analysis and modeling in gis

1. Analysis and Modeling in GIS

3. The Analysis Challenge Recognizing which generic GIS analytic capability (or combination) can be used to solve your problem: meet an operational need answer a question posed by your boss or your board address a scientific issue and/or test a hypothesis Send mailings to property owners potentially affected by a proposed change in zoning Determine if a crime occurred within a school�s �drug free zone� Determine the acreage of agricultural, residential, commercial and industrial land which will be lost by construction of new highway corridor Determine the proportion of a region covered by igneous extrusions Do Magnitude 4 or greater sub-oceanic earthquakes occur closer to the Pacific coast of South America than of North America? Are gas stations or fast food joints closer to freeways?

4. Availability of Capabilities in GIS Software Descriptive Focus: Basic Desktop GIS packages Data editing, description and basic analysis ArcView Mapinfo Geomedia Analytic Focus: Advanced Professional GIS systems More sophisticated data editing plus more advanced analysis ARC/INFO, MapInfo Pro, etc. Provided through extra cost Extensions or professional versions of desktop packages Prediction: Specialized modeling and simulation via scripting/programming within GIS VB and ArcObjects in ArcGIS Avenue scripts in ArcView 3.2 AMLs in Workstation ARC/INFO (v. 7) Write your own or download from ESRI Web site via specialized packages and/or GISs 3-D Scientific Visualization packages transportation planning packages e.g TransCAD ERDAS, ER Mapper or similar package for raster

5. Description and Basic Analysis(Table of Contents) Spatial Operations Vector spatial measurement Centrographic statistics buffer analysis spatial aggregation redistricting regionalization classification Spatial overlays and joins Raster neighborhood analysis/spatial filtering Raster modeling Attribute Operations record selection tabular via SQL �information clicking� with cursor variable recoding record aggregation general statistical analysis table relates and joins

6. Spatial measurements: distance measures between points from point or raster to polygon or zone boundary between polygon centroids polygon area polygon perimeter polygon shape volume calculation e.g. for earth moving, reservoirs direction determination e.g. for smoke plumes Spatial operations: Spatial Measurement Comments: Cartesian distance via Pythagorus Used for projected data by ArcMap measure tools Spherical distance via spherical coordinates Cos d = (sin a sin b) + (cos a cos b cos P) where: d = arc distance a = Latitude of A b = Latitude of B P = degrees of long. A to B Used for unprojected data by ArcMap measure tools possible distance metrics: straight line/airline city block/manhattan metric distance thru network time/friction thru network shape often measured by: Projection affects values!!!

7. Examples

8. Spatial operations: Spatial Measurement

9. Spatial Measurement: Calculating the Area of a Polygon

10. Spatial Operations:Centrographic Statistics Basic descriptors for spatial point distributions Two dimensional (spatial) equivalents of standard descriptive statistics (mean, standard deviation) for a single-variable distribution Measures of Centrality (equivalent to mean) Mean Center and Centroid Measures of Dispersion (equivalent to standard deviation or variance) Standard Distance Standard Deviational Ellipse Can be applied to polygons by first obtaining the centroid of each polygon Best used in a comparative context to compare one distribution (say in 1990, or for males) with another (say in 2000, or for females)

11. Centroid and Mean Center balancing point for a spatial distribution analogous to the mean single point representation for a polygon (centroid) single point summary for a point distribution (mean center) can be weighted by �magnitude� at each point (analogous to weighted mean) minimizes squared distances to other points, thus �distant� points have bigger influence than close points ( Oregon births more impact than Kansas births!) is not the point of �minimum aggregate travel�--this would minimize distances (not their square) and can only be identified by approximation. useful for summarizing change over time in a distribution (e.g US pop. centroid every 10 years) placing labels for polygons for weird-shaped polygons, centroid may not lie within polygon

14. Standard Distance Deviation single unit measure of the spread or dispersion of a distribution. Is the spatial equivalent of standard deviation for a single variable Equivalent to the standard deviation of the distance of each point from the mean center Given by: which by Pythagorasreduces to: ---the square root of the average squared distance ---essentially the average distance of points from the center We can also weight each point and calculate weighted standard distance (analogous to weighted mean center.)

15. Standard Distance Deviation Example

16. Standard Deviational Ellipse: concept Standard distance deviation is a good single measure of the dispersion of the incidents around the mean center, but it does not capture any directional bias doesn�t capture the shape of the distribution. The standard deviation ellipse gives dispersion in two dimensions Defined by 3 parameters Angle of rotation Dispersion along major axis Dispersion along minor axis The major axis defines the direction of maximum spreadof the distribution The minor axis is perpendicular to itand defines the minimum spread

17. Standard Deviational Ellipse: example

18. Spatial Operations: buffer zones region within �x� distance units buffer any object: point, line or polygon use multiple buffers at progressively greater distances to show gradation may define a �friction� or �cost� layer so that spread is not linear with distance Implement in Arcview 3.2 with Theme/Create buffers in ArcGIS 8 with ArcToolbox>Analysis Tools>Buffer Examples 200 foot buffer around property where zoning change requested 100 ft buffer from stream center line limiting development 3 mile zone beyond city boundary showing ETJ (extra territorial jurisdiction) use to define (or exclude) areas as options (e.g for retail site) or for further analysis in conjunction with �friction layer�, simulate spread of fire

19. Examples

20. Criteria may be: formal (based on in situ characteristics)e.g. city neighborhoods functional (based on flows or links): e.g. commuting zones Groupings may be: contiguous non-contiguous Boundaries for original polygons: may be preserved may be removed (called dissolving) Examples: elementary school zones to high school attendance zones (functional districting) election precincts (or city blocks) into legislative districts (formal districting) creating police precincts (funct. reg.) creating city neighborhood map (form. reg.) grouping census tracts into market segments--yuppies, nerds, etc (class.) creating soils or zoning map (class) Spatial Operations: spatial aggregation districting/redistricting grouping contiguous polygons into districts original polygons preserved Regionalization (or dissolving) grouping polygons into contiguous regions original polygon boundaries dissolved classification grouping polygons into non-contiguous regions original boundaries usually dissolved usually �formal� groupings

22. Spatial Operations: Spatial Matching: Spatial Joins and Overlays combine two (or more) layers to: select features in one layer, &/or create a new layer used to integrate data having different spatial properties (point v. polygon), or different boundaries (e.g. zip codes and census tracts) can overlay polygons on: points (point in polygon) lines (line on polygon) other polygons (polygon on polygon) many different Boolean logic combinations possible Union (A or B) Intersection (A and B) A and not B ; not (A and B) can overlay points on: Points, which finds & calculates distance to nearest point in other theme Lines, which calculates distance to nearest line Examples assign environmental samples (points) to census tracts to estimate exposure per capita (point in polygon) identify tracts traversed by freeway for study of neighborhood blight (polygon on lines) integrate census data by block with sales data by zip code (polygon on polygon) Clip US roads coverage to just cover Texas (polygon on line) Join capital city layer to all city layer to calculate distance to nearest state capital(point on point)

23. ERASE - erases the input coverage features that overlap with the erase coverage polygons.

24. Example: Spatial Matching via Polygon-on-Polygon Overlay: Union

25. Available in three places via Selection/Select by Location this selects features of one layer(s) which relate in some specified spatial manner to the features in another layer if desired, selected features may be saved later to a new theme via Data/Export Data Individual features are not themselves modified via Spatial Join (right click layer in T of C, select Join/Joins and Relates, then click down arrow in first line of Join Data window---see Joining Data in Help for details) Use for: points in polygon lines in polygon points on lines (to calculate distance to nearest line) points on points (to calculate distance to �nearest neighbor� point) operate on tables and normally creates a new table with additional variables, but again does not modify spatial features themselves via ArcToolbox Generally these tools modify geographic feature, thus they create a new layer (e.g. shape file) Tools are organized into multiple categories ArcToolbox Examples Dissolve features based on an attribute Combine contiguous polygons and remove common border ArcToolbox>Generalization>Dissolve Clip one layer based on another ArcToolbox>Analysis Tools>Extract>Clip Use one theme to limit features in another theme(e.g. limit a Texas road theme to Dallas county only) Intersect two layers (extent limited to common area) ArcToolbox>Analysis Tools>Overlay>Intersect Use for polygon on polygon overlay Union two layers (covers full extent of both layers) ArcToolbox>Analysis Tools>Overlay>Intersect Use for polygon on polygon overlay Implementing Spatial Matching in ArcGIS 9

26. Spatial Operations:neighborhood analysis/spatial filtering spatial convolution or filter applied to one raster layer value of each cell replaced by some function of the values of itself and the cells (or polygons) surrounding it can use �neighborhood� or �window� of any size 3x3 cells (8-connected) 5x5, 7x7, etc. differentially weight the cells to produce different effects kernel for 3x3 mean filter: 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 low frequency ( low pass) filter: mean filter cell replaced by the mean for neighborhood equivalent to weighting (mutiplying) each cell by 1/9 = .11 (in 3x3 case) smooths the data use larger window for greater smoothing median filter use median (middle value) instead of mean smoothing, especially if data has extreme value outliers

27. Spatial Operations:spatial filtering -- high pass filter high frequency (high pass) filter negative weight filter exagerates rather than smooths local detail used for edge detection standard deviation filter (texture transform) calculate standard deviation of neighborhood raster values high SD=high texture/variability low SD=low texture/variability again used for edge detection neighorhoods spanning border have large SD �cos of variability

28. Spatial Operations:raster�based modelling Relating multiple rasters Processes may be: Local: one cell only Neighborhood: cells relating to each other in a defined manner Zonal: cells in a given section Global: all cells ArcGIS implementation: All raster analyses require either the Spatial Analyst or 3-D Analyst extensions Base ArcView can do no more than display an image (raster) data set Suitability modeling Diffusion Modeling Connectivity Modeling

29. Attribute Operations: record selection or extraction--features selected on the map are identified in the table (and visa versa) Select by Attribute (tabular) Independent selection by clicking table rows: Open Attribute Table & click on grey selection box at start of row (hold ctrl for multiple rows) Create SQL query use Selection/Select by Attribute use table Relates /Joins to select specific data Select by Graphic Manually, one point at a time use Select Features tool within a rectangle or an irregular polygon use Selection/Select by Graphic within a radius (circle) around a point or points use Selection/Select by Location (are wthin distance) Select by Location By using another layer Use Selection/Select by Location (same as Spatial Matching discussed previously) Hot Link Click on map to �hot link� to pictures, graphs, or other maps Outputs may be: Simultaneously highlighted records in table, and features on map New tables and/or map layers Examples Use SQL query to select all zip codes with median incomes above $50,000 (tabular) identify zip codes within 5 mile radius of several potential store sites and sum household income (graphic) show houses for sale on map, and click to obtain picture and additional data on a selected house (hot link)

30. Attribute Operations:statistical analysis on one or more columns in table univariate (one variable or column) central tendency: mean, median, mode dispersion: standard deviation, min, max To obtain these statistics in ArcGIS: Right click in T of C and select Open attribute table Right click on column heading and select Statistics bivariate (relating two variables or columns) interval and nominal scale variables: sum or mean by category average crop yield by silt-sand-clay soil types To implement in ArcGIS, proceed as above but use Summarize two interval scale variables: correlation coefficients income by education ArcScripts are available for this on ESRI web site (or use Excel!) multivariate (more than two variables) usually requires external statistical package such as SAS, SPSS, STATA or S-PLUS

31. establishing/modifying number of classes and/or their boundaries for continuous variable. Options for ArcGIS natural breaks (default)(finds inherent inherent groups via Jenks optimization which minimizes the variances within each of the classes). quantile (classes contain equal number of records--or equal area under the frequency distribution) equal interval (user selects # of classes) (equal width classes on variable) Defined interval (user selects width of classes) (equal width classes on variable) standard deviation (categories based on 1,2, etc, SDs above/below mean) Manual (user defined) whole numbers (e.g. 2,000) meaningful to phenomena (e.g zero, 32o) aggregating categories on a nominal (or ordinal) variable pine and fir into evergreen No change in number of records (observations). Attribute Operations: variable recoding

32. Attribute Operations: record aggregation combining two or more records into one, based on common values on a key variable the attribute equivalent of regionalization or classification equivalent of PROC SUMMARY in SAS interval scale variables can be aggregated using mean, sum, max, min, standard deviation, etc. as appropriate ordinal and nominal require special consideration example: aggregate county data to states, or county to CMSA Record count decreases (e.g. from 12 to 2)

33. Attribute Operations: Joining and Relating Tablesassociating spatial layer to non-spatial table Join: one to one, or one to many, relationship appends attributes Associate table of country capitals with country layer: only one capital for each country (one to one) Associate country layer with type of government: one gov. type assigned to many countries--but each country has only one gov. type (one to many)

35. Attribute Operations: Joining and Relating Tablesassociating spatial layer to non-spatial table(contd.) Relate: many to one relationship, attributes not appended Associate country layer with its multiple cities (many to one) Note: if we flip these tables we can do a join since there is only one country for each city (one to many) For both Joins and Relates: Association exists only in the map document Underlying files not changed unless export data

36. Analysis Options: Advanced & Specialized(Table of Contents) Advanced Proximity/point pattern analysis nearest neighbor layer distance matrix layer surface analysis cross section creation visibility/viewshed network analysis routing shortest path (2 points) travelling salesman (n points) time districting allocation Convex Hull Thiessen Polygon creation (boundaries define the area that is closest to each point relative to all other points) Specialized Remote Sensing image processing and classification raster modeling 3-D surface modeling spatial statistics/statistical modeling functionally specialized transportation modeling land use modeling hydrological modeling etc.

37. Advanced Applications: Proximity Analysis Nearest Neighbor location (distance) relative to nearest neighbor ( points or polygon centroids) location (distance) relative to nearest objects of selected other types (e.g. to line, or point in another layer, or polygon boundary) Requires only one output column altho generalizable to kth nearest neighbor

38. Advanced Applications:Network Analysis Routing shortest path between two points direction instructions (locating hotel from airport) travelling salesman: shortest path connecting n points bus routing, delivery drivers Network-based Districting expand from site along network until criteria (time, distance, cost, object count) is reached; then assign area to district creating market areas, attendance zones, etc essentially network-based buffering Network-based Allocation assign locations to the nearest center based upon travel thru network assign customers to pizza delivery outlets draw boundaries (lines of equidistance between 2 centers) based on the above Network-based market area delimitation Essentially, network-based polygon tessellation (no gaps)

39. Advanced applications:Surface Analysis Slope Transform fit a plane to the 3 by 3 neighborhood around every cell, or use a TIN output layer is the slope (first derivative) of the plane for each cell Aspect Transform direction slope faces: (E-W oriented ridge has slopes with northern and southern aspects) aspect normally classified into eight 45 degree categories calculate as horizontal component of the vector perpendicular to the surface Cross-section Drawings and Volumes elevation (or slope) values along a line Volume & cut-and-fill calculation Cross-section easy to produce for raster, more difficult for vector especially if uses contours lines Viewshed/Visibility terrain visible from a specific point applications visual impact of new construction select scenic overlooks Military Contouring Lines joining points of equal (vertical) value From raster, massed-points or breakline data

40. Advanced Applications: Convex Hull Formally: the smallest convex polygon (no concave angles) able to contain a set of points Informally: a rubber band wrapped around a set of points Just as a centroid is a point representation for a polygon, the convex hull is the polygon representation for a set of points Go to the following web site for a neat application showing how convex hull changes as you move points around

41. Advanced Applications:Thiessen (Dirichlet, Voronoi) Polgonsand Delaunay Triangles polygons generated from a point layer such that any location within a polygon is closer to the enclosed point than to a point within any other polygon they divide the space between the points as �evenly� as possible used for market area delimitation, rain gauge area assignment, contouring via Delaunay triangles (DTs), etc. elevation, slope and aspect of triangle calculated from heights of its three corners DTs are as near equiangular as possible and longest side is as short as possible, thus minimizes distances for interpolation

42. Specialized Applications Remote Sensing/Digital Image Processing reflectance value (usually 8 bit; 256 values) collected for each bands (wavelength area) in the electro-magnetic spectrum 1 band for grey scale (Black & white) 3 for color up to 200 or so for �hyperspectral� permits creation of image �spectral signature�: set of reflectance values/ranges over available bands typifying a specific phenomena provides basis for identification of phenomena Location Science/Network Modeling Network based models for optimum location decisions for (e.g.) police beats School attendance zones Bus routes Hazardous material routing Fire station location Raster Modeling: 2-D use of direction and friction surfaces to develop models for: spread of pollution dispersion of forest fires Surface Modeling: 3-D flood potential ground water/reservoir studies Viewshed/visibility analysis Spatial Statistics/Econometrics analyses on spatial data which explicitly incorporates relative location or proximity property of observations Global (applies to entire study area) spatial autocorrelation Regressions adjusted for spatial autocorrelation Local (separately calculated for local areas) LISA (local indicators of spatial autocorrelation) Geographically weighted regression

43. Implementation of Advanced and Specialized Applications in ArcGIS 8/9 Extensions support many of the Advanced and some Specialized Applications Spatial Analyst extension provides 2-D modeling of GRID (raster) data (AV 3.2 and 8/9) 3-D Analyst extension provides 3-D modeling (AV 3.2 and 8/9) Geostatistical Analyst extension provides interpolation (ArcGis 8/9 only) Network Analyst extension (3.2 only) and ArcLogistics Route (standalone) for routing and network analysis Image Analyst extension for remote sensing applications in AV 3.2 Leica Image Analysis and Stereo Analyst for ArcGIS 8 (9 version not yet released-Fall �04) Spatial Statistics Tools in ArcToolbox provide spatial statistics (centroid, etc..) ArcScripts support other Advanced Applications and Specialized Applications ArcScripts (in Visual Basic, C++, etc.) are used to customize ArcGIS 8 A variety of scripts available at http://support.esri.com/ >downloads Note: ArcScripts written in Avenue work only in ArcView 3 and will not work in ArcGIS 8/9 Many functions previously requiring Avenue scripts for AV 3.2 are built into ArcGIS 8/9 Specialized Software Packages Remote Sensing packages such as Leica GeoSystems Imagine (formerly ERDAS Imagine) For links to some of these packages go to: http://www.utdallas.edu/~briggs/other_gis.html