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 A B Length of line A ------------------- Length of line 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 Regions: Vector Contiguous region Fragmented region Perforated region Hole or island

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

9. Measurement Regions: Vector Poly ID country A Fragmentland B Fragmentland C Fragmentland 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 Fragmented region A B C

10. Measurement Regions: Raster 0 11 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 No way to distinguish between contiguous, fragmented, and perforated regions unless we explicitly attribute each grid cell as part of a contiguous region

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

12. Measurement Calculating Raster Region Area for each individual contiguous region 0 11 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 - Meadow 1 - Forest How many grid cells where value = 1 0 11 1 1 0 0 1 1 0 0 0 0 1 0 0 2 2 0 0 0 2 2 0 0 0 - Meadow 1 - Forest stand 1 2 - Forest stand 2 How many grid cells where value = 2 reclassify

13. 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’ 0 11 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0

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

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. Measurement Calculating Simple Distance in Raster –Raster ‘spread’ operation defines a raster of distance from a point or many points 2 12 2 2 2 1 1 2 2 2 0 1 2 1 2 2 2 2 2 1 2 1 1 2

18. Measurement Calculating Functional Distance in Raster –raster ‘friction’ surface defines impedance value at each grid cell –relative barriers –absolute barriers 1 11 1 3 2 2 3 3 1 3 1 2 3 3 2 2 2 1 1 2 3 3 2 3 1 - open land (no impedance) 2 - small trees (relative barrier) 3 - large trees (absolute barrier) Difficulty for tank travel

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 1 1 3 1 3 1 1 1 1 1 1 1 1 3 1 1 3.8 4.8 4.4 3 4.2 2.4 2 3.8 2 3 1 0 2.4 4.4 1.4 1 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 Cost surfaceAccumulated cost

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.