Modelling sustainable urban development by the integration of constrained cellular automata and GIS

Cellular Automata (CA) have attracted growing attention in urban simulation because their capability in spatial modelling is not fully developed in GIS. This paper discusses how cellular automata (CA) can be extended and integrated with GIS to help planners to search for better urban forms for sustainable development. The cellular automata model is built within a grid-GIS system to facilitate easy access to GIS databases for constructing the constraints. The essence of the model is that constraint space is used to regulate cellular space. Local, regional and global constraints play important roles in a ecting modelling results. In addition, ‘grey’ cells are de ned to represent the degrees or percentages of urban land development during the iterations of modelling for more accurate results. The model can be easily controlled by the parameter k using a power transformation function for calculating the constraint scores. It can be used as a useful planning tool to test the e ects of di erent urban development scenarios. 1. Cellular automata and GIS for urban simulation Cellular automata (CA) were developed by Ulam in the 1940s and soon used by Von Neumann to investigate the logical nature of self-reproducible systems (White and Engelen 1993). A CA system usually consists of four elements—cells, states, neighbourhoods and rules. Cells are the smallest units which must manifest some adjacency or proximity. The state of a cell can change according to transition rules which are de ned in terms of neighbourhood functions. The notion of neighbourhood is central to the CA paradigm (Couclelis 1997), but the de nition of neighbourhood is rather relaxed. CA are cell-based methods that can model two-dimensional space. Because of this underlying feature, it does not take long for geographers to apply CA to simulate land use change, urban development and other changes of geographical phenomena. CA have become especially, useful as a tool for modelling urban spatial dynamics and encouraging results have been documented (Deadman et al. 1993, Batty and Xie 1994a, Batty and Xie 1997, White and Engelen 1997). The advantages are that the future trajectory of urban morphology can be shown virtually during the simulation processes. The rapid development of GIS helps to foster the application of CA in urban Internationa l Journal of Geographica l Information Science ISSN 1365-8816 print/ISSN 1362-3087 online  http://www.tandf.co.uk/journals/tf/13658816.html X. L i and A. G. Yeh 132 simulation. Some researches indicate that cell-based GIS may indeed serve as a useful tool for implementing cellular automata models for the purposes of geographical analysis (Itami 1994). Although current GIS are not designed for fast iterative computation, cellular automata can still be used by creating batch ® les that contain iterative command sequences. While linking cellular automata to GIS can overcome some of the limitations of current GIS (White and Engelen 1997), CA can bene® t from the useful information provided by GIS in de® ning transition rules. The data realism requirement of CA can be best satis® ed with the aid of GIS (Couclelis 1997). Space no longer needs to be uniform since the spatial di erence equations can be easily developed in the context of GIS (Batty and Xie 1994b). Most current GIS techniques have limitations in modelling changes in the landscape over time, but the integration of CA and GIS has demonstrated considerable potential (Itami 1988, Deadman et al. 1993). The limitations of contemporary GIS include its poor ability to handle dynamic spatial models, poor performance for many operations, and poor handling of the temporal dimension (Park and Wagner 1997 ). In coupling GIS with CA, CA can serves as an analytical engine to provide a  ̄ exible framework for the programming and running of dynamic spatial models. 2. Constrained CA for the planning of sustainable urban development Interest in sustainable urban development has increased rapidly in recent years. Unfortunately, the concept of sustainable urban development is debatable because unique de® nitions and scopes do not exist (Haughton and Hunter 1994). However, this concept is very important to our society in dealing with its increasingly pressing resource and environmental problems. As more nations are implementing this concept in their development plans, it has created important impacts on national policies and urban planning. The concern over sustainable urban development will continue to grow, especially in the developing countries which are undergoing rapid urbanization. A useful way to clarify its ambiguity is to set up some working de® nitions. Some speci® c and narrow de® nitions do exist for special circumstances but there are no commonly accepted de® nitions. The working de® nitions can help to eliminate ambiguities and ® nd out solutions and better alternatives to existing development patterns. The conversion of agricultural land into urban land uses in the urbanization processes has become a serious issue for sustainable urban development in the developing countries. Take China as an example, it cannot a ord to lose a signi® cant amount of its valuable agricultural land because it has a huge growing population to feed. Unfortunately, in recent years, a large amount of such land have been unnecessarily lost and the forms of existing urban development cannot help to sustain its further development (Yeh and Li 1997, Yeh and Li 1998). The complete depletion of agricultural land resources would not be far away in some fast growing areas if such development trends continued. The main issue of sustainable urban development is to search for better urban forms that can help to sustain development, especially the minimization of unnecessary agricultural land loss. Four operational criteria for sustainable urban forms can be used: (1 ) not to convert too much agricultural land at the early stages of development; (2 ) to decide the amount of land consumption based on available land resources and population growth; (3 ) to guide urban development to sites which are less important for food production; and (4 ) to maintain compact development patterns. The objective of this research is to develop an operational CA model for Modelling sustainable urban development 133 sustainable urban development. A number of advantages have been identi® ed in the application of CA in urban simulation (Wolfram 1984, Itami 1988). Cellular automata are seen not only as a framework for dynamic spatial modelling but as a paradigm for thinking about complex spatial-temporal phenomena and an experimental laboratory for testing ideas (Itami 1994 ). Formally, standard cellular automata may be generalised as follows: St+1 = f (St, N ) (1 ) where S is a set of all possible states of the cellular automata, N is a neighbourhood of all cells providing input values for the function f, and f is a transition function that de® nes the change of the state from t to t+1. Standard cellular automata apply a b̀ottom-up’ approach. The approach argues that local rules can create complex patterns by running the models in iterations. It is central to the idea that cities should work from particular to general, and that they should seek to understand the small scale in order to understand the large (Batty and Xie 1994a). It is amazing to see that real urban systems can be modelled based on microscopic behaviour that may be the CA model’s most useful advantage . However, the t̀op-down’ critique nevertheless needs to be taken seriously. An example is that central governments have the power to control overall land development patterns and the amount of land consumption. With the implementations of sustainable elements into cellular automata, a new paradigm for thinking about urban planning emerges. It is possible to embed some constraints in the transition rules of cellular automata so that urban growth can be rationalised according to a set of pre-de® ned sustainable criteria. However, such experiments are very limited since many researchers just focus on the simulation of possible urban evolution and the understanding of growth mechanisms using CA techniques. The constrained cellular automata should be able to provide much better alternatives to actual development patterns. A good example is to produce a c̀ompact’ urban form using CA models. The need for sustainable cities is readily apparent in recent years. A particular issue is to seek the most suitable form for sustainable urban development. The growing spread of urban areas accelerating at an alarming rate in the last few decades re ̄ ects the dramatic pressure of human development on nature. The steady rise in urban areas and decline in agricultural land have led to the worsening of food production and other environmental problems. Urban development towards a compact form has been proposed as a means to alleviate the increasingly intensi® ed land use con ̄ icts. The morphology of a city is an important feature in the c̀ompact city theory’ (Jenks et al. 1996). Evidence indicates a strong link between urban form and sustainable development, although it is not simple and straightforward. Compact urban form can be a major means in guiding urban development to sustainability, especially in reducing the negative e ects of the present dispersed development in Western cities. However, one of the frequent problems in the compact city debate is the lack of proper tools to ensure successful implementation of the compact city because of its complexity (Burton et al. 1996). This study demonstrates that the constrained CA can be used to model compact cities and sustainable urban forms based on local, regional and global constraints. 3. Suitability and constraints for sustainable urban forms using CA In this constrained CA model, there are three important aspects of sustainable urban forms that need to be consideredÐ compact patterns, land q