GEOGRAPHY:
SPATIAL ANALYSIS,
ADVANCED TOPICS
NRE501, SECTION 043 (3 credits)
SCHOOL OF NATURAL RESOURCES AND ENVIRONMENT
THE UNIVERSITY OF MICHIGAN
http://www.umich.edu
Class Resource Pages
http://www.snre.umich.edu/~sarhaus and follow links

Professor Sandra Arlinghaus (Ph.D.)
Winter, 1998
Wednesdays, 69 p.m.
Office in Dana: 2044
Research office: 1130 Hill Street (Community Systems Foundation)
Phone: 7611357 (research office); 9750246 (home, between 9 a.m. and
9 p.m.)
email: sarhaus@umich.edu (preferred method of communication)
Office Hours: Wednesday, 35p.m.; Friday, 9a.m.  3p.m.
Others by appointment.
MIDTERM: Wednesday, March 11. Party afterwards at Sandy's
home.
FINAL PRESENTATIONS: Wednesday, April 29. Party afterwards
at Sandy's home.
COURSE FLYER
Click
here
Overrides are available from an envelope hanging on the door of 2044
or from the instructor directly.
All software used is for the PC.
WEEK 1

Individual discussion with each student as to project interests

Overview of course, involving mechanics of evaluation and introduction
to web page

During week following: help to get each student a web page

Addresses for web pages (a number of students already had them); links:
WEEK 2 Centrality: from the classical to the modern

Discussion of individual needs as to mechanics of proceeding on project

Material on Central Place Theory.

Classical central place theory.

K=3 hierarchy, marketing principle

K=4 hierarchy, transportation principle

K=7 hierarchy, administrative principle

Fractal central place theory.

Illustration of exact fit of the two approaches, showing that the fractallygenerated
tiles fit together precisely to form the classical central place landscapes.
Related references by authors (listed below) appear in traditional published
formats:
Christaller, Walter (books); Losch, August (book);
Dacey, Michael (articles); Marshall, John U. (article, Geographical Analysis);
Arlinghaus, S. (article, Geografiska Annaler); Arlinghaus S. and Arlinghaus
W. (article, Geographical Analysis); S. Arlinghaus, Electronic Geometry,
(article, Geographical Reviewreprints available).
Related linksclick to go to article linked to the website of the
Institute of Mathematical Geography:
Beyond
the Fractal
Fractal
Geometry of Infinite Pixel Sequences: "Superdefinition" Resolution?"
Microcell
Hexnets
Related mappartially digitized Christaller map.
Draft
map
WEEK 3 Centrality and Fractals

Use of the Diophantine equation K=x^2+xy+y^2 to generate classes of
higher K values.

Partition of higher values into mutually exclusive, exhaustive classes
of Kvalues.

Complete determination of fractal generator shape, that will generate
a complete hierarchy, based solely on numbertheoretic properties of K.

Solution of sets of unsolved problems.

Fundamental theorems.
Slides:

Sample of a higher K value to illustrate the difficulty in figuring
out fractal generators to create the geometrically correct spatial hierarchy...Slide
17.

Oblique axes used to separate K values into a number of different subsets:
a. along the yaxis and elsewhere
b. along lines parallel to the line y=x
Statements of key theorems...all
on Slide 18.

Procedure for working with K values on the yaxis; note, therefore that
the square root of K is always an integer.
a. equations of horizontal line parallel to y=x
b. discriminant of the quadratic form
c. the integral value, j, used to crosscut the Diophantine equation.
All on Slide
19.

Chart illustrating how to determine the number of generator sides and
the fractal generator shape (in terms of "hexsteps") simply from the numbertheoretic
properties of K. That is, the entire central place hierarchy (its
geometry) can be generated by understanding the "genetic" code embodied
in K. Slide 20.

Algebraic Table illustrating calculations in detail: Slide
21, Slide 22.

Geometric Table illustrating, a set of K values on the yaxis, the determination
of generator shape and hierarchy type. Slide
23.

Geometric chart illustrating how to handle offyaxis Kvalues (nonintegral
square roots). Slide
24.

Fractal generators solve the problem (Dacey) of twin Kvalues:
49 can be generated by the pair (0,7) and (5,3). The procedure separates
these geometrically and generates the correct spatial hierarchies for each
of them. Slide 25.

Fractal dimension formula used to calculate spacefilling. Slide
26.

Some implications: from the urban to the electronic environment.
Slide 27.

Geometric suggestion of similar procedure for an environment of squares.
Slide 28.
WEEK 4 Scale issues. Graph theory and a realworld water
network; fractals and marina design.

Outline of material from the abstract to the practical. Slide
1. Slide 2.
Slide 3.

Definition of a vertex of attachment (Tutte), involving relative attachment,
as opposed to the concept of cutpoint, involving absolute location.
Slide 4.

Vertices of attachment, fixed subgraphs, network heart, and maximal
fragmentation. Network fragments created downstream from a central delivery
system. Slide 5.

Adding redundancy: maximizing capability of extra links.
Bipartite graphs. Slide
6.

Illustration of abstract material applied to a hypothetical realworld
water plant. Slide
7.

Results. The case of Detroit. See also reprint of article
by Arlinghaus and Nystuen (from Perspectives in Biology and Medicine).
Slide 8.

Fractal design for a marina: compact use of space; reprint address supplied
in class.

Animation software

Image compression software: see shareware.com, and search for
image compression

Translation site
WEEK 5 Spatial elements of communication

PowerPoint and the web, in Office 97

ArcView

Making 3D maps from 2D bitmaps

Website issues.
Use of PhotoShop; light backdrops behind webpages.
Use of index file.
Making tables
Copying URLs
Others, driven by conversation
WEEK 6 Continuation of week 5.

MapEdit detailed use of package, from local computer to the Internet.

Sources of maps on the web

File security issues

Others, driven by conversation
WEEK 7. Getting boundary files into shape. Linking Excel
spreadsheets with GIS databases.

Maps on the web

Headsup digitizing; use of a raster underlay
Opening a raster image
Matching map projections
Registration of electronic (vector) map to raster map
Tracing of map
Grabbing common borders
How many points are required?
How many points are too many points?
Zooming in to check
Editing initial work

Converting files from one GIS to another.
Atlas
GIS to ArcView converter
ArcView
to Atlas GIS converter

Headsup digitizing on the screen as opposed to use of a digitizer;
for many purposes headsup is just as good as using a digitizer (a digitizer
allows selection of an arbitrary number of control points; headsup does
not).

Primitive headsup "digitizing"...useful only in situations of extreme
duress.

Linking spreadsheets of data you find to existing GIS databases:
Cleaning the data base to fit with a GIS database
Traversing the software interface from Excel to:
Atlas GIS
ArcView.
WEEK 8. MAPPING AND REALWORLD APPLICATIONS

Child Infoa sample of GIS in current use (CSF work).

City of Ann Arbor maps

Sample CSF projects
WEEK 9. MIDTERMSTUDENT PRESENTATIONS During
the course of the term in which the course was offered, midterm presentations
were posted soon after they were presented. For archiving purposes,
only the final presentations appear on the website now.
audra

cnrennie

compgeek

dstutz

nibor; Transparency Display

rosscaff

siyer

WEEK 10. CONNECTION

Written communications. Samples of journal articles, abstracts,
magazines; scholarly and other documents.

Other connections

Download and install Beatnik.
Then you can listen to online music files in one Netscape window and browse
in another.

Beethoven's Moonlight
Sonata; in cases such as this one, try to track down the source.

Web strategy
1. If you link to another site, inform that site by email and offer
to disconnect if your site becomes a high volume site...at their request.
2. Grabbing an image
a. request permission to use and behave according to answer to request;
b. give cutoff date;
c. put in own directory to avoid bandwidth drain
d. cite source
3. Do not use an image if there are disclaimers on it;
4. U.S. Government materials; these do not generally require written
requests for printed materials...so, apparently, use them...cite source
and so forth and send a request if it indicates that one should be sent.
5. Link to search engines...do not inform them. Cite them:
"here's what Yahoo says about Leelanau...", copy link and paste...pass
along your search skills...can increase traffic on your site.
6. Enter course web page and individual web pages separately in search
engines.
7. Assemble on 501 web page and list that in search engine.
8. Student UM accounts can be kept past graduation (contact Alumni
Association)
9. Outside US copyright and related laws/ethics vary.
10.
Citations...be clear about where in the documents references are used.
11.
Concepts...tie to concepts...broad connections send broad message:
centrality, hierarchy, density, transformation,
distance, orientation, geodesic, minimization, connection, adjacency to
name a few.

Measuring Adjacency

Troubleshooting, as time permits

To capture the screen: Alt + PrintScrn

To multiply matrices in Excel (Office 97): Select region into
which matrix product is to fall, Function Wizard (Math/Trig), MMULT, fill
out appropriately, and then CTRL+SHIFT+ENTER
WEEK 11: MORE SCALE ISSUES. SCALE TRANSFORMATIONS

Dot Density Maps: use dot density maps to measure population or
other densities in irregularly shaped regions superimposed on these maps.

This map shows
a single Census variable, nonwhite population, mapped by Block Group.
One dot represents one person in a Block Group.
Within a Block Group, dots are scattered randomly. Thus, position
of dots within the block group is meaningless. However, taking a
smaller scale view, using Census Tracts, of the scatter at the Block Group
scale, shows where there is clustering within a tract.
Scale change can reveal pattern!

Formulas can be written in the GIS. Thus, comparisons can be made
using dots of different colors. Here
values satisfying the inquality
are green; values satisfying the inequality
are purple.

Spatial Autocorrelation. How are regions clustered in space?
Are similar ones next to each other or are dissimilar ones next to each
other. The text/article shows one way to measure spatial autocorrelation
using graph theory and adjacency matrices.

On this map, all
nonwhite Block Groups whose adjacent Block Groups are also only nonwhite
are light green.

All nonwhite Block Groups adjacent to white Block Groups are darker
green

All white Block Groups adjacent to nonwhite Block Groups are darker
purple.

All white Block Groups adjacent to only white Block Groups are light
purple.

This map shows
a pattern similar to the first one, but with adjacency counted through
two stages.

In both maps, when Block Group boundaries are removed, a continuous
pattern emerges.

Policy makers and municipal authorities may find maps such as these
useful in

siting locallyunwantedlanduses (see R. Saha)

matters of environmental justice (Saha)

matters involving transportation of schoolaged children
WEEK 12. INTERSECTION AND SIMILAR MATTERS.
WEEKS 13 AND 14. SELECTED MODELS, TRANSPORT COST, LOCATION,
AND CONTOURING

Agricultural Land Use Model, von Thunen (based loosely (partially) on
a description in Kolars and Nystuen)

Simplifying assumptions:

There is a single, isolated market at the center of the region

The region is a homogeneous plain

Labor costs are homogeneous

Transportation costs are homogeneous

The system is in economic equilibrium

The market price of a single commodity is fixed.

Fundamental Concept
Rent (as opposed to "rental"): net return associated with
a unit of land, rather than with a unit of commodity.

Conjecture
On any given parcel of land, the activity yielding the highest rent
will dominate all others.
In what follows, the conjecture will lead to certain consequences; whether
or not the conjecture can then be confronted with realworld evidence and
proven as a "theorem," has been, and remains, a matter of discussion.

Equations

Net return, r, on a unit of commodity, given
p is the market price
c represents production costs
d is distance to market
t is transport rate
(hence, dt is total transport cost)
is:

Rent (net return), R, on a unit of land is given by r times the yield
of the land (over a fixed time frame, such as a year). If Y is the
yield,
Rewriting the equation, setting
P = Y(p  c), profit on amount of crop produced per acre (market
margin)
T = Yt,
the equation becomes:

Implications of equations

Whether the return is measured for unit of commodity or for unit of
land, the measure of distance is invariant.

In rewriting the rent equation, it becomes clear that the equation is
of the linear slopeintercept form y = mx + b. That is, rent is expressed
as a linear function of distance R = f(d), in which the slope of the line
representing the equation is T and the intercept of the line with the
vertical axis is P. The units along the horizontal axis are "distance"
and those along the vertical axis are "rent".

Implications of the conjecture

Different crops give rise to different equations, based on the idea
that a given parcel will produce that which generates the greatest net
return (and the variability of transport rates for different types of crops).

Given an agricultural system
with three crops:
R = P1  T1 d
R = P2  T2 d
R = P3  T3 d
When the crop that yields the greatest rent is produced on all parcels
of land, the resulting land use pattern is one of concentric circles centered
on the market.

Directions for extension

Test model against reality: "prove" the conjecture. Here, GIS
can provide easy testing of large amounts of data.

Vary the simplifying assumptions: when, for example, is swamp
reclamation feasible?

Create nonlinear splitdomain Thunen functions. Here, concepts
of the calculus become important.

Industrial Location (in the manner of Weber)

Issue: Cities are foci of agricultural consumption (marketplaces)
and therefore have a strong influence on rural land use patterns.
Consider the parallel situation for industry. Cities are marketplaces
for industrial output. What influence does that fact have on the
location of facilities for resource processing and on consequent industrial
location patterns?

Simplifying Assumptions:

Assume a uniform plane

Assume a single urban market at a point

Assume resources are point locations

assume equal transport costs per unit of weight

Underlying Concept: The point of lowest total transport cost will
serve as an optimal location site for an industry. This total is
a sum of cost distances from resources and market.

Mechanical model, Weber's
weight analysis: the accompanying figure shows a mechanical model
of weights on strings. Weights may represent cost in transport; the
knot settles at the point minimizing total transport costs among the locations
(holes) on the uniform (circular) plane region.

Analysis: Given one market, M, and two resource supply sites,
R1 and R2

Contour the plane surrounding each point according to transport costs
from that point. Given the simplifying assumptions, the pattern will
be a set of concentric circles surrounding each point, evenly spaced, of
increasing value as one moves outward from the resource site or marketplace.

Model with equal transport costs (after Haggett)

isotims:
contours of equal transport costs surrounding single points

isodapanes:
contours of equal aggregate transport costs among a set of locations.

Model with unequal transport costs (modify the simplifying assumptions)
(after Haggett)

isotims:
contours of equal transport costs surrounding single points

isodapanes:
contours of equal aggregate transport costs among a set of locations.
In both cases, an optimal location (according to the Underlying Concept)
is found within the lowest contour on the resulting topographic map of
isodapanes.

Challenge to use GIS to consider this sort of analysis. Modifying
constraints on the fly, and seeing immediate spatial consequences, offers
richness in the analysis previously impossible.

References:
von Thunen, J. H. von Thunen's Isolated State, trans. Carla
M. Wartenberg, edited with an Introduction by Peter Hall, London: Pergamon
Press, 1966.
Weber, Alfred. Alfred Weber's Theory of the Location of Industries,
trans. C. J. Friedrich. Chicago: The University of Chicago
Press, 1928.
Textbooks (out of print; contact instructor)
Kolars and Nystuen, Human Geography; Haggett, Peter, Geography:
A Modern Synthesis; Abler, Adams, and Gould, Spatial Organization.

Maps revisited; the concepts you bring to the GIS determine
the depth of spatial analysis that can be performed: we have come
full circle.
WEEK 15: FINAL PRESENTATIONS: Introduction.
MAP MODELS...BASED ON STUDENT REQUEST
During the course of the term in which the course was offered, there
were direct hyperlinks to files; these files were simply used in some sort
of intermediate process (if at all) of coming to the final project and
so are not included here.
Robin C. Possible use of powering of matrices to track finds
over time (using the Excel grid). Then superimpose on map at
each stage to suggest diffusion?
Robin S.
Maps of various sorts analyzing proximity to
facilities on various bases.
MapInfo
Dave...the world, percent GDP in industrial (purple)
and service (green) sectorspie charts by country.
ArcView
Charles...Sleeping Bear Dunes, based on Prof.
Chuck Olson's base maps.
Atlas GIS
Ros...map of German states; all are in one layer.
Then new layers containing east and west are also formed.
Other
Dave suggested a really nice link for finetuning
of websites and an image compression package that lets you see how much
you are compressing an image, on the fly. It's called WebSiteGarage.
PKZIP
instructions for bridging a sequence of diskettes with a zipped file.
Audra...try these links:
http://www.kadets.d20.co.edu/~lundberg/dnapic2.html
http://www.kadets.d20.co.edu/~lundberg/dna.html
Frames model: http://www.snre.umich.edu/~sarhaus/501w/frames
and follow the directions from there.
COURSE MATERIALS

Web page and attached materials

Electronic handouts on computer in 2044

Reserve shelf in map library

Diskettes: each student should purchase a supply of high density
3.5 inch diskettes.

Each student is required to have an active email account; email will
be a critical tool

Each student is required to have an active web page, set up early in
the course.
EVALUATION:
Initial description of interests: 5% for a onepage statement
handed in on time, the first day.
Midterm oral presentation of about 15 minutes illustrating
progress to date; written statement (on diskette) of such to be handed
in. Students will be encouraged to capture their work in some sort of electronic
format for this presentation (such as PowerPointsay, 20 slides). This
presentation is worth 15% of the grade.
Midterm written project abstract, worth 10% of the grade.
Presentation of the final project (15 minutes for each,
as above). Presentation worth 35% of the grade.
Website displaying final project. (Students who do
not already know how to do this can get trained in this course, if they
wish). Worth 35% of the grade.
RELATED LINKS
RESERVE SHELF (Documents on reserve in the Map Library, 8th Floor,
Hatcher (graduate) library.
Selections from among (but not limited to):
Aldenderfer and Maschner, Anthropology, Space, and GIS
Kraak and Ormeling, Cartography: Visualization of Spatial
Data
Wood and Keller, Cartographic Design: Theoretical and Practical
Perspectives
Martin, David. GIS: Socioeconomic Applications
Monmonier, M. How to Lie with Maps, 2nd Edition
Monmonier, M. Drawing the Line
Thrower, Maps and Civilization
Clarke, Keith. Analytical and Computer Cartography
Robinson et al. Elements of Cartography, 6th Edition
Goodchild, M. et al. Environmental Modeling with GIS
Goodchild, M. GISPrinciples and Applications
Star and Estes, GIS: An Introduction.
INSTRUCTOR'S SELECTED PREVIOUS LECTURE FILES OF RELATED USE
Simple curve fitting and other material. Text files only for
entire series. Files with graphics available on computer in 2044 Dana Building.