GIS For Dummies

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The Neighborhood Function on an Individual Neighborhood

Defining your neighborhood’s size and shape

To create a simple search pattern, search for the eight neighboring cells around your target cell in a 3-x-3 matrix. That configuration is called an annulus (donut shape) with a search radius of one cell (as shown in Figure 17-7). An annulus could search two cells away from the target, three cells, or more.

The Neighborhood Function on an Individual Neighborhood

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You can also evaluate neighborhoods that include rectangles of all nine cells (including the target cell), wedges (pie shapes) in different directions, and circles (including the target cell). In short, you can choose from a few different geometries to define your neighborhood search area.

You select the geometry of your neighborhood for focal functions based on how far away from the target cell you need to go to evaluate grid cells. The distance is often a function of how the real environment you are modeling works (for example, how far from a gas leak you might encounter a fire hazard).

Focusing on focal flow

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You might be scratching your head, wondering how you might need all these different shapes for neighborhoods. Most people will never use all, or even most, of these shapes. Here are a few points about size and shape of impact areas to help you decide on your neighborhood geometries:

The size of your neighborhood area is based on the area of impact of the attributes you’re looking for. Sounds impressive, no? If you know, for example, that people can hear construction noise for ten miles from its point of origin, you can define your neighborhood as a circle with a radius of ten miles.

Circular shapes are common GIS search patterns. The circle is the most compact two-dimensional shape, and is easy to reproduce. The types of features that occur as circles and can take advantage of this circular search methodology are:

•Center-pivot irrigation circles

•Circular animal mounds and ant nests

•Exposed rock domes and salt domes

•Some archaeological sites and Indian mounds

•Coppice dunes

•Crop circles . . . okay, that’s a bit of a stretch — but crop circles exist, no matter who (or what!) creates them

You can search neighborhoods with rectangles because many human features occur in that shape. You’ve probably seen many housing subdivisions divided up into square blocks. You could certainly make a block of a certain size into a neighborhood.

Other shapes can simulate real-world shapes during search. Some shapes are more obscure than circles or rectangles, but some types of features, both natural and man-made, have these kinds of geometries:

•A ring of vegetation around the base of hills, or around ponds and small lakes, forms an annulus.

•Wedges might describe alluvial fans and river deltas, and even the pie-shaped crop types within a single center-pivot irrigation feature.

You can no doubt come up with other characteristics that define your neighborhoods. Each feature that you include in your search provides a reason for you to select the size and shape of your neighborhood. The exact syntax for how you make this selection varies with your GIS software, but essentially, you define the shape and the search size as part of your search strategy.

Comparing your neighborhood to the target cell

After you know the size and shape of your neighborhood (as I talk about in the preceding section), you need to decide what properties you want to use

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to compare your neighborhood cells to the target cell. You can use pretty much all the operators you have available in the local functions for focal functions, as well.

Figure 17-8 shows two simple 3-x-3 annulus examples, one that uses the majority and another that uses the maximum. The first search is a focal majority that returns the number that occurs most often in the annulus to (the eight-cell ring around) the target cell. The focal-maximum search returns the highest number that occurs in the eight-cell ring.

Exploring zonal functions

Unlike focal functions (discussed in the preceding section), zonal functions don’t create neighborhoods. They use zones, either from a single grid or from other layers to compare cells by either attribute (description) or shape (geometry). You need to define the zone with which you want to work. A zone is equivalent to what geographers call formal regions. Regions are areas or groups of areas that share common descriptive information. In a raster data model, a region (or zone) is a group of grid cells that have the same attributes.

Formal geographic regions can be contiguous (all in one chunk), perforated (with holes that have different attributes), or fragmented (like islands that share attributes).

Comparing zonal values

Like with local functions, you can apply a large array of quantitative and logical operators to zonal functions. The most common such operators include majority, minimum, maximum, mean, median, minority, range, standard deviation, sum, and variety.

The general approach to zonal functions follows these basic steps:

1.Create one input layer, called the zone layer (Ingrid 1 in Figure 17-9), as the top layer for comparison.

The zone layer defines the zone or zones that you want to evaluate.

2.Create another input layer that has the values you want to use to evaluate for each zone (Ingrid 2 in Figure 17-9).

3.Perform the comparison functions for each zone.

For example, you may want to find the variety for each different zone (as shown in Figure 17-10). Finding the variety tells you which zones (Ingrid 1) have the greatest number of different types of features based on the

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grid categories contained in each zone. Ecologists might use this type of function when they want to identify areas of high biodiversity (variety of habitat, for example).

The Neighborhood Function on an Individual Neighborhood

Value = no data

The Neighborhood Function on an Individual Neighborhood

In raster GIS, area is calculated by adding up the sizes of all the grid cells included in the zone. Details of calculating sizes of geographic features are outlined in Chapter 12:

Area: The number of grid cells multiplied by the area of the ground that each cell represents.

Perimeter: The sum of the widths of the outermost grid cells if they’re orthogonal (edge to edge) and the sum of the diagonals for each cell if they’re diagonal.

The zonal function can find the centroid (center of an area) for determining the orientation of a polygon (as discussed in Chapter 13). Identifying the centroid allows you to compare the centroid of one fragment or zone to another, which you can use to measure isolation (which I discuss in Chapter 12).

In raster, polygon means a collection of grid cells of the same value or attribute.

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Azonal area.

Expression: ZONALAREA(INGRID1)

Understanding block functions

Sometimes, you need to resample a set of grid cells to a coarser group of grids (bigger grid cells) so that the set matches other raster layers. For example, if a grid has 20-meter grid cells representing 1951 land use, and you want to compare that to Landsat Multi-Spectral Sensor (MSS) data representing 1975 land use in 80-meter pixels (think of these as grid cells derived from satellites), you can generalize the 1951 grid cells so that they match the 1975 pixels. You need to group blocks of grid cells and reclassify them so that they match the 80-meter pixels by using the block function.

The block function takes a uniform, non-overlapping block of grid cell values and changes them based on any of the following operators: mean, majority, maximum, minimum, median, minority, range, standard deviation, sum, and variety — the same operators that are available for zonal functions.

The following steps demonstrate how the block function works:

1.Define how big you want the neighborhood (the block) to be.

In the example (shown in Figure 17-12), I define a 3-x-3 block, but your blocks can be any size you want, as long as they stay the same throughout the whole grid.

2.Define the operator that you want to apply to the block.

In this example, I’m using a block maximum operation. So, for each nonoverlapping 3-x-3 block, the software looks over all the numbers and searches for the largest number in the block.

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3.Create an output grid and assign the values resulting from the operation to each cell in the block.

Now, the difference between focal and block functions becomes really clear. In focal functions (which you can read about in the section “Using focal functions,” earlier in this chapter), the software takes that maximum number and assigns it to a single focal cell in the output. In contrast, the block function assigns the maximum number to the entire block: All nine grid cells in each block get the maximum value.

Neighborhood (3X3)

Using global functions

Global functions are the exact opposite of local functions (as discussed in the section “Using local functions,” earlier in this chapter). Instead of seeing the database from a local function’s worm’s eye view, a global function takes the bird’s-eye view — it can see and operate on the entire study area at the same time. Global functions are very powerful and complex operations. Here are some examples:

Distance measures: Such as Euclidean distance, Manhattan distance

Surface functions: Such as finding basins, pour points, and drainage networks

Interpolation functions: Such as linear, nonlinear, trend surface, and exact

Hydrology functions: Such as water accumulation and flow direction

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You can also use two other groups of global functions — the groundwater global functions and the multivariate global functions.

The really geeky groundwater global function

The groundwater global functions are some of the most complex functions available in the standard GIS software package. They’re almost universally raster based and allow you to not only model the flow of liquids in different substrates (permeable material that fluids flow through), but also in different thicknesses of substrate (for example, underground aquifers), and with different amounts of head gradient (the amount of pressure based on the slope through which the underground water moves). These functions also allow you to analyze the movement of dissolved solids within these systems, which you might use to model point (occurring at a single source) and non-point source (occurring over an area) pollution.

Many hydrological engineering programs and specialized GIS software packages deal explicitly with subsurface flows and groundwater movement. Many general GIS packages are now incorporating some of these sophisticated operations to satisfy an increasing customer base. I don’t want to bog you . . .

or me . . . down in the gory detail of these models. If you’re a hydrologist, you can find documentation about these functions.

The radical fringe global functions

The multivariate functions of the GIS aren’t technically GIS functions at all — they’re a collection and implementation of traditional statistical functions, including some very sophisticated techniques familiar mostly to statisticians. I don’t go into detail about these functions, but you should know that most professional GIS packages have some of these functions built-in.

Formulating a Model

Whether you use map algebra or any other approach to GIS analysis, you probably use more than one map and more than one analytical technique to answer your questions. These combinations of maps and techniques are generally part of a complex set of ordered operations (operations done in a logical sequence) that GIS people call a model.

Some call this ordered operation and its output just a model, some a spatial model, some a GIS model, but the term most commonly applied by analysts is a cartographic model. It’s called a cartographic model partly because C. Dana Tomlin and Joe Berry coined that name years ago, but also because it just makes sense. You’re making models that result in maps. Mapmaking is cartography. So, you become, in essence, your own cartographer who makes and combines maps to answer questions. Hence, a cartographic model.