Chapter
14 - Query, measurement, and
transformation
14.1 Introduction: what is spatial analysis?
This
chapter begins a section of the book that reviews the scientific
core of GIS, the analysis of data beyond its
visualization. The first paragraph of this section is worth thinking
about: the skills and habits of thought you
learn in GIS can be applied to photographic, astronomic, and image
analysis as well as "mesoscale" human oriented investigations.
The
John Snow example is a perennial favorite of anyone trying to establish
the historical lineage of GIS as well as of medical geographers
pointing to the first explicit use of a spatially referenced database
in epidemiology.
The class assignments have already taken you fairly deeply into GIS analysis, although GTKAGIS postpones analysis to Chapter
9. In any case it is important that you relate the
sections of this chapter to operations we are doing in the assignments
and exercises; this is one of the advantages of working through
these two texts in
parallel.
For your reference, here is an outline of
the upcoming analytical topics of this chapter:
14.3
MEASUREMENTS
Distance & length
Shape
Slope and aspect
14.4
TRANSFORMATIONS
Buffering
Point
in polygon
Overlay
Interpolation
Thiessen
Inverse Distance
Weighting (IDW)
Kriging
Density estimation
15.2 DESCRIPTIVE SUMMARIES
Centers
Dispersion
Nearest-neighbor
Autocorrelation
Fragmentation |
14.2
Queries
You should be familiar with each of the catalog, map,
and table views of data, but consider how they give different views of
and access to the constituent databases, layers, and rows and columns.
We have also looked at histograms, and you should be aware that ArcMap
> Tools > Graphs > Create gives you access to a
variety of statistical visualizations, with some of the "dynamic link"
features shown in Figure
14.8. A query is usually a "Where is...?" question.
14.3
Measurements
It is always helpful to think
of the DATA to KNOWLEDGE hierarchy that GIS analysis affords. This logic
can be applied even to so simple a "toy" example as Figure 14.9 if you
think of transforming 4 data
points into a informational
mapped polygon whose area we then can know.
Study
the equation in Section 14.3.1 for a moment and appreciate not only its
power but that it can be applied to data in 3D and indeed any integral
dimension. In fact it is used as a metric to explain "distance" between
observations in multivariate space. I raise this point not only as a
mathematical insight but also to reinforce that, although we are
preoccupied with the data of geography, we are also learning about the
geography of data (think about that!).
The section
also introduced the term "polyline" which is also used by ESRI. To
inspect such an object look at the flight_path
data from GTKAGIS
Chapter 3, which is ___ lines linking ___ cities. If the number of
lines equals the number of points we have a "cycle" and Earhart would
have made it!
The
word "metric" is becoming quite popular and is often used to refer to
anything measured, but its more rigorous definition is some kind of
constructed variable that represents a phenomenon. In my environmental
work there are frequent references to "landscape metrics" such
as patch size and shape: fractal dimension,
diversity, heterogeneity, etc. I'm sure your own area of work/study has
similar concepts. Vice President Al Gore liked to invent them for
measuring government efficiency (and no, he didn't invent the
al-gor-ithm, but look up the etymology).
The subject
of shape is a rich area of fractal research. I had a George Mason
University graduate student write an MS thesis on the fractal analysis
of political districts (see Box
14.3). The simplest and most compact shape is a circle
(which is why bubbles are spheres), but for political districts
hexagons would be the next most desirable shape - if people were
spread uniformly on the land!
In GIS modeling slope
and aspect are commonly used as criteria for location (see GTKAGIS Chapter 20)
and we've also seen a related concept in the shaded relief data for the
Horn of Africa in Chapter 5.
14.4 Transformations
In the material world we and other animals are always making judgments
about spatial relationships (is that
apple attached to this
tree?), but it has taken a lot of difficult theoretical, algorithmic,
and programming work to implement these operations in GIS.
Much of this work has resulted in hundreds of various kinds of
transformations, some of which I've illustrated in a table
referenced earlier.
Among
the simplest transformations (but not always easy to implement for complex data) is
buffering, which is used extensively in GTKAGIS Chapter 12.
Note that almost any operation on vector data can also be done in the
raster domain. In fact, many of the operations in ArcGIS >
SpatialAnalyst take advantage of the speed and flexibility of raster
transformations, as simply illustrated in Figure 14.18 (which you should compare to Figure 6.9).
The first example in Section 14.4.2,
counting disease events among the population at risk in a region, is
the foundation of epidemiology and results in measures of prevalence
and incidence. If the pumps in John Snow's London had exclusive service
areas he could have used a GIS to make a choropleth of incidence and
easily focus on the source of the contaminated water.
To test your understanding of the polygon
overlay problem (and to refresh your memory of set theory) characterize
the 10
regions created in Figure
14.20. into 4
kinds. These operations cannot be done on the attribute data alone, but
only when the features are topologically defined and related in space.
And keeping Shrek from walking through Donkey requires gigabytes of RAM.
All of these operations are highly
scale-dependent. If a database has many small features, it will have
exponentially many overlay polygons. If it is generalized, the operation
will be much faster, although less precise. This is illustrated in Table 14.1 which is
not easy to understand unless you draw a vertical line between columns
6 and 7, separating the 5 individual layers from the 3 examples of
overlay. To see the kind of data being referred to, see Figures 12.8 and 15.13.
Spatial interpolation transforms
points into surfaces and objects into fields. Our Assignment #2 uses density estimation (Section 14.4.4.4). Each of the other sub-sub-sub sections is worth examining, at least for the graphics, but Kriging (Section 14.4.4.3) is only for the adventurous. To browse some excellent
examples of this, look at
C:\Program
Files\ArcGIS\Documentation\Geostatistical_Analyst_Tutorial.pdf
from
which Figures 14.23 and 30
are taken. This is a very technical field that nevertheless can result in quite elegant - and sometimes misleading -
transformations.
