Analysis of Operational Urban Cellular Automata Models

Transcription

1 Analysis of Operational Urban Cellular Automata Models SANTÉ, I., GARCÍA, A. M., MIRANDA, D., CRECENTE, R. Agroforestry Engineering Department Santiago de Compostela University Escuela Politécnica Superior, Campus universitario s/n Lugo SPAIN Abstract: - In recent years, cellular automata (CA) models for urban growth simulation have proliferated because of their simplicity, flexibility and capability for spatial and temporal modelling. However, the application of these models to real world urban planning issues involves a difficult selection or design of the most suitable CA model. For this reason, a review of the main operational urban CA-models is provided with an analysis of their strengths and weaknesses and a discussion of the needs for further research. Key-Words: cellular automata, urban model, urban planning, urban growth, urban simulation 1 Introduction In the 1980s, the first theoretical developments of cellular automata (CA) models for urban growth simulation appeared. A review of these theoretical bases can be found in [1]. These conceptual advances and the development of computing power led to the emergence of the first operational urban CA models [2] applied to real-world urban systems in the 1990s. Currently the application of these models to real world urban planning issues involves a difficult selection of the most suitable CA model, since there are too many available options. In order to present a structured overview that facilitates the choice of a particular method for an application problem, an analysis of various urban CA models has been performed. So they were classified according to their main characteristics, which allowed the identification of their strengths and weaknesses. 2 Characteristics of Urban CA Models A CA is defined as a discrete space formed by cells, each of which representing a possible state that changes depending on the current state and on the state of the cells by means of a set of transition rules. The background conventions of CA limit their ability to realistically simulate complex geographical phenomena. These phenomena usually force to make successive relaxations of these assumptions. Such relaxations have been expressed in the language of formal model theory by [3]. Among them, the following stand out: a finite and irregular space [4][5][6], a non-uniform cell space, an extended or non-stationary, more complex or non-stationary transition rules [7], growth constraints [8], and irregular or asynchronous time steps. 3 Analysis of Urban CA Models One of the first applications of urban CA to the simulation of real-world cases was carried out by [9]. However, the first widespread empirical application was the application suggested by [8], subsequently improved and applied to The Netherlands [10][11], San Diego [12], Lagos [13], Tokyo [14], and Brussels [15]. Other model that stands out because of its common application is SLEUTH, developed by [7] and frequently applied to North American cities as San Francisco, Washington/Baltimore [16][17], and San Joaquin [18], but also to European [19], South American [2] or Asiatic [21] regions. Other well-known models are those of F. Wu [22][23][24], X. Li and A.G.-O Yeh [25][26][27] and DINAMICA [28]. The main characteristics of these and other models are summarized as follows. i) Transition rules. Transition rules have been classified into five types. Yet some rules can be included in several groups. The first type comprises the orthodox transition rules, based exclusively on the state of the own cell and of its neighbours (Table 1). In the second group, the key driver of urban evolution is the transition potential or probability of each cell for a specific land use, which includes other factors in addition to the (Table 2). This type of rules breaks the CA assumptions of system closure to external events and of homogeneous space. Different methods can be used for the definition of the transition potential or probability; multi-criteria evaluation [26], logistic regression [29][24], statistical analysis [28][30], ISSN: ISBN:

2 economic theory [15] or a potential model [31]. The third type comprises the rules based on the urban shape and form which reproduce the urban spatial patterns (Table 3). The transitional functions (expander and patcher functions) of DINAMICA can also be included in this group because they are aimed at spatially simulating urban growth. The fourth type includes the rules based on artificial intelligence methods such as neural networks [25], data mining [27][32], kernel-based learning methods [33][34], or the CBR technique [35] (Table 4). The fifth type embraces the rules based on fuzzy logic, in which the driver factors of urban evolution are expressed through fuzzy variables (Table 5). Other possible classification of transition rules distinguishes between stochastic rules and deterministic rules. In the first ones, a distinction can be made between those that use a Monte Carlo process and others that include a parameter of stochastic disturbance. Despite the large variety of transition rules, the factors involved in these rules are usually repeated. The 81% of the reviewed models include accessibility to road network and more than 50% include distance to urban settlements. Next in frequency are slope, railway accessibility, urban zoning, different environmental factors, development suitability, and population density. ii) Objective. A distinction can be made between descriptive models, which analyze the dynamics that govern the evolution of urban land; predictive models, which simulate land-use change in a near future, and prescriptive models, aimed at obtaining the optimal allocation of land uses. iii) Cell space. It is composed of square cells of different resolutions (of 10 m to 1 km) in all the models, except for the model of [6], who used a space formed by cadastral parcels. [36] demonstrated the sensitivity of geographic CA to cell size. iv) State. Most models simulate transitions from nonurban to urban land uses, but some models extend these transitions to multiple land uses. This implies a higher complexity in the transition rules. [8] makes a distinction between fixed land uses, which remain stable, and functions, which can change to another state. Moreover, [13] differentiates between active and passive functions. v) Neighbourhood. Half of these models use the local of strict CA, with Moore being the most frequent one. The rest of the models extend the to a radius of 2 to 9 cells, in order to consider the action-at-distance effect. [12] showed that the type and size significantly affect the outcomes of the model. vi) Growth constraint. The total changed area is generated endogenously by the CA only in 7 models. In the rest of the models the total area is affected by an external constraint that can be obtained in different ways: i) by extrapolating the past urban growth trends or projecting the population growth, ii) through the integration with other models, or iii) according to the urban regulation. vii) Integration with other models. Other techniques are usually used to calculate growth constraints, for the definition of the transition rules, or for the calibration of the model. Table 1. Main characteristics of urban CA with strict transition rules Besussi et al. (1998) [41] Jenerette and Wu (2001) [40] Stevens and Dragicevic (2007) [6] Ward et al.(2000) [44] Yüzer (2004) [46] Objective* P-M D, P P-M D P-M Cell space 30 m cells 250, 75 m cells Cadastral parcels 50 m cells 100 m cells State Multiple land uses Multiple land uses Multiple land uses Urban, non urban Multiple land uses Neighbourhood Moore Moore Adjacent parcels Moore and von Neumann Square (6 cells) Transition rule Land value Transition Parcel attractiveness Development Transition potential transformation, urban functions transformation and function of the number of urban for residential, commercial or park use depends on the function of the number of urban is function of the land uses in the urban functions cells use of cells diffusion automatas and of the cell state cells and their distance Constraints** - - POP POP AGR or POP Other methods None GA None None None Calibration None Empirical and GA Empirical Visual Queries and studies Validation None Spatial indices None None None * D - Descriptive, P - Predictive, M multiple land uses, PC Prescriptive. **AGR annual urban growth rate, POP population growth projection, PLA urban regulation planning, MOD model mentioned in the row other methods, OTH other studies ISSN: ISBN:

3 Table 2a. Main characteristics of urban CA with transition rules based on transition potential or probability Almeida et al. Barredo et al. (2003) Caruso et al. (2005) Cheng and Masser Engelen et al. (1999) (2003) [28] [13] [15] (2004) [42] [10] Objective D-M D-M D D, P D-M, P-M Cell space 100 m cells 100 m cells 250, 500 m cells 10 m cells 100 m cells State Multiple land uses Multiple land uses Residential, agricultural Urban, non urban Multiple land uses Neighbourhood Moore Circular (8 cells) Moore, circular (3 and 5 cells) Circular (from 3 to 9 Circular (8 cells) cells) Transition rule Transition Transition potential Transition potential Transition potential Transition potential is function of the is function of the is function of an is function of a calculated using the accessibility, the commuting cost and indefinite number of stochastic weights of suitability for the the social and weighted factors and disturbance, the evidence approach. land use, the zoning, environmental constraints and a suitability for the Cells with higher probability are the effect, and a externalities of the stochastic variable land use, the zoning and the selected through two stochastic spatial functions disturbance effect Constraints AGR MOD AGR AGR OTH Other methods Weights of evidence Dynamic global model None None None Calibration Visual Visual Sensitivity analysis Empirical Sensitivity analysis Validation Multiple resolution Visual, fractal Spatial index, fractal Coincidence matrix Kappa index fitting procedure dimension, coincidence matrix and kappa index dimension, population density vs. distance and spatial index Table 2b. Main characteristics of urban CA with transition rules based on transition potential or probability He et al. (2006) [47] He et al. (2008) [31] Lau and Kam (2005) Li and Yeh (2002b) Li et al (2008) [38] [30] [26] Objective D, P D, P D-M PC D, PC Cell space 180 m cells 180 m cells 1 km cells 50 m cells Not explicit State Urban, non urban Urban, non urban Multiple land uses Development degree Urban, non urban Neighbourhood Not explicit Circular (5 cells) Moore Circular (2 cells) Not explicit Transition rule Development function of an Transition potential is function of the development indefinite number of suitability, the constraints and weighted factors, the effect, the inertia coefficient, and a stochastic disturbance effect, a stochastic disturbance, zoning and environmental constraints, and an urban expansion potential Transition potential is function of the suitability for the land use, the attribute effect, the inertia of the land use and the effect Development degree Model of [29] is function of the development suitability, the effect, a stochastic disturbance and the principal components (PC) of a set of factors Constraints MOD AGR and POP PLAN AGR Not explicit Other methods System dynamics Lineal regression Multivariate PC analysis GA model and potential model statistical tools Calibration Monte-Carlo method Monte-Carlo methodmanova and MDA Sensitivity analysis GA Validation Kappa index Kappa index Overall accuracy Sustainability indicesspatial indices and fractal dimension viii) Calibration. There are two traditional methods of calibration; those based on trial and error and those based on statistical techniques. The first ones require that the model is run many times, so they are computationally intensive. Among the second ones, the most common is the logistic regression, which sometimes cannot capture the complexity of the relationships. Because of this, in the last years ISSN: ISBN:

4 considerable research has been carried out into new, more developed methods [37], mainly into more efficient heuristic techniques as genetic algorithms (GA) or simulated annealing (SA). Both of them optimize a fitness function which can be defined from the total number of errors [38][39] or different spatial metrics [40]. In most of the models that use artificial intelligence techniques, the calibration and design of the transition rules occur simultaneously. ix) Validation. The most simple validation method consist in the visual analysis, which is usually complemented by quantitative methods that are frequently limited to evaluate overall accuracy, as the following ones; i) the ratio of simulated to real number of cells (or clusters) for a given land use, ii) overall accuracy, iii) regression analysis, and iv) confusion matrix and kappa index. However, as the objective of urban CA is to generate urban morphologies similar to real morphologies, the results must be analyzed in terms of spatial structure through: i) development profiles, ii) spatial metrics, iii) fractal analysis, or iv) the multiple resolution fitting procedure. It is also possible to validate the model by comparing its results with the output of another model or a null model. 4 Discussion All the models have advantages and drawbacks, so several of their most relevant characteristics have been analyzed separately. Table 2c. Main characteristics of urban CA with transition rules based on transition potential or probability Sui and Zeng (2001) [29] White and Engelen (2000) White et al. (1997) [8] Wu (1998; 2002) [23][24] [11] Objective D, P D-M, P-M D-M, P-M D, P Cell space 180 m cells 500 m cells 250 m cells 200 [23], 30 m [24] cells State Urban, non urban Multiple land uses Multiple land uses Urban, non urban Neighbourhood Von Neumann Circular (8 cells) Circular (6 cells) Moore Transition rule Transition Transition potential is Transition potential is Development probability function of elevation, function of the suitability, function of the suitability, is function of an indefinite slope, accessibility, shape the zoning, the inertia of the accessibility, the number of weighted index of the closest urban land uses,the accessibility, inertia of the land use, the factors and constraints patch, and the and a, and a an error term stochastic disturbance stochastic disturbance Constraints AGR-MOD MOD AGR AGR. Other methods Logistic regression Regional model None PC analysis [23], logistic regression [24] Calibration Logistic regression None Empirical Sensitivity analysis [23]. Logistic regression [24] Validation Total errors and spatial metrics None Visual, coincidence matrix, kappa index, fractal dimension Table 3. Main characteristics of urban CA with transition rules based on urban shape and form Clarke et al. (1997) [7] Li et al. (2003) [48] Objective D, P PC Cell space 300, 210 m cells 200 m cells State Urban, non urban Urban, non urban Neighbourhood Moore Moore Transition rule 4 types of growth rules (spontaneous, diffusive, organic, and road influenced growth,) and two selfmodification rules Constraints - POP Other methods None None Calibration Empirical in three phases of resolution Sensitivity analysis Validation 12 spatial metrics None Global accuracy, Moran I index, development profile [24] Cells are developed according to their population density, which increases in each step according to the population density of the cells ISSN: ISBN:

5 Table 4. Main characteristics of urban CA with transition rules based on artificial intelligence Li and Liu Li and Yeh Li and Yeh Liu et al. (2008) Liu et al. (2008) Yang et al. (2006) [35] (2002) [25] (2004) [27] [32] [33] (2008) [34] Objective D D, P; D-M, P-M D, P D, P D D, P Cell space Not explicit 50 m cells 30 m cells Not explicit 50 m cells 30 m cells State Urban, non urban Multiple uses Urban,non urban Urban, non urban Urban,non urban Urban,non urban Neighbourhood Not explicit Square (7 cells) Square (7 cells) Moore Moore Moore Transition rule Development defined through the Case-Based Reasoning (CBR), the effect and a set of constraints A neural network provides the development probability from the number of urban cells in and other cell attributes Explicit transition rules are defined by means of a data mining technique based on the information gain ratio Explicit transition rules are defined by means of a data mining technique based on an ant colony optimization algorithm Development function of a set of constraints, the effect and a kernel Fisher discriminant (KFD) model Development function of a stochastic variable, the effect, a set of constraints and a Support Vector Machines (SVM) function Constraints AGR AGR AGR AGR AGR AGR Other methods CBR Neural network Data mining Ant colony algorithm KFD and regression SVM Calibration Sensitivity Neural network Data mining Ant colony Empirical Empirical analysis, CBR training algorithm Validation Visual, confusionconfusion matrix Visual, global Visual, confusion Visual,confusion Visual, matrix, Moran I and overall accuracy and matrix, spatial matrix, total coincidence index, accuracy Moran I index indices and accuracy, kappa matrix, total comparison with comparison with index, spatial accuracy, kappa other models null model indices, other index, other models models Table 5. Main characteristics of urban CA with transition rules based on fuzzy logic Al-Ahmadi et al. (2009) [49] Al-kheder et al. (2008) [43] Wu (1996) [22] Objective D D-M, P-M PC-M Cell space 20 m cells 60 m cells 28.5 m cells State Urban, non urban Multiple land uses Multiple land uses Neighbourhood Is calibrated Moore Square (5 cells) Transition rule Development function of a stochastic disturbance and the development suitability, which depends on the fuzzy output of each factor Development potential is calculated through the fuzzy combination of fuzzy variables Transitions are function of fuzzy indicators, which are calculated from land uses in the and combined through the maximum method Constraints AGR - - Other methods Fuzzy logic, GA, SA Fuzzy logic Fuzzy logic Calibration GA and SA Sensitivity analysis Sensitivity analysis Validation Visual, confusion matrix, total accuracy and spatial indices Ratio of actual and simulated urban cells. Total accuracy Scenario evaluation i) Balance between realism and preservation of CA features. Although most of the analyzed models present some relaxation, with the exception of [41] and [40], some of them present more important modifications. For example, in the neural network of [25] the CA component is quite hidden. For the same reason, [28] define their model as a cell-space model more than a CA. In [27] and [32] the function was only one of the nine spatial variables used to define the transition rules. ii) Flexibility. The model capability to be adapted to different real-world urban situations depends on the flexibility of the transition rules, on the included factors, on the land uses modelled, and on the adaptability. Models that propose a general scheme within which multiple specific models can be defined [9][41] are more flexible. On ISSN: ISBN:

6 the opposite extreme we find the models that use neural networks, CBR or data mining, in which the resulting transition rules are closely adapted to local conditions. The rules constrained to some specific factors present less flexibility than those that allow to include any factor, although there is a risk that these factors are correlated [26]. With regard to the land uses modelled, [18] demonstrated that models that consider only one binary use (urban, non urban) oversimplify the dynamics. Regarding the, few models allow to implement different types of [6] and only some of them evaluate different s [15][42]. iii) Explanatory power. Descriptive models provide information about what happens but do not explain the causes [7][25][35], which does not affect their ability to predict urban growth. On the opposite extreme we find the explicit transition rules [27][32][43], which are transparent and easily understood by decision makers. An intermediate approach uses transition rules based on mathematical equations. The main advantage of the descriptive models, particularly those based on informing theories, is their ability to explore and validate hypothetical ideas and concepts related to urban dynamics. However, only a few of CA models are based on well-developed theoretical models [15][31]. iv) Data requirement. Data requirements depend upon the factors considered in the model, so this characteristic is usually in opposition to the flexibility previously described. v) Software availability. Most of the papers reviewed use the geographic information management capabilities of standard Geographic Information System and the CA is programmed by using generic programming languages [23][44][29] [42][30][32] [33][34] or macrolanguages [25][26]. In both cases, programming knowledge is needed to implement the models, which makes their implementation and use difficult for non-expert users. Very few of these software applications are available, among them are SLEUTH, freely downloadable at and DINAMICA, available at vi) Accuracy. In the validation of all these models the total area of the study area has been considered, although the percentage of cells that changed land use is usually low. In [17] the overall accuracy of 93% was reduced to 19% when the existing urban area was excluded. Therefore, if the area with a stable land use is not excluded in the validation, at least information should be provided about the percentage of the area in which land use changes. 5 Conclusion The strength of CA models lies in their ability to integrate the spatial and temporal dynamics, as well as in their simplicity and flexibility. However, this relative simplicity is also their main weakness, leading to relaxations that, when they are too extensive, can give rise to doubts about the CA condition of the model. Other shortcomings are the lack of a standard method for the definition of transition rules; the difficulty to define rules that reflect the urban complexity and simultaneously keep their simplicity; the lack of a theoretical basis; and the unavailability of software easily usable that allows non-expert users to implement these models. Much of the most recent research has been focused on improving the calibration by means of artificial intelligence techniques or on analyzing the influence of different model parameters (the type and size of the [12], the cell size [36], the land use classes modelled [18] or the temporal resolution [45]). However, the impact of other factors as the cell type, the stochastic component, etc. has not been studied yet. Other research lines are: the development of new validation methods that allow urban pattern recognition; the integration of other conventional urban theories in a CA framework; the integration with other techniques (multi-agent systems, transportation models, etc.) and the application of urban CA to planning issues to become a real Planning Support System. References: [1]R.M. Itami, Simulating spatial dynamics: cellular automata theory, Landscape and Urban Planning, Vol.30, 1994, pp [2]M. Batty, Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals, MIT Press, [3]H. Couclelis, From cellular automata to urban models: new principles for model development and implementation, Environment and Planning B: Planning and Design, Vol.24, 1997, pp [4]W. Shi, and M.Y.C. Pang, Development of Voronoi-based cellular automata an integrated dynamic model for Geographical Information Systems, International Journal of Geographical Information Science, Vol.14, No.5, 2000, pp [5]D. O`Sullivan, Exploring spatial process dynamics using irregular cellular automaton models, Geographical Analysis, Vol.33, No.1, 2001, pp ISSN: ISBN:

7 [6]D. Stevens, and S. Dragicevic, A GIS-based irregular cellular automata model of land-use change, Environment and Planning B: Planning and Design, Vol.34, 2007, pp [7]K. C. Clarke, S. Hoppen, and L. Gaydos, A selfmodifying cellular automaton model of historical urbanization in the San Francisco Bay area, Environment and Planning B: Planning and Design, Vol.24, 1997, pp [8]R. White, G. Engelen, and I. Uljee, The use of constrained cellular automata for high-resolution modelling of urban land-use dynamics, Environment and Planning B: Planning and Design, Vol.24, 1997, pp [9]Y. Xie, A generalizad model for cellular urban dynamics, Geographical Analysis, Vol.28, 1996, pp [10]G. Engelen, S. Geertman, P. Smits, and C. Wessels, Dynamic GIS and Strategic Physical Planning Support: a practical application to the IJmond/Zuid-Kennemerland region, in: Geographical Information and Planning (pp ). Springer-Verlag, [11]R. White, and G. Engelen, High resolution modelling of the spatial dynamics of urban and regional systems, Computers, Environment, and Urban Systems, Vol.24, 2000, pp [12]V. Kocabas, and S. Dragicevic, Assessing a cellular automata model behaviour using a sensitivity analysis approach, Computers, Environment and Urban Systems, Vol.30, 2006, pp [13]J.I. Barredo, L. Demicheli, C. Lavalle, M. Kasanko, N. McCormick, Modelling future urban scenarios in developing countries: an application case study in Lagos, Nigeria, Environment and Planning B: Planning and Design, Vol.32, 2004, pp [14]T. Arai, and T. Akiyama, Empirical analysis for estimating land use transition potential functions case in the Tokyo metropolitan region. Computers, Environment and Urban Systems, Vol.28, 2004, pp [15]G. Caruso, M. Rounsevell, and G. Cojocaru. Exploring a spatio-dynamic -based model of residential behaviour in the Brussels periurban area, International Journal of Geographical Information Science, Vol.19, No.2, 2005, pp [16]K.C. Clarke, and L.J. Gaydos, Loose-coupling a cellular automaton model and GIS: long-term urban growth prediction for San Francisco and Washington/Baltimore, International Journal of Geographical Information Science, Vol.12, No.7, 1998, pp [17]C.A. Jantz, S.J. Goetz, and M.K. Shelley, Using the SLEUTH urban growth model to simulate the impacts of future policy scenarios on urban land use in the Baltimore-Washington metropolitan area, Environment and Planning B: Planning and Design, Vol.30, 2003, pp [18] C. Dietzel, and K.C. Clarke, The effect of disaggregating land use categories in cellular automata during model calibration and forecasting, Computers, Environment and Urban Systems, Vol.30, 2006, pp [19]E.A. Silva, and K.C. Clarke, Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal, Computers, Environment and Urban Systems, Vol.26, 2002, pp [20]S. Leao, I. Bishop, and D. Evans, Simulating urban growth in a developing nation s region using a cellular automata-based model, Journal of Urban Planning and Development, Vol.130, No.3, 2004, pp [21]A.S. Mahiny, and M. Gholamalifard, Dynamic spatial modeling of urban growth through cellular automata in a GIS environment, International Journal of Environmental Research, Vol.1, No.3, 2007, pp [22]F. Wu, A linguistic cellular automata simulation approach for sustainable land development in a fast growing region, Computers, Environment, and Urban Systems, Vol.20, No.6, 1996, pp [23]F. Wu, SimLand: a prototype to simulate land conversion through the integrated GIS and CA with AHP-derived transition rules, International Journal of Geographical Information Science, 1998, Vol.12, No.1, pp [24]F. Wu, Calibration of stochastic cellular automata: the application to rural-urban land conversions, International Journal of Geographical Information Science, Vol.16, No.8, 2002, pp [25] X. Li, and A.G.-O. Yeh, Neural-network-based cellular automata for simulating multiple land use changes using GIS, International Journal of Geographical Information Science, Vol.16, No.4, 2002, pp [26] X. Li, and A.G.-O. Yeh, Urban simulation using principal components analysis and cellular automata for land-use planning, Photogrammetric Engineering & Remote Sensing, Vol.68, No.4, 2002, pp [27] X. Li, and A.G.-O. Yeh, Data mining of cellular automata s transition rules, International Journal of Geographical Information Science, Vol.18, No.8, 2004, pp ISSN: ISBN:

8 [28]C.M. Almeida, M. Batty, A.M.V. Monteiro, G. Camara, B.S. Soares-Filho, G.C. Cerqueira, and C.L. Pennachin, Stochastic cellular automata modeling of urban land use dynamics: empirical development and estimation, Computers, Environment and Urban Systems, Vol.27, 2003, pp [29]D.Z. Sui, and H. Zeng, Modeling the dynamics of landscape structure in Asia s emerging desakota regions: a case study in Shenzhen, Landscape and Urban Planning, Vol.53, 2001, pp [30]K.H. Lau, and B.H. Kam, A cellular automata model for urban land-use simulation. Environment and Planning B: Planning and Design, Vol.32, 2005, pp [31]C. He, N. Okada, Q. Zhang, P. Shi, and J. Li, J. Modelling dynamic urban expansion processes incorporating a potential model with cellular automata, Landscape and Urban Planning, Vol.86, 2008, pp [32] X. Liu, X. Li, L. Liu, J. He, and B. Ai, A bottom-up approach to discover transition rules of cellular automata using ant intelligence, International Journal of Geographical Information Science, Vol.22, No.11-12, 2008, pp [33]X. Liu, X. Li, X. Shi, S. Wu, and T. Liu, Simulating complex urban development using kernel-based non-linear cellular automata, Ecological Modelling, Vol.211, 2008, pp [34]Q. Yang, X. Li, and X. Shi, X., Cellular automata for simulating land use changes based on support vector machines, Computers & Geosciences, Vol.34, 2008, pp [35]X. Li, and X. Liu, An extended cellular automaton using case-based reasoning for simulating urban development in a large complex region, International Journal of Geographical Information Science, Vol.20, No.10, 2006, pp [36]A. Ménard, and D.J. Marceau, Exploration of spatial scale sensitivity in geographic cellular automata, Environment and Planning B: Planning and Design, Vol.32, 2005, pp [37]B. Straatman, R. White, and G. Engelen, Towards an automatic calibration procedure for constrained cellular automata, Computers, Environment and Urban Systems, Vol.28, 2004, pp [38]X. Li, Q. Yang, and X. Liu, Discovering and evaluating urban signatures for simulating compact development using cellular automata, Landscape and Urban Planning, Vol.86, 2008, pp [39]J. Shan, S. Alkheder, and J. Wang, Genetic algorithms for the calibration of cellular automata urban growth modeling, Photogrammetric Engineering & Remote Sensing, Vol.74, No.10, 2008, pp [40]G.D. Jenerette, and J. Wu, Analysis and simulation of land-use change in the central Arizona-Phoenix region, USA, Landscape Ecology, Vol.16, 2001, pp [41]E. Besussi, A. Cecchini, and E. Rinaldi, The diffused city of the italian north-east:identification of urban dynamics using cellular automata urban models, Computers, Environment and Urban Systems, Vol.22, No.5, 1998, pp [42]J. Cheng, and I. Masser, Understanding spatial and temporal processes of urban growth: cellular automata modelling, Environment and Planning B: Planning and Design, Vol.31, 2004, pp [43]S. Al-kheder, J. Wang, and J. Shan, Fuzzy inference guided cellular automata urban-growth modelling using multi-temporal satellite images, International Journal of Geographical Information Science, Vol.22, No.11-12, 2008, pp [44]D.P. Ward, A.T. Murray, and S.R. Phinn, A stochastically constrained cellular model of urban growth, Computers, Environment and Urban Systems, Vol.24, 2000, pp [45]X.H. Liu, and C. Andersson, Assessing the impact of temporal dynamics on land-use change modeling, Computers, Environment and Urban Systems, Vol.28, 2004, pp [46]M.A. Yüzer, Growth estimations in settlement planning using a Land Use Cellular Automata Model (LUCAM), European Planning Studies, Vol.12, No.4, 2004, pp [47]C. He, N. Okada, Q. Zhang, P. Shi, and J. Zhang, Modeling urban expansion scenarios by coupling cellular automata model and system dynamic model in Beijing, China. Applied Geography, Vol.26, 2006, pp [48]L. Li, Y. Sato, and H. Zhu, Simulating spatial urban expansion based on a physical process, Landscape and Urban Planning, Vol.64, 2003, pp [49]K. Al-Ahmadi, A. Heppenstall, J. Hogg, and L. See, A fuzzy cellular automata urban growth model (FCAUGM) for the city of Riyadh, Saudi Arabia. Applied Spatial Analysis, Vol.2, 2009, pp ISSN: ISBN: