1. Introduction to Geoinformatics L-9. Spatial Data Analysis
Dr. György SZABÓ associate professor
Budapest University of Technology and Economy
Department of Photogrammetry and Geoinformatics

2. Contents
OVERVIEW
This chapter is describing the geographic analysis and modeling methods. Examines methods constructed around the concepts of location, distance, and area.
LEARNING OBJECTIVES
Definitions of spatial data analysis .
Methods to examine distance effects, in the creation of clusters, hotspots, and anomalies.
Methods for measuring properties of areas.
Measures that can be used to capture the centrality of geographic phenomena.
Techniques for analyzing surfaces and for determining their morphologic properties.
Techniques for the support of spatial decisions and the design of landscapes according to specific objectives.
Longley, Goodchild, Maguire, Rhind (2011): Geographical Information Systems and Science
CH – 14. pp

3. What is spatial analysis?
Spatial analysis the engine of GIS because it includes all of the transformations, manipulations, and methods that can be applied to geographic data to add value to them, to support decisions, and to reveal patterns and anomalies that are not immediately obvious
Spatial analysis is the process by which we turn raw data into useful information

4. The first application of GIS in epidemiology
A redrafting of the map made by Dr. John Snow in 1854, showing the deaths that occurred in an outbreak of cholera in the Soho district of London
The first application of GIS in epidemiology

5. And the spatial analysis: Hypotesis: Source of the infection is the water > Broad street pump
Action: remove the Broad street pump head

6. Data sets: - location of the disease - Number of people at risk
The map made by Openshaw and colleagues by applying their Geographical Analysis Machine to the incidence of childhood leukemia in northern England.
A very large number
of circles of random sizes is randomly placed on the map, and a circle is drawn if the number of cases it encloses substantially exceeds the number expected in that area given the size of its population at risk
Data sets: - location of the disease
- Number of people at risk
(Source: International Journal of Geographical Information Systems)

7. Type of spatial analysis
Inductive: to examine empirical evidence in the search for patterns that might support new theories or general principles, in this case with regard to disease causation.
Deductive: focusing on the testing of known theories or principles against data
Normative: using spatial analysis to develop or prescribe new or better designs

8. Analysis of attributes
Selection of objects based on attribute values.
One way to examine this suspicion is to plot one variable against the other as a scatterplot.
Regression analysis focuses on finding the simplest relationship indicated by the data.
Relationships between variables can vary across space, which is an issue termed spatial heterogeneity (add thematic in Geomedia)

9. Geomedia-> Analysis->Attribute Query Cheap Pub (Price of beer =< 300 Ft
SQL script: SELECT <fields> FROM <tables> [WHERE <logical expressions>] [<grouping>] [<order by>];

10. A
Scatterplots of median house value (y axis) versus percent black (x axis) for U.S. counties in 1990, with linear regressions:
(A) California
(B) Mississippi B
(Source: U.S. Bureau of the Census)

11. Age-adjusted rates of mortality due to cancers of the trachea, bronchus, and lung, among white males between 1950 and 1969, by county

12. Geomedia: Legend ->Add Thematic Legend Entry Price level of pubs (cheap, medium, expensive)

13. Analysis of spatial properties
Topological relations:
Point in Polygon
Polygon Overlay
Spatial Joins
Analysis based on distance:
Measuring distance, length, area, peremiter
Buffering – point, line, area zone creation

14. The point in polygon problem, shown in the continuous-field case (the point must by definition lie in exactly one polygon, or outside the project area).
In only one instance (the orange polygon) is there an odd number of intersections between the polygon boundary and a line drawn vertically upward from the point.

15. Polygon overlay, in the discrete object case
Here the overlay of two polygons produces nine distinct polygons. One has the properties of both polygons, four have the properties of the yellow shaded polygon but not the blue (bounded) polygon, and four are outside the yellow polygon but inside the blue polygon.

16. Polygon overlay in the continuous-field case
Here a dataset representing two types of land cover (A on the left, B on the right) is overlaid on a dataset representing three types of ownership (the two datasets have been offset for visual clarity).

17. Geomedia: Analysis-> Spatial Query Topological relations of two object sets
The spatial relations:
TOUCH
COUNTAIN
ARE COUNTAINED BY
ENTIRELY CONTAIN
ARE ENTIRELY CONTAINED BY
OVERLAP
MEET
ARE SPATIALLY EQUAL
ARE WITHIN DISTANCE OF

18. Touch returns features that touch the defined features in any way-meeting, overlapping, containing, or being contained by.
Touch
with the Not qualifier
Contain returns features that surround defined features. Contained features can touch but not overlap the borders of the surrounding features. Points cannot contain other features.
Contain
with the Not qualifier

19. Are contained by returns features that fall completely within the defined features. Contained features can touch but not overlap the borders of the surrounding features.
Are contained by
with the Not qualifier
Entirely contain returns features that surround defined features. Contained features cannot touch or overlap the borders of the surrounding features. Points cannot entirely contain other features..
Entirely contain
with the Not qualifier

20. Overlap returns features that overlap the defined features.
Are entirely contained by returns features that fall completely within the defined features. Contained features cannot touch or overlap the borders of the surrounding features.
Are entirely contained by
with the Not qualifier
Overlap returns features that overlap the defined features.
Overlap
with the Not qualifier

21. Meet returns features that fall next to the defined features, touching without overlapping.
with the Not qualifier
Are spatially equal returns features that occupy the same space and location. Features must be of the same type to be spatially equal.
Are spatially equal
with the Not qualifier

22. Are within distance of returns features having any part located within the specified distance of the defined features. If either the starting or ending point of a linear feature, for example, falls within the specified distance, it is returned.
Are within distance of
with the Not qualifier

23. Spatial Intersection allows you to perform a spatial overlay on two feature classes or queries to find the intersecting areas, or areas of coincidence.
Original
After Spatial Intersection
The spatial operators available for this command are touch, contain, are contained by, entirely contain, are entirely contained by, overlap, meet, and are spatially equal. After you choose the two sets of input features to intersect and the type of spatial operation to perform, this command outputs the results as a new query.

24. Spatial Difference allows you to perform spatial masking, that is, to perform a difference operation on two sets of areas to produce resultant geometries.
This command takes as input two area feature classes or queries, the features to be masked or cropped (the from-feature), and the features to be used as a mask (the subtract-feature).

25. Geomedia -> Tools -> Validate Geometry, ->Validate Connectivity
Validate geometry: checking the point, line, area feature geometry consistency in a feature class
Validate connectivity: checking the topological relations of one feature class or between two feature groups

26. Geometry Validation Error Conditions

27. Validating Connectivity
Overshoot
This condition occurs when the end of a linear geometry extends beyond the point at which it should intersect with, and stop at, another geometry.
Undershoot
This condition occurs when the end of linear geometry or a point geometry falls short of intersecting another geometry.
Node Mismatch
This condition occurs when the end of a linear or point geometry falls short of intersecting with the end of another linear or point geometry.

28. Examples of Connectivity Conditions by Feature Class
Nearly Coincident
Overshoot
Node Mismach
Undershoot Node Mismach
Intersections Not
Coincident
Intersection Not Broken

29. Pythagoras’s Theorem and the straight-line distance between two points on a plane

30. The effects of the Earth’s curvature on the measurement of distance, and the choice of shortest paths

31. The length of a path as traveled on the Earth’s surface (red line) may be substantially longer than the length of its horizontal projection as evaluated in a two-dimensional GIS
(A) shows three paths across part of Dorset in the UK. The green path is the straight route, the red path is the modern road system, and the gray path represents the route followed by the road in 1886
(Courtesy Michael De Smith)

32. (Courtesy Michael De Smith)
(B) Shows the vertical profiles of all three routes, with elevation plotted against the distance traveled horizontally in each case. 1 ft m, 1 yd m.

33. Geomedia: Edit-> Attribute ->Update Attribute Static measurement of feature geometry: Line - LENGTH(Input.Geometry) Area - AREA(Input.Geometry), PERIMETER(Input.Geometry)

34. Buffers (dilations) of constant width drawn around a point, a polyline, and a polygon

35. Geomedia: Analysis-> Buffer Zone 100 m Buffer Zone of Pubs

36. Terrain surface representation and analysis
Digital Contourline Model (DCM),
Digital Surface Model (DSM),
Digital Elevation Model (DEM),
Digital Terrain Model (DTM)

37. Surface representation: 2, 2.5, 3D
DEM
DCM
DTM
DSM

38. Examples of applications that use the TIN data model
Landslide risk map for Pisa, Italy (Courtesy of Earth Science Department, University of Siena, Italy)
(B) Yangtse River, China
(Courtesy of Human Settlements Research
Center, Tsinghua University, China)

39. Sampling of Terrain Random: stochastic elements Systematic:
Homogenious (regular grid)
Inhomogenious (charasteristic points, break lines, form lines, extremal points)

40. Grid model
Systematic grid, or raster of spot height with constant density
Creation: direct measurement, derivation
Type: Grid, Cell, Point cloud
Advantage: easy representation and storage in matrix form
Disadvantage: heterogeneous terrain - > week representation or too much points

41. Grid interpolation Approximation: Linear Bilinear 2nd order 3rd order
Spline

42. TIN model Triangulated Irregular Network
Formation: Delaunay triangulation (dual definition - Voronoi Diagram): nearly equal side triangle structure
Advantage: more characteristics, represented the morphology of the real terrain forms
Disadvantage: complex structure, large storage and computational requirements

43. TIN Topology

44. TIN surface of Death Valley, California
“wireframe” showing all triangles
(B) shaded by elevation
(C) draped with satellite image

45. Tivadar – 2D contour line map

46. Tivadar – Digital Surface Model

47. Tivadar – Digital Terrain Model

48. Complex Model: Simulation of Bereg dam damage - 107m water level

49. Complex networks
Connections
Rules
Attributes

50. Model for movement over surfaces
Representation of route location on raster data
Complex surface representation of phenomena: water flow, drainage

51. Search for the best locations for a central facility to serve dispersed customers
the problem is solved in continuous space, with straight-line travel, for a warehouse to serve the 12 largest U.S. cities. In continuous space there is an infinite number of possible locations for the site.
a similar problem is solved at the scale of a city neighborhood on a network, where Hakimi’s theorem states that only junctions (nodes) in the network and places where there is weight need to be considered, making the problem much simpler, but where travel must follow the street network.

52. GIS can be used to find locations for fire stations that result in better response times to emergencies
(PhotoDisc/Getty Images)

53. Screenshot of the system used by drivers for Sears to schedule and navigate a day’s workload

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