1. WHAT IS SPATIAL ANALYSIS?

2. ANSWERING QUERIES

3. REASONING WITH GIS

4. MEASUREMENT WITH GIS

Methods for working with spatial data

to detect patterns, anomalies

to find answers to questions

to test or confirm theories (deductive reasoning)

to generate new theories and generalizations (inductive reasoning)

grounded in fundamental spatial concepts

pattern, cluster

anomaly

location, distance, shape

watershed, stream network

viewshed

what we think about when using GIS to analyze data

scale

uncertaint

see teachspatial.org

in doing scientific research

in trying to convince others

the machine does things the human finds too tedious, difficult, complex to do by hand

the human directs, makes interpretations and inferences

some methods are mathematically sophisticated

e.g. statistical tests

other methods are visual, intuitive, simple

making and examining maps

cholera outbreak in Soho, 1854

Dr John Snow and the pump

inference regarding the transmission mechanism for cholera

see www.jsi.com

updating Snow

Openshaw's map of childhood leukemia in N England

Basic spatial concepts

lie behind every type of spatial analysis

fundamental ideas about how the geographic world is structured

Types of spatial analysis

data types

discrete objects (points, lines, areas)

continuous fields

spatially intensive, spatially extensive

nominal, ordinal, interval, ratio, cyclic attributes

application domains

objectives

nominal

e.g. vegetation class
no implied order, no arithmetic operations
no average
"central" value is the commonest class (mode)

ordinal

e.g. ranking from best to worst
implied order, but no arithmetic operations
no average
"central" value has half of cases above, half below (median)

interval

e.g. Fahrenheit temperature
differences make sense
arbitrary zero point
"central" value is the mean

ratio

e.g. weight
ratios make sense
absolute zero point
"central" value is the mean

cyclic

scale repeats itself
e.g. aspect
be careful with arithmetic

average of 1 and 359 is 180

queries and reasoning

measurements

transformations

descriptive summaries

optimization

hypothesis testing

A GIS can present several distinct views

each view can be used to answer simple queries

hierarchy of devices, folders, datasets, files
map
table
metadata

example

map view
table view

linked views

histogram view
scatterplot view

percent owner occupied against median value by county

interactive methods to explore spatial data

use of linked views

finding anomalies
mining large masses of data

e.g. credit card companies
anomalous behavior in space and time

structured or standard query language

e.g. SELECT FROM counties WHERE median value > 100,000

We spend our lives in the vague world of human discourse

"is Santa Barbara north of LA?"

a GIS needs to know exactly what is meant by "north of"

is Reno east or west of San Diego?

we tend to think of the US as a square, with two N-S coasts

how to design a GIS to provide driving directions?

to direct people through airports?

a GIS would be easier to use if could "think" and "talk" more like humans

or if there could be smooth transitions between our vague world and its precise world

in our vague world, terms like "north of" are context-specific

geographically relevant terms like "across" or "in" have many meanings

spatial analysis is built on a formal, precise model of the world

not the comparatively vague, intuitive human view

Measurements are often difficult to make by hand from maps

measuring the length of a complex feature
measuring area

how did we measure area before GIS?

calculation from metric coordinates

straight-line distance on a plane

Pythagorean distance

d = sqrt ((x₁-x₂)²+(y₁-y₂)²)

distance on a spherical Earth

from (lat₁,long₁) to (lat₂,long₂)
R is the radius of the Earth, roughly 6378 km

d = R arccos [sin lat₁ sin lat₂ + cos lat₁ cos lat₂ cos (long₁ - long₂)]

add the lengths of polyline or polygon segments

if segments are straight, length will be underestimated in general

for lines and areas

lengths are measured in the horizontal plane

underestimated in hilly areas

applies to surveyed land also

how to measure area of a polygon?

proceed in clockwise direction around the polygon

for each segment

drop perpendiculars to the x axis
this constructs a trapezium
compute the area of the trapezium

difference in x times average of y

 keep a cumulative sum of areas

at the end, the sum will be the area of the polygon

an example of an algorithm

a set of rules executed in sequence to solve a problem
executed in this case in a GIS

when might the algorithm fail?

islands must all be scanned clockwise
holes must be scanned anticlockwise

holes have negative area

because of limited computer precision

results could be wrong if the area is very small and the coordinate values are very large

e.g. in UTM or SPC

need double precision for calculations
but not for results

applying the algorithm to a coverage

keep running total for each polygon

for each arc

proceed segment by segment from FNODE to TNODE

add trapezia areas to R polygon area
subtract from L polygon area

on completing all arcs, totals are correct areas

how to measure shape of an area?

a compact shape has a small perimeter for a given area

compare perimeter to the perimeter of a circle of the same area

shape = perimeter / [3.54 sqrt (area)]

what use are shape measures?

gerrymandering

creating oddly shaped districts to manipulate the vote

named for Elbridge Gerry

today GIS is used to design districts

the NC districting after the 1990 census

other types of districts designed with GIS

administrative regions

sales districts

the strangest-shaped county