Spatial Thinking in Planning Practice: An Introduction to GIS

49 ologies for performing a raster overlay (Chrisman 2002) 5 . 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 (Figure 9.4). It is o$en used in risk assessment studies where various layers are combined to produce an outcome map showing areas of high risk/reward. "e most common operators are addition, subtraction, multiplication, and division. In short, raster overlay simply uses arithmetic operators to compute the corresponding cells of two or more input layers together, uses Boolean algebra like AND or OR to !nd the pixels that !t a particular query statement, or executes statistical tests like correlation and regression on the input layers. "e Boolean connectors AND, OR, and XOR can be employed to combine the information of two overlying input raster datasets into a single output raster. Similarly, the relational raster overlay method utilizes relational operators (<, <=, =, <>, >, and =>) to evaluate conditions of the input raster datasets. In both the Boolean and re- lational overlay methods, cells that meet the evaluation criteria are typically coded in the output raster layer with a 1, while those evaluated as false receive a value of 0. "e simplicity of this methodology, however, can also lead to easily overlooked errors in interpretation if the overlay is not designed properly. Assume that a natural resource manager has two input raster datasets she plans to overlay; one showing the location of trees (“0” = no tree; “1” = tree) and one showing the location of urban areas (“0” = not urban; “1” = urban). If she hopes to !nd the location of trees in urban areas, a simple mathemat- ical sum of these datasets will yield a “2” in all pixels containing a tree in an urban area. Similarly, if she hopes to !nd the location of all treeless (or “non-tree,” nonurban areas, she can examine the summed output raster for all “0” entries. Finally, if she hopes to locate urban, treeless areas, she will look for all cells containing a “1.” Unfortunately, the cell value “1” also is coded into each pixel for nonurban, tree cells. Indeed, the choice of input pixel values and overlay equation in this example will yield confounding results due to the poorly devised overlay scheme. Figure 9.4 Mathematical Raster Overlay. http://2012books.lardbucket.org/books/geographic-information-sys- tem-basics/s12-geospatial-analysis-ii-raster-.html - Two input raster layers are overlain to produce an output raster with summed cell values. THE DIGITAL ELEVATION MODEL )DEM* "e United States Geologic Survey’s DEM is a popular raster !le format due to widespread availability, the simplicity of the model, and its extensive so$ware support. Each pixel value in these grid-based DEMs denotes 5 Chrisman, N. 2002. Exploring Geographic Information Systems . 2nd ed. New York: John Wiley and Sons. Chapter 9: Raster Data Models