On Some Fundamental Geographical Concepts

176B Lecture 3

Nystuen, J. D. (1963) “Identification of some fundamental spatial concepts”

• Search for a common geographical terminology to eliminate redundancy

• Basics: Distance, pattern, relative position, site and accessibility

• Advantages of abstract models and assumptions, e.g. isotropic surface

The mosque floor

Geographic primitives

• G = g (x, y, z, s, A, t)

• [x, y, z] = f(d• Geography also highly

dependent upon model

UCSBUCSBLat: 34.4087 Lon: -119.8447Lat: 34.4087 Lon: -119.8447

Projection, datum etc. for a 7.5 min quad

GIS basic geometric functions

• A GIS package must be able to move between– map projections– coordinate systems– datums– Ellipsoids

• A GIS must be able to GEORECTIFY• Not always a simple task!

Orthorectification

Georegistration: Control

Georectification

Conflation

Address matching

2123 South Main St.AnywhereCA 93901

4,312,205mN623,864mE

15N

Geographic information fundamentals

1. Volume

2. Dimensionality

3. Continuity

Volume

• 1 meter pixel

• 24 bit depth (8 bit R, 8 bit G, 8 bit B)

• California 3rd largest State A=158,706 square miles

• A= 411,046,653,039 square meters

• N=9.865x10^10 bytes

• 98 gigabyte image

Volume Issues: Tiles and Pyramids

Dimensionality

• Simple geographic features can be used to build more complex ones.

• Areas are made up of lines which are made up of points represented by their coordinates.

• Areas = {Lines} = {Points}

Areas are lines are points are coordinates

Continuity

• Attributes of the earth fall into different spatial “behaviors” over space and time

• Many phenomena are best treated as continuous fields– E.g. air temperature, atmospheric pressure,

population density

• Others have distinct spatial extent or edges– E.g. census tracts, buildings, roads

Field vs. Feature (object)

Fields are often rasters

Air Photos

Discontinuous irregular rasters: resampling

1929

Features are often vectors

Properties of Features

• Size

• Distribution/density

• Shape

• Scale

• Orientation

Size: Resolution and Extent

10cm, 25cm, 50cm, 1m

Resels: Non-uniform Support

Data structure conversion

Distribution

Geographical Clustering

Clusters on points/networks

Shape

Shape vs. Support

Shape measures/analysis

Scale: RF vs. Detail

Santa Barbara

Scaling behavior

Orientation: Objects & Frame

Tobler’s First Law of Geography

• “Everything is related to everything else but near things are more related than distant things” (Tobler, 1970)

• Variation of (x1 – x0)2

• Spatial autocorrelation

• Violates assumptions of statistics

Geographical relations

• Among features– Contains/overlaps/intersects

– Contiguity/Adjacency

– Proximity

– Trajectory

• Within fields– Neighborhood relation

– Pattern

– Process

Vector polygon overlay

O =

Raster overlay

01

& =

Buffering

Pattern

Pattern (Fourier) Analysis

Contiguity

http://www.clearproject.net/chapter10fig5.JPG (Clear Lake, Iowa)

Semivariogram

Most important, process…

•G = g (x, y, z, s, A, t)

t0 t1 t2 t3

Strands

Time-Space dynamics

Dynamics

1930 1950 1970 1980 1990

FROM

TO

Geography

The study of the earth and its features and of the distribution of life on the earth, including human life and the

effects of human activity.