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 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

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 Vegetation Area #patches Type 1 Beech 30 ha 2 Type 2 Birch 15 ha 2 Type 3 Mixed 8 ha 1 Type 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 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, 34) (14, 45.000, 31) (15, 41.000, 14) (17, 63.000, 82) (17, 66.000, 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

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

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

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

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

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

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 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 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

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 d = weight origin j  = distance decay parameter c = distance cost between origin 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 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