by the incorporation of explicit
decisionmaking processes. It is divided into four stages: project planning, site selection, local growth,
and temporal control. These four stages represent the interactions between top-down and bottom-up
decisionmaking involved in land development in large-scale projects. Project-based cellular automata
modelling is developed for interpreting the spatial and temporal logic between various projects that
form the whole of urban growth. Use of dynamic weighting is an attempt to model local temporal
dynamics at the project level as an extension of the local growth stage. As nonlinear function of
temporal land development, dynamic weighting can link spatial processes and temporal patterns.
The methodology is tested with reference to the urban growth of a fast growing city
ö
Wuhan, in the
People's Republic of China
ö
from 1993 to 2000. The findings from this research suggest that this
methodology can be used to interpret and visualise the dynamic process of urban growth temporally
and transparently, globally and locally.
DOI:10.1068/b2975
The first step in such decisionmaking is to identify the process of decisionmaking. This is
the same as in the area of information management, where we need to recognise the data
flowchart and model before establishing any operational information system.
Remote sensing and geographical information systems (GIS) have proven to be
effective means for extracting and processing varied resolutions of spatial information
for monitoring urban growth (Masser, 2001). However, they are still not adequate for
process-oriented modelling as they lack social and economic attributes, particularly at
a detailed scale. In developing countries, acquisition and integration of socioeconomic
data still have a long way to go. In such a situation, local knowledge (expert opinions,
historical documents), albeit only qualitative or semiquantitative, can be very valuable
in assisting us in understanding processes such as urban growth patterns, driving
forces, and the major actors involved. Hence, local knowledge should be incorporated
into simulation modelling at certain stages and in certain ways.
The use of cellular automata (CA), a technique developed recently, has been
receiving more and more attention in urban and GIS modelling because of its sim-
plicity, transparency, strong potential for dynamic spatial simulation, and innovative
bottom-up approach. When applied to real urban systems, CA models have to be
modified by including cell multistates, by relaxing the size of the neighbourhood with
distance-decay effects, probabilistic rules, and by linking them to complexity theory.
In fact, many
ö
if not all
ö
urban CA bear little resemblance to the formal CA model
(Torrens and O'Sullivan, 2001). The literature in the field of urban CA modelling
includes at least two classes of successful applications at various spatial and temporal
scales. One class concentrates on the study of artificial cities to test the theories of
complexity and urban studies (Batty, 1998; Benati, 1997; Couclelis, 1997; Wu, 1998a).
The other class focuses on real cities to provide decision support to urban planners at
the regional, municipal, and town levels (Besussi et al, 1998; Clarke and Gaydos, 1998;
Silva and Clarke, 2002; Ward et al, 2000; White and Engelen, 2000; Wu, 2002; Yeh
and Li, 2001). These studies have revealed that urban CA-like models are effective in
simulating the complexity of urban systems and their subsystems, from emergence,
feedback, and self-organisation. Nevertheless, the interpretation of transition rules,
which is highly important for urban planners, still receives little attention in urban
CA modelling, particularly in providing a link to the process of urban planning.
Moreover, previous studies of urban CA models ignore the fact that urban growth
is a dynamic process rather than a static pattern. For example, the urban growth model
of Clarke and Gaydos (1998) has attracted a lot of attention regarding urban growth
prediction (Silva and Clarke, 2002). Their CA model controls the evolution of city
growth by means of five coefficients (diffusion, breed, spread, slope, and roads). The
diffusion factor determines the overall outward dispersive nature of the distribution.
The breed coefficient specifies how likely it is that a newly generated detached settle-
ment will begin its own growth cycle. The spread coefficient controls how much
diffusion expansion occurs from existing settlements. The slope resistance factor influ-
ences the likelihood of settlement extending up steeper slopes. The road gravity factor
attracts new settlements toward and along roads. This is a successful simulation model
of patterns, focusing principally on spontaneous, organic, spread, road-influenced, and
diffusive patterns. It still lacks the ability to interpret causal factors in a complete
process model because similar patterns from the final output of CA simulation do
not indicate similar processes. Thus, the transition rules validated are not evidence to
explain the complex spatial behaviour behind the process. Therefore, process-oriented
rather than pattern-oriented simulation should be the main concern of urban growth
CA modelling. This point has been supported and recognised recently in some journals
(Torrens and O'Sullivan, 2001). Dragicevic et al (2001) apply fuzzy spatiotemporal
168 J Cheng, I Masser
interpolation to simulate changes that occurred between `snapshots' registered in a GIS
database. The main advantage of their research lies in its flexibility to create various
temporal scenarios of urbanisation processes and to choose the desired temporal
resolution. Dragiceivc et al also declared that the approach does not explicitly provide
causal factors; thus it is not an explanatory model.
Wu (1998b) developed a CA model driven by an analytical hierarchy process (AHP)
to simulate the spatial decisionmaking process of land conversion (AHPs were originated
by Saaty, 1980). In AHPs pair-wise comparisons are used to reveal the preferences of
decisionmakers and are an ideal means for calculating weight values from the qualitative
knowledge of local experts. This CA model is, in essence, a dynamic multicriteria
evaluation (MCE) as a dynamic neighbourhood (updated during model runs) is treated
as an independent variable. This model is successful in linking explicit decisionmaking
processes to CA. The adjustment of factor weights allows one to generate distinctive
scenarios. Hence, this model has a strong interpretive element. However, an AHP-driven
decisionmaking process is not spatially and temporally explicit as the weight values are
fixed for the whole study area and period modelled. They cannot be used to model
processes, especially temporal dynamics. The incorporation of spatially and temporally
explicit decisionmaking processes into CA models has not been reported to date.
In summary, we need to develop a new methodology based on present urban CA
that allows one to model and interpret spatial process and temporal dynamics and also
incorporate local knowledge to interpret these processes. With this in mind, we have
organised this paper into four sections. In the next section we introduce the concepts
that we meet in trying to understand urban growth: processes and dynamics, global
and local. We also discuss in detail a proposed methodology, that comprises mainly a
multistage framework and a dynamic weighting concept. The framework incorporates
explicit decisionmaking processes into the modelling of local spatial processes and
global temporal dynamics. The dynamic weighting concept allows the modelling of local
temporal dynamics by representing the dynamic interaction between pattern and process
at a lower level. CA-based simulation is developed to support and implement each
method. The mathematical foundations are described step by step. In section 3 we focus
on the implementation of the methodology by undertaking a case study of Wuhan City,
People's Republic of China. In section 4 we end the paper with further discussion and
conclusions regarding model calibration and validation, the visualisation of processes,
and process modelling.
2 Methodology
2.1 Complex processes and dynamics
Urban growth can be defined as a system resulting from complex interactions between
urban social and economic activities, physical ecological units in regional areas, and
future urban development plans. This interaction is an open, nonlinear, dynamic, and local
process, which leads to the emergence of global growth patterns. The urban growth process
is a self-organised system (Allen, 1997).
The term `process' generally refers to a sequence of changes in space and time
ö
spatial processes and temporal processes, respectively. It should be noted that, strictly
speaking, spatial and temporal processes cannot be separated precisely, as any geo-
graphical phenomenon is bound to have both a spatial and a temporal dimension.
An understanding of change through both time and space should, theoretically, lead
to an improved understanding of change and of the processes driving change (Gregory,
2002). However, a spatial process is much more than a sequence of changes. It implies
a logical sequence of changes being carried out in some definite manner that lead to a
recognisable result (Getis and Boots, 1978). To sum up, the key components of a process
Understanding spatial and temporal processes of urban growth 169
are change and logical sequence. `Change' is defined by a series of patterns, and `logical
sequence' implies an understanding of process. In contrast to pattern, process contains
a dynamic component.
An urban growth system consists of a large number of new projects on various
scales. Large-scale projects are characterised by dominant functions, heavy investment,
long-term construction, and the involvement of a number of actors; examples include
the construction of airports, industrial parks, and universities. In contrast, small-scale
projects are characterised by a single function, rapid construction, light investment,
and few actors; examples may be the construction of a private house or a small shop.
The project, as the basic unit of urban development, is the physical carrier of complex
social and economic activities.
The spatial and temporal heterogeneity of social and economic activities creates
massive flows of matter, people, energy, and information between new projects and
also between the projects and the other systems (developable, developed, and planned).
They are the sources of the complex interactions inherent in urban growth. As such,
the urban growth process consists of a spatial and temporal logic between various
scales of land development projects. The spatial and temporal organisation of projects
is the key to understanding these processes and dynamics. This understanding can
be based on two scales: the municipal (global) scale and the project (local) scale.
For instance, on the global scale, in space, projects can be organised into clustered
or dispersed patterns, `clustering' implying a self-organised process, and `dispersal'
a stochastic process. In time, projects can be organised into quick or slow patterns.
The term `local process' refers to spatial growth at the project level. The term `global
dynamics' refers to the temporal logic between the projects forming urban growth as a
whole, and the term `local dynamics' the temporal logic between only the spatial
factors or elements within a project.
The research reported in this paper has two specific objectives in terms of gaining a
systematic understanding of the spatial and temporal process of urban growth:
(1) to understand the local spatial process at the project level and the global temporal
dynamics with use of a multistage framework;
(2) to understand local temporal dynamics at the project level with use of the dynamic
weighting concept.
2.2 A conceptual model of global dynamics
The complexity of the urban growth process can intuitively be projected onto decision-
making processes and their spatial and temporal dimensions. The decisionmaking
process involves multiple actors and types of behaviour. The spatial and temporal
dimensions involve various spatial and temporal heterogeneities. Or, we can say, the
decisionmaking process is a cause, the spatial and temporal dimensions the effect and
projection. In consequence, we must start with the decisionmaking process in order to
understand the spatial and temporal processes of urban growth.
Decisionmaking in urban growth is related to plans, policies, and projects. Projects
consist of special land-use or development proposals usually by various types of actors
such as investors, planners, developers, landowners, and work units. They evolve in the
context of various levels of policy and plans. The project development process is a
dynamic, spatially nested, hierarchy of multiple decisionmaking procedures, from the
municipal to the building level, and vice versa. The global dynamics of urban growth
results from the interactions between the top-down and bottom-up processes of decision-
making. Top-down decisionmaking includes allocation of financial resources, master
planning, and the time schedule of projects; bottom-up decisionmaking includes building
style, building density, and plot ratios.
170 J Cheng, I Masser
Global patterns can be described as having a cumulative and an aggregate order
that results from numerous locally made decisions involving a large number of intelli-
gent and adaptive agents. At the municipal scale, the decisionmaking process can fall
into four stages: project planning, site selection, local growth, and temporal control, as
illustrated in figure 1.
The first (project-planning) stage answers the questions `how many large-scale
projects were planned in previous periods?' and `how much area was constructed in
each project?' This stage is a typical top-down decisionmaking process based on a
systematic consideration of physical and socioeconomic systems. Municipalities need
to plan land consumption according to their social and economic demand for develop-
ment. When land consumption is projected onto the physical land-cover system one
observes different scales of new projects. Land-development projects can be divided
into spontaneous and self-organisational types (Wu, 2000). `Spontaneous projects'
correspond to small-scale or sparse developments that may contain more stochastic
disturbance and involve lower-level actors such as individuals or organisations. `Self-
organisational projects' represent larger-scale projects with a dominant land use and
higher level actors. Such projects are the main concern at this project planning stage.
The project here can be called an `agent', which is a spatial entity linking with distinct
actors and spatial and temporal behaviour. In this sense, the project-based approach
proposed here is also a kind of agent-like modelling.
The first stage belongs to nonspatial modelling, resulting in proposals for development
projects. These new developments will be projected along their spatial and temporal
dimensions. Spatial complexity can be considered from two aspects: the location of
the site and the spatial interaction between sites.`Site location' concerns the issue of spatial
site selection or location, leading to the second stage. `Spatial interactions' relate to the
issue of local growth or the control of development density and pattern, the third stage
(a) (b)
(c) (d)
Project 1
Project 2
Project 3
Slow
t
1
Quick
t
3
Normal
t
2
Site
Direction of growth
Road
Built-up area
Figure 1. A conceptual model of the decisionmaking process: (a) project planning, (b) site selection,
(c) local growth, and (d) temporal control.
Understanding spatial and temporal processes of urban growth 171
of the framework. Temporal complexity, which is typically indicated by temporal
heterogeneity or the timing of local growth, will be described in the fourth stage.
The second (site-selection) stage deals with the question `where were the various sizes
(or scales) of the projects to be located?' This stage is a typical spatial decision process
involving municipal decisionmakers. The aim is systematically to optimise and balance
the spatial distribution of socioeconomic activities as each project has specific socio-
economic functions planned.This stage can be seen as the static projection of the projects
planned during the first stage. The rules of site selection are represented by multiple
physical, socioeconomic, and institutional factors, incorporating various global and local
constraints. Rules are delineated to differentiate between the various planned projects in
terms of influential factors, weights, and constraints. To some extent, this stage provides
growth boundaries and seeds for the next (local growth) stage and results in a number of
potential spatial subsystems through the top-down process.
The third (local growth) stage addresses the question `how did each project grow
locally?' The answer to this question includes consideration of development density,
intensity, and the spatial organisation of development units. After the spatial location
has been agreed, each project is developed based on a more local type of decisionmak-
ing involving landowners, investors, and individuals. This results in different spatial
processes. The outcomes of these local growth processes can be concentric, diffusive,
road influenced, and leapfrog in nature. They are affected by numerous factors, which
change their influential roles spatially and temporally. Spatial heterogeneity (hetero-
geneity in a spatial context means that the parameters describing the data vary from
place to place) suggests that spatial processes are locally varied. In spatial statistics,
global analysis is being complemented by local area analyses such as local indicators of
spatial association (LISA: Anselin, 1995) and geographically weighted regression
(GWR): Fotheringham and Rogerson, 1994). As for understanding local urban growth,
its spatial process depends mostly on local conditions such as physical constraints and
socioeconomic circumstances. Using CA we are able to explore the dominant causal
factors locally. This stage is dominated by the bottom-up approach.
The last (temporal-control) stage answers the question `how fast did each project
grow temporally?' This stage shifts to managing the local growth speed from a global
perspective. The image of the whole urban growth process comprises the temporal
sequences of all projects. For example, we can define such patterns as being quick,
basic or normal, or slow local growth, representing three identifiable timing modes.
The rate of local growth is governed by numerous factors resulting from top-down
and bottom-up decisionmaking. For example, top-down decisionmaking includes
allocation of financial resources from higher level organisations, and master and
land-use planning control. Bottom-up decisionmaking includes manpower allocation
and facility supply. The temporal land-demand amount decided at this stage should be
input for use as a guide or constraint at the local growth stage. Hence, the stage is
primarily a top-down procedure for controlling local temporal patterns and is conditioned
by a bottom-up procedure.
It should be noted that each stage described above involves interactions between
top-down and bottom-up decisionmaking. For example, although the land demand
of each project is planned by municipal organisations, actual consumption is influ-
enced by a number of local constraints. The whole process of urban growth should
contain numerous feedback loops between these at various spatial and temporal scales.
As the focus of our research aspects of top-down socioeconomic decisionmak-
ing at various stages of the decisionmaking process will be treated as the exogenous
variables.
172 J Cheng, I Masser
The framework described in this paper has been designed primarily for understanding
the dynamic processes of urban growth.When used for planning support, the first question
will become `how many large-scale projects will be planned in the coming years?' In
this case, the socioeconomic model for determining the land consumption of projects
should be included at this stage. Other questions arising at various stages will be
similarly modified. Such a multistage framework can offer a transparent and friendly
environment for constructing various scenarios for plans.
2.3 Land-transition models
The multistage framework discussed above conceptually breaks down the global
dynamics of the whole urban growth process into the local land-conversion processes
that result from large-scale projects. These local processes consist of complex spatial and
temporal interactions, which can be simulated by the urban CA approach. The identi-
fication of large-scale projects and their functions is of importance for understanding
the spatial behaviour of relevant actors. The term `large-scale' has two meanings, from a
spatial and a socioeconomic perspective, respectively. The spatial interpretation refers
to a certain scale of spatial clustering of new development units. A project defined in
this way may have no definite socioeconomic implications as it is not planned as a
complete spatial entity. This definition allows one to look at relative spatial division.
The socioeconomic interpretation refers to larger-area land development with special
socioeconomic functions, such as the construction of a car manufacturing centre.
A project defined in this way may have no ideal spatial agglomeration as the building
density may be low. In this paper, we wish to focus on the socioeconomic interpreta-
tion as it provides a link to the underlying socioeconomic activities. However, it should
be noted that spatial interpretations are also significant and necessary in some spatial
process modelling.
In the following, small-scale projects with mixed functions are merged into one
class conceptually. To identify large-scale projects, it was necessary to examine histori-
cal documents and to carry out interviews with local planning organisations. Last, as
the process of CA modelling is identical in each project, as an example we refer only to
project din the following description; the other projects are followed through the same
procedure.
2.3.1 Project planning
The simulated area of land for development from the starting time t1up to time
tn,L(t), is given as follows:
Ltj
tn
L
d
,(1)
where L
d
is the actual (or planned) area for land-development project d(from stage 1)
over the whole period (t1to tn). L
d
in principle should be the output from
traditional top-down socioeconomic models (for example, White and Engelen, 2000).
Here, it is assumed to be an exogenous variable (of known value from previous urban
growth analysis). For example, if a shopping centre is known to have occupied 5 ha
from 1993 to 2000 then L
d
5ha for that period. L(t)is the simulated are of land-
development project dup to time t, so L(1996) is the simulated land-transition area
from 1993 to 1996. Calculation of L(t)is described in section 2.3.4.
2.3.2 Constraint-based site-selection model
The constraint-based site-selection model is defined as follows:
SNCentrex,y, (2)
Understanding spatial and temporal processes of urban growth 173
where
Centrex,yY
I
i1
g
i
.(3)
Here, S, the site selected for a project, includes a central starting point, Centre(x,y),
and its surrounding area or neighbourhood, N. The location of the centre is determined
by various critical constraints g
i
. As in other research (Ward et al, 2000; Yeh and Li,
2001), constraints operate at the local, regional, and global levels. Global constraints
taking an account of the whole study area include physical aspects (for example,
ecological protection zones, accessibility to transport infrastructure, and city centres
and subcentres), economic aspects (for example, investment, and land value), social
aspects (for example, population density), and institutional aspects (such as master
planning). Regional constraints are defined by the availability of developable or devel-
oped land and its density in a neighbourhood. It should be noted that the regional level
has a varied spatial extent as the sizes of neighbourhood vary from project to project.
In some cases, we have to define multilevel regions (for example, Batty et al, 1999).
Local constraints refer to the physical conditions of a site or pixel, such as slope, soil
quality, and geological condition. Each of the criteria at each of the three levels varies
from project to project, and from case to case, so that one is able to interpret the
specific spatial behaviour of the actors involved in each project. For example, slope
does not take effect in a flat city. Equation (2) is based on the assumption that site
selection depends on a limited number of equally weighted constraints [equation (3)]
as, in practice, the decisionmaking process is primarily qualitative and simple for
decisionmakers. This stage is implemented by GIS analysis based on spatial operations
(for example, `find distance', `neighbourhood statistics', and `map calculation') and by
the use of heuristic rules (for example, if rule 1 and rule 2, then do ...) based on visual
programming. GIS visual functions can help modellers to test their systematic thinking;
that is, whether a particular rule can create ideal sites for a planned project.
2.3.3 Local growth model
Through this model we seek the major spatial determinants of local spatial processes
with use of bottom-up CA simulation. CA are dynamic discrete space and time
systems. A CA system consists of a regular grid of cells, each of which can be in one
of a finite number of possible states, updated synchronously in discrete time steps
according to a local, identical interaction rule. In this model, the cell state is binary
(1 indicates a land-cover transition from nonurban to urban; 0 indicates no such
transition), limited to the cellular space of each project, CA simulation is carried out
by dynamic evaluation and by updating the development probabilities for each cell
in the cellular space. The cells selected at each iteration will be changed from 0 to 1.
The development potential of each cell jat time t,P
j
(t), is defined as follows:
P
j
tX
k
i1
W
i
tV
ij
tY
I
ik1
o
i
,(4)
where W
i
(t)is the weight of constraint (or factor) iat time t,V
ij
(t)is the standardised
score of constraint (or factor) ifor cell jat time t,ando
i
is a restriction relating to
constraint i.
It is assumed that Iconstraints (14i4I) are considered, comprising knon-
restrictive and Iÿkrestrictive constraints. When (k1) 4i4I,o
i
is a binary
variable (taking a value 0 or 1) representing restrictive constraints at the local, regional,
and global levels: o
i
0indicates that a cell is absolutely restricted from transition to
urban use in relation to constraint i(for example, it may be at the centre of a large
lake). When l 4i4k,iis a nonrestrictive constraint and may be referred to as a
174 J Cheng, I Masser
factor in order to distinguish it from a restrictive constraint, o
i
. These factors are
complementary in contributing to the development potential of a cell.
The potential for transition depends on a linear weighted additive sum of develop-
ment factors. W
i
(t), the relative weight value of factor i, is calibrated from data.
Largely, W
i
(t)can be seen as representing the causal effects of the local growth process.
In the case of global temporal dynamics, W
i
(t)is treated temporally as a constant, W
i
.
The function W
i
(t)will be discussed in detail in section 2.3.4, on local temporal
dynamics.
V
ij
(t)is the standardised score (falling within the range 0 to 1) of factor ifor cell j
at time taccording to the following:
V
ij
t X
ij
tÿminX
ij
t
maxX
ij
t ÿ minX
ij
t ,04V
ij
t41, 1 4i4k,(5)
and
X
ij
texpÿfd
ij
,(6)
where X
ij
(t)is the value of factor ifor cell jat time t;min[X
ij
(t)] and max [X
ij
(t)] are,
respectively, the minimum and maximum values of X
ij
(t)among the cells to be
evaluated in relation to factor i;fis a distance-decay parameter; and d
ij
is the distance
from cell jto any spatial element defined in factor i, such as a major road network.
In urban growth, frequently considered factors include: (1) transport accessibility,
(2) accessibility to urban centres and subcentres, (3) suitability, (4) planning input, and
(5) the presence of dynamic neighbourhoods (Clarke and Gaydos, 1998; Ward et al,
2000; White et al, 1997; Wu, 1998b). In this paper, suitability analysis is applied at the
stage of site selection. The other four factors are used to evaluate P
j
(t)at this stage.
The quantification of master planning will be explained in section 3.
Accessibility measurement, such as accessibility to a major road, is a very active
field in GIS and modelling. Numerous methods have been published (see, for example,
Miller, 1999). In this study, a negative exponential function [equation (6)] is employed
to quantify the distance-decay effect. Urban modellers making use of economic theory
(Muth, 1969) and discrete choice theory (Anas, 1982) have made widespread use of the
negative exponential function. Previous research on the same case-study city (Cheng
and Masser, 2003) confirmed its effectiveness, although the inverse power function has
also frequently been successfully employed for quantifying the distance-decay effect
(Batty and Kim, 1992).
In this paper, fis the parameter controlling the distance-decay effect. Usually, we
can assume 0<f<1, and fvaries with factor i. A higher value of fmeans that the
influence on land transition will decrease more rapidly. The parameter fcan be
determined by means of a global exploratory data analysis of urban growth patterns
(Cheng and Masser, 2003), where fis the slope of the log ^ linear relationship between
the probability of transition and distance d
ij
. From equation (6) we calculate the
potential for land conversion contributed from proximity factors. In this study, acces-
sibility factors are fixed or static during the modelling period as the spatial factors
(such as road networks) are not updated temporally, so V
ij
(t)V
ij
.
In our model, neighbourhood size is not globally universal but locally parameterised
and varies for different projects, as each project has distinguishing social and economic
functions. The neighbourhood effect (`action-at-distance') is represented as a nonrestric-
tive factor in equation (4), which indicates the spatial influences of developed cells on
land conversion in surrounding sites. Developed cells come from the cells previously
transited or the old urban area. Strictly speaking, the further development of cells
that have already undergone a transition reflects the local spatial self-organisation of
Understanding spatial and temporal processes of urban growth 175
land conversion in each project as a dynamic variable that is updated in each iteration
[that is, V
ij
(t)6 V
ij
]. The development of old urban area depends on existing global
urban activities as a fixed spatial factor. These two types of development are treated as
two independent factors in this research.
In practice, restrictive and nonrestrictive constraints are relative classifications and
vary temporally. For example, ponds may have constituted a restrictive constraint in
1950 but may become nonrestrictive in 2000 as no large quantity of developable land
may be available in the later period. We may write:
P
0
j
t1lnx
a
P
j
t, (7)
and
DLtLtÿLtÿ1,L00,(8)
where P
0
j
(t)is the development potential of cell jat time t;DL(t)is the demand for
land from time tÿ1to time t;xis a random variable taking values in the range 0 to 1;
and ais a parameter controlling the size or strength of the stochastic perturbation.
Principally, land conversion is allocated according to the highest score of the
potential; however, practically, this is subject to stochastic disturbance and imperfect
information. To generate patterns that are closer to reality, a stochastic disturbance is
introduced, as 1ln (x)
a
(Li and Yeh, 2001). As in other CA applications (Ward et al,
2000; White et al, 1997; Wu and Webster, 1998), P
0
j
(t)in equation (7), representing the
probability of land transition at cell jat time t, is the major driving force of local
growth.
Whether or not a cell is to undergo transition over time tÿ1to time tdepends
on the probability P
0
j
(t)at each iteration. Selection will start from the maximum of
fP
0
j
(t)guntil it reaches the required number of cells
ö
that is DL(t)for the iteration
between time tÿ1and time t. The demand for land consumption DL(t)in equation (8)
will be calculated at the temporal control stage, as L(t)is the cumulative amount of
land development up to time t.
2.3.4 Temporal control model
Previous studies suggest that the urban development process represented by L(t)
in equations (1) and (8) follows a logistic curve over time (Herbert and Thomas,
1997). For example, Sui and Hui (2001) simulated the expansion trend of the desakota
regions between 1990 and 2010 by using a logistic equation, where the total number
of converted urban pixels was a logistic function of year. Here, the same principle is
applied for the temporal control of each project. A standard logistic curve is defined
as follows:
Lt a
1bexpÿct ,(9)
where a,b, and care unknown parameters, t(where t1, .::,n) is the time step, and
L(t)the amount of land development up to time t.Ifitisassumedthat
L0L
0
a
1b1,(10)
and
LnL
n
a
1bexpÿcnL
d
,(11)
176 J Cheng, I Masser
then nand L
d
are as defined in equation (1). Equation (9) can then be revised as
follows. If
zL
d
expÿcnÿ1
L
d
expÿcnÿ1,(12)
then
Lt z
1zÿ1expÿct.(13)
In equations (12) and (13) zimplies the long-term limit of L(t)behaviour. The shape of
the logistic curve usually represents the speed of project development over time, which
is controlled by the parameters c,n, and L
d
. Here, for simplicity, temporal control is
classified into three types
ö
slow growth, normal growth, and quick growth
ö
providing
three distinguishing scenarios. If it is assumed that
LtL
d
l,fortn
2,(14)
then
c2
nln L
d
ÿl
lÿ1.(15)
Further, L(t)may be a function of both time tand parameter lwhen nand L
d
are
fixed. Consequently, the value of lwill determine the shape of the logistic curve. As
such, we can define slow, normal, and quick growth according to l:
l
4
3,quick growth ;
2, normal growth;
4, slow growth.
8
>
>
<
>
>
:
(16)
Of course, we can define more classes, such as `very slow' or `very quick' by
assigning lvalues differently.
In figure 2 we provide an example of three modes, where L
d
500,n30, and
where lis 4/3, 2, and 4, respectively, for the three (quick, normal, and slow) patterns.
However, iteration time t(t1, .::,n) in simulation is different from the real time tin
Land area developed, L(t)
550
450
350
250
150
50
ÿ50 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Time, t
Quick
Normal
Slow
Figure 2. An illustration of temporal development patterns.
Understanding spatial and temporal processes of urban growth 177
years (1, .::,m) where the base year may be 1993 (t0) and the seventh year (t7)
2000. Let L
i
(t)denote the total growth of project iup to year t, a transition
from L
i
(t)to L
i
(t)may be established as follows:
L
i
thL
i
t,t1, 2, .::,m;t1, 2, .::,n;n>m.(17)
In previous research on CA applications, a linear function is applied, that is,
tDt.Here,Dis assumed to be a constant, which implies an equal growth rate.
For example, if when t5years, tcorresponds to 20 iterations this can be defined, in
the case of linear relationship, as t4t.So,L(t)j
t1
PL(t), 0 <t<5. In reality,
function h may be a nonlinear function of iteration number t, which may be tested
experimentally through qualitative understanding and visual exploration of the difference
between actual and simulated processes.
2.4 A conceptual model for local temporal dynamics
The multistage method can be used to understand the global temporal dynamics of the
whole study area rather than the local dynamics of each project. An understanding of
local dynamics requires a different perspective focusing on more detailed aspects
of spatial and temporal processes.
Heterogeneity in a temporal context means that the parameters describing any
geographical phenomena vary from phase to phase over the whole period studied.
For example, Wu and Yeh (1997) applied logistic regression methods for modelling
land-development patterns in two periods (1979 ^ 87 and 1987 ^ 92) based on parcel
data extracted from aerial photographs. They found that the major determinants of
land development have changed from distance from the city centre to closeness to the
city centre; from proximity to intercity highways to proximity to city streets; and are
more rather than less related to the physical condition of the sites. This suggests that
the roles of various factors are changing in the process of land development. Likewise,
if we shrink a longer period (1979 ^ 92) to a shorter period, such as 1993 ^ 2000, and
reduce the spatial extent, from looking at the whole city to looking at a smaller part
such as a large-scale project, the same principle should be working as well. Therefore,
temporal heterogeneity results in complex spatial and temporal processes, which need
to be identified in modelling. As similar patterns can result from numerous different
processes, the understanding of process is more important than the understanding of
pattern. Pattern is only a phenomenon but process is the essence.
In figure 3 we give an example of a spatial pattern and the processes involved in
urban growth. T
1
,T
2
, and T
3
indicate time series of land development with T
1
the
earliest, and T
3
the latest. The shading represents the temporal order of land develop-
ment: the darker the shading the later the development. The same spatial pattern
results from three (in reality, more) distinct spatiotemporal processes that reflect the
spatial and temporal interactions between road-influenced and centre-based local
(a) (b) (c)
T
1
T
2
T
1
T
3
T
2
T
1
T
2
T
2
T
1
Figure 3. Different spatiotemporal processes: (a) convergence, (b) a sequence, and (c) divergence.
Note: T
1
,T
2
, and T
3
are time sequences, from T
1
,theearliest,toT
3
,thelatest.
178 J Cheng, I Masser
growth patterns. The arrows indicate the trend of temporal development, from which we
can define them as three different processes (convergence, sequence, and divergence).
The basic principle behind the phenomena is that various physical factors such as
roads and centres play various roles over time during the course of local growth. In
figure 3(a), relating to convergence, at T
1
, the road is more important than the centre,
but it is less important at T
2
. This means that local growth occurs first along the road
and then moves to the centre. In figurer 3(c) we see the opposite effect. If we use Lto
denote the total amount of local growth, L
l
for the lower part along road, L
u
for the
upper part along road, L
c
for the centre part, and L
t
for the cumulative development
amount up to time t,wemaywrite:
LL
l
L
u
L
c
,(18)
and
W
i
tf
i
L
t
,ic,r. (19)
where W
r
and W
c
represent the weights of spatial factors `road' and `centre' respec-
tively. The rules detected are listed in table 1. The three cases imply that temporal
dynamics can be represented and understood through dynamic weighting concepts.
Dynamic weighting means that the factor weight is not a constant but is a function
of development amount over time [equation (19)].
To some extent, equation (19) suggests a dynamic feedback between W
i
(t)and L
t
,
representing the complex interaction between pattern and process. L
t
indicates the
temporal pattern in terms of area developed, and the process is described by the chang-
ing roles of multiple factors W
i
(t);infact,L
t
is also impacted by W
i
(t).Inprinciple,
the functions f
i
(L
t
should be continuous, which can be a step linear or a more
complicated nonlinear function, as in most cases W
i
(t)is not negatively or positively
linear with respect to L
t
. For example, in the case of the sequence (table 1), W
r
experiences a decrease from 1 to 0 over time and then an increase from 0 to 1 when t
changes from T
1
to T
3
. Apparently, W
r
is a nonlinear function of L
t
.When f
i
(L
t
)is
constant in relation to t,W
i
(t)also becomes constant over time, as in most CA
applications. However, although this treatment is effective for gaining an understand-
ing of global dynamics in section 2.3, it is not effective for looking at local dynamics at
the project level such as those illustrated in figure 3. The design of function f
i
(L
t
)is
critical. Empirical studies can be carried out based on a theoretical understanding of
interaction. Higher temporal resolution, such as a series of the actual values of L
t
,can
Table 1. Dynamics in the local spatiotemporal processes illustrated in figure 3.
Process T
1
T
2
T
3
Convergence W
r
!1, and W
c
!0, W
r
!0, and W
c
!1, Not applicable
if L
t
<L
l
L
u
if L
t
>L
l
L
u
Sequence W
r
!1, and W
c
!0, W
r
!0, and W
c
!1, W
r
!1, W
c
!0,
if L
t
<L
l
if L
t
>L
l
;if L
t
>L
l
L
c
,
and L
t
<L
l
L
c
and L
t
<L
Divergence W
r
!0, and W
c
!1, W
r
!1, and W
c
!0, Not applicable
if L
t
<L
c
if L
t
>L
c
;
and L
t
<L
Note: !, `approaching or close to'; L
l
,L
u
,L
c
, local growth on the lower, upper, and centre
part of the road, respectively; L
t
, cumulative development amount up to time t;L, total
amount of local growth; W
r
,W
c
, weights of spatial factors `road' and `centre', respectively;
T
1
,T
2
,andT
3
are time sequences, where T
1
is the earliest, and T
3
the latest.
Understanding spatial and temporal processes of urban growth 179
be used to calibrate the temporal rules W
i
(t). For simplicity, the functions f
i
(t)can be
discretised. This implies that the whole period can be divided into a few phases, T
1
to
T
N
, for which various weight values are defined with the assistance of local knowledge
or by calibration from data.
3 Implementation
A case study of Wuhan city, People's Republic of China, is used to test the method-
ology presented above for understanding the dynamic process of urban growth in a
rapidly growing metropolitan region.
3.1 Wuhan context
As the capital of Hubei Province, Wuhan is the largest city in central China and in the
middle reaches of the Yangtze River (figure 4). In 1999 it had an urban population of
around 4 million people, four times that in 1949. During the past five decades, Wuhan
has undergone rapid urban growth, from 3000 ha of builtup area in 1949 to 27515 ha
in 2000. As a result,Wuhan is a good case for gaining an understanding of the dynamic
processes of urban growth in a fast-developing country. In this paper, the urban growth
of Wuhan in the period 1993 ^ 2000 will be modelled based on the methodology
discussed in section 2.
Operational CA models need access to real databases for better simulation perfor-
mance to be achieved (Li and Yeh, 2001). The imagery employed here includes SPOT
PAN/XS for 2000, which covers the whole study area. The images are utilised as the
primary data source for creating a land-cover-change map from 1993 to 2000. The
topographic map (scale 1:10000) of 1993 was used for imagery geocoding registration
and also for producing the land-cover map for 1993. The secondary sources include
planning scheme maps, traffic and tourism maps, street boundary maps, the popula-
tion census, and the statistical yearbook. These were used to create the required spatial
factors (for example, proximity and density variables) for the CA modelling using
simple GIS operations such as overlay, buffering, and neighbourhood statistics. The
image processing for land-cover mapping was implemented through the ERDAS
IMAGINE 8.4 package, and onscreen digitising and spatial data analysis were carried
out in the ArcView environment (for details, see Cheng and Masser, 2003).
The land-cover transition from 1993 to 2000 shown in table 2 was calculated based on
the use of a 10 m 10 m cell size. It can be seen from this table that major land-use and
land-cover changes affected waters, towns and villages, and agricultural land, which were
physically or functionally transferred to urban builtup area. Towns and villages with the
highest annual transition rate were only functionally transferred to urban administration
Han River
Wuhan
Yangtze River
(a) (b)
Figure 4. Location of Wuhan municipality: (a) Hubei Province (shaded area), and (b) Wuhan
(shaded area) in relation to Hubei Province.
180 J Cheng, I Masser
because of the rapid expansion of Wuhan municipality. Agricultural land has experienced
the highest transition percentage. Water bodies include ponds and lakes. A higher per-
centage area occurred for the transition from ponds than from lakes (see figure 6 below).
The category `other' includes green areas, sands, and misclassified areas (misclassified
during image processing, and so on) which are omitted for modelling.
3.2 Project planning and site selection
With assistance from historical documents, local planners, and fieldwork, four large-
scale projects that were planned before or around 1993 were identified (WBUPLA,
1995). All small scale projects were merged into one class, resulting in five projects
[see table 3 (over); see also figure 6 below] as follows:
Project 1, Zhuankou: car manufacturing plant, planned from 1988;
Project 2, Wujiashan: Taiwanese investment zone, planned from 1992;
Project 3, Guanshan: high-technology development zone, planned from 1988;
Project 4, Changqing: large-scale residential zone, planned from 1994;
Project 5, `the rest': small-scale development (commercial, institutional, and residential).
In a GIS environment (ArcView 3.2a), we created the required spatial layers
(figure 5, over), including land cover for 1993, distance to road networks and to city
centres and subcentres, and population density. These layers were exported into a
computer program for testing different site-selection rules for each project according
to equation (2). As a result of a sensitivity analysis conducted in a visual programming
environment, we tested the constraints at three levels for each project
ö
global, regional,
and local
ö
as listed in table 3. The total amount of development L
d
(from the actual
urban growth shown in figure 6 below) and the temporal control mode (from documents
and interviews) are also displayed in this table.
After 1992, Wuhan entered a new wave of development characterised by more
actors, diverse functions, and a new industrial structure (Cheng and Masser, 2003).
We are able to explain the spatial behaviour of the actors involved in each project
in this table. For instance, the dominant actor in the Zhuankou, Wujiashan, and
Guanshan projects is Wuhan municipality, which obtained financial resources from
the central government, foreign investors, and local enterprises (WSB, 2000). Being the
owner of the land, the actor did not need to consider the costs of land utilisation.
Hence, for large-scale projects, the first rule is the availability of a certain amount of
developable land. Being orientated to manufacturing and tertiary industry, the second
rule concerns accessibility to major road networks. Strictly speaking, the second rule is
true not only for large-scale developments but also for small-scale land development
such as for commercial use. Moreover, accessibility to developed areas is crucial for the
economic development zone (Wujiashan) and the high-technology zone (Guanshan).
Table 2. Wuhan City: the land-cover transition from 1993 to 2000.
Major types Water Towns and Agricultural Other Total
villages land
Area in 1993 (ha) 30 258 8 669 51 585
Area undergoing transition:
hectares 1 131 1 530 3 527 72 6 260
percentage
a
18.1 24.4 56.3 1.2 100
Annual rate of transition (%) 0.5 2.3 0.9 na na
na, Not applicable.
a
Area of land undergoing transition in the given category as a percentage of the total amount
of land undergoing transition (6 260 ha).
Understanding spatial and temporal processes of urban growth 181
Access to research resources including nearly twenty universities is a prerequisite for the
location of a high-technology zone such as Guanshan (WBUPLA, 1995). In contrast,
the major actors in the Changqing housing project are local real estate companies
and the relevant work units (WSB, 2000). Land value is becoming an important
criterion, weakening the role of accessibility to city centres. Low-quality land cover
such as ponds is much cheaper than agricultural land. However, higher population
density can guarantee greater market demand and is an influential factor in residential
development. For small-scale projects, particularly within urban districts, more actors
are involved in the decisionmaking including local residents, investors, work units,
planners, and lower levels of local government. This results in a more stochastic
process of site selection, as a result of which the constraints become more uncertain
and fuzzy. However, generally speaking, accessibility to the city centre or subcentre and
to road networks are the key factors.
3.3 Local growth
The cell size used in this research is 100 m 100 m, which results in a 640 410 grid.
A smaller cell size (such as 10 m 10 m) would cause an overload in terms of model
computation. The state of the cells is binary (1 change, 0 no change). The initial
layer is the 1993 land cover.This includes developed land, agricultural land (A), village or
Table 3. Site-selection of the five projects studied.
Project
Zhuankou Wujiashan Guanshan Changqing `the rest'
Number of cells, L
d
1390 314 514 160 3710
Land use Manufacturing Economic High- Residential Mixture
zone technology
zone
Constraints
Global
must be <300 m to <300 m to <300 m to <300 m to Close to city
a major a major a major a major centres and
road road road road subcentres
must be ± ± <4.2 km <3.5 km to Close to
to university subcentres road
street network
must have ± ± ± >560 persons ±
per hectare
net population
density
Regional
density of developable land (%) in a square of
4:5km4:5km >62 ± ± ± ±
3km3km ± ± >68 ± ±
2km2km >90 ± ± ± ±
1km1km ± >69 ± >60 ±
density of developed area (%) in a
2km2km ± >18.7 ± >10 ±
a
Local
can transit if agricultural agricultural agricultural, agricultural agricultural
the land is: or village or village village, or pond village, pond
or hill or lake
Temporal control Quick Slow Quick Quick Normal
± This constraint is not relevant to the specified project.
a
Density should be higher than starting density.
182 J Cheng, I Masser
town land (V), ponds (P), lakes (L), and protected land (public green, parks, and sands). In
figure 5(a), the categories ponds and lakes are merged into the category `water'; and `other'
includes protected land. As described in section 3.1, only four types of land
ö
agricultural,
villages and towns, ponds, and lakes
ö
underwent much change. The pattern model
from another part of this research (Cheng and Masser, 2003) shows that the major
spatial determinants of urban growth in the period 1993 ^ 2000 included major road
networks, minor road networks, centres and subcentres, and master planning, as displayed
NN
N
N
505km 505km
505km
505km
Land cover
Population density
(persons per hectare)
Subcentre
Major centre
Minor road
Major road
University street
Land use
Built-up
Town or village
Agricultural
Water
Other
10 ± 200
200 ± 400
400 ± 600
600 ± 800
800 ± 1000
Residential
Industrial
Green
Street
Other
(a) (b)
(c) (d)
Figure 5. Spatial factors and constraints for site selection and cellular automata modelling:
(a) land cover per 1993; (b) population density (persons per hectare); (c) road networks and
centres and subcentres; (d) master plan for 1996 ^ 2020.
Understanding spatial and temporal processes of urban growth 183
in figure 5. They are selected here as nonconstrictive factors for evaluating the potential for
land conversion.
It should be noted that the classification of each layer is of great importance, as
the model is sensitive to classification, particularly when the study area is large and the
period is long. For instance, the construction of roads may occur during different
phases of the period to be modelled. Their construction time should be taken into
account. In this research, a major road connection (providing a link to the third bridge
over the Yangtze River) was completed in early 2000. This is clearly visible in the 2000
SPOT images. However, this major road is not included in the major road network
layer because it had no practical impact on urban development in the period 1993^
2000. This judgment is confirmed by very sparse and limited land-cover change
surrounding the road. Other layers were spatially defined by following similar rules.
Wuhan city can be treated as a flat landscape, its elevation ranging between
22 ^ 27 m above sea level, apart from a few hills. Hence, slope is not an influential
factor. Physical constraints comprise principally water bodies [see figure 5(a)]. Theoreti-
cally, water bodies should be completely excluded. However, in this case study, 18% of
the land-cover change comes from water bodies, which include ponds and lakes (see
table 2). As this change affects mostly small-scale ponds or the fringes of large lakes,
a general procedure can be designed for defining a specific layer (exclusion layer):
Step 1: select a water body cell from the land-cover layer of 1993.
Step 2: look at neighbourhood statistics (based on a circular neighbourhood with a
200 m radius).
Step 3: exclude the cell if the neighbouring 4 ha are also under water.
The layer will be utilised as a physical constraint on the water body, defining zones
excluded from transition. In the five CA models corresponding to the five projects, a
circular neighbourhood is chosen because it does not display significant directional
distortion. Its radius varies with different projects, ranging from 3 to 9 cells. The
selection of neighbourhood size for each project relies on empirical study and sensitiv-
ity analysis (see section 4.1). The heterogeneity of spatial processes is indicated by using
various combinations of influential factors, weight values, and parameters, to imply
differences in local spatial behaviour.
Given that local growth is impacted by the master plan to be implemented in the
period concerned, we must incorporate the master plan for 1996 ^ 2020 as an influential
factor (this scheme was initiated in 1990 and approved by the central government in 1996).
Owing to the rapid urban expansion at the fringe, some projects such as Changqing and
Wujiashan were not planned until their construction. These will be excluded from the
master planning analysis. Only the projects covered by master planning are considered
(that is, Guanshan, Zhuankou, and `the rest'). Each cell jis assigned a value X
j
,
representing the degree of influence of the planned land use on its land-cover transition
in a given project. If M
i
denotes the total area of land-use iin a specific project, C
i
denotes the part of M
i
undergoing a transition, then, C
i
=M
i
generally indicates the degree
of influence of land use i.Ifacelljwas planned for land use i,
X
j
C
i
M
i
. (20)
X
j
needs to be standardised according to equation (5) before it can be incorporated
into the evaluation formula [equation (4)]. The M
i
and C
i
=M
i
values of the major land
uses are listed in table 4. The code refers to the National Urban Land-use Classifica-
tion Standard (NULCS). From table 4 we can see that, in general, the master plan was
more successful in guiding large-scale projects in the fringe than it was in guiding
small-scale projects in urban districts. In figure 5(d), `residential' includes codes R
1
184 J Cheng, I Masser
and R
3
, `green' includes G
1
^G
3
, and `street' includes S
1
; the remaining coded areas
(C
1
,C
3
,C
4
,C
5
) are merged into `other'.
The calibration of parameters has proven a difficult task in urban CA modelling
(Clarke and Gaydos, 1998; Li and Yeh, 2001), particularly when there are many factors
and parameters to be considered. The difficulty lies in the fact that most urban CA
modelling takes the whole municipality into account in the calibration procedure,
resulting in intensive computational overload. In this research, project-based CA model-
ling has largely reduced the computational time of calibration as the spatial extent
of each project is much smaller than the whole study area, as shown in table 5 and
figure 6 (see over).
The factors and parameters for model calibration include six spatial factors,
neighbourhood size (radius), and stochastic disturbance a. Other parameters (for
example, the temporal pattern mode parameter, l, and iteration time t) are utilised
for sensitivity analysis (see section 4.1). The six spatial factors are `distance to minor
road', `distance to major road', `distance to centre or subcentres', `density of neighbour-
ing developed areas', `density of neighbouring new development', and `master planning'.
Their fparameters [see equation (6)] are taken from the global pattern model from a
logistic regression carried out in another part of this research (Cheng and Masser,
2003). Automatic search for the best-fit parameters was carried out by using a hier-
archical method
ö
that is, by reducing the step size in two stages over five loops, for
each of the six factors. For example, the step size of loops for calculating the weight
values was set first as 0.05
ö
that is, it was increased from 0.05 to 1.00 in steps of 0.05.
Once the scope of the parameter for the ideal accuracy was determined, such as from
0.20 to 0.25, we set a second step size (0.005) for finer calibration, so that the value was
increased from 0.20 to 0.25 in steps of 0.005.
The validation accuracy depends on the approach used to compare simulated with
actual patterns. The comparison is traditionally made by means of a coincidence
matrix generated by a cell ^ cell comparison of the two pattern maps. Some researchers
argue that CA simulations should not be assessed only on the goodness of fit (that is,
on a cell-by-cell basis) but should also be assessed on their feasibility and plausibility,
as urban systems are rather complicated and their exact evolution is unpredictable
Table 4 . Influential degree of master planning on land cover transition in the Zhuankou and
Guanshan projects, and `the rest'.
Code
a
Classification Zhuankou Guanshan `The rest'
C
i
=M
i
M
i
C
i
=M
i
M
i
C
i
=M
i
M
i
R
1
Low-rise residential 0.237 265 0.23 57 0.087 1082
R
3
Poorer environment ± ± ± ± 0.1333 149
M Industry 0.318 508 0.24 172 0.049 419
G
1
Public green 0.27 137 ± ± 0.0916 416
G
2
Protected land 0.147 58 0.33 112 0.041 222
G
3
Ecological agriculture ± ± ± ± 0.0216 82
C
1
Administration or offices 0.26 52 ± ± 0.0787 17
C
3
Cultural or recreational 0.528 16 ± ± ± ±
C
4
Sports facility ± ± 0.3 44 0.035 89
C
5
Hospital or health 0.742 33 ± ± ± ±
S
1
Street ± ± ± ± 0.069 354
± Value omitted as M
i
<15.
a
The code utilised in the National Urban Land-use Classification Standard.
Note: M
i
, total area in land-use i;C
i
, area of land in land use iundergoing transition; for more
details of the projects Zhuankou, Guanshan, and `the rest', see section 3.2 and table 3.
Understanding spatial and temporal processes of urban growth 185
(White and Engelen, 2000; Wu and Webster, 1998; Yeh and Li, 2001). Some global
measures that have been used for testing the validity of CA simulation include the
fractal index and Moran I index (Wu, 1998b), fractal analysis (Yeh and Li, 2001), and
the landscape metric (Soares-Filho et al, 2002). Wu (2002) emphasises the need to
validate the model through structural and cross-tabulation measures. Structural meas-
ures can be used to compare pattern (the outcome of the process) but not the spatial
location (or process). We consider spatial location match also to be of great importance
in support of planning decisionmaking, despite the difficulties imposed by CA model-
ling. Another reason lies in the fact that local processes at the project level require
more accurate cell-based measures, as their morphology is less definite compared with
those at the global level.
Clarke and Gaydos (1998) outline four ways to test the degree of historical fit
statistically (through three R
2
fits and one modified Lee^ Sallee shape index). For the
Lee ^ Sallee shape index (combining the actual and the simulated distributions as binary
urban or nonurban and by computing the ratio of the intersection over the union), they
reported that the practical accuracy is only 0.3. In this paper, we use consistency
coefficients, CC (the percentage of the matched over the actual) and the Lee ^ Sallee
index, LI for the evaluation of goodness of fit. As the total number of pixels is the same
in the simulation as in the actual pattern (that is, L
d
L
n
) we can write
LI CC
2ÿCC .(21)
Table 5. Cellular automata simulation of five projects.
Projects Zhuankou-1 Zhuankou-2 Wujiashan Guanshan Changqing Rest
Land demand, 1 390 1 390 314 514 160 3 710
L
d
(cells or ha)
Accuracy, CC 54 54 51.6 53.2 85 55
Lee ± Sallee 0.37 0.37 0.35 0.36 0.74 0.38
index, LI
Neighbourhood 6 6 5 8 3 7
size (radius in
no. of cells)
Temporal 4/3 4/3 4 4/3 4/3 2
pattern mode
parameter, l
Dynamic ± <15 15 ± 55 >55±±±±
weighting (%)
Major road
a
0.2 ± 0.5 0.05 0.325 ± 0.1 0.3
Minor road
b
0.3 ± 0.1 0.15 0.1 0.35 0.55 0.15
Centres
c
± 0.7 ± 0.5 ± ± ± 0.2
Neighbourhood
new 0.3 0.3 0.1 0.15 0.3 0.35 0.35 0.1
old ± ± ± ± 0.275 0.25 ± 0.2
Master planning 0.2 ± 0.3 0.15 ± 0.05 ± 0.05
Total (%) 100 100 100 100 100 100 100 100
± Not applicable.
a
Distance-decay parameter: f0:000765.
b
Distance-decay parameter: f0:0012.
c
Distance-decay parameter: f0:000272.
Note: a1% (parameter controlling strength of stochastic pertubation), n50 (number of
iterations); for details of Zhuankou-1 and Zhuankou-2, see section 3.5.
186 J Cheng, I Masser
ForexamplewhenCC0:57,LI0:4. Following this formula, the Lee ^ Sallee
indices for five projects were computed and are listed in table 5. The overall accuracy
based on the weighted combination (L
d
) of the five projects, is 0.554 in CC and 0.383
in LI, greater than the measures of Clarke and Gaydos.
3.4 Temporal control
With local knowledge, we were able to identify the patterns of temporal development
of each project (see table 3). In 1993 Zhuankou was still completely rural. By 1995
nearly half was developed. There was not much change from 1997 and 2000. Therefore,
its temporal growth pattern is defined as `quick' (l4=3). The small-scale projects,
`the rest', are a mixture of all three patterns. Some may be quick, others slow (l4).
On average, it is reasonable to classify them as `normal' (l2). The numb er of i te ra-
tions is defined as n50 because the greater the number the finer the discriminative
capacity of the models.
In figure 7 (over) we show the trajectories of temporal development for the five
projects according to the results of the validated CA simulations. As described by
equation (17), the output of CA simulation is L
i
(t)(t1, 2, .::,n), which is different
from the yearly actual amount L
i
(t)(t1, 2, .::,m) for each project i. We need a
transition from L
i
(t)to L
i
(t). The transition function h in equation (17) should be based
on an understanding of the actual temporal development process, which is determined
by its socioeconomic development. For the sake of simplicity, we use an equal time
Project
Village
Agricultural
Lake
Pond N
707km
1994 1995 1996
1997 1998 1999
2000 Actual
Figure 6. Simulated (1994 ^ 2000) patterns and actual pattern.
Understanding spatial and temporal processes of urban growth 187
interval
ö
that is, a linear function: tt=7.Astranges from 1 to 50 (n50) and t
from 1 to 7 (m7),
L
i
(t)XL
i
t,for t7tÿ11, .::,7t. (22)
A series of new created layers for the whole study area corresponding to the seven-year
urban growth (from 1993 to 2000; see figure 6) were imported into animation software
(Animagic32, Right to Left Software, New York) for dynamic visualisation. This
animation is helpful for exploring and comparing the temporal dynamics of spatial
processes.
In table 5 we list the spatial heterogeneity of the causal factors, which vary spatially
in terms of their weight values. The neighbourhood effect is represented by neighbour-
hood size and by the weight values of new and old developed areas. Table 5 suggests
that there are some similarities and some dissimilarities between the five projects. The
weight values of the major roads, minor roads, city centres and subcentres, and master
planning also show some differences. Major roads played a greater role in `the rest' and
Wujiashan projects, and less important roles in the Changqing and Guanshan projects.
Conversely, minor roads played a greater role in the Changqing and Guanshan projects
than in `the rest' and Wujiashan projects. By linking the site-selection rules shown
in table 3, it can be seen that the road network system actually plays various roles
during different phases of urban growth. The major road network is the key at the
site-selection stage and remains important for some areas at the local growth stage.
However, the minor road network is active only at the local growth stage. This is
because of the fact that minor road networks are created after the site-selection stage
together with the new growth. Relatively, city centres and subcentres are influential
only for `the rest' as the other projects are located at the urban fringe. Master planning
is less influential for `the rest' than it is for the other projects. The spatial heterogeneity
described above suggests that the causal effects of urban growth vary from place to
place. Local process modelling may offer deeper insights into urban growth processes.
3.5 Local temporal dynamics
For each project we focus on local temporal dynamics. The following examples may be
highlighted.
Land developed up to time t,L
t
(cells or ha)
4000
3500
3000
2500
2000
1500
1000
500
0
ÿ500
Project:
1 5 9 1317 2125 293337 414549
t
`The rest'
Changqing
Zhuankou
Guanshan
Wujiashan
Figure 7. Temporal control patterns of the five projects.
188 J Cheng, I Masser
(a) Compared with the major road network, minor roads, especially in new zones that
are also new development units, may occur at different phases of the period studied:
that is, between T
0
and T
n
, but not immediately from T
0
.
(b) The spatial impacts of various factors such as roads and centres do not affect local
growth simultaneously.
(c) Neighbourhood effects may show temporal variation; for example, they may be
stronger at T
0
than at T
n
, or vice versa.
These examples show qualitatively the complex pattern and process interaction as
discussed in section 2.4. The two models for the Zhuankou project (table 5) have
similar model accuracy and similar patterns. However, their spatiotemporal processes
are quite different, as shown quantitatively in figure 8 (over). Model 1 exhibits a more
random process. Model 2 shows a more self-organised process. Model 2 is based on the
assumption that new development in Zhuankou first occurred at the centre, then along
the major road, and then finally spread from the centre. The assumption corresponds to
a temporal dynamics that is spatially controlled by three sets of weight values (table 5).
To calibrate this process-oriented CA model, manual tests based on the moeller's
understanding of local growth processes and the visual exploration of model outputs
(temporal patterns) are very important for reducing parameter ranges and making
rough estimates of dynamic weight values. Limited automatic search can be followed
for the best (or ideal) combination of parameters.
To some extent, the dynamic weighting implies the temporal lag of the spatial
influences of locational factors on urban growth. This example suggests that local
temporal dynamics can enable us to understand better organised local growth. If we
explore the changes in weight values, it can be found that major changes are seen in
major roads and centres. As described by equation (19), the weight values should be
nonlinear functions of temporal land-development demand. In table 5 it can also
be seen that the functions are highly complex in reality. They are frequently phased.
Model 2 is based on local knowledge. The other projects can be calibrated temporally
by the same procedures as those followed in the Zhuankou project.
4 Discussion and conclusions
4.1 Model calibration and validation
Li and Yeh (2001) report a calibration procedure for CA modelling involving use of
an artificial neural network. In their method, the neural network is utilised to obtain
the optimal parameter values automatically, based on the training of empirical data; the
parameter values thus calibrated are then used to carry out CA simulations on new
data. In CA models of this kind, the transition rules represented by the neural network
structure are not transparent to users. Consequently, this method can be used for
prediction by using the same set of rules but is not ideal for interpreting the logic of
land conversion or spatiotemporal processes; it is a `black box' (Wu, 2002).
It has been found in this research that visual tests offer a useful and quick way of
calibrating and verifying CA models (Clarke et al, 1997; Ward et al, 2000), particularly
with respect to sensitivity analysis. In this project-based CA modelling exercise, cali-
bration did not prove to be a severe problem in terms of computation time. However,
the optimal combination of parameters from automatic searches may not give the best
results, as socioeconomic systems essentially produce no `best' solution. Consequently,
the calibrated results need further confirmation with respect to their interpretation
and the plausibility of their spatial and temporal processes. In table 6 (over), we take
the Wujiashan project as an example to illustrate this issue. When neighbourhood size
(radius) is set as 5 cells, the optimal parameters for accuracy (i
CC
) 52.8% are calculated
from an automatic search (the step size for the weight value is 0.005), together with the
Understanding spatial and temporal processes of urban growth 189
Minor road
Major road
Iteration t
1±8
9±14
15 ± 28
(a)
(b)
N
N
10123km
10123km
Figure 8. Local temporal dynamics of (a) Zhuankou-1 and (b) Zhuankou-2 (see table 5).
190 J Cheng, I Masser
other parameter combinations. However, the spatial processes produced by the set of
weight values (0.2, 0.1, 0.45, 0.25) are not the same as the real temporal pattern based
on visual comparison. Conversely, another combination of weight values (0.325, 0.1,
0.3, 0.275) is able to create more satisfactory temporal patterns, although its model
accuracy (51.6% in i
CC
) is lower. Consequently, visual tests are still a necessary means
for process modelling in contrast to pattern modelling.
Another aspect of calibration is sensitivity analysis as the results of CA simulation
are very sensitive to the parameter values (for example, neighbourhood size, weight
values, l,andn). This is an issue of uncertainty in CA simulation that is not given
enough attention in most applications. For the Wujiashan project, before accepting the
weight values (0.325, 0.1, 0.275), we need to test the stability of this set by slightly, or
greatly, adjusting the weight values and other parameters, such as neighbourhood size,
as shown in table 6. The changes (slight or great) in validation accuracy that are
identical to those observed in the parameters assure the reliability of this set.
4.2 Visualisation of processes
To implement site-selection and CA modelling, a loose coupling strategy is frequently
adopted for various applications (Bell et al, 2000; Clarke and Gaydos, 1998). In general,
loose coupling means that a data-transfer procedure is implemented between a CA
model, GIS, and an animation module. This loose-coupling strategy sacrifices the
`friendly' interface but improves the computational efficiency of CA simulation.
Here, the site-selection rules and the CA model are programmed in object-oriented
programming language. Spatial data analysis and visual exploration tasks are imple-
mented under a GIS environment (the ArcView platform). Each layer produced is
exported as an ASCI raster file. A subprocedure is programmed to read and write
the ASCII raster files between the CA and ArcView. The major parameters include the
weight values, the temporal pattern control parameter l, the neighbourhood size, and
the stochastic perturbation a. The validation results are stored into a text file and an
ASCII raster file. A validated urban growth layer (for the period 1993 ^ 2000) from the
simulation is separated into a series of maps, each corresponding to one year. The layers
created are exported as a JPG file or any other type of image file. These are inserted as
an individual frame into the animation file for visual checking of the spatial process.
However, a major deficiency of this strategy is that it is not a very `friendly' environment
for the immediate visualisation of spatial temporal processes, although it is effective for
Table 6 . Calibration of cellular automata modelling and sensitivity analysis: the Wujiashan
project.
Accuracy, i
CC
(%) 52.8 51.6 51.3 50.8 29.5 46 49 50 50
Neighbourhood size 5 5 5 5 5 8 6 4 5
a
(radius in cells or ha)
Major road
b
0.2 0.325 0.325 0.225 0.375 0.1 0.325 0.325 0.325
Minor road
c
0.1 0.1 0.05 0.25 0.3 0.3 0.1 0.1 0.1
Neighbourhood
new 0.45 0.3 0.35 0.15 0.3 0.4 0.3 0.3 0.3
old 0.25 0.275 0.375 0.025 0.2 0.275 0.275 0.275
Total (%) 100 100 100 100 100 100 100 100 100
Note: a1%, n50, l4.
a
Temporal pattern mode paraemter: l4:5.
b
Distance-decay parameter: f0:000765.
c
Distance-decay parameter: f0:0012.
Understanding spatial and temporal processes of urban growth 191
model calibration. In the future, CA modelling tightly coupled with GIS and animation
should be further studied to enhance its visualisation function with regard to spatial
temporal processes.
4.3 Process modelling
To some extent, the accuracy of a simulation model depends on the complexity and
stochasticity of the real city and on the availability of detailed information. Although
the overall accuracy of the five CA models run here is only 55%, on a cell-by-cell
municipal and project basis, the methodology proposed in this paper illustrates the
potential for gaining an understanding of spatial processes and their temporal
dynamics at the level. The spatial clustering of land-development projects indicates
a self-organising process. The timing schedule of various projects exhibits global tem-
poral dynamics. Dynamic weighting is an important concept in the simulation of
process, in contrast to the situation for the simulation of pattern. Spatial classification
based on the project concept is subjective but transparent to urban planners. The spatio-
temporal processes explored by project-based modelling can easily be interpreted with
reference to socioeconomic and decisionmaking processes. To be a true process model,
CA modelling, as suggested in this research, should incorporate dynamic weighting
methods, although there is still much difficulty in systematically defining these functions
in practice.
From a local spatial modelling point of view, a possible future direction lies in
applying a moving window or kernel in defining a project for each cell, so that
generalised local process modelling can be repeatedly applied to each cell. This is a
similar principle to that applied in GWR modelling. This idea can result in universally
localised process modelling. The parameters for understanding local processes vary by
cell. Users can redefine interesting projects for further interpretation by focusing on a
`hot spot'.
From the perspective of spatial data analysis, the methodology can be utilised to
discover hidden processes in an integrated spatial database regarding temporal urban
growth. This has been one of the major concerns in the field of spatial data mining or
knowledge discovery. When socioeconomic data become available at detailed levels,
project-based CA modelling can be further linked to microscale multiagent and eco-
nomic modelling. Such integration may allow an exploration of the spatial and economic
behaviour of various actors at the microscale.
The major purpose of CA simulation is to generate alternative scenarios for
decision support for smart-growth management. The methodology developed here
can be extended in this direction. In this case, stages 1 and 4 need to incorporate
top-down socioeconomic models for predicting the demand for new land development
in the future [that is, for predicting L
d
in equation (1)]. Stages 2 and 3 are subject to
some modification in quantification. The construction of plan scenarios is based on
soft-system thinking, which stresses the role of user subjectivity. In this way, the
intentions of local planners can be transformed into spatially and temporally explicit
weight values and into certain parameters (for example, see Wu, 1998b). With a user-
friendly visualisation environment, the framework tested in this research can be used to
facilitate decisionmaking regarding urban spatial development.
We cannot ignore the fact that any advanced modelling technique, including CA
must be based on a proper understanding and abstraction of the systems studied. The
better the understanding the more accurate the modelling is likely to be. Planning will
never be a hard science, for it is built on humanistic assumptions, values, and goals
(Shmueli, 1998). Our understanding of the new urban reality will ultimately be based
upon a combination of the use of computers and human judgment (Sui, 1998).
192 J Cheng, I Masser
CA form a simulation tool only for testing a decisionmaker's understanding. Limited
by existing GIS theory and methods, the identification of various spatial and temporal
heterogeneity cannot be completed without the assistance of local knowledge. This implies
that local knowledge is an important ancillary data source for CA modelling, especially
under the framework presented in this paper. During the modelling process, project
planning, site selection and temporal control needs more input from local experts. For
dynamic weighting, because of the limited temporal resolution, local knowledge is an
essential source of qualitative information. It has been stressed in this research that a
soft-system methodology, stressing the roles of decisionmakers, and feedback between
modellers and users and between various stages of the decisionmaking process is helpful,
especially when complete information resources are not guaranteed.
Acknowledgements. This research was financially supported by the project DSO-SUS, involving
the International Institute for Geo-Information Science and Earth Observation, Enschede, and the
School of Urban Studies, Wuhan University, between the Netherlands and China. It was also
partially assisted by the national Natural Science Funding (NSF) project (50238010), China. Thanks
are also extended to three anonymous reviewers for their constructive and critical comments, which
helped create the current version.
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194 J Cheng, I Masser
