1. Geospatial Modeling Maps and Animated Geography E. Lynn Usery Professor, University of Georgia Research Geographer, U.S. Geological Survey

2. Models Scale - Differs from reality only in size –Iconic - Miniature copies of reality –Analog - Alter size, some properties - glacier model with clay Conceptual -- Diagrammatic process model –Usually with boxes and arrows, i.e., flowchart Mathematical - Allows prediction –Probabilistic - Assumes components are related in random fashion -Subject to chance, express initial assumptions as set of probabilities and use probability theory. –Deterministic - Behavior controlled by natural laws.

3. Geospatial Models Definition and Classification A geospatial model is a simplified representation of geographic reality. Model Types –Spatial – Generally static, model distributions Examples include maps, GIS databases, and cartographic models (based on Map Algebra) –Process – Static or dynamic, model processes Growth or accumulation –urban growth, climate change, sea level rise Flows –spatial interaction, gravity model, location-allocation

4. Spatial Models -- Maps Scale models, i.e., generalized representations of geographic phenomena No map is accurate; all contain three types of errors from transformations –Spherical to plane –Three-dimensions to two-dimensions –Generalization Selection Simplification Symbolization Induction

5. Global Landcover – Mollweide Projection

7. Spatial Models--Cartographic Models Map themes again geographically registered but combined with a sequence of operations (map algebra) that generate a desired result from a set of basic input data layers Map layers become variables in map algebra with operators on and between variables Operators include point, neighborhood, and global Most commonly implemented with raster data layers

14. Cartographic Model for Profitability

16. Cartographic Model of Human Effects on Animal Activity Measure animal activity over different time periods Determine change over time Determine human activities over samespace and time Compare the two activity levels to determine effects

20. Spatial Models-- GIS Databases Map model placed in computer representation Includes all error inherent in the map model Usually include multiple maps of individual themes registered to a common spheroid, datum, projection, and coordinate system with associated attributes linked to geographic object (point, line, area) identifiers commonly stored in a relational database

22. Entity Model What is it – attributes, theme Where is it – location, space When is it – time What is its relation to other entities – proximity, connectivity (topology)

23. Classes of Operations for Entities Attribute operations Distance/location operations Topological operations

24. Attribute Operations U i = f(A,B,C,D,…) –Where U i is the derived attribute –A,B,C,D,… are attributes combined to derive U i –F ( ) is a function of one or more of: Logical (Boolean) Arithmetical Univariate statistics Multivariate statistics Multicriteria methods

27. Land Suitability Model Soil mapping units of texture and pH A is set of mapping units of Oregon Loam B is set of mapping units for pH >= 7.0, then –X = A AND B finds all occurrences of Oregon Loam with pH >= 7.0. –X = A OR B finds all occurrences of Oregon Loam and all mapping units with pH >=7.0. –X = A XOR B finds all units that are either Oregon Loam or have a pH >= 7.0, nut not in combination –X = A NOT B finds all mapping units that are Oregon Loam where the pH is less than 7.0.

28. Retrieving Entities with Only Attributes

29. Retrieval and Recode

30. Reclassification

31. Deriving New Attributes Empirical Regression Models –Temperature as function of elevation –T = 5.697 – 0.00443*E where, T is temperature in degrees Celsius and E is elevation in meters Multivariate clustering

32. Polygon Overlay – Sliver Problem

33. Distance Operators Spatial Buffering Determine the number of fast food restaurants within 5 km of the White House. Investigate the potential for water pollution in terms of proximity of filling stations to natural waterways. Compute the total value of the houses lying within 200 m of the proposed route for a new road. Compute the proportion of the world popultaion lying within 100 km of the sea.

34. Spatial Buffering

35. Connectivity Operators

36. Geospatial Process Models Often use results of GIS Databases as steps in a process Non-point Source Pollution -- AGNPS Sea Level Rise Urban Growth -- SLEUTH

37. AGNPS Agricultural Non-Point Pollution Source

38. Introduction -- AGNPS Operates on a cell basis and is a distributed parameter, event-based model Requires 22 input parameters Elevation, land cover, and soils data are the base for extraction of input parameters

41. Input Parameter Generation 22 parameters; varying degrees of computational development –Simple, straightforward, complex

42. Input Parameter Generation

43. Details on Generation of Parameters Cell Number Receiving Cell Number SCS Curve Number –Uses both soil and land cover to resolve curve number

44. Details on Generation of Parameters Slope Shape Factor

45. Extraction Methods Used object-oriented programming and macro languages –C/ C++ and EML Manipulated the raster GIS databases with Imagine Extracted parameters for each resolution for both boundaries using AGNPS Data Generator

46. Creating AGNPS Output AGNPS creates a nonpoint source (“.nps”) file ASCII file like the input; tabular, numerical form

47. AGNPS Output

49. Creating AGNPS Output Images Output Image Creation –Combined “.nps” file with Parameter 1 to create multidimensional images –Users can graphically display AGNPS output –Process: create image with “x” layers, fill layers with AGNPS output data, set projection and stats for image –Multi-layered (bands) images per model event

50. Creating AGNPS Output Images

51. Creating AGNPS Images

52. Model of Sea Level Rise Data inputs –Elevation – Gtopo 30 –Population -- Landscan –Land Cover – Global Land Cover 30 arc-sec resolution cells (approximately 1 km at the Equator) Most accurate global data available Model for eastern North America only

58. Urban Growth -- SLEUTH Model of converting land to urban from other uses Cellular Automata model based on probabilities from Monte Carlo stochastic simulation Model begins with an existing urban base (i.e, some cells are urban and others non- urban based on historical land cover data)

59. Urban Growth -- SLEUTH Non-urban cells change to urban based on 7 controlling variables (GIS layers) and user specified parameters controlling growth Variables: Slope, Land Cover, Elevation, Urban, Transportation, Hillshade Types of growth: –Spontaneous GrowthSpontaneous Growth –New Spreading CentersNew Spreading Centers –Edge GrowthEdge Growth –Road-Influenced GrowthRoad-Influenced Growth