SHARAF ALKHEDER & JIE SHAN GEOMATICS ENGINEERING AREA SCHOOL OF CIVIL ENGINEERING

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 Indiana GIS Conference, March 7-8, 2006

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

3. INTRODUCTION • Urban growth process is complex in its nature. • Urban growth modeling is a necessity for each municipality. • 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) for 2D spatial modelling. Indiana GIS Conference, March 7-8, 2006

4. STATEMENT OF THE PROBLEM • Urban areas undergo accelerated urban growth rates. • Multi-temporary images are useful resource. • 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. 1973 1987 2003 Indiana GIS Conference, March 7-8, 2006

5. FOCUS OF OUR WORK • Development and calibration of CA model. • Spatial & temporal calibration algorithm design. • 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. • Integrate with commercial GIS (ArcGIS, VBA). 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: 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. • 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. • 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). Indiana GIS Conference, March 7-8, 2006

7. CELLULAR AUTOMATA (CA) THEORY • The neighborhood function is defined as: 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: 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 : Indiana GIS Conference, March 7-8, 2006

8. CA FOR URBAN GROWTH MODELLING • CA mechanism: complex phenomenon can be modeled by a # of simpler ones. • CA composed of cell, state, neighborhood and transition rules. • The future state of a cell depends on: - Its current state. - Neighborhood states. - Transition rules. 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. • 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. • CA design is based on the effect of each land use. E.g., roads encourage and drive the urban development. Indiana GIS Conference, March 7-8, 2006

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

11. ARTIFICIAL CITY CA URBAN GROWTH • 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. • CA simulates urban growth at 0, 25, 50 and 60 growth steps. • Effect of road and lakes in driving growth. • Pollution source buffer zones. • Conservation of water. Indiana GIS Conference, March 7-8, 2006

12. REAL CITY (INDIANAPOLIS) CA GROWTH • Extending the artificial city CA model for real city. • Complex structure and interaction of development factors result in growth pattern. • Careful design of CA transition rules. • Model calibration and evaluation is needed. • 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. 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). • Images are projected to UTM NAD1983 zone 16N & registered. • Ground reference data are used to classify the images. • 7 classes are defined: water, road, commercial, forest, residential, pasture and row crops. • High classification accuracy (>92%). • Commercial and residential classes represent urban class. Indiana GIS Conference, March 7-8, 2006

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

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

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

18. CA ALGORITHM DESIGN • Spatial calibration at 1982 on a township basis. • Rules are calibrated based on township site specific features. • Evaluate urban class per region for simulated and real images at 1982. • Calculate region & average accuracy as a ratio between simulated and real urban amount. 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. • Run the simulation again from 1973 to 1982 and evaluate. • Run till simulated results closely estimate real growth. • 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). Indiana GIS Conference, March 7-8, 2006

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

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

22. CA MODELING RESULTS - CALIRATION Temporal calibration Effect. Indiana GIS Conference, March 7-8, 2006

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

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

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

26. CONCLUSIONS • Multitemporal imagery is a rich source for urban growth modeling. • 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. • Importance of spatial calibration on township basis to improve the spatial prediction accuracy. • Temporal calibration to adapt the growth pattern over time. Indiana GIS Conference, March 7-8, 2006

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