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Chapter 17: Map Algebra and Model Building 271

 

I’ve talked to literally hundreds of people who specialize in cartographic mod-

 

eling. Nearly everyone has told me that the key to good cartographic modeling

GIS

is to formulate the model through the use of flowcharting techniques. They

also tell me that you should normally create the flowcharts even before you

 

 

know what’s in your database. Such formulations have helped me decide what

 

should go into the model in the first place.

Making a formulation flowchart

The easiest way to formulate a model is by creating a formulation flowchart — a set of graphics and arrows showing steps in the modeling process. A formulation flowchart starts with the final desired product (the spatial information product), breaks it up into sub-models, and finally outlines the actual map elements that you need. Your software may have built-in flowcharting capabilities, you may have your own flowcharting software, or you can even (hold onto your hat here) use a pencil and paper. (Sometimes, this old pencil-and- paper way is the fastest.)

Suppose that you want to put up some solar panels to generate electricity. You call the map that you want to create solsites, meaning sites where you should place solar panels. You need to make sure that you fulfill three requirements of your solar-panel placement:

Each site must be at least 2 miles from town.

Each site should be on slopes of at least 30 degrees but less than 55 degrees.

The slopes must face south to get as much sun as possible.

Figure 17-13 shows your formulation flowchart.

 

 

 

needed

 

 

final output

submodel

operations

elements

 

 

good

south

elevation

 

 

aspect

aspect

 

 

 

Figure 17-13:

 

 

slope

 

A for-

solsites

good

elevation

mulation

slope

30-55

 

 

flowchart

 

 

 

 

for the sol-

 

good

dist>2mi

citylimits

sites model.

 

 

distance

 

 

 

 

272 Part IV: Analyzing Geographic Patterns

Expanding your sphere of influence

Allocation, which also works with networks (as I talk about in Chapter 15), involves finding all the areas within your sphere of influence, or your territory. Say that you and your brother decide that you want to put up small grocery stores at opposite ends of your town. You want to know which part of the town will visit your store and which part will visit your brother’s store. In other words, you want to allocate part of the town, and your brother wants to allocate the rest.

You can allocate portions of space to individual facilities in vector systems by using Thiessen

polygons, but you have a nice easy-to-under- stand way of doing it by using raster systems. First, identify the two targets (your grocery stores). The software starts moving out from each of those places to decide which grid cells it allocates to your store and which it allocates to your brother’s store. Say that your store has a value of 2, and your brother’s store has a value of 1 (see the figure). Depending on your software, it might start its search from your store or from your brother’s, but generally, the algorithm that the software uses alternates between the two of them.

1

1

1

1

1

1

1

1

 

1

1

1

1

1

1

1

 

 

1

1

1

1

1

1

 

 

Allocation

 

 

 

 

 

 

 

2

1

1

1

1

1

 

 

2

2

2

1

1

1

2

 

2

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1

 

Source Grid

 

 

Allocation Grid

 

 

When the software knows the locations of the target cells, it measures distance outward from those locations: 1 for each orthogonal cell and 1.414 for each diagonal cell. It examines each grid cell in the entire database. When it selects each cell away from the target, it compares its distance from each target-cell location. If a grid cell is closer to your store, the software

assigns it the same value as your store (2), but if the cell is closer to your brother’s store, the software assigns it a value of 1 to correspond to his store. Software differs in how it deals with ties, but most software assigns values based on the order in which it finds the cells. Consult your software documentation to figure out how it assigns ties.

Chapter 17: Map Algebra and Model Building 273

In Figure 17-13, notice how the final spatial information product on the left (solsites) breaks down into submodels that identify searchable aspects of the GIS data:

Good aspect and good slope: You can derive both of these submodels from manipulations and reclassifications of the same starting map element — topography (essentially, a Digital Elevation Model, or DEM). In this case, you want a south-facing aspect and a slope between 30 and 55 degrees.

Good distance: To determine an area that fits the good distance submodel, you measure 2 miles from the outside perimeter of the City polygon on a map layer containing city limits data.

You use the GIS software to combine the sub-models by using a map overlay operation (discussed in Chapter 16) called intersection, which means that it finds only those areas that include all the elements (2 miles from the city, slopes between 30 and 55 degrees, and a south aspect) for your solsites locations.

This basic model has all the elements that you need to make more complex models. You can break models into smaller pieces, and each of the pieces requires one or more map elements to produce it. And you can use the same map element to create multiple derived maps. Cool, huh?

Basing your database on your flowchart

When you finish a formulation flowchart, you know exactly what map elements you need to create the maps you want. Instead of relying on an existing database, you can make all the decisions about what maps, at what scales, and with what classifications you need to get your answer. You’re not even restricted by whether the maps exist. You’re creating a best-case scenario, and the most effect and most accurate models start with this kind of model-specific data.

Always take the time to develop a formulation flowchart of your cartographic model that includes everything you want to see the model contain without worrying about whether the data are available.

Implementing a Model

Implementing a cartographic model is really just the reverse of formulating it, but with one major difference. You can no longer assume that you have all the best data and all the map elements that you need to do the job. If you assume that you have all the layers at the appropriate scales and classification levels for your solsites model, you simply need to reverse the flowchart so that it moves from basic map element input to the final product (see Figure 17-14).

274 Part IV: Analyzing Geographic Patterns

Some GIS software has built-in flowcharting programs that do more than provide you with a flowchart. They actually populate the portions of the flowchart with data and take that data through its paces. Programs such as the ESRI Model Builder allow you to run the model many times, changing and modifying its formulas and its contents until it performs in exactly the way you want. Such flowcharting programs provide both documentation for how you constructed the model, and an efficient and repeatable way to reproduce it.

No matter what software you use, or whether it contains a modeling tool, your cartographic models probably don’t have the exact data, with the precise level of scale, containing exactly the categories available to you. You can deal with inadequate or improper data in three ways:

Find better data, if you can. Getting better data is always the best way to deal with inadequate data. In an ideal situation, you’d have the time to collect primary data specific to your needs. Time and resources may limit your ability to collect this kind of data, however. Consult with other GIS users in your area who may possess data that would work for you. If no one has any data that he’ll give you for free, you may have to purchase data from a commercial vendor.

Adapt the model to fit available data. Although it’s not the best solution, you can modify your model to adapt to what data you do have. You may have to leave parts of the model incomplete, be more general in your conclusions, or modify how the model arrives at its conclusions.

Employ surrogates. The final solution to data issues in cartographic modeling is to find data that you can substitute for the data that you really need. Such spatial surrogates (replacement data) might include housing in place of population, power lines for missing roads, and fire patterns to indicate wind direction and intensity.

You often have to use spatial surrogates based on rather anecdotal evidence. If it’s available to you, try to use literature, expert opinion, or even experimental evidence to make the strongest possible linkage between surrogates and the data for which they substitute. You can do

so by determining — and supporting with evidence — that one value is a reasonable approximation of the other.

Some of these techniques may require a leap of faith on your part, but remember, no kind of modeling is an exact science. So, I’m providing a disclaimer — I’m not responsible for the improper use of the output! You might want to include a complete explanation of the methods employed to create the output so that the user knows how reliable the model is.

Chapter 17: Map Algebra and Model Building 275

 

elements

operations

output

operations

final output

Figure 17-14:

elevation

south

good

 

 

aspect

aspect

 

 

 

 

 

An imple-

 

 

 

 

 

mentation

elevation

slope

good

combine

solsites

flowchart

30-55

slope

(union)

 

 

for the sol-

 

 

good

 

 

sites model.

citylimits

dist>2mi

 

 

distance

 

 

 

 

 

 

 

Testing a Model

No model is perfect. In many cases, you can’t get any correct answers — only defensible and indefensible ones. An often-neglected part of cartographic modeling involves testing the output. A true test of modeling often requires a truth set (a known correct answer) against which you test the output.

Unfortunately, visiting a location that you modeled probably can’t yield answers about whether your model is correct. Imagine, for example, trying to test a model that predicts the population distribution of your city in 2020. Unless you have a time machine, you can’t figure out whether the model is a perfect predictor of the distribution.

Over the years, I’ve discovered four aspects of GIS modeling that you can examine without the need for a time machine. The following sections cover these points in detail:

Is the software working correctly (giving you the correct numbers based on the algorithms)?

Does the model produce answers that aren’t too limiting or too general?

Is the outcome logical and consistent with the real world?

Is the user satisfied with the product?

Determining whether the software is working correctly

When you need to figure out whether the software algorithms are working correctly, you can most easily perform an analysis on a very small part of the database and check it against a manual computation of the same area.

276 Part IV: Analyzing Geographic Patterns

Assessing whether the model gives adequate results

You need to carefully consider whether the constraints that you put into your model give you adequate results. I’ve run models that attempt to show the most appropriate place to put a planned development only to have the model tell me that the majority of the unoccupied portion of the city will do nicely. If you get this kind of result, you need to rethink your model and tighten the rules and constraints. I also created a model to show the best

location for winter movement of troops, and the output gave me a blank map because I made the constraints too tight. Adjusting model constraints takes finesse; consult the user when you make adjustments so that you don’t violate the spirit or purpose of the model.

Gauging whether your model makes sense

Models must make sense. I can’t tell you how to determine whether a model makes sense because I’m probably not an expert in your particular field or discipline. Use your own background to assess whether the logic is consistent with how your portion of the real world works. To make this determination, you (and often the user) need to be able to interpret the model. Making your cartographic model understandable, you may need to provide ample documentation, make sure that the model employs easy-to-understand functions and operations, include flowcharts, and even keep the model simple and general enough that users can easily figure out its purpose and function.

Ensuring that your model satisfies the user

Most real-world GIS operations employ consulting firms to do their cartographic modeling (although this fact is changing). The users must be satisfied with the model. They might find a really accurate model worthless because

it doesn’t provide the answers that they want or expect, they can’t read or interpret the output (bad map design), the output is in the wrong format (for example, a travel log versus a map), or the GIS doesn’t deliver the model and output on time.

I don’t have any easy answers to potential problems of model-user dissatisfaction, but I do have one suggestion: Make sure that you always keep the lines of communication open with the users. If you keep the users involved throughout the process, they’re much more likely to accept the final product. A correct model is a useful model only if the user accepts it. Keep the user involved in every phase of your GIS work.

Part V

GIS Output and

Application

In this part . . .

AGIS analysis is only as good as its ability to communicate the results to the user. In this part, I show

you how you can use GIS to create traditional map output. Or you might opt for some radically different types of maps (called cartograms), which are sometimes even more effective at communicating your message.

But GIS output isn’t limited to maps; this part also introduces other types of output, including travel directions, lists, tables, animations, and flythroughs — all of which help boost your understanding of how to present the results of your analyses. Finally, this part offers a guide for how you can efficiently incorporate the GIS technology into your organization and take advantage of its transforming power.

Chapter 18

Producing Cartographic Output

In This Chapter

Finding your way around a traditional map

Understanding the usefulness of cartograms

In the past, trained cartographers in cartographic production shops made almost all the maps created. Their products were hard copy maps done

on parchment, paper, Mylar, or other surfaces, depending on the technology of the day. Today, large production shops are still available in government agencies such as the National Geospatial-Intelligence Agency (NGA) or in businesses (such as Rand McNally) that specialize in maps. Many professional cartographers do both production and cartographic design work for GIS companies, as well.

These large shops will likely be around for some time. They can always find a market for large volumes of well-designed maps, ranging from the general reference and atlas maps to content-specific thematic maps. Although the shops have staying power, their role in producing cartographic output is quickly and permanently changing because of the ready availability and rapidly increasing numbers of GIS software users.

When you work with GIS software, you’re the cartographer. Unfortunately, you don’t automatically inherit the training and experience that professional cartographers possess because you own the latest and greatest GIS software. GIS software provides you access to the cartographer’s toolkit, but many of those tools have specialized uses that require instruction and particular conditions under which you can and should use them.

The cartographic product of your GIS work is important. You can do the most elaborate and impressive GIS models in the world, but when you’re done, you need to produce a map that the user accepts and, more importantly, that exactly communicates the analysis.

This chapter shows some basic ideas behind how you can produce good maps. I show you some bad maps and describe how they detract from the quality of your GIS work. The more you work with GIS, the more maps you

280 Part V: GIS Output and Application

see. While you see more and more quality maps, you can begin to appreciate all the hard work that goes into them. More importantly, you start to see how the application of some basic principles can lead to effective map output.

Exploring Traditional Maps

Traditional maps are the most common forms of maps and generally the most easily understood by the general public. Reading and interpreting maps is much easier if the scales, symbology, classes, and graphic design elements are all focused on visual communication. (See Chapter 2 for more about how maps show information.) These principles hold true for computer displays, just like they do for maps put on silk, papyrus, or other non-computer surfaces.

Here are the five basic characteristics of good map design (the cardinal rules of mapping):

Make sure that the map meets users’ needs. Always make this characteristic rule number one. If the user can’t interpret the map or the map presents the wrong information, all your time and the results of your analysis are wasted.

Make the map easy to use and understand. Avoid confusion at all costs.

Accuracy is essential to good map design. As much as possible, avoid data errors, unintended data and graphic distortions, and misinterpretations.

The method of map presentation should relate correctly to the data.

Make sure that you use the right type of map — one with the right symbols, correct classes, scales, projections, and so on.

Allow the user to review and interact with the map during production.

Make sure the user understands what the map is all about, that it meets his or her needs, and that it communicates the information correctly.

Mapping qualitative data

Sometimes, when you create a map, you map qualitative (descriptive or nominal) data, which generally requires that you pick unique symbols for each category.

Many software programs set their default so that when you open your map of a certain set of polygons, the map contains the borders for each polygon, but the polygons themselves are all the same color. You may find this layout confusing the first time you see it, but don’t worry. All your information is there. The software defaults to this layout so that you can determine the colors and patterns you want to use for your map, as shown in Figure 18-1.

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