166 The Future of Water in African Cities
complex dynamics across spatial scales and have been increasingly used since the 1990s following the increasing availability of computing power (Santé et al., 2010). Four categories of urban models have emerged over the last several decades (Landis, 2001). In addition to cellular automata models, there are spatial interaction models that model choices for sitting firms and houses using economic and travel distance (for example, Wegener, 1998); agentbased modeling where a reduced set of representative decision makers populate the landscape and convert land uses based on a set of rules largely focused on the household- or firm-level (for example, UrbanSim designed by Waddell, 2002); and urban future models that model sitelevel transitions based on spatial relationships such as neighborhood statistics, distance to infrastructure, demography, economic conditions, and regulatory conditions (for example, California Urban Futures; Landis, 2001). One particular model that has been widely studied and used is the SLEUTH model (Clarke et al., 1997). This model defines rules for cell transitions from nonurban to urban based on a core set of determinants and iterates over time. SLEUTH stands for slope, land use, exclusion, urban, transportation, and hillshade, describing the core input data sets that drive the model behavior. This form of cellular automata model simulates growth in time steps, and uses historical data sets to calibrate model parameters for forecasting in the future. Monte Carlo simulations are run and the results averaged to give a best estimate of future urbanization. This modeling effort used a simplified cellular automota approach that was necessitated by limits in suitable consistent historical data over all cities, and a limit in computational resources. The first step in the modeling approach was to define the suitability of each cell to urbanization based on site characteristics and neighborhood relationships. Suitability was defined as a combination of enablers and constraints on future growth. The primary enablers of urban growth are proximity to existing urban areas and transportation infrastructure, while the primary constraints on urban growth are slope, water, and exclusionary land use zoning (Clarke et al., 1997). Population growth determined the area of suitable land that might be urbanized, as this growth is the primary driver of urbanization. Once the suitability rankings were mapped, additional populated areas based on measured urban densities and projected urban growth were allocated to successively decreasing suitability levels. Next, the stages of suitability calculation are described, followed by the method of urban area allocation.