5.3: Overlay Analysis

Overlay is one of the most common and powerful GIS functions. It investigates the spatial association of features by “vertically stacking” feature layers to investigate geographic patterns and determine locations that meet specific criteria.

It is the best-known GIS function, but examples of overlay predate computers and GIS. A simple but powerful example was described in Chapter 1: Dr. Snow overlaid water pumps over cholera deaths to see a spatial pattern and infer a connection between water and the disease. Other, more sophisticated, overlay analyses also occurred before the advent of GIS. In the 1960s, Ian McHarg sought a better way to plan land use, taking into account the physical environment and human factors. In Design with Nature (1969), McHarg formalized his site planning process based on overlay transparencies. He created hard-copy transparent maps for each relevant human (historic values, scenic vistas, social costs, etc.) and physical (slope, surface drainage, riparian areas, susceptibility to erosion, etc) factor. Each transparency included shades ranging from dark tones (areas with high values) to light tones (areas with low values). Physically, the transparencies were superimposed upon each other over the study area’s base map. A composite map revealed dark tones over areas where multiple layers had high values (high impacts) and light tones in regions with low impact values. McHarg felt that planners needed to undertake this process to determine which areas should be left natural and which places were suitable for development. His book and method were so popular that many of the first GIS projects attempted to formalize his technique using GIS.

Today, there are many types of GIS overlay. Vector and raster models both perform overlay, but their overlay functions differ considerably and thus will be discussed separately.

Vector (Logical) Overlay

Vector overlay predominantly overlays polygons in one layer over polygons in another layer, but it can also be used to overlay point or line features over polygon layers. Sometimes referred to as topological or logical overlay, it is conceptually and mathematically more demanding than raster overlay. There are three types of vector overlay operations:

Polygon on polygon is where one polygon layer is superimposed over another polygon layer to create a new output polygon layer. The resultant polygons may contain some or all of the attributes from the polygons in which they were created. Several types of polygon on polygon overlay exist, including intersection (A and B), union (A or B), and clip (A not B). These Boolean operators work both on the attribute table and the geography.

• Intersection computes the geometric intersection of all of the polygons in the input layers (see Figure 5.9). Only those features that share a common geography are preserved in the output layer. Any polygon or portion of a polygon that falls outside of the common area is discarded from the output layer. The new polygon layer can possess the attribute data of the features in the input layers.

Figure 5.9: Intersection of two layers.

• Union combines the features of input polygon layers (see Figure 5.10). All polygons from the input layers are included in the output polygon layer. It can also possess the combined attribute data of the input polygon layers.
  

Figure 5.10: Union of two layers.

• Clip removes those features (or portions of features) from an input polygon layer that overlay with features from a clip polygon layer (Figure 5.11). The clip layer acts as a cookie cutter to remove features (and portions of features) that fall inside the clip layer.

Figure 5.11: Clipping one layer from another.

Point in polygon is where a layer of point features is superimposed over a layer of polygon features. The two layers produce a point layer that includes attributes from the surrounding input layer polygons (Figure 5.12). Alternatively, you can tally the number of point features falling within each polygon and store the sum as a new attribute in the polygon layer. Other point attributes can be aggregated (summed, averaged, etc.) and included as attributes in the polygon’s data file. The transferring of attributes based on their geographic poistion is called a spatial join.

Figure 5.12: Point in Polygon.

Line on polygon is similar to point in polygon, but lines are superimposed on polygons. This type of spatial join either appends polygon attributes to line features falling within them or counts and aggregates line attribute data to the polygon layer’s data file.

Raster (Arithmetic) Overlay

Raster overlay superimposes at least two input raster layers to produce an output layer. Each cell in the output layer is calculated from the corresponding pixels in the input layers. To do this, the layers must line up perfectly; they must have the same pixel resolution and spatial extent. If they do not align, they can be adjusted to fit by the preprocessing functions discussed in Chapter 3. Once preprocessed, raster overlay is flexible, efficient, quick, and offers more overlay possibilities than vector overlay.

Raster overlay, frequently called map algebra, is based on calculations which include arithmetic expressions and set and Boolean algebraic operators to process the input layers to create an output layer. The most common operators are addition, subtraction, multiplication, and division, but other popular operators include maximum, minimum, average, AND, OR, and NOT. In short, raster overlay simply uses arithemetic operators to compute the corresponding cells of two or more input layers together, uses Boolean algebra like AND or OR to find the pixels that fit a particular query statement, or executes statistical tests like correlation and regression on the input layers (see Figure 5.13).

Figure 5.13: Raster Overlay. Using layers 1 and 2, all sorts of overlay are possible.

Correlation and Regression

Correlation and Regression are two ways to compute the degree of association between two (or sometimes more) layers. With correlation, you do not assume a causal relationship. In other words, one layer is not affecting the spatial pattern of the other layer. The patterns may be similar, but no cause and effect is implied.

Regression is different; you make the assumption that one layer (and its variable) influences the other. You specify an independent variable layer (sometimes more than one) that affects the dependent variable layer. Figure 5.14 shows a precipitation (dependent) and elevation (independent) as the layers.

Figure 5.14: Is there a spatial relationship between these two layers? Correlation and regression tests allow you to overlay layers to test their spatial relationship.

With both statistical tests, you compute a correlation coefficient, which ranges from -1 to +1. Positive coefficients indicate that the two layer’s varaibles are associated in the same direction. As one variable increases, the other variable increases (both can simultaneously decrease too). The values closer to +1 describe a stronger association than those closer to zero. A negative coefficient depicts two layer’s variables that are associated but in opposite directions. As one variable increases, the other variable decreases. Values closer to -1 have a strong negative association. If the correlation coefficient is near zero, there is little to no association. Both of these processes are raster based.