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Geographical analysis
Overlay, cluster analysis, autocorrelation, trends, models,
network analysis, terrain analysis
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?)
Example overlay
• Two subdivisions with labeled regions
soil
Soil
Soil
Soil
Soil
vegetation
type
type
type
type
1
2
3
4
Birch forest
Beech forest
Mixed forest
Birch forest
on soil type 2
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
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
Result of overlay
• New subdivision or map layer, e.g. for
further processing
• Table with combined data
• Count, surface area
Soil
Type
Type
Type
Type
….
1
2
3
4
Vegetation
Area
Beech
Birch
Mixed
Beech
….
30
15
8
2
ha
ha
ha
ha
#patches
2
2
1
1
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
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
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
Overlay in vector
• E.g. the plane sweep algorithm as given in
Computational Geometry (line segment
intersection)
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
Elevation
Annual precipitation
Types of rock
Overlay: partitioning
based on the three themes
Analysis point set
• Points in an attribute space: statistics, e.g.
regression, principal component analysis,
dendrograms
(area, #population, #crimes)
(12, 34.000,
(14, 45.000,
(15, 41.000,
(17, 63.000,
(17, 66.000,
……
……
#crimes
#population
34)
31)
14)
82)
79)
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
For example: craters in a region; crimes in a city
Analysis point set
• Points in geographical space with value: autocorrelation (~ up to what distance are measured
values “similar”, or correlated).
11 10
12
13
12
19
14
16
18
21
21
20
22
17
15
16
n points 
(n choose 2) pairs;
each pair has a
distance and a
difference in value
difference 2
Average
difference 2
 observed
expected
2
difference
distance
Classify distances and
determine average per class
distance
Observed variogram
Average
2
difference
 observed
expected
2
difference
Model variogram (linear)
σ
distance
sill
2
range
distance
Smaller distances 
more correlation, smaller variance
Importance auto-correlation
• Descriptive statistic of a data set
• Interpolation based on data further away than
the range is nonsense
11
10
12
20
13
16
14
??
21
16
19
18
21
range
12
22
15
17
Analysis subdivision
• Nominal subdivision: auto-correlation
(~ clustering of equivalent classes)
• Ratio subdivision: auto-correlation
PvdA
CDA
VVD
Auto-correlation
No auto-correlation
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
PvdA
CDA
VVD
• E(CDA adj. PvdA) = 5.33; reality
once
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)
Geographical models
• Functions of models:
- psychological (for understanding,
visualization)
- organizational (framework for definitions)
- explanatory
- constructive (beginning of theories, laws)
- communicative (transfer scientific ideas)
- predictive
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
Forest fire
Wind, speed 3
Forest; burn factor 0.8
Heath; burn factor 0.6
Road; burn factor 0.2
Museum
Soil
humidity
Origin
< 3 minutes
< 6 minutes
< 9 minutes
> 9 minutes
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)
Network analysis
• When distance or travel time on a network
(graph) is considered
• Dijkstra’s shortest path algorithm
• Reachability measure: potential value
potential (i )   d c

j ij
j
d j = weight origin j
 = distance decay parameter
c ij= distance cost between
origin j and destination i
Example reachability
• Law Ambulance Transport: every location
must be reachable within 15 minutes (from
origin of ambulance)
Example reachability
• Physician’s practice:
- optimal practice size: 2350 (minimum: 800)
- minimize distance to practice
- improve current situation with as few changes
as possible
Current
situation: 16
practices,
30.000 people,
average 1875
per practice
Computed,
improved
situation: 13
practices
Example in table
Original
New
16
13
Number of practice locations
9
7
Number of practices < 800 size
2
0
3957
4624
Average travel distance (km)
0,9
1,2
Largest distance (km)
5,2
5,4
Number of practices
Number of people > 3 km
Analysis elevation model
• Landscape shape
recognition:
- peaks and pits
- valleys and ridges
- convexity, concavity
• Water flow, erosion,
watershed regions,
landslides, avalanches