High-resolution integrated modelling of the
spatial dynamics of urban and regional systems
R. White
a,
*, G. Engelen
b
a
Department of Geography, Memorial University of Newfoundland, St. John's, Newfoundland,
Canada A1B 3X9
b
Research Institute for Knowledge Systems, Postbus 463, 6200 AL Maastricht, The Netherlands
Received 5 May 1999; received in revised form 17 December 1999; accepted 21 January 2000
Abstract
An emerging branch of geocomputing involves the modelling of spatial processes. A variety
of techniques are being used, the most important being traditional regionalized system
dynamics approaches, multi-agent systems, and cellular automata (CA). The techniques are
frequently combined to model processes operating at dierent spatial scales. Urban and
regional models based on CA give good representations of the spatial dynamics of land use.
In a current application, a cellular model of The Netherlands at 500 m resolution is driven by
a macro-scale dynamical spatial interaction model de®ned on 40 economic regions; this model
is in turn driven by national planning projections and policy goals. Given the national totals,
the macro-scale model generates regional demands for population and a number of economic
activities. These demands are translated into demands for cell space, which the CA then
attempts to locate. In turn, information on conditions at the cellular level, such as the quan-
tity and quality of land available to various activities and actual densities at the cellular scale,
are returned to the regional model to modify parameter values there. Linking the two models
operating at the two scales improves the performance of both. The results of high-resolution
modelling of spatial dynamics raise several methodological issues. One of the most pressing
concerns evaluation of the results. Another issue concerns predictability. To the extent that
these models capture the evolving nature of real cities and regions, they cannot be strictly
predictive. # 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Cellular automata; Land use; Integrated models; Process models; Spatial dynamics
Computers, Environment and Urban Systems
24 (2000) 383±400
www.elsevier.com/locate/compenvurbsys
0198-9715/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0198-9715(00)00012-0
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* Corresponding author. Fax: +1-709-737-3119.
E-mail address: roger@plato.ucs.mun.ca (R. White).
1. Introduction
Most geocomputation currently deals with the processing of spatial data in order
to show us the world as it is; but of course the world can be seen from many points
of view, and one of the great strengths of geographical information systems (GIS) is
that it allows us continually to recon®gure the data in the ways that are most
appropriate for our changing needs and points of view. Spatial statistics by and
large tend to perform the same sort of task, but in a more abstract way, allowing us
to make generalizations about what we see in the data, to extract hypotheses from it,
or, ®nally, to use it to test hypotheses.
But the data that is stored and process ed in a GIS contains, so to speak, the seeds
of its own destruction. The patterns of land cover and land use, and of social, eco-
nomic, and demographic characteristics, constantly change, both because the spatial
structures are themselves inherently unstable, and because they are typically exposed
to external phenomena that also force change. This problem is dealt with by pro-
grammes for periodic data collection and updating, but such a response is not su-
cient for all purposes, since at best it gives us only a regularly updated pictur e of
current conditions. Planners and decision makers need to know not only the current
state of aairs, they also require some idea of future conditions. Ideally they would
like to be able to see the possible consequences of the plans and policies they may
have under consideration. These considerations point to another class of geo-
computation techniques Ð speci®cally, predictive computational models. To the
extent that these models embody dynamics capturing the endogenous instabilities of
existing spatial con®gurations, they can be thought of as dynamical GIS.
The favoured techniques for implement ing high-resolution models of spatial
dynamics are cellular automata (CA) and multi-agent systems (MA). CA are
attractive for a number of reasons:
1. they are inherently spatial; typically they are de®ned on a raster cell space and
are thus compatible, or can be made compatible, with most spatial data sets;
2. they are dynamic, and can thus represent spatial processes in a direct way;
3. they are highly adaptable Ð they can be set up to represent a very wide range
of situations and processes;
4. they are rule based, and can thus capture a wide variety of spatial behaviours;
5. they are simple, and thus computationally ecient; and
6. in spite of their simplicity, they can exhibit extraordinarily rich behaviour;
some simple CA have been shown to be formally equivalent to a Turing
machine, i.e. these CA can represent and execute any possible algorithm.
MA systems also have attractive features:
1. they provide a straightforward way to represent spatial entities or actors hav-
ing relatively complex properties or behaviours;
2. they provide inheritance of properties from class to subclass, so that they
represent hierarchical systems in a natural way; and
384 R. White, G. Engelen / Comput., Environ. and Urban Systems 24 (2000) 383±400
3. they capture directly the interactive properties of many natural and human
systems, as well as the complex system behaviour that emerges from this
interaction.
The two approaches overlap to some degree; indeed, CA are occasionally con-
sidered to be a type of MA system. In the context of geocomputation, MAs are most
commonly used together with CA to represent, for example, individuals moving
around in a cell space endowed with its own CA dynamics (Benenson, 1998; Portu-
gali & Benenson, 1997), or to represent clusters of cells which may be generated by
the dynamics of a CA, and which as a cluster maybe acquire emergent properties.
However, MAs can be used on their own, e.g. to model the dynamics of an urban
system containing a variety of types of urban centres (Bura, Guerin-Pace, M athian,
Pumain & Sanders, 1996; Sanders, Pumain & Mathian, 1997).
In this paper we focus on CA. Tobler (1979) was the ®rst to suggest the use of CA
in geographical modelling. He was followed by Phipps (1989, 1992), who focused on
theoretical problems of cluster formation, and Couclelis (1985, 1988, 1989), who in
this early work used the technique to explore theoretical issues such as complexity
and structure formation. In more recent work, both (Couclelis, 1997; Phipps &
Langlois, 1997) have continued to pursue theoretical problems associated with CA
representations of geographical systems. Cecchini and Viola (1990) were also among
the ®rst to adopt CA for spatial modelling, and ha ve continued to work in this area
(Cecchini, 1996). Papini and Rabino (1997) have used CA to model urban form.
Since CA can be considered an extension of GIS, in which a dynamics is imposed on
the data structures, the link between the two has attracted a certain amount of
attention: Itami (1994), Wagner (1997), White and Engelen (1994), and Wu (1998b)
have all considered this issue. Theobald and Gross (1994) have gone further and
discussed the integration of GIS, CA, and System Dynamics techniques (Stella);
they thus support the approach taken in this paper, which emphasizes integrated
modelling using all three types of approaches.
More recently, there have been a number of applications of CA that are aimed at
developing the technique as one which can be applied to practical problems in such
areas as land use planning, social policy, and impact assessment. Clarke, Hoppen
and Gaydos (1997) used a CA to model the historical development of urbanization
in the San Francisco Bay area. Batty and Xie (1994, 1996) and Xie (1996) developed
several urban models, one of which was applied to the development of a residential
area on the fringe of Bualo, USA. The work of Wu (1998b) is also directed at
developing planning applic ations. Portugali and Benenson (1995, 1997) and Portu-
gali, Benenson and Omer (1994, 1997) have emphasized empirical realism in highly
detailed models which combine land use dynamics with models of socio-economic
and ethnic group formation; these are applied in Tel Aviv, Israel. Finally, Engelen,
White and Uljee (1997), Englelen, Uljee and White (1997), Engelen, White, Uljee
and Wargnies (1996), Uljee, Engelen and White (1996), White and Engelen (1993,
1997a, b), and White, Engelen and Uljee (1997, 1999) have developed several CA
and CA-based integrated models designed as prototypes of Spatial Decision-
Support Systems for urban and regional planning and impact analysis (fully functional
R. White, G. Engelen / Comput., Environ. and Urban Systems 24 (2000) 383±400 385
demos of several of these models can be downloaded from www.riks.nl/RiksGeo/
freestu.htm).
The cumulative eect of this work is to demonstrate that CA are remarkably
eective at generating realistic simulations of both land use patterns and other spa-
tial structures. Unlike conventional System Dynamics techniques, they have proven
able to handle high-resolution applications easily, and thus to combine the precision
of high-quality data sets typically resi dent in GIS with the realism of dynamics to
yield convincing predictions of the future states of spatial systems.
2. Characteristics of CA
CA are perhaps the simplest type of dynamic spatial model. Essentially, they
consist of:
1. a grid or raster space;
2. a set of states which characterize the grid cells;
3. a de®n ition of the neighbourhood of a cell;
4. a set of transition rules that determine the state transitions of each cell as a
function of the states of neighbouring cells; and
5. a sequence of discrete time steps, with all cells updated simultaneously.
The most ba sic CA, like Game of Life and the one-dimensional CA used for fun-
damental research in the properties of dynamical systems, embody these character-
istics in a straightforward way. In Game of Life, for example, the cell space is a two-
dimensional rectilinear grid, there are two possible cell states, alive and dead, and the
transition rules are simple, e.g. if a dead cell has exactly three live cells in its eight-cell
neighbourhood, then at the next iteration it changes state to alive. But the CA that
have been developed to model geographical systems typically are much more com-
plex, and relax these de®ning characteristics in a number of ways in order to come as
close as possible to a faithful repres entation of the system being modelled. Thus, it is
worthwhile to examine some of these variations on the CA theme and the reasons
why they are useful in a geocomputational setting.
2.1. The grid space
Grid space is typically assumed to be two dimensional, rectilinear, and homo-
geneous; but these assumptions are frequently dropped. While it is clear that for
most geographical applications invo lving land use and land cover it is natural to use
a two-dimensional grid, for some applications it may be more straightforward to
use grids with other dimensions. Some of the most advanced urban trac models,
for example (Nagel, Rasmussen & Barrett, 1997), have been developed using one-
dimensional CA, although in these models the linear CA are concatenated in order
to represent the network structure of the road system. Similarly, it might be useful to
386 R. White, G. Engelen / Comput., Environ. and Urban Systems 24 (2000) 383±400
model dense, multi-story urban areas with three-dim ensional CA, although to date
this has not been done.
Rectilinear grid systems have obvious advantages both in terms of compatibility
with raster-based data systems and in terms of computational eciency. However,
the regula r structure in principle may introduce artifacts into the spatial structures
generated by the CA, and so some authors have proposed using a hexagonal tiling
or even randomizing the grid coordinates in order to minimize or eliminate the
macroscopic asymmetries that characterize a square lattice. So far there seem to be
no geographical applications that make use of such a randomization procedure.
There are other reasons to depart from a regular grid. In current applications, cell
sizes range from 500 m down to tens of metres. If the space to be modelled is already
subdivided into functionally relevant units that approximate the scale of the grid,
then these units will provide a better representation of the space than will grid cells.
For example, if land use modell ing is to be carried out at a resolution approximating
the scale of cadastral or land ownership units, then using cadastral units rather than
grid cells will result in a better conformation of model results to actual land use
boundaries, although there will of course be a loss of computational eciency, as
well as a complication of the de®nition of the `cell' neighbourhood. Batty and Xie
(1994) have employed cadastral units in a model of land use changes in a suburban
area of Bualo, USA.
For typical geographical applications, the most important grid space assumption
to relax is that of homogeneity. Realistically, the space on which the state dynamics
is played out is far from homogeneous. If the states represent land use, then it is
clear that a number of factors other than the land use of neighbouring cells Ð fac-
tors such as slope, soil quality, and zoning regulations Ð may be impor tant deter-
minants of land use change. Such factors can be thought of as ch aracterizing the cell
space itself. In this view, then, each cell is characterized by an intrinsic suitability for
each particular land use, or state, which acts in addition to the standard cellular
neighbourhood eect in determining the cell state transitions. These suitabilities may
also include non-local factors that are not represented in the cell space neighbour-
hood, such as accessibility to a transportation network or to key points in the region
like a city centre or an airport.
A number of CA models have been developed in which the cell space is inhomo-
geneous (Engelen, White & Uljee, 1993; White & Engelen, 1997a; White, Engelen &
Uljee, 1997). The idea of including suitabilities in the characterization of the cell
space emphasizes the importance of the link between CA modelling and GIS, since
the suitabilities are typically calculated within a GIS and imported into the cellular
model. However, when suitabilities consist of weighted sums of cell characteristics, it
is frequently the case that the proper values of the weights are not known. In this
case determination of the precise values of the weights becomes part of the calibra-
tion process of the CA, and it is convenient to have a software tool that sits be tween
the GIS and the CA and faci litates the process of calibrating the weights. In any
case, the weights, or more accurately, the suitabilities determined by them, form part
of the boundary conditions of the CA, i.e. they are read in during the initialization
of the model and remain ®xed during execu tion. In principle the weights might also
R. White, G. Engelen / Comput., Environ. and Urban Systems 24 (2000) 383±400 387
