1. Modeling Urban Land-use with Cellular Automata Geog 232: Geo-Simulation Sunhui(Sunny) Sim February 7 th, 2005

2. Modeling Urban Land-use with Cellular Automata 4.1 Introduction 4.2 Cellular Automata as a Framework for Modeling Complex Spatial Systems 4.3 Raster but not Cellular Automata Models …Urbanization Potential as a Self-existing Characteristic of a Cell 4.4. From Markov Models to Urban Cellular Automata 4.5. Integration of CA and Markov Approaches at a Regional Level 4.6 Conclusion

3. Urbanization Potential as a Self-existing Characteristic of a Cell Potential: An intermediate characteristic in order to compare land units regarding possible changes Also, the previous estimates of potential which influence land changes together with the actual land-uses. Above-neighborhood Three standard levels of the urban hierarchy-land unit, neighborhood, and city are sufficient for representing and formalizing urban dynamics. It is expressed by the dependence of cell transitions on distance to urban networks. ⇒ In a theoretical sense, Can explain emergence of secondary urban centers Can reflect the influence of urban networks as well as emerging urban zones

4. Potential Can explain emergence of secondary urban centers The standard CA framework is extended and the cell transitions at t+1 become dependent on the state of the neighborhood both at moments t and t-1 Positive dependence of potential on a rate of increase can result in poly-centricity. In probabilistic CA, probabilities of transition between cell states have the same meaning as potentials.

5. Example of Potential-Based Models Yeh and Li(1998~2002): Characteristics: employ the constrained CA follows an urban-non-urban dichotomy of land-use concentrates on transition rules An assumption: the potential of transition of cell C from agricultural into urban use accumulates in time Potential: is defined by the characteristics of neighborhood and depends on external factors (distance from C to a main urban center or distance to the closest subcenter, exogenous factor such as soil quality or slope) The results of implementation of CA models… Different real-world cities and regions are likely simulated based on similar factors “likely” transition function might be sufficient for correct modeling

6. 4. 3 Raster but not Cellular Automata Models ….Urbanization as a diffusion process The CA tradition: “cell-centered” the cell stated is influenced by the neighborhood. An opposing view: cells as affecting their neighbors roots in urban dynamics as a diffusion process 1. Game of Life in urban context => urbanization Urban cells can be in urban and nonurban states each cell can give birth to new cells or die. 2. Spread of urban spatial patterns Not only unitary cells, but also diffusion of more complex urban entities. Goal: to build a general and simple tool for high-resolution simulation of urban growth The input : slope, land cover, exclusion, urban, transportation, and hillshade

7. 4. 3 Raster but not Cellular Automata Models ….From Fixed Cells to Varying Urban Entities The network interpretation of CA: Basic: nodes as cells, and edges as denoting neighborhood relations. Advantages: offer additional degrees of freedom for establishing new urban units new units can have specific shape and orientation, and relationships between neighbors can be altered during model run. Example: A model by Erickson and Lloyd-jones(1997) The model works with land objects ( street, road, house, garden) All objects are allocated in the continuous space of a growing city. The Difference between the CA and object-based model determine the type and location of new objects based on correlation between the kind, location and orientation of new and existing ones.

8. 4.4. From Markov Models to Urban Cellular Automata The simplest Markov model: Ignores neighbors’ influence considers cell states at t+1 as a function of cell state at t alone. A Markov standpoint is most general and seems ideal for the “unbiased” researcher The standard way of tuning CA models is in varying coefficients of theoretically established transition rules and making comparison between simulated and observed land-use patterns Why not justify transition rules empirically… The lack of connection between Ca and Markov models => content of a land cell Land use data enhancements => Converge

9. 4.4. From Markov Models to Urban Cellular Automata ….From Remotely sensed images to Markov models The tradition of Markov models demands statistical confirmation of the relationships between land use changes and environmental factors By assuming that transition probabilities are not constant, but linearly depend on environmental factors, and tuning the coefficients of this dependency, good correspondence between actual and predicted land-uses is achieved. The idea of neighborhood-dependence and extension of Markov models toward CA become unavoidable if we consider land use changes as part of landscape system dynamics.

10. 4.4. From Markov Models to Urban Cellular Automata ….The Link Example Turner(1988) modified a standard Markov model in a way that is very close to the constrained CA. She assumed the ‘likelihood’ of cell C transformation…so the transition is one of maximum likelihood. This approach can be just constrained CA with empolyment of a sequential transition rule. But, it provides strong support for further investigation of abilities of asynchronous(sequential) CA for description of land use dynamics.

11. 4.5. Integration of CA and Markov Approaches at a Regional Level Several attempts to integrated Markov and CA approaches 1. Flat models Probabilities of land unit changes are established directly in each region delegate the overall changes generated all factors are equal candidates in influencing land use changes. 2. Hierarchical models describe interregional relationships actually constitutes the bulk of urban models, each apply at a specific hierarchical level of partition.

12. 4.6 Conclusion Geographic CA …..Several stages 1. An initial boom : 1960s 2. Tobler’s formulation : 1979 3. Progress: end of 1980s 3. Established : 1990s ~ present Modern geographic modeling follows the idea of constrained CA Use of “potential of change Stochasticity of transitons Neighborhoods of several orders with different levels Factors at above-neighborhood level The partition of urban space in the models can change The Geographic Automata System idea incorporates human urban objects, thus provide a general framework for portraying and modeling all components of urban systems.