GIS For Dummies

In the clustered condition, some points are closer together than others. Put another way, the points in the clusters have many close neighbors, whereas the remaining neighbor distances are much farther apart. The mathematical technique that the GIS uses to make this determination is called, not surprisingly, the nearest neighbor statistic.

Figure 3-7:

GIS can determine whether this tornado pattern is clustered or random.

To determine whether a pattern of points is regular, random, or clustered, your GIS software follows these steps:

1.Find the random nearest neighbor distance by dividing one by twice the square root of the density of points.

In the tornado example, you realize when performing your analysis that the number of tornados for Illinois isn’t the same from one season to the next or from one year to the next. You need a measurement of the average nearest distance that would occur if the distribution were random.

That measurement is based on the density (number of points per unit area) of the distribution, which you identify with this simple equation: Random nearest neighbor distance = 1/(2 × square root of the density)

In this case, density is the number of tornados per square mile. The average nearest distance changes with the density but always gives you the nearest neighbor distance for a random pattern.

2.Calculate the average pair-wise nearest neighbor distance of your points.

The pair-wise part of this term indicates that each point (denoting a tornado location) is matched with only one other point as its nearest neighbor. And this statistic is pretty easy to calculate. The GIS software finds the x- and y-coordinates for each tornado location, measures the distance to every other location, and determines which location is the nearest neighbor. After collecting this data, the program calculates the average of these pair-wise nearest neighbors.

3.Divide the calculated average pair-wise nearest neighbor distance by the random nearest neighbor distance to compare distances for randomness.

After the software calculates the average pair-wise nearest distance, you need a way to compare the standard for random distributions with other types of distributions — regular and clustered. You just have to compare the measured nearest neighbor distance to the random distribution by dividing the measured (calculated in Step 2) by the random (calculated in Step 1).

4.Compare the number to 0 and 1, where 1 is perfectly random and 0 is perfectly clustered.

Numbers larger than 1 indicate a more regular pattern.

If you calculate the mean of all the nearest neighbor distances and divide that number by the random nearest neighbor distance — and you get a value of 1.0 — the measured nearest neighbor distance shows a perfectly random distribution. If the value you get is 0.0, this measurement is perfectly clustered (meaning as clumped together as you can get). If you get a value greater than 1, your distribution becomes more regular (more dispersed) as the number grows larger. No absolute value exists for determining perfectly regular distributions because the values you get depend on the density of points.

You can determine whether the values that you get from your analysis occur by chance or whether they’re truly meaningful, but you may want to leave that job for the statisticians in the crowd. You need to know only the nature of the distribution.

The nearest neighbor analysis is an effective tool for determining the pattern of point objects, but you can also use this analysis to evaluate the distribution of line objects, and even area and volume objects. You just need to let the software calculate the center of each line — or each polygon or volume feature — and then do the same calculation that you perform for point objects (for example, nearest neighbor). You use nearest neighbor statistics to make sure that what your eye has already told you is real and not a figment of your imagination.

Identifying even more patterns

Some calculations can help you identify different types of patterns. You can use certain techniques to determine the average direction of linear objects, such as tornado paths, fallen trees, boulder distributions, shelterbelts (protective barriers such as windbreaks), and many other objects. Without going into the trigonometry, it simply gives you a summary statement of the direction in which these events and objects occur. This calculation might, for example, tell you the direction of wind during storms, the movement of a glacier while it leaves debris behind, or the way that farmers line up planted trees to protect their crops from the wind.

Beyond these calculations of position and dispersion, you can find techniques for calculating the connectivity or circuitry of networks, the ratios of streams branching, the sinuosity of streams, the isolation of forest patches, and many more available inside the GIS software. In most cases, you can find these techniques simply by knowing the appropriate terms describing the condition of the geographic features you wish to examine (connectivity, isolation, and so on) and what they mean, and then searching for them in the help menu. The best part is that most GIS software not only tells you how the commands work, but it also frequently provides short tutorials that explain what the statistics do.

Interpreting the Results

and Making Decisions

Maps show many types of patterns and distributions. As you read more maps, you become more familiar with them and often recognize that many of the patterns are distinctive in their configuration, distribution, or location. The GIS provides you with a mathematical means to quantify and categorize these patterns so that you know they really exist. Although wielding such quantitative power is cool, you don’t use GIS just for fun unless, like me, you really like patterns.

Each pattern exists because of underlying forces, whether those forces are natural or human, random or focused, static or dynamic. After you become familiar with the idea of seeing and recognizing patterns for your own specialty, you next need to use your specialized knowledge to identify the reasons they exist. A process creates every pattern, and every pattern has an effect on the process that created it. As trees reseed themselves in a single plot of land, the density of trees increases. As the density of trees increases, the competition for space increases, and some trees die, thus reducing the density.

Part II

Geography Goes

Digital

In this part . . .

We live in a digital world, and that world is filled with all sorts of geographic features, surfaces, and dis-

tributions. In this part, I explain how getting the geography into digital form requires that you understand the different data models. You see how each model works and discover its impact on the way you store, retrieve, edit, and analyze geographic data. Dive into this part and get ready to feel much more comfortable with digital map data.

Chapter 4

Creating a Conceptual Model

In This Chapter

Compensating for your computer’s lack of map-reading skills

Understanding how to select the right maps for your GIS

Figuring out what you want in your maps

Inputting map data into your computer

Maps are complex devices that hold tons of information. Some of that information appears outright in the symbols, but a map imparts much

information more subtly, almost covertly. A single shading pattern that represents the distribution of a soil type explicitly shows where the soil is located. But such shading patterns also tell you what soils are adjacent to other types of soils, the relative amounts of each soil type, and even how often the types occur in a single piece of land.

For another example, if your map has point symbols that represent the locations of churches, each point symbol links explicitly to a church’s absolute map coordinates. And when you look at a church symbol on an area map, you can also see a measurable distance to other churches and to potential churchgoers, how many churches are in the area, and their locations within the area’s topography. If you’re looking for the Church on the Hill, you can probably find it on a hill.

Maps are complex, and human map readers (like you) interpret much of the information that those maps contain. So, to create a GIS that has both complex and useful information, you have to show the computer how to think like you do as a map reader.

Formulate a conceptual model (a picture in your mind) of how you plan to tell the computer all the information that you glean from a map. In this chapter, you can discover how to think very precisely about a map so that you can transfer that precision into your GIS projects.

Helping Computers Read Maps

A traditional map shows the properties of its features as a picture, and skilled cartographers do a good job of drawing the picture. When you see, read, and interpret the map, you often recognize properties because you know what the symbols in the picture mean. You might easily understand that topographic contour lines are close together on a map when the slope is steep, and they’re farther apart when the slope is more gradual. When you see a church on a hill, you know that it’s on a hill and that the people have to go up that hill to get there.

Then, along comes a computer, which really can’t read a map at all on its own. To the computer, contour lines are just a graphic representation of numbers located in its files. It doesn’t understand that the lines represent elevation values. Likewise, the computer doesn’t understand the kind of information that you glean from the map at a glance — for example, that a certain symbol represents a church, that the church is on a hill, that the roads leading up to the church must go uphill, and that those roads connect to a network of other roads leading to the people who attend that church.

You have to tell the computer all this stuff by constructing a conceptual model. You first figure out how the map was constructed and why it was made that way. You determine what decisions went into selecting the map areas, the categories of features included, and the graphics that represent the features. With these details in place, you can make a model that even your computer will love (or, at least, understand).

Embracing the Model-Creation Process

You can’t create useful GIS projects until you have a grasp of what you want to produce. In other words, you start the model-creation process with the big picture by asking what your final product needs to be. Then, you break down, or decompose, the final product into the general types (themes) of maps that you need to use. The last stage in the process involves determining which aspects of each map you need to examine. This final stage actually defines the map elements (features and their related data) that you ultimately plan to combine to create your final map.

Each GIS project has its own map elements, and each has its own proposed outcome. To decide what map features you need, you can just draw a simple flowchart (which is what I like to do), starting with the final outcome and successively breaking it down into themes and individual elements. I recommend that you create this flowchart without thinking about whether these data are available. That way, you devise the most detailed model with no compromises.