Chapter 16 - Spatial modeling with GIS

Because GIS represents the real world in some way, it is part of a vast and deep area of human activity called modeling. This chapter, however, is a bit more restricted in that it discusses how GIS can be used to simulate real-world processes; hence there is almost always some notion of time at least implicit in GIS modeling.

16.1 Introduction

The concept of modeling, introduced in Longley et al Chapter 8, is here more fully developed. We are all familiar with a map as a model, as well as those 3D (actually 2½D)  relief models you have seen at parks, etc. Not often considered in GIS modeling, however, is the idea that time deserves equal attention in developing models.

The concept of spatial resolution is fundamental in digital modeling. For raster data it is simple: the width in the real world of a pixel.  (For example, use the Measure Tool in ArcMap to measure the width of a pixel in GTKArcGIS\Chapter04\Bathymetry\seafloor.tif, or look at its Properties > Source > Raster Information > Cellsize. But resolution for vector data is more complicated because, for example, a line can be represented as any number of points the data collector has time and money to collect. (In the case of Chapter04/flightpath.shp the shortest line segment is at the beginning of the polyline and appears to be about 110 kilometers, so we could estimate the resolution of this data as about 100 kilometers, but it also depends on how accurately and precisely the cities are measured.

A very simple model I developed shows how 16 agents might interact as they move among 32 cells; a red (infected) agent infects any blue agent with which it shares a cell. A vastly more complicated model is the Santa Barbara evacuation simulation discussed in Box 16.2 and cited at several other points in the textbook. Figure 16.6 shows an approach to the resolution problem for polylines.

16.2 Types of model

Although modeling is a universal activity, there are ways of categorizing models as illustrated by the arguments of this section. An introductory chapter of my PhD dissertation develops a taxonomy of models depending upon whether they are:
  • static v. dynamic
  • hierarchical v. non-hierarchical
  • stochastic v. deterministic, and
  • spatial v. non-spatial
    • making 24 = 16 possibilities. Using these criteria, what kind of model is discussed in Box 16.3? Note that GTKAGIS Chapter 20 shows you how to use ModelBuilder to carry out the operations of Chapters 11 and 12.

    Simple cellular automata (CA) illustrate the fundamental GIScience ideas of what/where/when by reducing reality to a grid of binary-valued (0/1) cells that evolves in integer time. The easiest way to understand cellular automata is to search on 'the game of life' and play with the original CA developed by John Conway in 1970 (or go to the website in Box 16.5). Cellular models are used by the USGS in urban simulation in the Chesapeake Bay Watershed (among other places) and the techniques - even the metaphysics - of cellular automata are extensively developed by Stephen Wolfram in his A New Kind of Science book and associated software.

    Although the basics of map algebra discussed at the end of the section was developed by Dana Tomlin, much of its functionality has been incorporated into ArcGIS > Toolbox > Spatial Analyst Tools, where you can inspect the operations.

    16.3 Technology for modeling

    If you haven't made or used models then discussing the concept of "meta-models" (i.e. models about models) can seem fairly dry. Until you may do so, think of the GIS exercises, assignments, and projects you are doing as building a model of reality in silico, and you are invited to speculate about how your models fit into a particular scheme or taxonomy.

    16.4 Multicriteria methods

    The application of GIS to decisionmaking has evolved from a well-developed post-World War II field of "programming" that attempts to apply engineering and mathematics to complex real-world problems. Such systems as linear programming, PERT-charting, Delphi collaboration, etc. constitute an area of hard/soft scientific collaboration. As with GIS, debates continue to rage about how effective such techniques are and, more importantly, whether they can ever take into account all of the criteria that people find important but difficult to express, let alone quantify (beauty, sympathy, spirituality, etc). But you should read the part of this section that makes the quite valid point that modeling (GIS or otherwise) can bring diverse "stakeholders" to the table to argue explicitly over what they may not have been able even to consider, let alone bargain about.

    And the claim that n factors have n(n - 1) / 2 pairs doesn't begin to account for the fact that these factors can actually be combined in n2 ways.

    I think that J. Ron Eastman (Box 16.6 and Figure 16.15) is one of the great GIS leaders, and would be quite happy to teach using Idrisi, which has much of the power of ArcGIS but is much less expensive.

    16.5 Accuracy and validity: testing the model

    We have discussed the problem of uncertainty in Chapter 6, and hopefully you are experienced enough with the incredible mistakes that fast but dumb computers make so that you retain a healthy skepticism about their results. This class is intended to extend that skepticism to such GIS products as maps and predictions. Because you now have some experience with manipulating spatial models you can see how dependent they are on the choices made by their users, the quality of their data, and the operations they are designed to carry out. When you have made a map and discussed its implications, ask yourself if you would trust it as a foundation for an important decision. The answer is rarely an unqualified "yes." But as this section argues, there are many ways to test models so that their results can be less trustworthy.