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

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:
• audra
• cnrennie
• compgeek
• dstutz
• nibor
• rosscaff
• siyer

• 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
• calculation of distance between competing next nearest neighbors
• superimposed layers of hierarchy
• K=4 hierarchy, transportation principle
• calculation of distance between competing next nearest neighbors
• superimposed layers of hierarchy
• K=7 hierarchy, administrative principle
• calculation of distance between competing next nearest neighbors
• superimposed layers of hierarchy
• Fractal central place theory.
• K=3 hierarchy
• K=4 hierarchy
• K=7 hierarchy
• Illustration of exact fit of the two approaches, showing that the fractally-generated tiles fit together precisely to form the classical central place landscapes.
• K=3 hierarchy
• K=4 hierarchy
• K=7 hierarchy

Related links--click to go to article linked to the website of the Institute of Mathematical Geography:
    Beyond the Fractal
    Fractal Geometry of Infinite Pixel Sequences: "Super-definition" Resolution?"
    Micro-cell Hex-nets

Related map--partially 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 K-values.
• Complete determination of fractal generator shape, that will generate a complete hierarchy, based solely on number-theoretic properties of K.
• Solution of sets of unsolved problems.
• Fundamental theorems.

• 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:

• Procedure for working with K values on the y-axis; note, therefore that the square root of K is always an integer.

• Chart illustrating how to determine the number of generator sides and the fractal generator shape (in terms of "hex-steps") simply from the number-theoretic 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 y-axis, the determination of generator shape and hierarchy type.  Slide 23.
• Geometric chart illustrating how to handle off-y-axis K-values (non-integral square roots).  Slide 24.
• Fractal generators solve the problem (Dacey) of twin K-values:  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 space-filling.  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.

• 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 real-world 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

• PowerPoint and the web, in Office 97
• ArcView
• Making 3D maps from 2D bitmaps
• Website issues.

• MapEdit detailed use of package, from local computer to the Internet.
• Sources of maps on the web
• File security issues
• Others, driven by conversation

• Maps on the web
• Heads-up digitizing; use of a raster underlay

• Converting files from one GIS to another.

• Heads-up digitizing on the screen as opposed to use of a digitizer; for many purposes heads-up is just as good as using a digitizer (a digitizer allows selection of an arbitrary number of control points; heads-up does not).
• Primitive heads-up "digitizing"...useful only in situations of extreme duress.
• Linking spreadsheets of data you find to existing GIS databases:

• Child Info--a sample of GIS in current use (CSF work).
• City of Ann Arbor maps
• Sample CSF projects

• 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 e-mail 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
• Graph-theoretic adjacency
• Adjacency matrix
• Powering of matrices
• Application from British History:  drawing space and time together
• Transportation application
• Spatial autocorrelation
• Trouble-shooting, 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

• 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, non-white 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
Non-white - white > 0
are green; values satisfying the inequality
Non-white - white < 0
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 non-white Block Groups whose adjacent Block Groups are also only non-white are light green.
• All non-white Block Groups adjacent to white Block Groups are darker green
• All white Block Groups adjacent to non-white 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 locally-unwanted-landuses (see R. Saha)
• matters of environmental justice (Saha)
• matters involving transportation of school-aged children

• Set intersection
• Venn diagrams
• Splitting regions:  abstract approach
• Splitting regions:  GIS approach
• Splitting regions:  real-world interpretation, ArcticArc.
• One thing leads to another...

• 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 real-world 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:
r = p - c - dt
• 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,
R = rY = Y(p - c) - Ydt.
Rewriting the equation, setting
P = Y(p - c), profit on amount of crop produced per acre (market margin)
T = Yt,
the equation becomes:
R = P - Td
• 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 slope-intercept 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 non-linear split-domain 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.

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) sectors--pie 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 fine-tuning 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 e-mail account; e-mail will be a critical tool
• Each student is required to have an active web page, set up early in the course.

• U.S. Dep't. of Transportation, Bureau of Geographic Information Services
• The Transport Web
• Detroit Traffic http://campus.merit.net/mdot/largeview.html
• Michigan Department of Transportation http://www.mdot.state.mi.us/maps/adt/adtfront.pdf
• Bodleian Library Map Room
• Cartographic Materials Home Page: Canada
• CIESIN: Consortium for International Earth Science Information Network
• Australian Centre of Asian Spatial Information and Analysis Network
• Rutgers--Center for Remote Sensing and Spatial Analysis
• West Chester University -- Center for GIS and Spatial Analysis
• Environmental Management Technical Center (EMTC)
• SpORE (Spatially Oriented Research in Ecology)
• Entergy Spatial Analysis Research Laboratory, Tulane University
• ESRI Home Page
• Federal Geographic Data Committee Internet site
• James Ford Bell Library at the University of Minnesota
• National Atlas Information Service, Canada
• National Geographic Society
• National Imagery and Mapping Agency
• National Oceanic and Atmospheric Administration
• National Spatial Data Infrastructure
• NCGIA Home Page
• Numerical Cartography Laboratory, The Ohio State Universtiy
• Ryhiner Map Collection, Berne, Switzerland.
• Spatial Odyssey, NCGIA, University of Maine
• Subway Navigator
• Surf Your Watershed, EPA
• United States Geological Survey
• U.S. Census Bureau data Access Tools
• U.S. Gazetteer
• USGS National Mapping Information
• The Virtual Geomorphology
• Xerox Parc Map Viewer
• International Society of Spatial Sciences

Links to education-oriented sites:

• School demographic data (contributed by Robin Saha)
• High School level presentation of the Mathematics of Cartography.
• Social Studies Connection: Website of Craig A. Robinson.
• The Island Project; University of Chicago Laboratory Schools, project of a fifth grade class
Links keep coming...
• http://www.nwf.org/nwf/news/dirty_water/dirt3.html
• http://www.nwf.org/nwf/kids/cool/index.html
• http://www.great-lakes.net/envt/water/hydro.html
• http://www.great-lakes.net/envt/water/flows.html
• http://www.great-lakes.net/envt/water/flowfuct.html
• http://www.great-lakes.net/ecosystem/ecosys.html
• http://city.net/indexes/top_maps.html
• http://www.yahoo.com/Education/K_12/School_Districts
• http://www.reji.com/reji/base/relocation/washington/wwframe.shtml
• http://www.unesco.org
• http://www.netrail.net/~howder/dcmaps.html
• http://www.ncdc.noaa.gov/ncdc.html
• http://www.info.usaid.gov/

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.  GIS--Principles 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.

• Simple curve fitting
• Cubic splines
• Applications of the exponential
• Logistic curve
• Application of Feigenbaum's graphical analysis
• Illustration of calculations for graphical analysis
• Variations...Gompertz....
• Graph theory,