2. 1 Spatial Analysis in GIS EAA 502 MSc. Course Lecture 3 Dr Mohd Sanusi

3. 2 What is spatial analysis? What is spatial analysis? n Methods for working with spatial data –to detect patterns, anomalies –to find answers to questions –to test or confirm theories »deductive reasoning –to generate new theories and generalizations »inductive reasoning n "a set of methods whose results change when the locations of the objects being analyzed change"

4. 3 What is Spatial Analysis (cont.) n Methods for adding value to data –in doing scientific research –in trying to convince others n Turning raw data into useful information n A collaboration between human and machine –Human directs, makes interpretations and inferences –Machine does tedious, complex stuff

5. 4 Objectives of Spatial Analysis n Queries and reasoning n Measurements –Aspects of geographic data, length, area, etc. n Transformations –New data, raster to vector, geometric rules n Descriptive summaries –Essence of data in 1 or 2 parameters n Optimization - ideal locations, routes n Hypothesis testing - sample to entire pop.

6. 5 Types of Spatial Analysis n Retrieval (spatial query) / reclassification / measurement n Overlay operations with polygons, lines, points n Neighbourhood operations: –search, interpolation,contouring, thiessen polygons, surface generation n Connectivity functions: –contiguity measures, network analysis, spread and seek functions, intervisibility

7. Classes GIS Spatial Analytical Operations

8. 1. Reclassifying Maps

9. 2. Overlaying Maps

10. 9

11. 10 Operations n Raster Overlay faster than vector overlay

12. 11 Operations n Vector overlay –calculate new nodes, arcs and polygons

13. 12 3. Transformations n BUFFERING n POINT IN POLYGON n POLYGON OVERLAY n SPATIAL INTERPOLATION n DENSITY ESTIMATION Produce new objects and data sets from existing objects and data sets

14. 13Buffering n buffering takes points, lines, or areas and creates areas n every location within the resulting area is either: –in/on the original object –within the defined buffer width of the original object

15. Buffering to Find Regions The overlay of the 60m buffer with the parcels helps to identify which parcels are selected.

16. 15 Applications n find all areas of National Forest beyond 1 km from a road n find all households within 1 km of a proposed new freeway –and send them notification of proposal n find all cyber cafe within 500m of a school –and notify them of a proposed change in the law

17. 16 Variants n vary the object's buffer width according to an attribute value –e.g. noise buffers depending on road traffic volume n vary the rate of spread according to a friction field

18. 17 Point-in-Polygon n Determine whether a given point lies inside or outside a given polygon –assign a set of points to a set of polygons –e.g., count numbers of accidents in counties –e.g., whose property does this phone pole lie in? n Algorithm –draw a line from the point to infinity –count intersections with the polygon boundary –inside if the count is odd –outside if the count is even

19. 18 Point-in-Poly Algorithm n inside if the count is odd n outside if the count is even n what if the point lies on the boundary?

20. 19 4. Spatial Measurement n often difficult to make by hand from maps –measuring the length of a complex feature –measuring area –how did we measure area before GIS? n Distance and length –calculation from metric coordinates –straight-line distance on a plane

21. 20 Distance (cont.) n Simplest distance calculation in GIS n d = sqrt ((x 1 -x 2 ) 2 +(y 1 -y 2 ) 2 ) - works for lat/long??

22. 21 Distance (cont.) n GIS needs more complex spherical calculations n distance on a spherical Earth n from (lat 1,long 1 ) to (lat 2,long 2 ) n R is the radius of the Earth, roughly 6378 km n d = R cos -1 [sin lat 1 sin lat 2 + cos lat 1 cos lat 2 cos (long 1 - long 2 )]

23. 22 Length n add the lengths of polyline or polygon segments n Two types of distortions (1) if segments are straight, length will be underestimated in general

24. 23 Length (cont.) n Two types of distortions (2) line in 2-D GIS on a plane considerably shorter than 3-D Area of land parcel based on area of horiz. projection, not true surface area

25. 24 Area n how to measure area of a polygon? n proceed in clockwise direction around the polygon n for each segment: –drop perpendiculars to the x axis –this constructs a trapezium –compute the area of the trapezium –difference in x times average of y –keep a cumulative sum of areas

26. 25 Area (cont.) n Green, orange, blue trapezia n Areas = differences in x times averages of y n Subtract 4th to get area of poly

27. 26 Algorithm n when might the algorithm fail? –“islands” must all be scanned clockwise –“holes” must be scanned anticlockwise –holes have negative area n Wrong result if area is very small and the coordinate values are very large (UTM) n need double precision for calculations but not for results! Area of poly - a “numerical recipe” a set of rules executed in sequence to solve a problem

28. 27 Applying the Algorithm to a Coverage n keep running total for each polygon n for each arc: n proceed segment by segment from FNODE to TNODE n add trapezia areas to R polygon area n subtract from L polygon area n on completing all arcs, totals are correct area are correct area

29. 28 Shape n how to measure shape of an area? n a compact shape has a small perimeter for a given area n compare perimeter to the perimeter of a circle of the same area n shape = perimeter / [3.54 sqrt (area)]

30. 29 What Use are Shape Measures? n “Gerrymandering” –creating oddly shaped districts to manipulate the vote –named for Elbridge Gerry, governer of MA and signatory of the Declaration of Independence –today GIS is used to design districts After 1990 Census