1 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals Analysis and Modeling in GIS 2 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals GIS and the Levels of Science Description: Using GIS to create descriptive models of the world representations of reality as it exists. Analysis: Using GIS to answer a question or test an hypothesis. Often involves creating a new conceptual output layer, (or table or chart), the values of which are some transformation of the values in the descriptive input layer. e.g. buffer or slope or aspect layers Prediction: Using GIS capabilities to create a predictive model of a real world process, that is, a model capable of reproducing processes and/or making predictions or projections as to how the world might appear. e.g. flood models, fire spread models, urban growth models 3 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals 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? 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 Capabilities move ‘down the chain’ over time. In earlier generation GIS systems, use of advanced applications often required learning another package with a different user interface and operating system (usually UNIX). 5 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals 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 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals 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!!! perimeter area x 3.54 = 1.0 for circle = 1.13 for square Large for complex shape ArcGIS geodatabases contain automatic variables: shape.length: line length or polygon perimeter shape.area: polygon area Automatically updated after editing. For shapefiles, these must be calculated e.g. by opening attribute table and applying Calculate Geometry to a column (AV 9.2) Distances depend on projection. Perimeter to area ratio differs 22 )()( jijiij YYXXd −+−= 7 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals Spatial operations: Spatial Measurement SHAPE AREA PERIMETER CNTY_ CNTY_ID NAME FIPS Shape Index Polygon 0.265 2.729 2605 2605 Anderson 48001 1.50 Polygon 0.368 2.564 2545 2545 Andrews 48003 1.19 Polygon 0.209 2.171 2680 2680 Angelina 48005 1.34 Polygon 0.072 2.642 2899 2899 Aransas 48007 2.78 Polygon 0.233 1.941 2335 2335 Archer 48009 1.14 Polygon 0.233 1.941 2103 2103 Armstrong 48011 1.14 Polygon 0.299 2.278 2870 2870 Atascosa 48013 1.18 Polygon Polygon 0.224 1.900 2471 2471 Dallas 48113 1.13 Polygon 0.222 1.889 2481 2481 Dawson 48115 1.13 Polygon 0.368 2.580 2106 2106 Deaf Smith 48117 1.20 Polygon 0.072 1.421 2386 2386 Delta 48119 1.50 Area and Perimeter measures are automatically maintained in the attributes table for a Geodatabase or coverage. For a shapefile, you need to apply Calculate Geometry to an appropriate column in the attribute table (or convert to a geodatabase) . The shape index can be calculated from the area and perimeter measurements. (Note: shapefile and shape index are unrelated) 8 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals Spatial Measurement: Calculating the Area of a Polygon )/2YY ( )X-(X 2112 1i n + ∑ = 0 10 5 0 10 5 0 10 5 0 10 5 2,3 7,7 7,3 6,2 4,7 Area=(2 x 4)/2=4 Area=(3 x 4)=12 Area=(5 x 1)/2=2.5 5 0 10 5 5 0 10 5 = - A CB = - The actual algorithm used obtains the area of A by calculating the areas of B and C, and then subtracting. The actual formulae used is as follows: Its implementation in Excel is shown below. The area of the above polygon is 18.5, based on dividing it into rectangles and triangles. However, this is not practical for a complex polygon. Area of triangle = (base x height)/2 9 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals 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) 10 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals 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 centroid outside polygon n Y Y n X X n i i n i i ∑∑ == == 11 , Note: many ArcView applications calculate only a “psuedo” centroid: the coordinates of the bounding box (the extent) of the polygon Can be implemented via: ArcToolbox>Spatial Statistics Tools>Measuring Geographic Distributions>Mean Center [...]... 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) – • 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... UTDallas • 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 GISC 6381 GIS Fundamentals 34 Advanced Applications: Proximity Analysis Nearest Neighbor • • location (distance) relative to nearest neighbor ( points or polygon... Note: the definition of Union in GIS is a little different from that in mathematical set basin Drainage Basins Atlantic A theory In set theory, the union contains everything that belongs to any input set, but original set membership is lost In a GIS union, all original set memberships are Another example explicitly retained In set theory terms, the outcome 1 2 3 of the above would simply be: GIS Union... (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... 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:... variable recoding • • 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) Implement in ArcGIS via: – equal interval... UK Const Monarchy 20 Argentina Republic 10 Saudi Arabia Absolute Monarchy 15 Sweden Const Monarchy 45 Portugal Parliamentary Democracy Layer Attribute Table after Join GISC 6381 GIS Fundamentals 31 Single most common error in GIS Analysis intending a one to one join of attribute to spatial table getting a one to many join of attributes to spatial table Spatial After joining attribute to spatial data... the input coverage features that overlap with the erase coverage polygons GISC 6381 GIS Fundamentals 21 Example: Spatial Matching via Polygon-on-Polygon Overlay: Union Land Use a c b The two layers (land use & drainage basins) do G Gulf not have common boundaries GIS creates combined layer with all aA bA cA Combined layer possible combinations, bG aG cG permitting calculation of land use by drainage... 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 noncontiguous regions – original boundaries usually dissolved – usually ‘formal’ groupings Implement in ArcView 9 thru ArcToolbox>Generalization>Dissolve... phenomena (e.g zero, 32o) Standard Deviation -2 aggregating categories on a nominal (or ordinal) variable – pine and fir into evergreen -1 0 -.68 0 1 68 2 Equal interval score Equal area score No change in number of records (observations) 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals 29 Attribute Operations: record aggregation • • • • • • combining two or more records into one, based on common . Briggs, UTDallas GISC 6381 GIS Fundamentals Analysis and Modeling in GIS 2 07/07/14 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals GIS and the Levels of Science Description: Using GIS to create. 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. 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