Calibration and Assessment of Multitemporal Image-based Cellular Automata for Urban Growth Modeling

This paper discusses the calibration and assessment of a cellular automata model for urban growth modeling. A number of transition rules are introduced in the cellular automata model to consider the most influential urbanization factors, such as land-cover maps obtained from satellite images and population density from the census. The transition rules are calibrated both spatially and temporally to ensure the modeling accuracy. Spatially, each township (about 6 miles 3 6 miles) in the study area is used as a calibration unit such that the spatial variability of the urban growth process can be taken into account. The temporal calibration is performed by using a sequence of remote sensing images from which the land-cover information at different years is extracted. As for the assessment, fitness (for urban level match) and two types of modeling errors (for urban pattern match) are introduced as the evaluation criteria. The study shows that the use of images reduces the need for a large number of input data. Evaluation on the rule variogram reveals that the transition rule values are correlated spatially and vary with the urbanization level. The paper reports the study outcome over the city of Indianapolis, Indiana for the past three decades using Landsat images and the population data. Introduction Remarkable progress has been achieved in urban dynamic modeling to understand the urban growth process (Meaille and Wald, 1990; Batty and Xie, 1994a and 1994b). Some urbanization models focus more on the physical aspects of the urban growth process (Wilson, 1978), while others on social factors (Jacobs, 1961). An example of the physical models is the land-use transition model of Alonso and Muth in landscape economics (Wilson, 1978). Social models simulate the urbanization process according to the difference between individuals’ intentions and their behavior (Clarke et al., 1997; Portugali et al., 1997). According to Clarke et al. (1997), urban growth models can be designed either for a specific geographical location such as BASS II which models Calibration and Assessment of Multitemporal Image-based Cellular Automata for Urban Growth Modeling Sharaf Alkheder and Jie Shan the urbanization process for the San Francisco Bay area only (Landis, 1992), or as general models such as humaninduced land transformations (HILT) where its growth rules are designed to be general enough to consider different city structures. Yang and Lo (2003) classify the urban dynamic models into three categories: “cellular automata-based models” such as Clarke et al. (1997); “probability-based models” such as Veldkamp and Fresco (1996); and “GIS weighted models” like the Pijanowski et al. (1997) model. The “cellular automatabased models” are becoming popular in recent literature mainly because of their ability to model and visualize spatial complex phenomena (Takeyama and Couclelis, 1997). Urban “cellular automata models” perform better as compared to the conventional mathematical models (Batty and Xie, 1994a) and simplify the simulation of complex systems (Wolfram, 1986; Waldrop, 1992). The fact that the urban process is entirely local in nature also makes the cellular automata a preferred choice (Clarke and Gaydos, 1998). Many urban cellular automata models are reported. The model of White and Engelen (1992a and 1992b) involves reduction of space to square grids, based on which a set of initial conditions is defined. The transition rules are implemented recursively until the reference data are matched by the modeling results. Cellular automata has been used by Batty and Xie (1994a) to model the urban growth of Cardiff of Wales, and Savannah of Georgia. Later, Batty et al. (1999) develop a model that tests many hypothetical urban simulations to evaluate the different model structures. Based on the previous work (von Neumann, 1966; Hagerstrand, 1967; Tobler, 1979; Wolfram, 1994), Clarke et al. (1997) propose the SLEUTH model, which is able to modify the parameter settings when the growth rate exceeds or drops below a critical value. Clarke and Gaydos (1998) use SLEUTH to model the urban growth in the San Francisco Bay Area and Washington D.C./ Baltimore, Maryland corridor. Yang and Lo (2003) use the SLEUTH model to simulate the future urban growth in Atlanta, Georgia with different growth scenarios. Wu (2002) develops a stochastic cellular automata model to simulate rural-tourban land conversions in the city of Guangzhou, China. Calibration of cellular automata models is essential to achieve an accurate modeling outcome. However, it has been ignored until recent efforts were made to develop PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING Decembe r 2008 1539 Sharaf Alkheder is with the Queen Rania’s Institute of Tourism and Heritage, The Hashemite University, Jordan, and formerly with the Geomatics Engineering, School of Civil Engineering, Purdue University, West Lafayette, IN 47907. Jie Shan is with Geomatics Engineering, School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907 ([email protected]). Photogrammetric Engineering & Remote Sensing Vol. 74, No. 12, December 2008, pp. 1539–1550. 0099-1112/08/7412–1539/$3.00/0 © 2008 American Society for Photogrammetry and Remote Sensing 07-003.qxd 11/13/08 9:22 PM Page 1539