1. Application of a CA Model to Simulate the Impacts of Road Infrastructures on Urban Growth Nuno Pinto and António Antunes, University of Coimbra with Josep Roca, Technical University of Catalonia Workshop 3 “Stakeholder Scenario Building: Imagining Urban Futures” Lisbon, July 9 th, 2010

2. Outline 1.Introduction to cellular automata models 2.Model presentation 3.Model results I.Calibration for Coimbra II.Simulation of the impacts on land use of a new road in 2021 4.Future developments

3. Introduction to CA Models [1.History]  Urban models started to being used on the 1950s  A models is a simplified representation of reality in which one or more phenomena can be considered  Models can be  Static – if there is no temporal evolution; these models can be useful for assessing important data on a given issue  Dynamic – if they aim to simulate evolution in time; they intend to capture historical trends in order to prospectively forecast future evolutions  Three key issues  Spatial resolution  Temporal resolution  Decision making complexity

4. Introduction to CA Models [1.History]  The concept of Cellular Automata (CA) has its origins in the work of von Neumann and Ulam, two mathematicians that were facing (independently) the problem of devising mathematical rules for biological systems and evolution  Automata comes from the consideration of theoretical mechanisms capable of universally process any given code (defined by a set of states) – the Universal Turing machine  Important dates  1940s – the work of von Neumann and Ulam (mathematical approach)  1970 – Conway’s Game of Life  1979 – “Cellular Geography”, Waldo Tobler  1980s – Stephen Wolfram’s work on CA (mathematical approach and a wide set of applications)  1985 – dissemination of Geographical CA, Helen Couclelis  1990s, 2000s – Intensive research on Geographical/Urban CA

5. Introduction to CA Models [1.History]  Waldo Tobler introduced the concept of cellular models to geography  He stated the first law of geography – Everything is related with everything else but near things are more related than distant things Tobler, W. (1979), “Cellular geography”, in Gale and Olsson (Eds.) Philosophy in Geography,, D. Reidel, Boston, 379-386

6. Introduction to CA Models [2.Concept] “…an automaton is a processing mechanism with characteristics that change over time based on its internal characteristics, rules and external input…” (Benenson and Torrens, 2004)  Mathematical formulation of a 2D CA Each cell A (an automaton) is defined by a given state from a finite set of cell states S and evolves in time according to a set of transition rules T, considering an external input I If we consider the neighborhood R of cell A and the cross influence of every cell state of every cell in R in the state of A than we have the definition of CA

7. Introduction to CA Models [2.Concept]  Five components  Cells and Cell Structure  Neighborhood  Cell States  Transition Rules  Time  Mathematical Approach  1D (vector) or 2D (matrix) cell space  Contiguous neighborhoods (n cells)  Binary cell states (1 or 0)  Probabilistic transition rules

8. Introduction to CA Models [2.Relaxations] Couclelis, H., 1997, "From cellular automata to urban models: New principles for model development and implementation“, Environment and Planning B: Planning and Design 24(2) 165-174

9. Model Presentation [1.Components]  Approach – Constrained CA model with land use demand based on population density calibrated by an optimization procedure (Particle Swarm)  Five major CA components  Cell and Cell Structure  Neighborhood  Cell States  Transition Rules  Time time

10. Model Presentation [2.Transition Potential]  State transition occurs following the variation of the transition potential for each cell at each time step, that takes into account three components  Accessibility  Land Use Suitability – binary variable (admissible 1, non-admissible 0)  Neighborhood effect  Transition Potential

11. Model Presentation [2.Calibration]  High number of calibration parameters (48)  Strong interdependence => Optimization  Particle Swarm (PS) algorithm  Computational intensive  Objective function – to maximize the value of agreement measure k mod between model and reality

12. Model Presentation [2.Calibration]  Measure of agreement between modeled and reference maps  k mod doesn’t take into account cells that can’t change state m ij – number of cells modeled in state I and classified in reality is state j s – total number of cell states k mod Agreement < 0.00poor 0.00 - 0.20very week 0.21 - 0.40week 0.41 - 0.60moderate 0.61 - 0.80substantial 0.81 - 1.00perfect

13. Model Results [1.Previous Appplications] Calibration Prospective Analysis Calibration

14. Model Results [2.Coimbra Dataset] Reference Map 1991Reference Map 2001

15. Model Results [2.Coimbra Model Calibration] Reference Map 2001Simulation Map 2001, k mod 0,767

16. Model Results [2.Coimbra Scenarios] BaselineAnel Pedrulha Growth Rates

17. Model Results [2.Coimbra Baseline] Reference Map 2001Simulation Map 2011

18. Model Results [2.Coimbra Baseline] Simulation Map 2011Simulation Map 2021

19. Model Results [2.Coimbra Anel Pedrulha] Reference Map 2001Simulation Map 2011

20. Model Results [2.Coimbra Anel Pedrulha] Simulation Map 2011Simulation Map 2021

21. Model Results [2.Coimbra Sc Comparison] Baseline Simulation Map 2021Anel Pedrulha Simulation Map 2021

22. Future Developments of the Model  Multiscale approach  Neighborhood, dynamic, discontinuous  Different transition rules  New measures of agreement  Use multimodal accessibility measures  Logit model to establish the rank for transition potential

23. Application of a CA Model to Simulate the Impacts of Road Infrastructures on Urban Growth Nuno Pinto and António Antunes, University of Coimbra with Josep Roca, Technical University of Catalonia Workshop 3 “Stakeholder Scenario Building: Imagining Urban Futures” Lisbon, July 9 th, 2010