Schedule

Four sessions:

Sunday June 25th:

8:00am - 9:45am

10:15am - 12:00pm

Lunch

1:30pm - 3.00pm

3:30pm - 5:00pm

Michael F. Goodchild is Professor of Geography at the University of California, Santa Barbara; Chair of the Executive Committee, National Center for Geographic Information and Analysis (NCGIA); Associate Director of the Alexandria Digital Library Project; and Director of NCGIA’s Center for Spatially Integrated Social Science. He received his BA degree from Cambridge University in Physics in 1965 and his PhD in Geography from McMaster University in 1969. After 19 years at the University of Western Ontario, including three years as Chair, he moved to Santa Barbara in 1988. He was Director of NCGIA from 1991 to 1997. In 1999 he was awarded an honorary doctorate by Laval University. In 1990 he was given the Canadian Association of Geographers Award for Scholarly Distinction, in 1996 the Association of American Geographers award for Outstanding Scholarship, and in 1999 the Canadian Cartographic Association’s Award of Distinction for Exceptional Contributions to Cartography; he has won the American Society of Photogrammetry and Remote Sensing Intergraph Award and twice won the Horwood Critique Prize of the Urban and Regional Information Systems Association. He was Editor of Geographical Analysis between 1987 and 1990, and serves on the editorial boards of ten other journals and book series. In 2000 he was appointed Editor of the Methods, Models, and Geographic Information Sciences section of the Annals of the Association of American Geographers. His major publications include Geographical Information Systems: Principles and Applications (1991); Environmental Modeling with GIS (1993); Accuracy of Spatial Databases (1989); GIS and Environmental Modeling: Progress and Research Issues (1996); Scale in Remote Sensing and GIS (1997); Interoperating Geographic Information Systems (1999); and Geographical Information Systems: Principles, Techniques, Management and Applications (1999); in addition he is author of some 300 scientific papers. He was Chair of the National Research Council’s Mapping Science Committee from 1997 to 1999, and is currently a member of NRC's Commission on Physical Sciences, Mathematics, and Applications. His current research interests center on geographic information science, spatial analysis, the future of the library, and uncertainty in geographic data.

For a complete CV see the NCGIA web site www.ncgia.ucsb.edu under Personnel
Other related web sites: UCSB Geography www.geog.ucsb.edu, Alexandria Digital Library alexandria.ucsb.edu

Outline:

1. What is Spatial Analysis?

        Basic GIS data models

        GIS function descriptions

 2. Spatial Statistics

        Spatial interpolation

        Exploratory spatial analysis

3. Spatial Interaction Models

4. Spatial Dependence

5. Spatial Decision Support

        Spatial search

        Districting

What is Spatial Analysis?

GIS is designed to support a range of different kinds of analysis of geographic information: techniques to examine and explore data from a geographic perspective, to develop and test models, and to present data in ways that lead to greater insight and understanding. All of these techniques fall under the general umbrella of "spatial analysis". The statistical packages like SAS, SPSS, S, or Systat allow the user to analyze numerical data using statistical techniques—GIS packages like ArcInfo give access to a powerful array of methods of spatial analysis.
 
 

Purpose of the Course

The course will introduce participants with some knowledge of GIS to the capabilities of spatial analysis. Each of the five major sections will cover a major application area and review the techniques available, as well as some of the more fundamental issues encountered in doing spatial analysis with a GIS.
 
 

Outline

Section 1 - What is spatial analysis? - Basic GIS concepts for spatial analysis - GIS functionality - Integrating GIS and spatial analysis - Issues of error and uncertainty:

• Definition of spatial analysis, major types and areas for application.

• How should an analyst view a spatial database? Fields and discrete objects, attributes, relationships

• How to organize the functions of a GIS into a coherent scheme.

• Levels of integration of GIS and spatial analysis - loose and tight coupling, and full integration. Scripts and macros, lineage and analytical toolboxes.

• The uncertainty problem - why is it such an issue in spatial analysis? What can we do now about data quality?

• Measures of spatial form - centrality, dispersion, shape.

• Spatial interpolation - intelligent spatial guesswork - spatial outliers.

• Exploratory spatial analysis - moving windows, linking spatial and other perspectives.

• Hypothesis tests - randomness, the null hypothesis, and how intuition can be misleading.

• The Huff model and variations.

• Site modeling for retail applications - regression, analog, spatial interaction.

• Modeling the impact of changes in a retail system.

• Calibrating spatial interaction models in a GIS environment.

• Spatial autocorrelation - what is it, how to measure it with a GIS.

• The independence assumption and what it means for modeling spatial data.

• Applying models that incorporate spatial dependence - tools and applications.

• Shortest path, traveling salesman, traffic assignment.

• What is location/allocation, and where can it be applied?

• Modeling the process of retail site selection. Criteria.

• Electoral districting and sales territories.

• What is an SDSS? What are its component parts? How does it compare to a GIS or a DSS? Why would you want one? Building SDSS.

• Examples of SDSS use - site selection, districting.

Section 1 - What is spatial analysis? - Basic GIS concepts for spatial analysis - GIS functionality - Integrating GIS and spatial analysis - Issues of error and uncertainty:

• Definition of spatial analysis, major types and areas for application.

• How should an analyst view a spatial database? Objects, layers, relationships, attributes, object pairs, data models.

• How to organize the functions of a GIS into a coherent scheme.

• Levels of integration of GIS and spatial analysis - loose and tight coupling, and full integration. Scripts and macros, lineage and analytical toolboxes.

• The uncertainty problem - why is it such an issue in spatial analysis? What can we do now about data quality?

A set of techniques for analyzing spatial data

"A set of techniques whose results are dependent on the locations of the objects being analyzed"

Some books on spatial analysis:

• Anselin L (1988) Spatial Econometrics: Methods and Models. Kluwer
• Bailey T C, Gatrell A C (1995) Interactive Spatial Data Analysis. Harlow: Longman Scientific & Technical
• Berry B J L, Marble D F (1968) Spatial Analysis: A Reader in Statistical Geography. Prentice-Hall
• Boots B N, Getis A (1988) Point Pattern Analysis. Sage
• Burrough P A, McDonnell R A (1998) Principles of Geographical Information Systems. New York: Oxford University Press
• Cliff A D, Ord J K (1973) Spatial Autocorrelation. Pion
• Cliff A D, Ord J K (1981) Spatial Processes: Models and Applications. Pion
• Fischer M, Scholten H J, Unwin D J, editors (1996) Spatial Analytical Perspectives on GIS. London: Taylor & Francis
• Fotheringham A S, O'Kelly M E (1989) Spatial Interaction Models: Formulations and Applications. Kluwer
• Fotheringham A S, Rogerson P A (1994) Spatial Analysis and GIS. Taylor and Francis
• Fotheringham A S, Wegener M (2000) Spatial Models and GIS: New Potential and New Models. London: Taylor and Francis
• Getis A, Boots B N (1978) Models of Spatial Processes: An Approach to the Study of Point, Line and Area Patterns. Cambridge University Press
• Ghosh A, Imgene C A (1991) Spatial Analysis in Marketing: Theory, Methods, and Applications. JAI Press
• Ghosh A, Rushton G (1987) Spatial Analysis and Location-Allocation Models. Van Nostrand Reinhold
• Goodchild M F (1986) Spatial Autocorrelation. CATMOG 47, GeoBooks
• Griffith D A (1987) Spatial Autocorrelation: A Primer. Association of American Geographers
• Griffith D A (1988) Advanced Spatial Statistics. Special Topics in the Exploration of Quantitative Spatial Data Series. Kluwer
• Haggett P, Chorley R J (1970) Network Analysis in Geography. St Martin's Press
• Haggett P, Cliff A D, Frey A (1977) Locational Methods. Wiley
• Haggett P, Cliff A D, Frey A (1978) Locational Models. Wiley
• Haining R P (1990) Spatial Data Analysis in the Social and Environmental Sciences. Cambridge University Press
• Harries K (1999) Mapping Crime: Principle and Practice. Washington, DC: Crime Mapping Research Center, Department of Justice
• Haynes K E, Fotheringham A S (1984) Gravity and Spatial Interaction Models. Sage
• Hodder I, Orton C (1979) Spatial Analysis in Archaeology. Cambridge: Cambridge University Press
• Leung Y (1988) Spatial Analysis and Planning under Imprecision. Amsterdam: North Holland
• Longley P A, Batty M, editors (1996) Spatial Analysis: Modelling in a GIS Environment. Cambridge: GeoInformation International
• Mitchell, A (1999) The ESRI Guide to GIS Analysis, Volume 1: Geographic Patterns and Relationships. ESRI Press
• Odland J (1988) Spatial Autocorrelation. Sage
• Raskin R G (1994) Spatial Analysis on the Sphere: A Review. Santa Barbara, CA: National Center for Geographic Information and Analysis
• Ripley B D (1981) Spatial Statistics. Wiley
• Ripley B D (1988) Statistical Inference for Spatial Processes. Cambridge University Press
• Taylor P J (1977) Quantitative Methods in Geography: An Introduction to Spatial Analysis. Houghton Mifflin
• Unwin D (1981) Introductory Spatial Analysis. Methuen
• Upton G J G, Fingleton B (1985) Spatial Data Analysis by Example. Wiley

Landsat image of New York area

Indianapolis database

Snow map of Soho, 1854

Openshaw GAM map of NE England

Atlantic Monthly mystery map

Northridge earthquake epicenters

Environmental justice in LA

World map

England and Wales demography

South Wales demography

Vandenberg service station

Service station subsurface

Service station plume
 
 

What tools exist for helping/conceptualizing/problem-solving?

Assumption: these (analysis, modeling, decision-making) are the primary purposes of GIS technology.
 

GIS components:
 
 

		Issues
Input	Digitizing Scanning	cost
Storage	Data structures	volume vs speed raster vs vector objects vs layers spatial vs object indexing
Manipulation	Analysis Modeling	algorithms response time menus vs commands
Output	Plot Print Display	cartographic design visualization

 

The cost of input to a GIS is high, and can only be justified by the benefits of analysis/modeling/decision-making performed with the data.

• Query (if it is faster than manual lookup)
• very repetitive
• highly trained user

• Analyses which are simple in nature but difficult to execute manually
• overlay (topological)
• map measurement, particularly area
• buffer zone generation
• Analyses which can take advantage of GIS capabilities for data integration
• global science
• Browsing/plotting independently of map boundaries and with zoom/scale-change
• seamless database
• need for automatic generalization
• editing
• Complex modeling/analysis (based on the above and extensions)

• List of generic GIS functions has 75 entries

• A taxonomy/classification of GIS functions
• A customized view of a spatial database designed for the needs of the analyst/modeler
• A set of tools to support analysis and database manipulation
• Associated tools for defining needs in the analysis/modeling area, and testing systems against those needs
• Methods for dealing with problems associated with analysis/modeling of spatial databases, particularly error/inaccurac

There are two distinct ways of conceiving of the geographical world.

In the field view, the world is conceived as a finite set of variables, each having a single value at every point on the Earth's surface (or every point in a three-dimensional space; or a four-dimensional space if time is included).

Examples of fields: elevation, temperature, soil type, vegetation cover type, land ownership

raster (a rectangular array of homogeneous cells)

grid (a rectangular array of sample points)

irregular points

digitized contours

polygons

TIN

The field view underlies the following ESRI implementation models:

coverage

TIN

grid

in the Arc8 Geodatabase the distinction can be implemented in object behaviors

In the discrete object view an otherwise empty space is littered with objects, each of which has a series of attributes. Any point in space (two, three, or four dimensional) can lie in any number of discrete objects, including zero, and objects can therefore overlap, and need not exhaust the space.

Field and discrete object views can be implemented in either raster or vector forms

the distinction concerns how the world is conceived, and the rules governing object behavior

a field can be represented as raster cells, points (e.g., spot heights), triangles (TIN), lines (contours), or areas (land ownership)

in many of these cases the primitive elements are not real (cannot be located on the ground), but are artifacts of the representation

buffer makes sense only for discrete objects

interpolation makes sense only for fields

Attributes can be of several types:
 

numeric
alphanumeric

quantitative
qualitative

nominal
ordinal
interval/ratio
cyclic
 

Spatial objects are distinguished by their dimensions or topological properties:

        points (0-cells)
        lines (1-cells)
        areas (2-cells)
        volumes (3-cells)
 

A class of objects is a set with the same topological properties (e.g. all points) and with the same set of attributes (e.g. a set of wells or quarter sections or roads). In the Arc8 Geodatabase a class also has the same behaviors, and may inherit behaviors from other classes. A class is associated with an attribute table.

Geodatabase introduces a consistent set of terms for primitive geometric objects

When a class represents a field, certain rules apply to the component objects. The objects belonging to one class of area or volume objects will fill the area and will not overlap (they are space-exhausting, they partition or tesselate the space, they are planar enforced).

         the layer provides one value at every point (recall the definition of a field)

• e.g. soil type
• e.g. elevation
• e.g. zoning

Spatial objects are abstractions of reality. Some objects are well-defined (e.g. road, bridge) but others are not. Objects representing a discrete entity view tend to be well-defined; objects representing a field are not.

• A TIN or DEM is an approximation to a topographic surface, with an accuracy which is usually undetermined. Even if accuracy is known at the sampled points, it is unknown between them.

• We assume that all of the points within an area object have the attributes ascribed to the object. In reality the area inside the object is not homogeneous, and the boundaries are zones of transition rather than sharp discontinuities (e.g. soil maps, climatic zones, geological maps).
 

Slides: Elevation model options

digital elevation model (raster)

digitized contours

triangular mesh

TIN

• sampling intensity can adapt to local variability

• many landforms are approximated well by triangular mosaics

• uniform sampling intensity is suited to automatic data collection via e.g. analytical stereoplotter

• many applications require uniform-sized spatial objects.

A spatial database consists of a number of classes of spatial objects with associated attribute tables.
 

The methods used to store the attribute and locational information about the objects are not of immediate concern to the analyst/modeler.

• Relationships between objects of different classes

• Relationships between objects of the same class

A cartographic data structure stores no spatial relationships among objects.

• ID of left and right polygons stored as attributes of shared boundaries (requires planar enforcement, so is associated with representation of a field).

• ID of incident links stored as attributes of nodes in line networks

An object pair is a combination of objects of the same or different types/classes which may have its own attributes.

Examples of object pairs:

• Matrix of distances between pairs of objects

• Hydrologic flows

• Traffic flows between origin/destination pairs

Object pairs in ESRI products

turntable (link-link pairs)

distance matrix (first object, second object, distance)

association class in UML

attributed relationship class in Geodatabase

Visio example

Example: Data Model for Traffic Routing

What are the essential components of a data model for route planning in a complex street network?

1. Links - attributes: length, street name, traffic count, terminal nodes. A street can be represented by a single link with attributes which include <one-way?> or by a pair of links with associated directions - one of the pair being omitted in the case of one-way streets.

2. Nodes or intersections - attributes: incident links, presence of traffic light.
 

•  Turn prohibitions - are attributes not of nodes or links but of link/link object pairs ("turntable")

•   Stop signs - are attributes of link/node object pairs.

1. Design a database to capture and analyze data on recreational fishing in the Scottish Highlands, to support decision-making by the tourist industry and regulatory agencies. The database should be able to represent the following:

• locations of fishing (rivers, lakes)

• locations of accommodation (hotels, guest houses)

• preferences and rights (fishing locations owned by hotels, locations accessible to hotels)

3. Design a database to support water resource analysis and planning for complex hydrographic networks that include streams, rivers, lakes and reservoirs.

GEOGRAPHIC INFORMATION SYSTEM FUNCTION DESCRIPTIONS
 

A. BASIC SYSTEM CAPABILITIES

A1 Digitizing (di)

Digitizing is the process of converting point and line data from source documents to a machine-readable format.

A2 Edgematching (ed)

Edgematching is the process of joining lines and polygons across map boundaries in creation of a "seamless" database.† The join should be topological as well as graphic, that is, a polygon so joined should become a single polygon in the data base, a line so joined should become a single line segment.

A3 Polygonization (po)

Polygonizing is the process of connecting together arcs ("spaghetti") to form polygons.

A4 Labelling (la)

This process transfers labels describing the contents (attributes) of polygons, and the characteristics of lines and points, to the digital system.† This input of labels must not be confused with the process of symbolizing and labelling output described below.

A5 Reformatting digital data for input from other systems (rf)

Data previously digitized are made accessible through an interface or converted by software to the system format, and made to be topologically useful as well as graphically compatible.

A6 Reformatting for output to other systems (ro)

This function is the inverse of the previous one. Internal data is reformatted to meet the requirements of other systems or standards.

A7 Data base creation and management (db)

Data is typically digitized from map-sheets, and may be edgematched. The creation of a true "seamless" database requires the establishment of a map sheet directory, and may include tiling to partition the database.

A8 Raster/vector conversion (rv)

The ability to convert data between vector and raster forms with grid cell size, position and orientation selected by the user.

A9 Edit and display on input (ei)

This function allows continuous display and editing of input data, usually in conjunction with digitizing.

A10 Edit and display on output (eo)

The ability to preview and edit displays before creation of hard copy maps.

A11 Symbolizing (sy)

To create high quality output from a GIS, it is necessary to be able to generate a wide variety of symbols to replace the primitive point, line and area objects stored in the database.

A12 Plotting (pl)

Creation of hard copy map output.

A13 Updating (up)

Updating of the digital data base with new points, lines, polygons and attributes.

A14 Browsing (br)

Browse is used to search the data base to answer simple locational queries, and includes pan and zoom.
 
 

B. DATA MANIPULATION AND ANALYSIS FUNCTIONS

B1 Create lists and reports (cl)

This is the ability to create lists and reports on objects and their attributes in user-defined formats, and to include totals and subtotals.

B2 Reclassify attributes (ra)

Reclassification is the change in value of a set of existing attributes based on a set of user specified rules.

B3 Dissolve lines and merge attributes (dm)

Boundaries between adjacent polygons with identical attributes are dissolved to form larger polygons.

B4 Line thinning and weeding (lt)

This process is used to reduce the number of points defining a line or set of lines to a user defined tolerance.

B5 Line smoothing (ls)

Automatically smooth lines to a user-defined tolerance, creating a new set of points (compare B4).

B6 Complex generalization (cg)

Generalization which may require change in the type of an object, or relocation in response to cartographic rules.

B7 Windowing (wi)

The ability to clip features in the database to some defined polygon.

B8 Centroid calculation and sequential numbering (cn)

Calculate a contained, representative point in a polygon and assign a unique number to the new object.

B9 Spot heights (sh)

Given a digital elevation model, interpolate the height at any point.

B10 Heights along streams (hs)

Given a digital elevation model and a hydrology net, interpolate points along streams at fixed increments of height.

B11 Contours (isolines) (ci)

Given a set of regularly or irregularly spaced point values, interpolate contours at user-specified intervals.

B12 Elevation polygons (ep)

Given a digital elevation model, interpolate contours of height at user-specified intervals.

B13 Watershed boundaries (wb)

Given a digital elevation model and a hydrology net, interpolate the position of the watershed between basins.

B14 Scale change (sc)

Perform the operations associated with change of scale, which may include line thinning and generalization.

B15 Rubber sheet stretching (rs)

The ability to stretch one map image to fit over another, given common points of known locations.

B16 Distortion elimination (de)

The ability to remove various types of systematic distortion generated by different input methods.

B17 Projection change (pc)

The ability to transform maps from one map projection to another.

B18 Generate points (gp)

The ability to generate points and insert them in the database.

B19 Generate lines (gl)

The ability to generate lines and insert them in the database.

B20 Generate polygons (ga)

The ability to generate polygons and insert them in the database.

B21 Generate circles (gc)

The ability to generate circles defined by center point and radius.

B22 Generate grid cell nets (gg)

The ability to generate a network of grid cells given a point of origin, grid cell dimension and orientation.

B23 Generate latitude/longitude nets (gn)

The ability to generate graticules for a variety of map projections.

B24 Generate corridors (gb)

This process generates corridors of given width around existing points, lines or areas.

B25 Generate graphs (gr)

Create a graph illustrating attribute data by symbols, bars or fitted trend line.

B26 Generate viewshed maps (gv)

Given a digital elevation model and the locations of one or more viewpoints, generate polygons enclosing the area visible from at least one viewpoint.

B27 Generate perspective views (ge)

From a digital elevation model, generate a three-dimensional block diagram.

B28 Generate cross sections (cs)

Given a digital elevation model, show the cross-section along a user-specified line.

B29 Search by attribute (sa)

The ability to search the data base for objects with certain attributes.

B30 Search by region (sr)

The ability to search the data base within any region defined to the system.

B31 Suppress (su)

The ability to exclude objects by attribute (the converse of selecting by attribute).

B32 Measure number of items (mi)

The ability to count the number of objects in a class.

B33 Measure distances along straight and convoluted lines (md)

The ability to measure distances along a prescribed line.

B34 Measure length of perimeter of areas (mp)

The ability to measure the length of the perimeter of a polygon.

B35 Measure size of areas (ma)

The ability to measure the area of a polygon.

B36 Measure volume (mv)

The ability to compute the volume under a digital representation of a surface.

B37 Calculate - arithmetic (ca)

The ability to perform arithmetic, algebraic and Boolean calculations separately and in combination.

B38 Calculate bearings between points (cb)

The ability to calculate the bearing (with respect to True North) from a given point to another point.

B39 Calculate vertical distance or height (ch)

Given a digital elevation model, calculate the vertical distance (height) between two points.

B40 Calculate slopes along lines (gradients) (al)

The ability to measure the slope between two points of known height and location or to calculate the gradient between any two points along a convoluted line which contains two or more points of known elevation.

B41 Calculate slopes of areas (sl)

Given a digital elevation model and the boundary of a specified region (e.g., a part of a watershed), calculate the average slope of the region.

B42 Calculate aspect of areas (aa)

Given a digital elevation model and the boundary of a specified region, calculate the average aspect of the region.

B43 Calculate angles and distances along linear features (ad)

Given a prescribed linear feature, generalize its shape into a set of angles and distances from a start point, at user-set angular increments, and constrained to any known points along the linear feature.

B44 Subdivide area according to a set of rules (sb)

Given the corner points of a rectangular area, topologically subdivide the area into four quarters.

B45 Locations from traverses (lo)

Given a direction (one of eight radial directions) and distance from a given point, calculate the end point of the traverse.

B46 Statistical functions (sf)

The ability to carry out simple statistical analyses and tests on the database.

B47 Graphic overlay (go)

The ability to superimpose graphically one map on another and display the result on a screen or on a plot.

B48 Point in polygon (pp)

The ability to superimpose a set of points on a set of polygons and determine which polygon (if any) contains each point.

B49 Line on polygon overlay (lp)

The ability to superimpose a set of lines on a set of polygons, breaking the lines at intersections with polygon boundaries.

B50 Polygon overlay (op)

The ability to overlay digitally one set of polygons on another and form a topological intersection of the two, concatenating the attributes.

B51 Sliver polygon removal (sp)

The ability to delete automatically the small sliver polygons which result from a polygon overlay operation when certain polygon lines on the two maps represent different versions of the same physical line.

B52 Line of sight (ln)

The ability to determine the intervisibility of two points, or to determine those parts of pairs of lines or polygons which are intervisible.

B53 Nearest neighbor search (nn)

The ability to identify points, lines or polygons that are nearest to points, lines or polygons specified by location or attribute.

B54 Shortest route (ps)

The ability to determine the shortest or minimum cost route between two points or specified sets of points.

B55 Contiguity analysis (co)

The ability to identify areas that have a common boundary or node.

B56 Connectivity analysis (cy)

The ability to identify areas or points that are (or are not) connected to other areas or points by linear features.

B57 Complex correlation (cx)

The ability to compare maps representing different time periods, extracting differences or computing indices of change.

B58 Weighted modelling (wm)

The ability to assign weighting factors to individual data sets according to a set of rules and to overlay those data sets and carry out reclassify, dissolve and merge operations on the resulting concatenated data set.

B59 Scene generation (sg)

The ability to simulate an image of the appearance of an area from map data. The image would normally consist of an oblique view, with perspective.

B60 Network analysis (na)

Simple forms of network analysis are covered in Shortest route and Connectivity. More complex analyses are frequently carried out on network data by electrical and gas utilities, communications companies etc. These include the simulation of flows in complex networks, load balancing in electrical distribution, traffic analysis, and computation of pressure loss in gas pipes. In many cases these capabilities can be found in existing packages which can be interfaced to the GIS database.
 
 

Other groupings of GIS functions:

Berry, J.K., 1987, "Fundamental operations in computer-assisted map analysis". International Journal of GIS 1 119-36.

• Reclassifying maps

• Overlaying maps

• Measuring distance and connectivity

• Characterizing neighborhoods

• (see below)

• Focal: operations that process a single cell

• Local: operations that process a cell and a fixed neighborhood

• Zonal: operations that process an area of homogeneous characteristics

• Global: operations that process the entire map

• Capture

• Transfer

• Validate and Edit

• Store and Structure

• Restructure

• Generalize

• Transform

• Query

• Analyze

• Present

Integration of GIS and Spatial Analysis

1. Full integration (embedding)

• spatial analysis as GIS commands

• requires modification of source code
• difficult with proprietary packages
• analysis is not the strongest commercial motivation
• third party macros

• what we have now

• unsatisfactory
• hooks too awkward
• loss of higher structures in data

• transfer of simple tables

• better hooks

• common data models

• discretization problem
• discretization often not explicit in models
• e.g. slope, length

• user interface design
• models easy to use?
• the user-friendly grand piano
• user community is already frustrated

Section 2 - Spatial statistics - Simple measures for exploring geographic information - The value of the spatial perspective on data - Intuition and where it fails - Applications in crime analysis, emergencies, incidence of disease:

• Measures of spatial form - centrality, dispersion, shape.

• Spatial interpolation - intelligent spatial guesswork - spatial outliers.

• Exploratory spatial analysis - moving windows, linking spatial and other perspectives.

• Hypothesis tests - randomness, the null hypothesis, and how intuition can be misleading.

How to sum up a geographical distribution in a simple measure?
 

Two concepts of space are relevant:
 

Continuous:

• travel can occur anywhere

• travel can occur only on a network

• only certain locations (on the network) are feasible
• all distances (between all possible pairs of locations) can be evaluated using any measure (travel time, cost of transportation etc.)

A metric is a means of measuring distance between pairs of places (in continuous space)

• e.g. straight lines (the Pythagorean metric)

Definitions of center:

The centroid

• the average position

• computed by taking a weighted average of coordinates

• the point about which the distribution would balance

• the basis for the US Center of Population (now in MO and still moving west)
 

• this is the bivariate median

• this is the point of minimum aggregate travel (MAT), sometimes called the median (very confusingly)

• for many years the US Bureau of the Census calculated the Center of Population as the centroid, but gave the MAT definition

• there is a long history of confusion over the MAT

• no ready means exist to calculate its location
• the MAT must be found by an iterative process
• an interesting way of finding the MAT makes use of a valid physical analogy to the resolution of forces - the Varignon frame

• on a network, the MAT is always at a node (junction or point where there is weight)
 

• for tracking change in geographic distributions, e.g. the march of the US Center of Population westward is still worth national news coverage

• for identifying most efficient locations for activities
• location at the MAT minimizes travel
• a central facility should be located to minimize travel to the geographic distribution that it serves
• should we use continuous or discrete space?
• this technique was considered so important to central planning in the Soviet Union in the early 20th century that an entire laboratory was founded
• the Mendeleev Centrographic Laboratory flourished in Leningrad around 1925

• centers are often used as simplifications of complex objects
• at the lower levels of census geography in many countries
• e.g. ED in US, EA in Canada, ED in UK
• to avoid the expense of digitizing boundaries
• e.g. land parcel databases
• or where boundaries are unknown or undefined
• e.g. ZIPs

• in the census examples, common practice is to eyeball a centroid

• some very effective algorithms have been developed for redistributing population from centroids
 

• what you would want to know if you could have two measures of a geographical distribution

• the spread of the distribution around its center

• average distance from the center

• measures of dispersion are used to indicate positional accuracy
• the error ellipse
• the Tissot indicatrix
• the CMAS

• a measure which increases with the weight of geographic objects and with proximity to them

• calculated as:
 
V = summation of (w(i)/d(i))

where i is an object, d is the distance to the object and w is its weight

the summation can be carried out at any location

V can be mapped - a "potential" map

• the market share obtainable by locating at a point

• the best location is the place of maximum potential

• population pressure on a recreation facility

• accessibility to a geographic distribution
• e.g. a network of facilities

• potential measures omit the "alternatives" factor
• imply that market share can potentially increase without limit

• potential measures have been used as predictors of growth
• economic growth most likely in areas of highest potential

• potential calculation exists as a function in SPANS GIS

• the objects used to calculate potential must be discrete in an empty space
• adding new objects will increase potential without limit
• it makes no sense to calculate potential for a set of points sampled from a field
• potential makes sense only in the object view

think of a scatter of points representing people

how to map the density of people?

replace each dot by a pile of sand, superimposing the piles

the amount of sand at any point represents the number and proximity of people

the shape of the pile of sand is called the kernel function

Measures of shape:
 

• shape has many dimensions, no single measure can capture them all

• many measures of shape try to capture the difference between compact and distended
• many of these are based on a comparison of the shape's perimeter with that of a circle of the same area
• e.g. shape = perimeter / (3.54 * sqrt(area))
• this measure is 1.0 for a circle, larger for a distended shape

• all of these measures based on perimeter suffer from the same problem
• within a GIS, lines and boundaries are represented as straight line segments between points
• this will almost always result in a length that is shorter than the real length of the curve, unless the real shape is polygonal
• consequently the measure of shape will be too low, by an undetermined amount
• shape (compactness) is a useful measure to detect gerrymanders in political districting

Spatial Interpolation

Spatial interpolation is defined as a process of determining the characteristics of objects from those of nearby objects

• of guessing the value of a field at locations where value has not been measured

The attributes are most often interval-scaled (elevations) but may be of any type

From a GIS perspective, spatial interpolation is a process of creating one class of objects from another class

Spatial interpolation is often embedded in other processes, and is often used as part of a display process

Distance-weighted interpolation

Known values exist at n locations i=1,...,n

The value at a location x_i is denoted by z(x_i)

We need to guess the value at location x, denoted by z(x)

The guessed value is an average over the known values at the sample points

• the average is weighted by distance so that nearby points have more influence.

Let w[d] denote the weight given to a point at distance d in calculating the average.
 
 

The estimate at x is calculated as:
 

z(x) = summation over every point i (w[d(x_i,x)] z(x_i)) / summation over every point i (w[d(x_i,x)])
 

in other words, the average weighted by distance.
 

The simplest kind of weight is a switch - a weight of 1 is given to any points within a certain distance of x, and a weight of 0 to all others

w[d] = d^-2

All of the distance weighted methods (e.g IDW) share the same positive features and drawbacks. They are:

• easy to implement and conceptually simple

• adaptable - the weighting function can be changed to suit the circumstances. It is even possible to optimize the weighting function in this sense:

Suppose the weighting function has a parameter, such as the size of the window

Set the window size to some test value

Then select one of the sample points, and use the method to interpolate at that point by averaging over the remaining n-1 sample values

Compare the interpolated value to the known value at that point. Repeat for all n points and average the errors

Then the best window size (parameter value) is the one which minimizes total error

In most cases this will be a non-zero and non-infinite value.
 
 

• all interpolated values must lie between the minimum and maximum observed values, unless negative weights are used
• This means that it is impossible to extrapolate trends
• If there is no data point exactly at the top of a hill or the bottom of a pit, the surface will smooth out the feature

• the interpolated surface cannot extrapolate a trend outside the area covered by the data points - the value at infinity must be the arithmetic mean of the data points
 

Polynomial surfaces

A polynomial function is fitted to the known values - interpolated values are obtained by evaluating the function
 

e.g. planar surface - z(x,y) = a + bx + cy

e.g. cubic surface - z(x,y) = a + bx + cy + dx² + exy + fy² + gx³ + hx²y + ixy² + jy³

• easy to use

• useful only when there is reason to expect that the surface can be described by a simple polynomial in x and y

• very sensitive to boundary effects

Most real surfaces are observed to be spatially autocorrelated - that is, nearby points have values which are more similar than distant points.

The amount and form of spatial autocorrelation can be described by a variogram, which shows how differences in values increase with geographical separation

Observed variograms tend to have certain common features - differences increase with distance up to a certain value known as the sill, which is reached at a distance known as the range.
 

To make estimates by Kriging, a variogram is obtained from the observed values or past experience

• Interpolated best-estimate values are then calculated based on the characteristics of the variogram.

• perhaps the most satisfactory method of interpolation from a statistical viewpoint

• difficult to execute with large data sets

• decisions must be made by the user, requiring either experience or a "cookbook" approach

• a major advantage of Kriging is its ability to output a measure of uncertainty of each estimate
• This can be used to guide sampling programs by identifying the location where an additional sample would maximally decrease uncertainty, or its converse, the sample which is most readily dropped.

Some of the most satisfactory methods use a mosaic approach in which the surface is locally defined by a polynomial function, and the functions are arranged to fit together in some way

With a TIN data structure it is possible to describe the surface within each triangle by a plane

• Planes automatically fit along the edges of each triangle, but slopes are not continuous across edges

• This can be arranged arbitrarily by smoothing the appearance of contours drawn to represent the surface

• Alternatively a higher-order polynomial can be used which is continuous in slopes.
 

Exploratory Spatial Analysis

The primary aim of spatial analysis should be to explore data from a spatial perspective, to gain insight and understanding

This does not require techniques with great mathematical sophistication

Many simple techniques can be devised to reveal patterns and trends in data

In statistics, Exploratory Data Analysis was devised in the 1970s for a similar purpose

• one of its aims is to identify outliers - cases that are surprising in some way

• in the spatial case, are there spatial outliers - cases that stand out from the regional trend?

• is there something we might call an Exploratory Spatial Analysis?

• how is it more than simply a user-friendly graphic interface to GIS?
 

• ESA should be easy to use and understand

• it should be aimed at revealing patterns and trends in data that are not easy to discern using conventional maps

• in this way it should exploit the capabilities of GIS and the digital environment

• easy change of scale - zooming in and out of data

• zooming discontinuously between levels in a hierarchy

• linking different data media - text, graphics, sound, images

• generalized relationships
• maps show the spatial relationships of proximity and adjacency well, but not linkages established by interaction, cultural affinity, trade, social networks
 

• animation can be used to convey time dependence

• it is much easier to create different shades of color and intensity in the digital environment
• these have always created difficulty in cartography

• 3D
• using specialized technology
• by animating 2D displays of solid objects
 

John Haslett, Trinity College, Dublin (REGARD)

• assume we have data of some socioeconomic nature, at more than one level of spatial resolution
• e.g. data on social deprivation patterns in a major city
• data is available at Census Tract (average 2,000 households) and at Block Group (average 100 households) levels of aggregation

• open several windows on the screen
• e.g. one window shows deprivation at the Census Tract level
• a second window shows the same variable mapped at the Block Group level

• the windows are linked
• pointing to a Census Tract in one window highlights the tract, and also highlights all Block Groups in the second window that are members of that tract
 
• suppose we wish to explore the relationship between deprivation and some other variable
• e.g. average number of years of formal education of household head

 
• one common difficulty in exploring data of this nature is that intuition is often misleading over the effects of scale
• the "ecological fallacy" occurs when an inference drawn at one scale is falsely applied at another scale
• e.g. if deprivation and education are related at the tract level, it is wrong to assume that they must therefore be related at other levels
• e.g. it would be wrong to assume that poorly educated individuals are necessarily socially deprived

• window 3 shows a scatter plot of the relationship at the tract level

• window 4 shows a similar scatter plot at the block group level, i.e. one point on the plot per block group

• all windows are linked logically
• pointing to a tract on the tract map highlights the tract, all block groups in the tract on the block group map, the point on the tract scatter plot and all points representing block groups in that tract on the block group scatter plot
• tracts that are outliers on the tract plot (e.g. deprivation too high given their income) may not be outliers at all on the block group plot
• interesting insights come from exploring relationships in multi-level data in this way

• spatial outliers

• hierarchical relationships

• temporal change

• integration over user-defined areas
• tell me how many people live in this area, or in a circle of defined radius around this point?

• complex patterns of interaction
• e.g. commuter travel patterns
• interaction is difficult to display using conventional static maps

• - ???

• compare patterns against the outcomes expected from well-defined processes

• if the fit is good, one may conclude that the process that formed the observed pattern was like the one tested
• unfortunately, there will likely be other processes that might have formed the same observed pattern
• in such cases, it is reasonable to ignore them as long as a) they are no simpler than the hypothesized process, and b) the hypothesized process makes conceptual sense

• the best known examples concern the processes that can give rise to certain patterns of points
• attempts to extend these to other types of objects have not been as successful

• a commonly used standard is the random or Poisson process
• in this process, points are equally likely to occur anywhere, and are located independently, i.e. one point's location does not affect another's

• a real pattern of points can be compared to this process
• most often, the comparison is made using the average distance between a point and its nearest neighbor
• in a random pattern (a pattern of points generated by the Poisson process) this distance is expected to be 1/(2 * sqrt(density)) where density is the number of points per unit area, and area is measured in units consistent with the measurement of distance
• when the number of points is limited, we would expect to come close to this estimate in a random pattern
• theory gives the limits within which average distance is expected to lie in 95% of cases
• if the actual average distance falls outside these limits, we conclude that the pattern was not generated randomly

• the pattern is clustered
• points are closer together than they should be
• the presence of one point has made other points more likely in the immediate vicinity
• some sort of attractive or contagious process is inferred

• the pattern is uniformly spaced
• points are further apart than they should be
• the presence of one point has made other points less likely in the vicinity
• some sort of repulsive process is inferred, or some sort of competition for space
 

• the process that generated the pattern may be non-random, but not sufficiently so to be detectable by this test
• this false conclusion is more likely reached when there is little data - the more data we have, the more likely we are to detect differences from a simple random process
• in statistics, this is known as a Type II error - accepting the null hypothesis when in fact it is false

• the process may be non-random, but not in either of the senses identified above - contagious or repulsive
• points may be located independently, but with non-uniform density, so that points are not equally likely everywhere

• it is possible to hypothesize more complex processes, but the test becomes progressively weaker at confirming them

Section 3 - Spatial interaction models - What they are and where they're used - Calibration and "what-if" - Trade area analysis and market penetration:

• The Huff model and variations.

• Site modeling for retail applications - regression, analog, spatial interaction.

• Modeling the impact of changes in a retail system.

• Calibrating spatial interaction models in a GIS environment.

• a model used to explain, understand, predict the level of interaction between different geographic locations

• examples of interactions:
• migration (number of migrants between pairs of states)
• phone traffic (number of calls between pairs of cities)
• commuting (number of vehicles from home to workplace)
• shopping (number of trips from home to store)
• recreation (number of campers from home to campsite)
• trade (amount of goods between pairs of countries)

• interaction is always expressed as a number or quantity per unit of time

• interaction occurs between defined origin and destination
• these may be the same or different classes of objects
• e.g. the same class in the case of migration between states
• e.g. different classes in the case of journeys to shop or work
• the matrix of interactions can be square or rectangular

 

• some measure of the origin (its propensity to generate interaction)

• some measure of the destination (its propensity to attract interaction)

• some measure of the trip (its propensity to deter interaction)

• these measures are assumed to multiply
 

I_ij = a E_i A_j C_ij
 

• that is, interaction can be predicted from the product of a constant, emissivity, attraction and deterrence

• such ideas of social physics have long since gone out of fashion, but the name is still sometimes used

• even in the form above, the model bears some relationship to Newton's Law of Gravitation
 

• e.g. the value of a might be unknown in a given application

• its value would be calibrated by finding the value that gives the best fit between the observed interactions and the interactions predicted by the model

• the conventional measure of fit is the total squared difference between observation and prediction, that is, the summation over i and j of (I_ij - I*_ij)²

• this is known as least squares calibration

• other unknowns might be the method of calculating deterrence (C_ij) from distance, or the attraction value to give to certain retail stores

C_ij

• deterrence is often strongly related to distance
• the further the distance, the less interaction and thus the lower C_ij

• a common choice is a decreasing function of distance:
C_ij = d_ij^-b            (C_ij = 1 / d_ij^b)
or C_ij = exp (-bd_ij)            (exp denotes 2.71828 to the power)

• generally the fit of the model is not sufficiently good to distinguish between these two, that is, to identify which gives the better fit

• the negative exponential has a minor technical advantage in not creating problems when d_ij = 0 (origin and destination are the same place)

• the b parameter is unknown and must be calibrated
• its value depends on the type of interaction, and also probably on the region
• b has units in the negative exponential case (1/distance) but none in the negative power case

• other measures of deterrence include:
• some function of transport cost
• some function of actual travel time
• in either case the function used is likely to be the negative power or negative exponential above
• there are examples where distance has a positive effect on interaction

• how to measure the propensity of each origin to emit interaction?

• gross population P_i

• some more appropriate measure weighting each cohort, e.g. age and sex cohorts
• some cohorts are more likely to interact than others

• gross income

• E_i could be treated as unknown and calibrated
 

• the propensity of each destination to attract interaction

• could be unknown and calibrated

• for shopping models, gross floor area of retail space is often used

• some forms of interaction are symmetrical
• flow from origin to destination equals reverse flow
• e.g. phone calls
• requires E_i and A_j to be the same, e.g. population

I_ij = E_i A_j C_ij / summation over j (A_j C_ij )

 
• summing interaction to all destinations from a given origin:
I_ij = E_i

• that is, total interaction from an origin will always equal E_i regardless of the number and locations of destinations
• flow will now be partially diverted from existing destinations to new ones
• E_i is now the total outflow, can be set equal to the total of observed outflows from origin i

• the Huff model is consistent with the axiom of Independence of Irrelevant Alternatives (IIA)
• the ratio of flows to two destinations from a given origin is independent of the existence and locations of other destinations

• population of a neighborhood increases by x%

• ethnic mix of a neighborhood changes

• a new bridge is constructed

• an earthquake takes a freeway out of operation

• a mall adds new space

• an anchor store moves out

• a store changes its signage
 

• the business done by a new store or an old store operating under changed circumstances is best estimated by finding the closest analog in the chain

• requires a search

• criteria include:
• physical characteristics of each store
• intangibles such as management, signage
• local market area
• a GIS can help compare market areas (local densities, street layouts, traffic patterns)
• a multi-media GIS can help with the intangibles
• bring up images of site, layout, signage...

• identify all of the factors affecting sales, and construct a model to predict based on these factors

• an enormous range of factors can affect sales

• some factors are exogenous
• determined by external, physical, measurable variables
• some of these travel with the store if it moves (site factors), others are attributes of place (situation factors)

• other factors are endogenous
• determined by crowding, types of customers, trends, advertizing
• unpredictable, determined by the state of the system
 

• site layout - on a corner? parking spaces, etc.

• inside layout

• trade area - number of households in primary, etc

• characteristics of neighborhood

Sales per 2-week period for convenience store:
 

$12749
+ 4542 if gas pumps on site
+ 3172 if major shopping center in vicinity

+ 3990 if side street traffic is transient

+ 3188 per curb cut on side street

+ 2974 if store stands alone

- 1722 per lane on main street

• use of surrogate variables

• problems in use of model for prediction in planning
 

• many different circumstances

• major issues involved in calibration

• specific tools are available
• SIMODEL

• possible to use standard tools in e.g. SAS, GLIM

• calibration possible using aggregate flows or individual choices
 

• suppose the E_i are known, the A_j unknown
• the constant a can be absorbed into the A_j (i.e. find aA_j)

• suppose we use the negative power deterrence function
 I_ij = E_i A_j / d_ij^b

• move the E_i to the left:
I_ij/E_i = A_j / d_ij^b

•   now a trick - introduce a set of dummy variables u_ijk, set to 1 if j=k, otherwise zero:

• now the left hand side is all knowns, the right hand side is a linear combination of unknowns (the logs of the As and b)

• the model can now be calibrated (the unknowns can be determined) using ordinary multiple regression in a package like SAS

• it may be easier to avoid linearizing altogether by using the nonlinear regression facilities in many packages

• normally, we would try to maximize the fit of the observed and predicted interactions

• linearization changes this
• e.g. we minimize the squared differences between observed and predicted values of log (I_ij/E_i) if ordinary regression is used on the linearized form above
• this is easy in practice, but makes no sense

• intuitively, an error of 30 in a prediction of 1000 trips is much more acceptable than an error of 30 in a prediction of 10 trips

• these ideas are formalized in the technique of Poisson regression, which assumes that I_ij is a count of events, and sets up the objective function accordingly
• the function minimized to get a good fit is roughly the difference between observed and predicted, squared, divided by the predicted flow

Section 4 - Spatial dependence - Looking at causes and effects in a geographical context:

• Spatial autocorrelation - what is it, how to measure it with a GIS.

• The independence assumption and what it means for modeling spatial data.

• Applying models that incorporate spatial dependence - tools and applications.

Spatial dependence

• what happens at one place depends on events in nearby places

• all things are related but nearby things are more related than distant things (Tobler's first law of geography)

• positive spatial dependence:
• nearby things are more alike than things are in general

• negative spatial dependence:
• nearby things are less alike than things are in general
• conceptual problems with negative spatial dependence
• e.g. the chessboard

• spatial autocorrelation measures spatial dependence
• an index, rather than a parameter of a process
• dependence between discrete objects, or dependence in a continuous field?

• calculates the product of values in neighboring objects

• related to Geary but not in a simple algebraic sense

Calculation of the Geary index of spatial autocorrelation

a is the mean of x values

w_ij = 1 if i,j adjacent, else 0

c is 1 if neighbors vary as much as the sample as a whole

c < 1 if neighbors are more similar than the sample as a whole (positive dependence)

c > 1 if neighbors are less similar (negative dependence)

• i.e. neighboring values are slightly more similar than one would expect if the values were randomly allocated to the four areas

• IDRISI calculates autocorrelation over a raster

• code has been written to calculate autocorrelation in ARC/INFO (see NCGIA Technical Paper 91-5)

• contact Dan Griffith, Syracuse University; Luc Anselin, West Virginia University

• some of these fail to take advantage of GIS capabilities, for generating input data and displaying output
 

• suppose there is a relationship between number of AIDS cases and number of people living in an area

• the form of this relationship will vary spatially
• in some areas the number of cases per capita will be higher than in others
• we could map the constant of proportionality

• spatial heterogeneity describes this geographic variation in the constants or parameters of relationships

• when it is present, the outcome of an analysis depends on the area over which the analysis is made
• often this area is arbitrarily determined by a map boundary or political jurisdiction

• a technique of ESA

• a user-defined window is moved over the map

• analysis occurs only within the window
 

 
• e.g. regression analysis assumes that the observations (cases) are statistically independent

• this violates the first law of geography

• in general, analysis in space is very different from conventional statistical analysis (although this is very often carried out on spatial data)
 

• the relationship between land devoted to growing corn and rainfall in a Midwestern state like Kansas

• rainfall available at 50 weather stations

• percent of land growing corn available for 100 counties

• use a method of spatial interpolation to estimate rainfall in each county from the weather station data

• plot one variable against the other, and perhaps fit a regression equation

• how many data points are there?
• the more data points, the more significant the results
• 100 (the number of counties)?
• 50 (the real number of weather observations)?
• something in between?

• more data points can be invented by intensifying the sample network using spatial interpolation, but no more real data has been created by doing so

• both variables are strongly spatially autocorrelated, violating an assumption of regression

• the significance of the analysis is now uncertain

• methods of spatial regression try to overcome this problem in a systematic way
• see earlier references to available code

A related issue - the MAUP
 

• many statistics are reported by averaging or summing over polygons - e.g. populations of counties, average elevation

• it is commonly necessary to interpolate such values to new polygons which do not coincide
• e.g. from census tracts with known populations to school districts
• source zones have known populations
• populations of target zones are unknown

• the best method of solving this problem is to create a continuous surface from the source data, then to integrate this surface to the new target areas

• density is constant within source zones

• density is constant within target zones

• density is constant within some third set of control zones

• density varies smoothly (Tobler's Pycnophylactic interpolation)

• e.g. Openshaw and Taylor

• 99 counties of Iowa

• two variables - % over 65, and % Republican
• correlation for the counties was .3466
 

6 Republican-proposed congressional districts .4823

6 Democrat-proposed congressional districts .6274

6 existing congressional districts .2651

6 urban/rural regional types .8624

6 functional regions .7128
 

• e.g. 48 regions - correlations between -.548 and +.886

• e.g. 12 regions - correlations between -.936 and +.996

• evaluate the range?

• are we asking the right question?
• is scale part of the question rather than a mere matter of implementation?

Section 5 - Site selection - Locational analysis and location/allocation - Other forms of operations research in spatial analysis - Spatial decision support systems - Linking spatial analysis with GIS to support spatial decision-making:

• Shortest path, traveling salesman, traffic assignment.

• What is location/allocation, and where can it be applied?

• Modeling the process of retail site selection. Criteria.

• Electoral districting and sales territories.

• What is an SDSS? What are its component parts? How does it compare to a GIS or a DSS? Why would you want one? Building SDSS.

• Examples of SDSS use - site selection, districting.

A spatial database can be used to support the solution of a variety of network problems, including optimal location, routing and vehicle scheduling

Shortest path problem
Traveling salesman problem and variants
Trans-shipment problem
Hitchcock transportation problem
Traffic assignment problem

P-median problem
Coverage problems
Minimax location problems
Plant location problem
• many of these are implemented in current GIS, e.g. NETWORK in ARC/INFO, TransCAD and GIS*PLUS from Caliper Corp.
• additional code interfaced with GIS has been developed

• solution of many of these problems raises a number of issues of data modeling
• some of these have been raised earlier in the example of modeling a street network for shortest path analysis
 

• oil extraction from the field generates large quantities of waste fluid

• there are 14 active producers in the field, each operating a single extraction facility

• the only effective method of disposal is by pumping to a formation below the oil producing layer

• options include:
• a single, central disposal facility
• requiring each producer to install a facility
• some intermediate configuration of shared facilities

• maximum capital cost

• zero transport cost

• minimum capital cost

• maximum transport cost

Pipe cost:
 

C1 = A D₀ / B + C

A installed cost per metre

D₀ distance in metres

B pipe life in years

C pump cost per year

C2 = E D V₀ / (365 F) + Q V₀ (H + D₀/(1000P)) / G

E holding period, days

D holding capacity, m³

V₀ volume of brine, m³ per year

F life of holding capacity, years

Q truck cost, $/hour

H time to load and unload truck

P speed of truck in km/hour

G truck load, m³

New well - $50-$75,000

Success rate 60-80%

Buildup of residual hydrocarbons

Corrosion of pipes

Slide: Transport cost functions
 

GIS implementation:

Network of streets and rights of way - potential routes for trucks/pipes

Links with attributes of length

Nodes with attributes of volume produced - producer sites plus other potential well locations

GIS database with nodes and links and associated attributes:

• data input functions (editing)

• data display - graphics, plots

• storage of geographic data

• provides data to the analysis module
 

• obtains nodes and links from the GIS

• performs analysis, reports results directly to the user

• includes several heuristic methods for solving the optimization problem

• allows the user access to the display/analysis functions of the GIS
 

Location-allocation analysis module:

Vehicle routing and scheduling

Traffic modeling

Corridor location for pipelines/powerlines/highways

Runoff modeling based on DEM

Load balancing in electrical networks

Spatial search

Boolean search

Forest stands - area object type, non-overlapping

Two or more coverages can be overlayed to obtain new object types with concatenated attributes. This allows Boolean search and related operations to be conducted on multiple object types, i.e. with more information available.

Example:

A buffer zone allows Boolean searches to include criteria based on distance

Example:

In many cases criteria are not commensurate and cannot be summed.

Example

Single Utility Functions (SUFs) for each criterion

Multiple Utility Functions (MUFs) to combine criteria.
 
 

Both SUFs and MUFs can be determined by experimental designs involving groups of decision-makers

Decision theoretic methods can be incorporated into GIS technology. The GIS is used to evaluate the criteria for each alternative, then to weigh them using SUFs and MUFs to arrive at a decision.
 
 
 

A model for spatial analysis with a GIS
 

Example of multi-stage GIS analysis

Generation of a Recreation Opportunity Spectrum (ROS) map for a National Forest 1:24,000 quad (7.5 minute)
 
 

Problem: generate zones and associated ROS classes for Forest Service land based on distance from transportation features, with urban exclusions.
 

Data needed:

D1: Roads and railways (1:24,000) - line objects

D2: Forest Service ownership map (1:24,000) - area objects

D3: City and town boundaries map (1:24,000) - area objects

Reclassify attributes (B2)

Dissolve and merge (B3)

Generate corridors (B24)

Topological overlay (B50)

Measure size of areas (B35)

Centroid calculation and sequential numbering (B8)

Plot (A12)

Create list and report (B1)

SPM                forest land, non-urban and within 0.5 miles of road/rail

SPN                 forest land, non-urban, outside 0.5 mile and inside 1.0 mile corridors

P                      forest land, non-urban, outside both 0.5 mile and 1.0 mile corridors (B2)

Initial data sets: D1, D2, D3

1. B2 on D2 -> E1

2. B3 on E1 -> E2

3. B24 on D1 -> E3

4. B24 on D1 -> E4

5. B50 on E2, E3, E4 -> E5

6. B50 on E5, D3 -> E6

7. B2 on E6 -> E7

8. B3 on E7 -> E8

9. B35 on E8 -> E9

10. B2 on E9 -> E10

11. B8 on E10 -> E11

12. A12 on E11, D1, D3

13. B1 on E11
 
 

Many GIS applications require complex decision rules in reclassification operations.

Districting

• GIS technology useful in designing sales areas, analyzing trade areas of stores

• similar applications occur in politics
• design of voting districts (apportionment, gerrymandering) has enormous impact on outcome of elections
• major interest in reapportionment after 1990 census

• GIS applications in these areas are still at early stage

• scale:
• street centerline, census reporting zones - i.e. 1:24,000 and smaller
• data at block group/enumeration district scale (250 households) is needed for locating smaller commercial operations like gas stations and convenience stores
• data at census tract scale (2,000 households) is good for the location of larger facilities like supermarkets and fast food outlets

• data sources:
• much reliance on existing sources of digital data
• especially TIGER and DIME
• similar data available in other countries
• additional data added to standard datasets by vendors
• e.g. updating TIGER files by digitizing new roads, correcting errors
• e.g. adding ZIP code boundaries, locations of existing retailers

• functionality:
• dissolve and merge operations, e.g. to build voting districts out of small building blocks
• modeling, e.g. to predict consumer choices, future population growth
• overlay operations, e.g. to estimate populations of user-defined districts, correlate ZIP codes with census zones
• point in polygon operations, e.g. to identify census zone containing customer's residence
• mapping, particularly choropleth and point maps of consumers
• geocoding, address matching

• data quality:
• more concern with accuracy of statistics, e.g. population counts, than accuracy of locations

• districting
• designing districts for sales territories, voting
• objective is to group areas so that they have a given set of characteristics
• "geographical spreadsheets" allow interactive grouping and analysis of characteristics
• e.g. Geospreadsheet program from GDT

• site selection
• evaluating potential locations summarizing demographic characteristics in the vicinity
• e.g. tabulating populations within 1 km rings
• searching for locations that meet a threshold set of criteria
• e.g. a minimum number of people in the appropriate age group are within trading distance

• market penetration analysis
• analyzing customer profiles by identifying characteristics of neighborhoods within which customers live

• targeting
• identifying areas with appropriate demographic characteristics for marketing, political campaigns

• many data vendors and consulting companies active in the field, many large retailers

• no organization unique to the field

• American Demographics is influential magazine
 

• GIS has applications in design of electoral districts, sales territories, school districts

• each area of application has its own objectives, goals

• this example looks at designing school districts

• the Catholic school system of London, Ontario, Canada provides elementary schools for Kindergarten through Grade 8 to a city of approx. 250,000
• about 25% of school children attend the Catholic system
• 27 elementary schools were open prior to the study

• population data is available for polling subdivisions from taxation records
• approx. 700 polling subdivisions have average population of 350 each

• forecasts of school age populations are available for 5, 10, 15 years from the base year at the polling subdivision level

• children are bussed to school if their home location is more than 2 miles away, or if the walking route to school involves significant traffic hazard

• minimal changes to the existing system of school districts

• minimal distances between home and school, and minimal need for bussing

• long-term stability in school district boundaries

• preservation of the concepts of community and parish - if possible a school should serve an identifiable community, or be associated with a parish church

• maintenance of a viable minimal enrollment level in each school, defined as 75% of school capacity and > 200 enrollment

• digitized boundaries of the polling subdivision "building blocks"

• an attribute file of building blocks giving current and forecast enrollment data
• for forecasting, we must include developable tracts of land outside the current city limits, plus potential "infill" sites within the limits
• 748 polygons
• development tracts are isolated areas outside the contiguous polling subdivisions
• infill sites are shown as points

• the ability to merge building blocks and dissolve boundaries to create school districts
• school districts are not required to be conterminous
• if necessary a school can serve several unconnected subdistricts

• a table indicating whether walking or bussing is required for each building-block/school combination

Current districts

Projections of enrollment based on current school districts

• rapid increase in developing areas, e.g. St Joseph's (#3), St Thomas More (#4) NW

• decrease in maturing areas of periphery, e.g. St Jude's (#8) - SW area

• rejuvenation in some inner-city schools due to infilling, e.g. St Martin's (#15) - lower center

• stagnation in other inner-city schools, e.g. St Mary's (#17), decline e.g. St John's (#14) - center

• general strategy - begin with current allocations, shift building blocks between districts in order to satisfy objectives

• requires interaction between graphic display and tabular output
• quick response to "what if this block is reassigned to the school over here?"

• implementation allowed School Board members to make changes during meetings, observe results immediately
• using map on digitizer tablet, tables on adjacent screen

• one of the alternative plans developed

• note:
• assumes closure of 6 schools
• rise in enrollment as percent of capacity
• stability of projections through time
• reduction in number of "non-viable" schools (<200 enrollment)
• increase in percent not assigned to nearest school
• increase in average distance traveled

Slide: Planned enrolments