1. Indiana GIS Conference, March 7-8, 2006 1 URBAN GROWTH MODELING USING MULTI-TEMPORAL IMAGES AND CELLULAR AUTOMATA – A CASE STUDY OF INDIANAPOLIS SHARAF ALKHEDER & JIE SHAN GEOMATICS ENGINEERING AREA SCHOOL OF CIVIL ENGINEERING PURDUE UNIVERSITY

2. Indiana GIS Conference, March 7-8, 2006 2 OUTLINE Introduction. Introduction. Statement of the problem. Statement of the problem. Focus of our work. Focus of our work. Cellular Automata (CA) urban growth modeling: Cellular Automata (CA) urban growth modeling:  Artificial city modeling (synthetic data).  Real city modeling (Indianapolis). Conclusions. Conclusions. Work in progress. Work in progress.

3. Indiana GIS Conference, March 7-8, 2006 3 INTRODUCTION Urban growth process is complex in its nature. Urban growth process is complex in its nature. Urban growth modeling is a necessity for each municipality. Urban growth modeling is a necessity for each municipality. Simulation & prediction of urbanization process help infrastructure planning. Simulation & prediction of urbanization process help infrastructure planning. Cellular Automata (CA) is promising due to its ability to learn and simulate complex processes that not possible with mathematical models. Cellular Automata (CA) is promising due to its ability to learn and simulate complex processes that not possible with mathematical models. Cellular Automata (CA) for 2D spatial modelling. Cellular Automata (CA) for 2D spatial modelling.

4. Indiana GIS Conference, March 7-8, 2006 4 STATEMENT OF THE PROBLEM Urban areas undergo accelerated urban growth rates. Urban areas undergo accelerated urban growth rates. Multi-temporary images are useful resource. Multi-temporary images are useful resource. The objective is to use CA with satellite images to model the spatial & temporal growth of Indianapolis. The objective is to use CA with satellite images to model the spatial & temporal growth of Indianapolis. CA for complex processes modeling in a grid space. CA for complex processes modeling in a grid space. 197319872003

5. Indiana GIS Conference, March 7-8, 2006 5 FOCUS OF OUR WORK Development and calibration of CA model. Development and calibration of CA model. Spatial & temporal calibration algorithm design. Spatial & temporal calibration algorithm design. CA rules calibration: CA rules calibration:  Using Multi-temporal data.  Based on neighborhood structure and input data.  Based on modeling error feedback (over/under estimate). Township based evaluation. Township based evaluation. Integrate with commercial GIS (ArcGIS, VBA). Integrate with commercial GIS (ArcGIS, VBA).

6. Indiana GIS Conference, March 7-8, 2006 6 CELLULAR AUTOMATA (CA) THEORY CA introduced by Ulam and von Neumann in 1940s to study the behaviour of complex systems. CA introduced by Ulam and von Neumann in 1940s to study the behaviour of complex systems. CA: An iterative dynamical discrete system in space and time that operates on a uniform grid under certain rules. CA: An iterative dynamical discrete system in space and time that operates on a uniform grid under certain rules. Four components of CA: Cells/pixels, States, Neighborhood & Transition rules. Four components of CA: Cells/pixels, States, Neighborhood & Transition rules. Let I represents integers set. For a cellular space over the set IxI ; the neighborhood function for cell α is defined as: Let I represents integers set. For a cellular space over the set IxI ; the neighborhood function for cell α is defined as: Where; δi(i = 1…n) is index of the neighborhood pixels. Where; δi(i = 1…n) is index of the neighborhood pixels. The CA system in a symbolic notation is defined as: The CA system in a symbolic notation is defined as: Where; is distinct element of cellular states V & is the local transition function. (rules on neighborhood). Where; is distinct element of cellular states V & is the local transition function. (rules on neighborhood).

7. Indiana GIS Conference, March 7-8, 2006 7 CELLULAR AUTOMATA (CA) THEORY The neighborhood function is defined as: The neighborhood function is defined as: Where; are the current states of tested pixel and its neighborhood. Where; are the current states of tested pixel and its neighborhood. Relation between the state of cell α at time (t+1) and its neighborhood states at time t is expressed as: Relation between the state of cell α at time (t+1) and its neighborhood states at time t is expressed as: represents the CA transition rules defined on α and neighborhood states to drive the modelling process. represents the CA transition rules defined on α and neighborhood states to drive the modelling process. The neighborhood (e.g. square) over the IxI space presented as a city-block metric : The neighborhood (e.g. square) over the IxI space presented as a city-block metric :

8. Indiana GIS Conference, March 7-8, 2006 8 CA FOR URBAN GROWTH MODELLING CA mechanism: CA mechanism: complex phenomenon can be modeled by a # of simpler ones. complex phenomenon can be modeled by a # of simpler ones. CA composed of cell, state, neighborhood and transition rules. CA composed of cell, state, neighborhood and transition rules. The future state of a cell depends on: The future state of a cell depends on: - Its current state. - Its current state. - Neighborhood - Neighborhood states. states. - Transition rules. - Transition rules.

9. Indiana GIS Conference, March 7-8, 2006 9 ARTIFICIAL CITY CA URBAN GROWTH OBJECTIVES: Mimic the reality by introducing complex structures for an urban system. Mimic the reality by introducing complex structures for an urban system. To test the effect of a number of factors and constraints on urban growth. To test the effect of a number of factors and constraints on urban growth. To design the CA system transition rules as a function of neighborhood structure. To design the CA system transition rules as a function of neighborhood structure. CA design is based on the effect of each land use. E.g., roads encourage and drive the urban development. CA design is based on the effect of each land use. E.g., roads encourage and drive the urban development.

10. Indiana GIS Conference, March 7-8, 2006 10 ARTIFICIAL CITY CA URBAN GROWTH 200x200 pixels image input to the CA algorithm. 200x200 pixels image input to the CA algorithm. The CA rules are defined with the The CA rules are defined with the motivation that they represent each motivation that they represent each land use effect on the growth process. land use effect on the growth process. Growth constraints are take into Growth constraints are take into consideration in rules definition. consideration in rules definition. CA rules: for tested pixel CA rules: for tested pixel  IF it is river, road, lake, urban or pollution source, THEN no growth. or pollution source, THEN no growth.  IF it is non-urban AND 1 or more of neighborhood are pollution, of neighborhood are pollution, THEN keep non-urban. THEN keep non-urban.  IF it is non-urban AND the # urban pixels in the neighborhood is >= than 3 AND there is no pollution pixel THEN change it to urban.  IF non-urban AND 1 or more of the neighborhood road AND 1 or more urban AND no pollution pixel, THEN change to urban.

11. Indiana GIS Conference, March 7-8, 2006 11 ARTIFICIAL CITY CA URBAN GROWTH CA rules (cont’d): CA rules (cont’d):  IF non-urban AND 1 or more of the neighborhood are lake AND 1 or more are urban AND no pollution pixel, THEN change to urban.  ELSE keep non-urban. Moore 3 by 3 rectangle neighborhood. Moore 3 by 3 rectangle neighborhood. CA simulates urban growth at 0, 25, 50 and 60 growth steps. CA simulates urban growth at 0, 25, 50 and 60 growth steps. Effect of road and lakes in driving growth. Effect of road and lakes in driving growth. Pollution source buffer zones. Pollution source buffer zones. Conservation of water. Conservation of water.

12. Indiana GIS Conference, March 7-8, 2006 12 REAL CITY (INDIANAPOLIS) CA GROWTH Extending the artificial city CA model for real city. Extending the artificial city CA model for real city. Complex structure and interaction of development factors result in growth pattern. Complex structure and interaction of development factors result in growth pattern. Careful design of CA transition rules. Careful design of CA transition rules. Model calibration and evaluation is needed. Model calibration and evaluation is needed. Indianapolis is located in Marion County at latitude 39°44'N and longitude of 86°17'W. Indianapolis is located in Marion County at latitude 39°44'N and longitude of 86°17'W. Grown from part of Marion in 70’s to the whole County and parts of the neighboring in 2003. Grown from part of Marion in 70’s to the whole County and parts of the neighboring in 2003.

13. Indiana GIS Conference, March 7-8, 2006 13 INDIANAPOLIS CA GROWTH - INPUT DATA 1. Multitemporal Satellite Imagery: 5 historical MSS/TM satellite images : (1973, 1982, 1987, 1992 and 2003). 5 historical MSS/TM satellite images : (1973, 1982, 1987, 1992 and 2003). Images are projected to UTM NAD1983 zone 16N & registered. Images are projected to UTM NAD1983 zone 16N & registered. Ground reference data are used to classify the images. Ground reference data are used to classify the images. 7 classes are defined: water, road, commercial, forest, residential, pasture and row crops. 7 classes are defined: water, road, commercial, forest, residential, pasture and row crops. High classification accuracy (>92%). High classification accuracy (>92%). Commercial and residential classes represent urban class. Commercial and residential classes represent urban class.

14. Indiana GIS Conference, March 7-8, 2006 14 INDIANAPOLIS CA GROWTH - INPUT DATA 2. Population Density Maps: Another input to CA model. Another input to CA model. A population density model for each growth year is prepared. A population density model for each growth year is prepared. 2000 Census tract map is used. 2000 Census tract map is used. Area for each census tract Area for each census tract is calculated. is calculated. Population density is Population density is computed per census tract. computed per census tract. (Source, IGS)

15. Indiana GIS Conference, March 7-8, 2006 15 INDIANAPOLIS CA GROWTH - INPUT DATA 2. Population Density Maps: An exponential model is fitted between density and distance from city center. An exponential model is fitted between density and distance from city center. The model is used to calculate population density per pixel for entire image for each growth year. The model is used to calculate population density per pixel for entire image for each growth year. Model parameters are updated yearly based on population growth rate. Model parameters are updated yearly based on population growth rate. Population density is used as another CA input. Population density is used as another CA input.

16. Indiana GIS Conference, March 7-8, 2006 16 CA TRANSITION RULES CA rules based on: Land use effect: growth constraints. Land use effect: growth constraints. Closeness to city: Closeness to city: positive effect. positive effect. Population density. Population density.  3 by 3 Moore neighborhood.  CA calibration involves two aspects: Spatial and Temporal calibration. Future

17. Indiana GIS Conference, March 7-8, 2006 17 CA ALGORITHM DESIGN CA Modelling in ArcGIS through VBA. CA Modelling in ArcGIS through VBA. CA transition rules are defined as a function of neighborhood structure and population density. CA transition rules are defined as a function of neighborhood structure and population density. Two set of multitemporal imagery: Two set of multitemporal imagery: - Training images 1982 & 1987 to calibrate the CA rules. - Training images 1982 & 1987 to calibrate the CA rules. - Testing images of 1992 and 2003 for validation purposes only. - Testing images of 1992 and 2003 for validation purposes only. CA rules are initialized to run the simulation from 1973 till 1982. CA rules are initialized to run the simulation from 1973 till 1982.

18. Indiana GIS Conference, March 7-8, 2006 18 CA ALGORITHM DESIGN Spatial calibration at 1982 Spatial calibration at 1982 on a township basis. on a township basis. Rules are calibrated based Rules are calibrated based on township site specific on township site specific features. features. Evaluate urban class per Evaluate urban class per region for simulated and region for simulated and real images at 1982. real images at 1982. Calculate region & Calculate region & average accuracy as a ratio average accuracy as a ratio between simulated and between simulated and real urban amount. real urban amount.

19. Indiana GIS Conference, March 7-8, 2006 19 CA ALGORITHM DESIGN IF over/under estimate increase/decrease urban growth rate through modifying the rules, respectively. IF over/under estimate increase/decrease urban growth rate through modifying the rules, respectively. Run the simulation again from 1973 to 1982 and evaluate. Run the simulation again from 1973 to 1982 and evaluate. Run till simulated results closely estimate real growth. Run till simulated results closely estimate real growth. For temporal calibration, Recalibrate again spatially at 1987 to adapt growth pattern over time. For temporal calibration, Recalibrate again spatially at 1987 to adapt growth pattern over time. Predict urban growth at 1992 (from 1987) for 5 years interval and 2003 for 11 years interval (from 1992). Predict urban growth at 1992 (from 1987) for 5 years interval and 2003 for 11 years interval (from 1992).

20. Indiana GIS Conference, March 7-8, 2006 20 ARCGIS-CA TOOL DEVELOPMENT

21. Indiana GIS Conference, March 7-8, 2006 21 CA MODELING RESULTS - CALIRATION Close Close match match Spatial Spatialcalibrationeffect.

22. Indiana GIS Conference, March 7-8, 2006 22 CA MODELING RESULTS - CALIRATION TemporalcalibrationEffect.

23. Indiana GIS Conference, March 7-8, 2006 23 CA MODELING RESULTS – PREDICTION (1992) Short term prediction (5 years). Short term prediction (5 years). Good Good accuracy accuracy

24. Indiana GIS Conference, March 7-8, 2006 24 CA MODELING RESULTS – PREDICTION (2003) Good Good accuracy accuracy Pattern Pattern match match

25. Indiana GIS Conference, March 7-8, 2006 25 CA PREDICTION RESULTS ACCURACY Higher Higher accuracy for accuracy for short term. short term. Township effect Township effect on improving on improving accuracy. accuracy. Low variability. Low variability.

26. Indiana GIS Conference, March 7-8, 2006 26 CONCLUSIONS Multitemporal imagery is a rich source for urban growth modeling. Multitemporal imagery is a rich source for urban growth modeling. CA show great potential to model the 2D growth process. CA show great potential to model the 2D growth process. Error model of comparing the real and simulated images on a township basis is the basis of calibration process. Error model of comparing the real and simulated images on a township basis is the basis of calibration process. Importance of spatial calibration on township basis to improve the spatial prediction accuracy. Importance of spatial calibration on township basis to improve the spatial prediction accuracy. Temporal calibration to adapt the growth pattern over time. Temporal calibration to adapt the growth pattern over time.

27. Indiana GIS Conference, March 7-8, 2006 27 WORK IN PROGRESS…. Fuzzy CA modeling to preserve the continuous nature of the growth process. Fuzzy CA modeling to preserve the continuous nature of the growth process. Genetics algorithms for efficient and automatic CA transition rules calibration. Genetics algorithms for efficient and automatic CA transition rules calibration.

28. Indiana GIS Conference, March 7-8, 2006 28 Thanks For Listening. Questions!! SHARAF ALKHEDER & JIE SHAN GEOMATICS ENGINEERING AREA SCHOOL OF CIVIL ENGINEERING (salkhede,jshan )@ecn.purdue.edu PURDUE UNIVERSITY