Chapter 3 - Representing geography

In spite of its relatively short length, this chapter introduces some of the fundamental concepts you should take away from geographic information science (GIScience). (Plus it talks about fractals!) Probably the most important reason this course is offered to you is the growing consensus that geographic science - as presented in the tools of GIS - is central to environmental studies.

What is represented on page 61: what data, where, and what direction is north?

3.1 Introduction

The argument behind Figure 3.1 appears in many places throughout geography, and can be traced as well to Feynman diagrams (cf. Wikipedia). Although the "map" obscures the idea, think of the volume as 3 having dimensions: (X, Y) in physical space and T vertically as time. So if you move to the north at a high velocity your green line is steep and moves to the upper-right on the page. Question: what if the agent were confined to a 1-dimensional spatial line?

3.2 Digital representation

Everything is a digit, and there are even (sane, intelligent) people who think that the universe is a computer (e.g. Stephen Wolfram). Although any map can rightly be called a geographic information system, it's not strictly a GIS, which has got to be in a computer somehow.

The box on binary numbers is worth reading with a pencil: 0 = 0, 1 = 1, 10 = 2, 11 = 3, 100 = 4 and so forth. Imagine how you would count if you had only 3 fingers with finger #1 counting up to 1, finger #2 up to 2 and finger #3 up to 4. How high could you count (what if all 3 fingers were up)?

3.3 Representation for what and for whom?

Although "geographic representation" is by definition concerned with the Earth, GIS techniques are universal: Google is now mapping Mars; I have an astronomy program that maps galaxies; and I've used ArcGIS to analyze an MRI. I'd be comfortable saying that any representation of something that exists in space and time could be considered an example of GIS. But again, I'm not a GIS enthusiast (though I guess I sound like one!).

To extent this argument, GIS is concerned with modeling objects and fields in space

3.4 The fundamental problem

Consider in detail the measurement on pp. 68-69 in light of the S/T/P paradigm I mentioned earlier:

SPACE  LONGITUDE:   120°  0' W  
 LATITUDE:    34° 45' N
TIME  TIME: 12:00 (GMT -8)
PHENOMENON  TEMPERATURE: 34° 

I shall often insist that we think clearly in this Where/When/What trichotomy; it will make planning original research much easier. And these dimensions aren't always clear - is that daylight savings? Is temperature in Celsius? Is longitude measured first?

Extra where is that location?

I'm not sure why Box 3.3 doesn't have a table:

LEVEL EXAMPLE VISUALIZATION TYPICALITY
Binary Developed/undeveloped  Table Mode
Nominal Los Angeles Table (pie?) Mode
Ordinal Poor < OK < Improved Bar plot Median
Continuous  50 kg. Histogram Mean

These are extremely important concepts ignorance of which can get you into big analytical trouble; e.g. you can't run a histogram on nominal data (but what similar tool can be used?) Begin with the distinction between nominal v. continuous data and break each one down further.

Two other "qualities" beyond S/T/P (SPACE/TIME/PHENOMENON) I add are scale and uncertainty, which inhere in all data. If you zoomed in on Figure 3.3 you'd eventually see the 250m pixels (how big is that measurement in terms of the room you're sitting in - unless you are outside?). The raster image has a resolution that cannot be improved upon: there's no more data beyond the 1/4 kilometer square.

3.5 Discrete objects and continuous fields

An innovation of GIScience is the distinction between objects and fields - or "things" and "stuff" as I like to call them. In a GIS these are usually (but, alas, not always) represented as vectors and rasters. Here's a table from an article I wrote:

OBJECT FIELD
GIS Vector Raster
Language Things Stuff
Example Fire hydrant Temperature
Figure 8.4 3.12

And this distinction lends itself well to the basic questions: You would ask "Where is y?" about an object but "What is at x?" about a field (try asking them about the Examples in the above table). You can also relate the above table to the discussion in Table 3.3 of the book (but note that the columns are reversed).

Objects lend themselves well to the usual spatial/attribute GIS distinction: Figure 3.5 is a picture of female BEAR 002 who can be found at about (X, Y) = (489, 5258) or perhaps as a dot in Figure 8.4 but she's too small to be seen in Figure 8.5 (note the coordinates at the bottom left of the image, in meters UTM, which I've rounded to kilometers above).

3.6 Rasters and vectors

Think of a raster as an often quite large rectangular table of numbers (or perhaps nominal values, as in Figure 3.8). Such GIS data structures may also be called an "array, matrix, image," etc. The simplest possible kind of raster would have binary values (0 or 1, black or white, etc). TASK Find an example of a binary array in Chapter 4.

It may also be helpful to think of objects as having explicit locations (e.g. EAST and NORTH, as in Table 3.1) but fields as having implicit locations (as in COLUMN and ROW, as in Figure 3.8).

Task For the westernmost Douglas fir cell, what is its ROW ________ and COLUMN ________?

By now you may be able to tell that a lot of my "highlighting" comments on the text relate to graphics. I do read the text, but a considerable amount of the meat of this book is in its excellent exhibits (tables and especially figures). For example, Figure 3.11 is a concise "cartoon" showing six different ways of representing a field. Frames A and C are regular samples (shown as points and cells); B is an irregular sample and could also be used to "partition" space as in E or as the basis for "interpolation" as in F. And so forth.

In other words, study the section headings, skim the text for topics of interest, study the graphics and the associated text. reading cover-to-cover is not recommended, but if you become familiar with the content the text will become an excellent reference manual.

3.7 The paper map

Remember that GIS is thousands of years old if you think of all maps (even ones drawn in the dirt outside a cave) as a way of managing spatial data. Consider the following scenario. "I saw the tree with the ripe berries on it about this far from the big rock at the bend of the river over the hill." So she is relating the objects (which?) to their spatial arrangement in her experience, using marks in the dirt. All without taking this class!

The all-important matter of scale is treated rather lightly here. Consider the USGS map of Redding (California!) in Figure 3.14. If it is actually shown at a scale of 1:24,000 (as is the paper map you can buy from USGS), then the distance from Manzanita School to Magnolia school, which is 3 cm. on the page, is 24000 × .03 meters = 750 meters on the ground. TASK What is the length of the Benton Airport runway in feet?

The figure is a representation of a digital raster graphic (DRG) in which objects are first drawn on a plate, then printed, then scanned to make a raster; but the original map is a representation of vector objects. (Then of course the image is digitally inserted in the file from which the textbook is printed...)

Anyway, the paper map will continue to be with us for a long time. I never go kayaking without a paper map (OK, perhaps a plastic map, but certainly not a computer map, though I often take my GPS receiver).

3.8 Generalization

This is an extremely deep subject that guides decisions about how much information to display on a map or analyze in a model. Section 3.8.1 lists a few of the several techniques used in "data reduction" and Figure 3.15 uses "toy" examples to illustrate some of them. Meditate on the "Refinement" frame showing how to generalize a river network (or tree?). How many creeks, brooks, streams, tributaries, etc can you leave out before you lose the river entirely? TASK Think about why you would want to do this in the first place?

You could also think about generalization in the phenomenon dimension (remember S/T/P?) by reducing a database of animals counted in a region from counts of Monarch Butterflies. You might just count all butterflies and generalize at the Family level:

Kingdom: Animalia (Animals)
    Phylum: Arthropoda (Arthropods)
        Class: Insecta (insects)
            Order: Lepidoptera (butterflies)
→            Family: Danaidae (Milkweed butterfly family)
                    Genus: Danaus
                        Species: Plexippus

You might even generalize to the level of just "insects" (but never say "bugs" which is Order Hemiptera within Insecta!).

A nice example of generalization in more detail is shown in Figure 3.17 which is a "toy" case of a line simplification algorithm actually used in ArcGIS (though I don't think we have that particular extension in our software). The generalization proceeds from top to bottom, representing the line (say a river) first as 15 points and eventually as 7 points. We'll encounter this idea again in Box 4.6.