1. Elementary Spatial Analysis GEOG 370 Instructor: Christine Erlien

2. Overview Spatial Analysis Flowcharting Query Defining spatial characteristics Higher-level objects –Centroids –Nodes –Boundaries –Networks –Regions

3. Spatial Analysis Spatial analysis: Way in which we turn raw data into useful information –A set of techniques whose results are dependent on the locations of the objects being analyzed –Variety of methods –Powerful computers –Intelligent users

4. Preparing a Spatial Analysis: Flowcharting Flowchart tools provided by: ESRI’s Model Builder, ERDAS’s GIS Modeler, etc.) Objective – systematizing thinking and documenting procedures about a GIS application/project InputOutput Operation (Plus conditions) General form of most GIS flowcharts: From Fundamentals of Geographic Information Systems, Demers (2005)

5. GIS Data Query Important, useful tool associated with DBMS Why? –Narrowing down information –Better understanding of map Complexity How entities of interest spatially related to other data layers –Ability to make further measurements, comparisons Total numbers  relative numbers (e.g., density) What might you want to know? –Which features occur most often –How often they occur –Where are they located?  spatial pattern

6. GIS Data Query What is it? –Using tools to find records meeting specific criteria How? –Select criteria –Use operators to define expression Simple Complex And: Intersection of sets Ex.: ([area] > 1500) and ( [b_room] > 3) Or: Union of sets Ex: ([age] 65) Not: Subtracts one set from another set Ex.: ([sub_region] = "N Eng") and ( not ( [state_name] = "Maine"))

7. Successive Querying Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University

8. Examining vector entities’ attributes –Check spatial objects’ properties Using identify tool Using find tool Performing queries GIS Data Query: Vector

9. GIS Data Query: Raster Examining raster attributes –Unique colors assigned to attribute values –Tabulating results  # of grid cells in each category For those interested in landscape ecology  fragmentation statistics

10. Raster Data Query: Fragmentation Statistics Landscape Composition –Proportional Abundance of each Class –Richness: Number of different patch types –Evenness: Relative abundance of different patch types Landscape Configuration –Patch size distribution and density –Patch shape complexity –Isolation/Proximity See Fragstats website: http://www.umass.edu/landeco/research/fragstats/fragstats.html

12. Defining Spatial Characteristics: Points Nominal, Ordinal, Interval/ratio data Define, separate, retrieve on the basis of: –Category –Class –Magnitude Examining classes of data & the individuals within each class –Distance between features in same category, class –Distribution: Clustered vs. random or regular Examining relationships between point objects & other objects

13. Dr. John Snow & the Cholera Map http://en.wikipedia.org/wiki/Image:Snow-cholera-map.jpg

14. http://www.unl.edu/nac/conservation/atlas/Map_Html/Demographics/National/Minority_Operated_Farms/1997.htm

16. Defining Spatial Characteristics: Lines Define, separate, retrieve on the basis of: –Category –Class –Magnitude Single line entity –Attribute values may change along length Lines in relation to their surroundings –Easiest in vector, using topological data Length, Azimuthal direction, Shape/sinuosity –For entire line or its individual segments

17. http://forest.mtu.edu/staff/mdhyslop/gis/sinuosity.html Sinuosity information is used in developing stream classifications Defining Spatial Characteristics: Lines

18. http://clerk.ci.seattle.wa.us/~ordpics/115137At10TRFigA4.gif

19. Defining Spatial Characteristics: Areas Define, separate, retrieve on the basis of: –Category –Class –Magnitude Shape: Deviation from particular geometry (e.g., circle or square) Elongation: Ratio between long & short axes Orientation Size  perimeter, area, length Contiguity: Measure of wholeness (vs. perforation) Heterogeneity: Measure of how much map area is in contact with polygonal features sharing same attributes

20. Defining Spatial Characteristics: Areas Major axis Along longest part of polygon Must divide polygon in two equal parts Minor axis Along shortest part of polygon Must divide the polygon in two equal parts Major axis / Minor axis ratio Values > 1 denote elongated polygon Value = 1 denotes uniform polygon Major axis Minor axis 1.5 2.5 R = 1 3.5 R = 2.33 2.5 Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University

21. Defining Spatial Characteristics: Areas Perimeter –Length of all segments of closed polygon –Length of the contact surface of a feature with other features Lake shoreline Fence Area Perimeter Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University

22. Defining Spatial Characteristics: Areas Shape Perimeter to Area Ratio –perimeter/area –Expression of the geographical complexity of a polygon High ratio  complex Low ratio  simple Area = 25 sqr miles Perimeter = 7 miles CI = 7 / 25 = 0.28 Area = 25 sqr miles Perimeter = 15 miles CI = 15 / 25 = 0.60 Graphic: Dr. Jean-Paul Rodrigue, Dept. of Economics & Geography, Hofstra University

23. Higher Level Objects Higher-level objects: Need to be determined rather than being encoded through digitizing Types –Points –Lines –Areas

24. Higher-level Point Objects Types –Centroids –Nodes Centroid: Indicates geographic center of polygon –Simplest to calculate for simple shapes (e.g., rectangle, circle) –Not well-suited to raster –Calculated using the trapezoidal rule Polygon separated into overlapping polygons Each polygon’s centroid calculated, then weighted- average calculated

25. From Fundamentals of Geographic Information Systems, Demers (2005) Higher-level Point Objects: Centroids

26. Types of Centroid: –Simple centroid: Absolute geographic center of polygon –Center-of-gravity centroid (mean center): Central point of distribution –Weighted mean center: Centroid calculated on basis of location & associated weighting factor

27. From Fundamentals of Geographic Information Systems, Demers (2005) Centroid Types

28. Centroid Types: Mean Center Mean Center (Center of gravity) Average individual X &Y coordinates for all points in the coverage/layer Result: Single pair of X, Y values representing the central point of distribution From Fundamentals of Geographic Information Systems, Demers (2005)

29. Centroid Types: Weighted Mean Center Characteristics from attribute table used as additional weighting factor Weighting factor –Each X, Y coordinate multiplied by a weight –Weighted mean center derived from sum of weighted coordinates divided by number of points

30. From Fundamentals of Geographic Information Systems, Demers (2005) Centroid Types: Weighted Mean Center

31. Higher-level Point Objects: Nodes Locators along line & area entities Generally encoded during input –Difficulties arise when coded as point rather than node Used to isolate line segments

32. Higher-level Line Objects Types –Boundaries/borders: Major change in single or multiple attribute values as move across –Networks: Interconnected line entities whose attributes share a common theme related to flow

33. Higher-level Line Objects: Networks Types: –Straight line network –Branching network –Circuit Networks can be directed or undirected –Directed: Flows move only in a single direction –Undirected: Flows can go back and forth along the network in either direction If attribute data are lacking  limits ability to use linear features as higher-level objects

34. From Fundamentals of Geographic Information Systems, Demers (2005)

35. Higher-level Area Objects Regions: Areas of uniform content within a coverage –Homogeneous sets or homogeneous combinations of factors –Types: Contiguous: Wholly contained in a single polygon Fragmented: Comprised of more than 1 polygonal form separated by intervening space that doesn’t share same attributes Perforated: Uniform polygon interspersed with smaller polygons not sharing the same mix of attributes –Region: Matrix –Perforations: Smaller internal polygons that don’t share same attributes

36. Higher-level Area Objects From Fundamentals of Geographic Information Systems, Demers (2005)

37. Wrapping up: You should know The purpose of flowcharting The why & how of using attributes in search/query What higher-level attributes are & what they can be used for –Centroids –Nodes –Boundaries –Networks –Regions