An
Analytical Framework for GIS Modeling
Joseph
K. Berry1 and Shitij Mehta2
1Keck Scholar in Geosciences, Department of
Geography, University of Denver, Denver, Colorado; jkberry@du.edu Website: www.innovativegis.com/basis/
2Former Graduate Teaching Assistant at the
University of Denver; currently Product Engineer, Geoprocessing
Team, Environmental Systems Research Institute (ESRI), Redlands, California
Abstract:
The U.S.
Department of Labor has identified Geotechnology as
one of three mega technologies for the 21st century noting that it
will forever change how we will conceptualize, utilize and visualize spatial
information. Of the spatial triad
comprising Geotechnology (GPS, GIS and RS), the spatial analysis and modeling
capabilities of Geographic Information Systems provides the greatest untapped
potential, but these analytical procedures are least understood. This paper develops a conceptual framework
for understanding and relating various grid-based map analysis and modeling
procedures, approaches and applications.
Discussion topics include; 1) the nature of discrete versus continuous
mapped data; 2) spatial analysis procedures for reclassifying and overlaying
map layers; 3) establishing distance/connectivity and depicting neighborhoods; 4) spatial statistics procedures for surface
modeling and spatial data mining; 5) procedures for communicating model
logic/commands; and, 6) the impact of spatial reasoning/dialog on the future of
Geotechnology.
Keywords:
Geographic Information Systems, GIS modeling, grid-based map analysis, spatial
analysis, spatial statistics, map algebra, map-ematics
This
paper presents a conceptual framework used in organizing material presented in
a graduate course on GIS Modeling presented at the University of Denver. For more information and materials see http://www.innovativegis.com/basis/Courses/GMcourse11/.
<Click here>
for a printer- friendly version of this paper (.pdf)
|
Table
of Contents |
||
|
Section |
Topic |
Page |
|
Introduction |
2 |
|
|
Nature of Discrete
versus Continuous Mapped Data |
4 |
|
|
Spatial Analysis
Procedures for Reclassifying Maps |
6 |
|
|
Spatial Analysis
Procedures for Overlaying Maps |
8 |
|
|
Spatial Analysis
Procedures for Establishing Proximity and Connectivity |
10 |
|
|
Spatial Analysis
Procedures for Depicting Neighborhoods |
13 |
|
|
Spatial Statistics
Procedures for Surface Modeling |
15 |
|
|
Spatial Statistics
Procedures for Spatial Data Mining |
17 |
|
|
Procedures for
Communicating Model Logic |
18 |
|
|
Impact of Spatial
Reasoning and Dialog on the Future of Geotechnology |
20 |
|
|
|
Further Reading and
References |
23 |
____________________________
Historically information relating to
the spatial characteristics of infrastructure, resources and activities has
been difficult to incorporate into planning and management. Manual techniques of map analysis are both
tedious and analytically limiting. The
rapidly growing field of Geotechnology
involving modern computer-based systems, on the other hand, holds promise in
providing capabilities clearly needed for determining effective management
actions.
Geotechnology refers to
“any technological application that utilizes spatial location in visualizing,
measuring, storing, retrieving, mapping and analyzing features or phenomena
that occurs on, below or above the earth” (Berry, 2009). It is recognized by the U.S. Department of Labor as one of the “three mega-technologies for the 21st
Century,” along with Biotechnology and Nanotechnology (Gewin,
2004). As depicted in the left inset of
figure 1 there are three primary mapping disciplines that enable Geotechnology—
GPS (Global Positioning System)
primarily used for location and navigation, RS
(Remote Sensing) primarily used to measure and classify the earth’s cover,
and GIS (Geographic Information Systems/Science/Solutions)
primarily used for mapping and analysis of spatial information.
The interpretation of the “S” in GIS
varies from “Systems” with an emphasis on data management and the computing
environment. A “Science” focus
emphasizes the development of geographic theory, structures and processing
capabilities. A “Solutions” perspective
emphasizes application of the technology within a wide variety of disciplines
and domain expertise.
Figure 1. Overview organization of components, evolution and types of tools
defining Map Analysis.
Since the 1960s the
decision-making process has become increasingly quantitative, and mathematical
models have become commonplace. Prior to
the computerized map, most spatial analyses were severely limited by their manual
processing procedures. Geographic
information systems technology provides the means for both efficient handling
of voluminous data and effective spatial analysis capabilities. From this perspective, GIS is rooted in the
digital nature of the computerized map.
While today’s
emphasis in Geotechnology is on sophisticated multimedia mapping (e.g., Google Earth, internet mapping, web-based
services, virtual reality, etc.), the early 1970s saw computer mapping as a
high-tech means to automate the map drafting process. The points, lines and areas defining
geographic features on a map are represented as an organized set of X,Y coordinates. These
data drive pen plotters that can rapidly redraw the connections at a variety of
colors, scales, and projections. The map
image, itself, is the focus of this automated cartography.
During the early
1980s, Spatial database management systems
(SDBMS) were developed that linked computer mapping capabilities with
traditional database management capabilities.
In these systems, identification numbers are assigned to each geographic
feature, such as a timber harvest unit or sales territory. For example, a user is able to point to any
location on a map and instantly retrieve information about that location. Alternatively, a user can specify a set of
conditions, such as a specific vegetation and soil combination, and all
locations meeting the criteria of the geographic search are displayed as a map.
As Geotechnology
continued its evolution, the 1990s emphasis turned from descriptive “geo-query”
searches of existing databases to investigative Map Analysis. Today, most GIS
packages include processing capabilities that relate to the capture, encoding,
storage, analysis and visualization of spatial data. This paper describes a conceptual framework
and a series of techniques that relate specifically to the analysis of mapped
data by identifying fundamental map analysis operations common to a broad range
of applications. As depicted in the
lower portion of the right inset in figure 1, the classes of map analysis
operations form two basic groups involving Spatial
Analysis and Spatial Statistics.
Spatial Analysis extends the basic set of discrete map features of points, lines and
polygons to surfaces that represent continuous geographic space as a set of
contiguous grid cells. The consistency
of this grid-based structuring provides a wealth of new analytical tools for
characterizing “contextual spatial relationships,” such as effective distance,
optimal paths, visual connectivity and micro-terrain analysis. Specific classes of spatial analysis
operations that will be discussed include Reclassify,
Overlay, Proximity and Neighbors.
In addition, it
provides a mathematical/statistical framework by numerically representing
geographic space. Whereas traditional
statistics is inherently non-spatial as it seeks to represent a data set by its
typical response regardless of spatial patterns, Spatial Statistics
extends this perspective on two fronts.
First, it seeks to map the variation in a data set to show where unusual
responses occur, instead of focusing on a single typical response. Secondly, it can uncover “numerical spatial
relationships” within and among mapped data layers, such as generating a
prediction map identifying where likely customers are within a city based on
existing sales and demographic information.
Specific classes of spatial statistics operations that will be discussed
include Surface Modeling and Spatial Data Mining.
By organizing primitive analytical
operations in a logical manner, a generalized GIS modeling approach can be
developed. This fundamental approach can
be conceptualized as a “map algebra” or “map-ematics”
in which entire maps are treated as variables (Tomlin and Berry, 1979; Berry,
1985; Tomlin, 1990). In this context,
primitive map analysis operations can be seen as analogous to traditional
mathematical operations. The sequencing
of map operations is similar to the algebraic solution of equations to find
unknowns. In this case however, the
unknowns represent entire maps. This
approach has proven to be particularly effective in presenting spatial analysis
techniques to individuals with limited experience in geographic information
processing.
2.0 Nature of Discrete versus Continuous Mapped
Data
For
thousands of years, points, lines and polygons have been used to depict map
features. With the stroke of a pen a
cartographer could outline a continent, delineate a highway or identify a
specific building’s location. With the
advent of the computer and the digital map, manual drafting of spatial data has
been replaced by the cold steel of the plotter.
In
digital form, mapped data have been linked to attribute tables that describe
characteristics and conditions of the map features. Desktop mapping exploits this linkage to
provide tremendously useful database management procedures, such as address
matching, geo-query and network routing.
Vector-based data forms the foundation of these techniques and
directly builds on our historical perspective of maps and map analysis.
Grid-based data, on
the other hand, is a less familiar way to describe geographic space and its
relationships. At the heart of this
procedure is a new map feature that extends traditional irregular discrete Points, Lines and Polygons
(termed “spatial objects”) to uniform continuous map Surfaces.
The
top portion of figure 2 shows an elevation surface displayed as a traditional
contour map, a superimposed analysis frame and a 2-D grid map. The highlighted location depicts the
elevation value (500 feet) stored at one of the grid locations. The pop-up table at the lower-right shows the
values stored on other map layers at the current location in the Analysis Frame. As the cursor is moved, the “drill-down” of
values for different grid locations in the Map
Stack are instantly updated.
Figure 2.
Grid-based map layers form a geo-registered stack of maps that are
pre-conditioned for map analysis.
Extending
the grid cells to the relative height implied by the map values at each
location forms the 3-dimensional plot in the lower-left portion of the
figure. The result is a “grid” plot that
depicts the peaks and valleys of the spatial distribution of the mapped data
forming the surface. The color zones
identify contour intervals that are draped on the surface. In addition to providing a format for storing
and displaying map surfaces, the analysis frame establishes the consistent
structuring demanded for advanced grid-based map analysis operations. It is the consistent and continuous nature of
the grid data structure that provides the geographic framework supporting the
toolbox of grid-based analytic operations used in GIS modeling.
In
terms of data structure, each map layer in the map stack is comprised of a
title, certain descriptive parameters and a set of categories, technically
referred to as Regions. Formally stated, a region is simply one of
the thematic designations on a map used to characterize geographic
locations. A map of water bodies
entitled “Water,” for example might include regions associated with dry land,
lakes or ponds, streams and wetlands.
Each region is represented by a name (i.e., a text label) and a
numerical value. The structure described so far, however, does not account for
geographic positioning and distribution.
The handling of positional information is not only what most
distinguishes geographic information processing from other types of computer
processing; it is what most distinguishes one GIS system from another.
As
mentioned earlier, there are two basic approaches in representing geographic
positioning information: Vector, based on sets of discrete line segments, and
Raster, based on continuous sets of grid cells.
The vector approach stores information about the boundaries between
regions, whereas raster stores information on interiors of regions. While this difference is significant in terms
of implementation strategies and may vary considerably in terms of geographic
precision, they need not affect the definition of a set of fundamental
analytical techniques. In light of this
conceptual simplicity, the grid-based data structure is best suited to the
description of primitive map processing techniques and is used in this
paper.
The
grid structure is based on the condition that all spatial locations are defined
with respect to a regular rectangular geographic grid of numbered rows and
columns. As such, the smallest
addressable unit of space corresponds to a square parcel of land, or what is
formally termed a Grid Cell, or more
generally referred to as a “point” or a “location.” Spatial patterns are represented by assigning
all of the grid cells within a particular region a unique Thematic Value. In this way,
each point also can be addressed as part of a Neighborhood of surrounding values.
If
primitive operations are to be flexibly combined, a processing structure must
be used that accepts input and generates output in the same format. Using the data structure outlined above, this
may be accomplished by requiring that each analytic operation Involve—
- retrieval of
one or more map layers from the map stack,
- manipulation of
that mapped data,
- creation of a
new map layer whose categories are represented by new thematic values
derived as a result of that manipulation, and
- storage of
that new map layer back into the map stack for subsequent processing.
The cyclical nature of the
retrieval-manipulation-creation-storage processing structure is analogous to
the evaluation of “nested parentheticals” in
traditional algebra. The logical
sequencing of primitive map analysis operations on a set of map layers forms a
spatial model of specified application.
As with traditional algebra, fundamental techniques involving several
primitive operations can be identified (e.g., a “travel-time map”) that are
applicable to numerous situations.
The use of these primitive map
analysis operations in a generalized modeling context accommodates a variety of
analyses in a common, flexible and intuitive manner. It also provides a framework for
understanding the principles of map analysis that stimulates the development of
new techniques, procedures and applications.
3.0 Spatial Analysis Procedures for
Reclassifying Maps
The first and in many
ways the most fundamental class of map analysis operations involves the
reclassification of map categories. Each
of the operations involves the creation of a new map by assigning thematic
values to the categories/regions of an existing map. These values may be assigned as a function of
the initial value, position, size, shape
or contiguity of the spatial
configuration associated with each map category (figure 3). All of the reclassification operations
involve the simple repackaging of information on a single map layer and results
in no new boundary delineations. Such
operations can be thought of as the “purposeful re-coloring” of maps.
