INTRODUCTION TO SPATIAL ANALYSIS

Michael F. Goodchild

1. HOW TO ORGANIZE THE POSSIBILITIES

1. HOW TO ORGANIZE THE POSSIBILITIES

A list of GIS functions

75Multistage visualization2,000

anything one can think of doing on spatial data

boxes are data sets, links are operations

ERDAS ImagineScripting languagesESRI Spatial Modeler

Stella

describe analysis as a linear sequence of operationsBy object type

e.g. Bailey and GatrellBy six classesInteractive spatial data analysisHarlow, UK: Longman Scientific and Technical (1995):A. Point patterns

B. Spatial continuous data (fields of interval/ratio variables)

C. Area dataspatially intensive or spatially extensiveD. Spatial interaction datathe cartographic problem

how to model spatial interaction?<origin object, destination object, attributes>

queries and reasoningmeasurements

transformations

descriptive summaries

optimization

hypothesis testing

2. QUERIES AND REASONING

Interacting with views

catalog viewSQLiconsmap viewlocationtable viewhistogram, pie chart

scatterplot

linked views

exploratory spatial data analysis

SELECT... FROM... WHERE...Spatial reasoning

e.g. route-finding directions

www.mapquest.comDriving directions from 909 West Campus Lane to 1401 De La Vina Stmap view

Go that way (pointing) and turn right at the fence. When the road curves to the right head straight, under the big coral tree. Turn left at the first stop sign, pass the daycare center on the right, and turn right at the stop sign at the end. At the light head straight through, and follow Storke through two more lights (the second one is Hollister). At the third light turn right to take the ramp onto 101 South (it's actually heading east at this point). In about eight miles take the Mission Street exit, and turn left at the bottom of the ramp. Go through three lights, watch out for the sharp dip in the road at Bath, and turn right on De La Vina. 1401 is at the corner of Sola, one block after the light at Micheltorena.

3. MEASUREMENTS

The original motivation for GIS

the Canada Geographic Information System of 1965Distance metricsmeasurement of area

planimetryoverlay of layers to obtain joint areasdot counting

PythagoreanBias in the length of a polyline

relative to a true lineArea of a polygon

Shape

Elbridge Gerry and the salamanderIn 1992, following the release of population data from the 1990 Census, new boundaries were proposed for the voting districts of North Carolina. For the first time race was used as an explicit criterion, and districts were drawn that as far as possible grouped minorities (notably African Americans) into districts in which they were in the majority. The intent was to avoid the historic tendency for minorities to be thinly spread in all districts, and thus to be unable to return their own representative to Congress. African Americans were in a majority in the new 12th District, but in order to achieve this the district had to be drawn in a highly contorted shape.

The new district, and the criteria used in the redistricting, were appealed to the U.S. Supreme Court. Writing for the 5-4 majority, and striking down the new districting scheme, Chief Justice William Rehnquist wrote that "A generalized assertion of past discrimination in a particular industry or region is not adequate because it provides no guidance for a legislative body to determine the precise scope of the injury it seeks to remedy. Accordingly, an effort to alleviate the effects of societal discrimination is not a compelling interest."

perimeter for a given areashape = perimeter / (3.54 sqrt area)1 for a circle (most compact)

>1 otherwise

4. TRANSFORMATIONS

Buffering

dilationPoints in polygonserosion

Polygon overlay

the discrete object caseSpatial interpolation

estimation of the value of a field variable at a location where it has not been measuredDensity estimationat all locationsinverse distance weightingcontouring

Kriging

estimation of the density of discrete objectsreplacing each object by a suitably weighted kernel functionresult depends on the radius of the kernel

5. DESCRIPTIVE SUMMARIES

Statistics that summarize a distribution

and satisfy the test for whether a method of analysis is spatialBy analogy to one dimension:reducing a potentially complex system to a few numbers

that are relevant to a question or application

measures of central tendencyTwo-dimensional versions of the mean and their variational propertiesmeasures of dispersion

skewness, kurtosis

centroidApplications of centersminimizing distance squaredmedianthe balance point

means of coordinates

minimizing distancebivariate medianminimizing Manhattan distance

summarizing change through timeDispersionwestward march of the US population centroidsite selectionthe Mendeleev Centrographic Laboratory

mean distance from centerMeasures of spatial dependence

the First Law of GeographyMeasures of fragmentationall things are related but nearby things are more related than distant thingsGeary and Moran statisticsendemic in geographic information

Type II errors

variograms

FRAGSTATSMeasures of fractional dimension

Measures of clustering

the K function

6. OPTIMIZATION

Design to achieve specific objectives

pointsLocation of central point-like facilities

lines

areas

to serve dispersed demandLocation of linear facilitieslocation-allocation methods

central facilities location

retailing

agency offices

emergency facilities

recreation facilities

delivery routes

power lines, highways, transmission corridorsLocation of areas

political districting

7. HYPOTHESIS TESTING

Application of inferential methods

based on traditional statistical methodsInferencenull hypothesistest statistic

known distribution under the null hypothesis

alpha level

Type I and Type II errors

from a sample to a populationThe independence assumptionsample is drawn randomly and independently

geographic objects as samples

the entire population is often analyzedinference about what population?

and the First Law of GeographyRandomization tests