1. Geographical analysis
Overlay, cluster analysis, auto-correlation, trends, models, network analysis, terrain analysis

2. Geographical analysis
Combination of different geographic data sets or themes by overlay or statistics
Discovery of patterns, dependencies
Discovery of trends, changes (time)
Development of models
Interpolation, extrapolation, prediction
Spatial decision support, planning
Consequence analysis (What if?)

3. Example overlay Two subdivisions with labeled regions soil vegetation
Soil type 1 Soil type 2 Soil type 3
Soil type 4
Birch forest
Beech forest
Mixed forest
Birch forest on soil type 2

4. Kinds of overlay
Two subdivisions with the same boundaries - nominal and nominal Religion and voting per municipality - nominal and ratio Voting and income per municipality - ratio and ratio Average income and age of employees
Two subdivisions with different boundaries Soil type and vegetation
Subdivision and elevation model Soil type and precipitation

5. Kinds of overlay, cont’d
Subdivision and point set quarters in city, occurrences of violence on the street
Two elevation models elevation and precipitation
Elevation model and point set elevation and epicenters of earthquakes
Two point sets money machines, street robbery locations
Network and subdivision, other network, elevation model

6. Result of overlay
New subdivision or map layer, e.g. for further processing
Table with combined data
Count, surface area
Soil Vegetation Area #patches
Type 1 Beech 30 ha 2
Type 2 Birch 15 ha 2
Type 3 Mixed ha 1
Type 4 Beech 2 ha 1
…. ….

7. Buffer and overlay
Neighborhood analysis: data of a theme within a given distance (buffer) of objects of another theme
Sightings of nesting locations of the great blue heron (point set)
Rivers; buffer with width 500 m of a river
Overlay  Nesting locations great blue heron near river

8. Overlay: ways of combination
Combination (join) of attributes
One layer as selection for the other Vegetation types only for soil type 2 Land use within 1 km of a river

9. Overlay in raster
Pixel-wise operation, if the rasters have the same coordinate (reference) system
Pixel-wise
AND
Forest
Population increase
above 2% per year
Both

10. Overlay in vector
E.g. the plane sweep algorithm as given in Computational Geometry (line segment intersection)

11. Combined (multi-way) overlays
Site planning, new construction sites depending on multiple criteria
Another example (earth sciences): Parametric land classification: partitioning of the land based on chosen, classified themes

12. Elevation
Annual precipitation

13. Types of rock
Overlay: partitioning based on the three themes

14. Analysis point set
Points in an attribute space: statistics, e.g. regression, principal component analysis, dendrograms
(area, #population, #crimes)
(12, , 34) (14, , 31) (15, , 14) (17, , 82) (17, , 79) …… ……
#crimes
Een regressielijn minimaliseert de som van de kwadraten van de vertikale afstanden van de (rode) datapunten tot de (blauwe) regressielijn. Bij principale componentenanalyse wordt de richting gezocht waarin de meeste variantie voorkomt. Een dendrogram is een hierarchische opdeling van de data gebaseerd op een vergelijkingsmaat van twee objecten.
#population

15. Analysis point set
Points in geographical space without associated value: clusters, patterns, regularity, spread
Actual average nearest
neighbor distance versus expected Av. NN. Dist. for this number of points in the region
Werkelijke average nearest neighbor distance kan met behulp van Voronoi diagrammen in O(n log n) tijd bepaald worden. De verwachte average nearest neighbor distance kan met behulp van Monte Carlo simulatie benaderd worden.
For example: craters in a region; crimes in a city

16. Analysis point set
Points in geographical space with value: auto-correlation (~ up to what distance are measured values “similar”, or correlated). 11 10 12 12
n points  (n choose 2) pairs; each pair has a distance and a difference in value 13 19 21 14 20 16 22 17 18 16 21 15

17. Classify distances and determine average per class2
difference
Average difference  observed expected difference 2 2
distance
distance
Classify distances and determine average per class

18. Model variogram (linear)
Observed variogram
Model variogram (linear)
Average difference  observed expected difference 2
sill 2
distance
distance
range
Smaller distances  more correlation, smaller variance

19. Importance auto-correlation
Descriptive statistic of a data set
Interpolation based on data further away than the range is nonsense 11 10 12
range 13 20 16 21 ?? 14 16 22 17 19 18 12 21 15

20. Analysis subdivision
Nominal subdivision: auto-correlation (~ clustering of equivalent classes)
Ratio subdivision: auto-correlation
PvdA
CDA
VVD
Auto-correlation
No auto-correlation

21. Auto-correlation, nominal subdivision
22 neighbor relations among provinces
Pr(VVD adj. VVD) = 4/12 * 3/11
E(VVD adj. VVD) = 22 * 12/132 = 2
Reality: 4 times
E(CDA adj. PvdA) = 5.33; reality once
PvdA
CDA
VVD

22. Geographical models
Properties of (geographical) models: - selective - approximative (simplification, more ideal) - analogous (resembles reality) - structured - suggestive (usable, analyzable, transformable) - re-usable (usable in related situations)

23. Geographical models
Functions of models: - psychological (for understanding, visualization) - organizational (framework for definitions) - explanatory - constructive (beginning of theories, laws) - communicative (transfer scientific ideas) - predictive

24. Example: forest fire
Is the Kröller-Müller museum well enough protected against (forest)fire?
Data: proximity fire dept., burning properties of land cover, wind, origin of fire
Model for: fire spread
Time neighbor pixel on fire: [1.41 *]
b * ws * (1- bv) * (0.2 + cos )
b = burn factor
ws = wind speed
 = angle wind – direction pixel bv = soil humidity

25. Forest fire Wind, speed 3 Soil humidity Origin Forest; burn factor 0.8
< 3 minutes < 6 minutes < 9 minutes > 9 minutes
Forest; burn factor 0.8
Heath; burn factor 0.6
Road; burn factor 0.2
Museum

26. Forest fire model
Selective: only surface cover, humidity and wind; no temperature, seasonal differences, …
Approximative: surface cover in 4 classes; no distinction in forest type, etc., pixel based so direction discretized
Structured: pixels, simple for definition relations between pixels
Re-usable: approach/model also applies to other locaties (and other spread processes)

27. Network analysis
When distance or travel time on a network (graph) is considered
Dijkstra’s shortest path algorithm
Reachability measure: potential value
d = weight origin j  = distance decay parameter
c = distance cost between origin j and destination i j ij

28. Example reachability
Law Ambulance Transport: every location must be reachable within 15 minutes (from origin of ambulance)

29. Example reachability
Physician’s practice: - optimal practice size: 2350 (minimum: 800) - minimize distance to practice - improve current situation with as few changes as possible

30. Current situation: 16 practices, 30
Current situation: 16 practices, people, average 1875 per practice
Computed, improved situation: 13 practices

31. Example in table Original New Number of practices 16 13
Number of practice locations
Number of practices < 800 size
Number of people > 3 km
Average travel distance (km) 0, ,2
Largest distance (km) 5, ,4

32. Analysis elevation model
Landscape shape recognition: - peaks and pits - valleys and ridges - convexity, concavity
Water flow, erosion, watershed regions, landslides, avalanches