1. Spatial Modeling with GIS Longley et al., Chapter 16

2. Spatial Modeling with GIS Introduction Types of Model Modeling Technology Multicriteria Methods Accuracy and Validity

3. Spatial modeling Modeling: An overworked term data model a template for data relational, object-oriented, coverage, shapefile Model concerned with how the world looks Model also a representation of some real-world process Concerned with how the world works

4. Spatial modeling Manipulation of geographic information in multiple steps Steps may represent stages in some complex analysis Calculation of indicators over space (potentials) Steps may represent time Dynamic model Iterative analysis Geocomputation (see www.geocomputation.org)

5. Analog or Digital Modeling? Analog use of a scale model Analogous process Varignon frame Need a digital process represented in 0s and 1s program in C GIS script in VBA Python

6. Scaled Real Models

7. Army Corps of Engineers:WES

8. Varignon Frame

9. “Live” table: Pollution demo

10. Scale in a digital model? Spatial resolution/extent Temporal resolution/extent Define what is left out of the model Leave out uncertainty about model data, predictions Model must run faster than the real world Ecological fallacy

11. Why model? Support some design process Allow the user to experiment with a replica Investigate what-if scenarios To understand change and dynamics Test sensitivity and confidence

12. Analysis vs. Modeling To analyze or model? Evacuation scenarios –Tom Cova's analysis –Church's simulations –LANL

13. Analysis

14. Modeling LANL TRANSIMS Individual vehicle-based traffic simulation of entire cities

15. Limits of Analysis Static, one point in time Search for patterns, anomalies Generating hypotheses Revealing what would otherwise be invisible Form vs. process

16. Modeling multiple stages Perhaps different points in time Implementing ideas and hypotheses Experimenting with policy options Scenario based planning

17. Types of Model Static models and indicators Combining GIS layers through overlay e.g., using ModelBuilder Universal Soil Loss Equation A = R x K x LS x C x P DRASTIC model of groundwater vulnerability Karst groundwater protection model

18. DRASTIC

19. Santa Barbara Regional Impacts of Growth Study: 2040 forecasts

20. Karst groundwater protection model in Model Builder

21. Model result

22. Modeling Approach Individual vs. Aggregate models Is it possible to model every individual element in the system? Every molecule of groundwater? Every person in a crowd? Autonomous agent models

23. Mass Behavior: Problems Twenty-one Hajj pilgrims trampled Wednesday, February 12, 2003 Posted: 2:33 PM EST (1933 GMT) MINA, Saudi Arabia -- Another 21 people were trampled to death Wednesday on their way to one of the rituals of the Hajj, the annual Muslim pilgrimage to Mecca, Saudi officials said. Wednesday's deaths happened on a bridge as the throngs of pilgrims were heading to throw stones at one of three pillars representing Satan's temptation of Abraham, the officials said. The stoning represents a rejection of evil deeds. On Tuesday, a similar incident killed 14 pilgrims.

24. Notting Hill Carnival

25. Cellular Models Work on a raster: Good match to GIS Initial conditions Each cell in one of a number of states Rules of state transition at each timestep based on states of cell and neighbors Conway’s Game of Life SLEUTH land use change model

26. (Universal) Turing machine

27. Cellular automata Framework for systems experiments Simplest way to demonstrate complex systems behavior Wolfram: Formal framework {Cells, States, Initial conditions, Neighborhood, Rules, Time} Conway’s LIFE

28. The game of life Grid of square cells extending infinitely in every direction. A cell can be live or dead. Each cell in the grid has a neighborhood consisting of the eight cells in every direction including diagonals. To apply one step of the rules, we count the number of live neighbors for each cell. –A dead cell with exactly three live neighbors becomes a live cell (birth). –A live cell with two or three live neighbors stays alive (survival). –In all other cases, a cell dies or remains dead (overcrowding or loneliness).

29. Some examples

30. More examples

31. Urban Growth as a CA

32. SLEUTH applied to Santa Barbara

33. Technology for Modeling in GIS Graphic user interface e.g. GISMO in ERDAS ModelBuilder –access to all ArcGIS functions –no looping at present Scripts ARC/INFO AML ArcView 3.x Avenue ArcGIS –Visual Basic for Applications –Perl –Python –JScript –ArcScripts

34. Model Coupling linking model software to GIS Loose coupling –Exchanging files –Entering results Tight coupling –Common files –Common interface –Common code Modeling languages

35. Multcriteria Methods Multiple factors affect decisions Weighted by difference levels of importance Karst case –slope > 5% –land use = cropping –distance from stream < 300m Simple binary decision How to assign weights to each factor? Stakeholders may disagree on weights MCDM = multicriteria decision making

36. Analytical Hierarchy Process Devised by Thomas Saaty Each stakeholder compares each pair of factors Assigns comparative weights –e.g., slope 7 times as important as land use –e.g., distance from stream 1/2 as important as slope forming a complete matrix Weights must sum to one SlopeLand useDistance from Stream Slope 72 Land use 1/71/3 Distance from Stream 1/23

37. AHP example:Idrisi

38. Model accuracy and validity How do we know if the model is correct? How do we know that forecasts are accurate? Results from a computer are often trusted implicitly How to calibrate the model? –Hindcasting –Boostrapping A model is never more than an approximation to reality but how good/bad is the approximation? Important to provide measures of confidence in results

39. Sensitivity testing Varying the inputs to observe effects on outputs Some inputs affect outputs more than others These are the inputs that most need to be correct Error propagation Examining the impacts of input errors on outputs Mostly by simulation