Literature Review and Methodology

AI techniques can be used to tackle complex and dynamic problems in urban studies. Wu and Silva (2010) reviewed several AI techniques that can be utilised to understand urban and land dynamics processes as well as the associated emerging challenges. In this review we solely focus on the evolution, development and calibration of CA rules.

CA was developed in the late 1940s by S. Ulan and J. Von Neumann based on Turing machine, placed at each cell of a lattice and connected together (Sante et al., 2010). CA models for urban growth simulation have proliferated because of their simplicity, flexibility, intuitiveness, and particularly because of their ability to incorporate the spatial and temporal dimensions of the process (Sante et al., 2010). The ability of CA to simulate urban growth is based on the assumption that past urban development affects future patterns through local interactions among land uses. CA-based models have abilities to fit complex spatial nature using simple and effective rules for urban simulation and are also integrated with Geographical Information Systems (Itami, 1994; Wagner, 1997) with better computational efficiency at higher spatial resolutions. Most CA models capturing the urban growth process are based on states, neighbourhood and simple and effective transition rules that are capable of modelling evolution of complex spatial patterns. Development of CA model involves rule definition and calibration to produce results that are consistent with historical data. The same rules are also used for future prediction (Clarke et al., 1997; White and Engelen 1993). Sante et al. (2010) provide a detailed structured overview of CA models for urban growth, with new advances and the strengths and weaknesses of the different models. Wolfram (1984) demonstrated how complex natural phenomena can be modeled using CA that laid the foundations for a theory of CA (Wolfram, 2002) on the premise that these are discrete dynamic systems wherein local interactions among components generate global changes in space and time (Clarke and Gaydos, 1998). Tobler (1979) first proposed the application of cellular space models to geographic modeling. The first theoretical approach to CA-based models for the simulation of urban expansion appeared in the 1980s followed by other such studies (Batty and Xie, 1994; Couclelis, 1985; White and Engelen, 1994). Itami (1994) reviewed CA theory and its application to the simulation of spatial dynamics, and Batty (2005) provided an analysis of diverse applications for modelling urban growth using CA.

In other similar studies, Liu et al., (2008) and Yang et al., (2008) adopted kernel-based techniques and support vector machines (SVM) for transition rules. One of the earliest, widely used and most well-known model is CA-SLEUTH (Slope, Land use, Exclusion, Urban extent, Transportation and Hillshade) model (Wolfram, 1994), based on four major types of data: land cover, slope, transportation, and protected lands (Clarke et al., 1997). A set of initial conditions in SLEUTH is defined by ‘seed’ cells which are determined by locating and dating the extent of various settlements identified from historical maps, atlases, and other sources. These seed cells represent the initial distribution of urban areas. However, the disadvantage is that sets of complex behaviour rules are developed, that involve many steps such as selecting a seed location randomly, investigating the spatial properties of the neighboring cells, and urbanising the cell based on a set of probabilities. Silva and Clarke, (2002) used SLEUTH developed with predefined growth rules, applied spatially to gridded maps of the cities in a set of nested loops. Here, urban expansion was modelled in a modified two-dimensional regular grid and the problem of equifinality, and parameter sensitivity to local conditions were addressed. This model is difficult to calibrate to the actual ground conditions and requires many parameters to be accounted in the rules’ development. Most of these CA models are usually designed based on individual preference and application requirements, where transition rules are defined in an ad hoc manner (Li and Yeh, 2003; Pinto and Antunes, 2007). In fact, the transition rules of a formal CA consider only the current state of the cell and its neighbours. However, a variety of factors influence urbanisation processes, such as suitability for land use, accessibility, socioeconomic conditions, urban planning, etc. The transition rules of strict CA are static, although the processes that govern land use change may vary over time and space. This necessitates developing transition rules adapting to specific characteristics of each area and time interval, where the spatial and temporal variations can be achieved through calibration (Geertmanet al., 2007; Li et al., 2008).

The discussion so far has been based on studies pertaining to the design and development of increasingly complex models and simulations of urban dynamics that have in general ignored the process of calibration involving heuristic approaches. Most of the developed CA models need intensive computation to select the best parameter values for accurate modelling. Furthermore, calibration has largely been used for estimation and adjustment of model parameters and constants to bring the model output as close to the reality as possible. Therefore, the selection of CA transition rules remains an active research topic. This motivates development and implementation of an effective CA-based urban growth model that is easy to calibrate and which simultaneously takes the spatial and temporal dynamics of urban growth into account. The objectives of this study are as follows:

Spatially, the model is locally calibrated to take the effect of site specific features into account while the temporal calibration is set up to adapt the model to the changes in the growth pattern over time. Calibration provides optimal values for the transition rules to achieve accurate urban growth modelling. The input to the urban growth model consists of two types of data: (i) classified images of 1973, 1992 and 2006 where each pixel represents one of the four land use classes – urban, vegetation, water and others, (ii) population density maps represented by pixels in a raster format for the years 1973 and 1992.

CA generates transition rules for each pixel. This depends on the current state of the pixel’s category (in terms of the class of land usage) and its population density value. The job of the transition rule is to decide the state of the pixel (in terms of land usage) from one time epoch to the next, which in this case happens to be from 1973 to 1992 and from 1992 to 2006.