Intro to Spatial Analysis

1. Intro to Spatial Analysis • Most GIS support simple spatial analysis tasks such as selecting, counting, and generating descriptive statistics such as mean and standard deviation • More sophisticated spatial analysis (e.g. regression, analysis of spatial relationships between objects, etc.) often necessitate linking to other software (e.g. a statistical package) and/or significant programming by the user

2. Intro to Spatial Analysis • Finding and returning information about an object • what objects have a certain attribute value? • what is the attribute value of a certain object? • What locations have a certain attribute value? • What is the attribute value at a certain location?

3. Intro to Spatial Analysis • Basic spatial properties of objects (besides location) • Point • Line • length • orientation • sinuosity • Polygon • area • perimeter • shape • eccentricity (elongation) • orientation

4. Measurement • Vector Line Length • Length of straight line calculated by pythagorean theorem using beginning and ending point locations • length of a curvillinear line calculated by adding lengths of individual line segments • Raster Line Length • Number of grid cells x length of grid cell • Can incorporate greater distance for diagonal orientation

5. Measurement • Sinuosity of a Line Length of line A ------------------- Length of line B A B

6. Measurement • Vector Polygon Area • Break complex polygon into simpler geometric shapes such as right triangles and rectangles whose area can be calculated • Raster Region Area • Count number of grid cells with certain attribute value • May have to define a separate raster layer to find areas of contiguous regions of a certain attribute value

7. Measurement Hole or island • Regions: Vector Fragmented region Perforated region Contiguous region

8. Measurement • Regions: Vector Vector data layer that describes agricultural land cover Polygons B and C and not agricultural land but they are polygons and still appear in the relational table Poly ID Crop A corn B C B A C Perforated region

9. Measurement • Regions: Vector Vector data layer that describes countries Polygons A, B, and C are islands that compose one country, but in relational table each polygon is a separate record Poly ID country A Fragmentland B Fragmentland C Fragmentland A C B Fragmented region

10. 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 Measurement • Regions: Raster No way to distinguish between contiguous, fragmented, and perforated regions unless we explicitly attribute each grid cell as part of a contiguous region

11. 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 Measurement 0 - Meadow 1 - Forest • Raster Region Area How many grid cells where value = 1

12. 0 0 0 0 0 0 2 1 2 1 0 0 0 0 0 0 1 2 1 2 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 Measurement 0 - Meadow 1 - Forest stand 1 2 - Forest stand 2 • Calculating Raster Region Area for each individual contiguous region 0 - Meadow 1 - Forest reclassify How many grid cells where value = 1 How many grid cells where value = 2

13. 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 Measurement • Calculating Vector Polygon Perimeter • calculate lengths of all component lines • Calculating Raster Region Perimeter • find ‘boundary’ grid cells • calculate lengths of all component ‘lines’

14. Measurement • Calculating Polygon Eccentricity Length of A -------------- Length of B B A

15. Measurement • Calculating Distance • Simple distance assumes an isotropic surface in Euclidean space • Functional distance incorporates ‘cost’

16. Measurement • Calculating Simple Distance • Between 2 points • Pythagorean theorem • Between 2 polygons • measure distance between centroids using Pythagorean theorem • measure distance between polygons bounding box

17. 2 2 2 2 2 2 1 1 1 2 2 1 0 1 2 2 1 1 1 2 2 2 2 2 2 Measurement • Calculating Simple Distance in Raster • Raster ‘spread’ operation defines a raster of distance from a point or many points

18. 1 2 3 3 2 1 2 3 3 2 1 1 1 2 2 1 3 2 2 1 3 3 3 3 1 Measurement • Calculating Functional Distance in Raster • raster ‘friction’ surface defines impedance value at each grid cell • relative barriers • absolute barriers Difficulty for tank travel 1 - open land (no impedance) 2 - small trees (relative barrier) 3 - large trees (absolute barrier)

19. Measurement • Calculating a Least Cost Path in Raster • choose a starting point and search nearest neighbors for easiest route

20. Measurement • Calculating a Least Cost Path in Raster • accumulated cost from one point to each cell in the grid to find least cost path between two points Cost surface Accumulated cost From 4,4 to 2,2 0.5 (1.4 x 1) = 0.7 0.5 (1.4 x 3) = 2.1 + (prev val) 1.4 4.2 1 1 3 1 4.8 3.8 4.4 3 1 3 1 1 3.8 4.2 2.4 2 3 1 1 1 4.4 2.4 1.4 1 1 1 1 1 3 2 1 0

21. Measurement • Least Cost Path Can be Applied to Vector Networks • each line has a cost associated with it • to find a least cost path between two points is exhaustive (must try all paths before determining the shortest) and therefore time consuming • costs on a street network include speed limit, traffic lights, stop signs, dead ends, cul de sacs, wait to make a left turn at a busy intersection, etc.