Geographical analysis

Overlay, cluster analysis, auto-correlation, 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 type 1Soil type 2Soil type 3Soil type 4

Birch forestBeech forestMixed forest

Birch forest on soil type 2

soil vegetation

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 boundariesSoil type and vegetation

• Subdivision and elevation modelSoil type and precipitation

Kinds of overlay, cont’d

• Subdivision and point setquarters in city, occurrences of violence on the street

• Two elevation modelselevation and precipitation

• Elevation model and point setelevation and epicenters of earthquakes

• Two point setsmoney 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 Vegetation Area #patches

Type 1 Beech 30 ha 2Type 2 Birch 15 ha 2Type 3 Mixed 8 ha 1Type 4 Beech 2 ha 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 2Land use within 1 km of a river

Overlay in raster

• Pixel-wise operation, if the rasters have the same coordinate (reference) system

Forest Population increaseabove 2% per year

Pixel-wiseAND

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)

#population

#crimes (12, 34.000, 34)(14, 45.000, 31)(15, 41.000, 14)(17, 63.000, 82)(17, 66.000, 79) …… ……

Analysis point set

• Points in geographical space without associated value: clusters, patterns, regularity, spread

Actual average nearestneighbor 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: auto-correlation (~ up to what distance are measured values “similar”, or correlated).

2014

13

1012

11

16

18

2115

17

16

22

2119

12 n points (n choose 2) pairs;each pair has a distance and a difference in value

distance

difference

distance

Classify distances and determine average per class

Averagedifference observed expected difference

2

2

2

distance distance

sill

range

2σ

Observed variogram Model variogram (linear)

Smaller distances more correlation, smaller variance

Averagedifference observed expected difference

2

2

Importance auto-correlation

• Descriptive statistic of a data set• Interpolation based on data further away than

the range is nonsense

20

14

13

101211

16

18

21 15

17

16

22

21

1912

range

??

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

• E(CDA adj. PvdA) = 5.33; reality once

PvdA

CDA

VVD

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

b * ws * (1- bv) * (0.2 + cos )b = burn factorws = wind speed = angle wind – direction pixelbv = soil humidity

Time neighbor pixel on fire: [1.41 *]

Forest fire

Forest; burn factor 0.8Heath; burn factor 0.6Road; burn factor 0.2Museum

Soilhumidity

Origin< 3 minutes< 6 minutes< 9 minutes> 9 minutes

Wind, speed 3

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

j

ijjcdi )(potentiald = weight origin j = distance decay parameterc = distance cost betweenorigin j and destination i

j

ij

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

Number of practices 16 13

Number of practice locations 9 7

Number of practices < 800 size 2 0

Number of people > 3 km 3957 4624

Average travel distance (km) 0,9 1,2

Largest distance (km) 5,2 5,4

Analysis elevation model

• Landscape shape recognition:- peaks and pits- valleys and ridges- convexity, concavity

• Water flow, erosion,watershed regions,landslides, avalanches