Issue link: http://read.dmtmag.com/i/29869
Fruit Salad That’s where a “mixed-fruit” scale comes in. As depicted in the top portion of Figure 2, elevation on the left and slope on the right have unique raw data distributions that can’t be directly compared. The figure’s middle portion illustrates this, using the standard normal variable (SNV) equation to “normalize” the two maps to a common scale. This involves retrieving the map value at a grid location, subtracting the mean from it, and then dividing by the standard deviation and multiplying by 100. The result is a rescaling of the data to the percent varia- tion from each map’s average value. The rescaled data no longer are “apples and oranges,” but a mixed-fruit salad that uses the standard normal curve as a common reference, where +100 percent locates areas that are one standard deviation above the typical value, and -100 percent locates areas that are one standard deviation below. Because only scalar numbers are involved in the equation, neither the spatial nor the numeric relationships in the mapped data are altered—like converting temperature readings from degrees Fahrenheit to Celsius. The middle/lower portion of Figure 2 describes the comparison of the two SNV-normalized maps. The normalized values at a grid location on the two maps are retrieved and then subtracted, and the absolute value is taken to “measure” how far apart the values are. For example, if Map 1 had a value of -100 (one standard deviation below the mean), and Map 2 had a value of +200 (two standard deviations above the mean) for the same grid location, the absolute difference would be 300—indicating very different information occurring at that location. Standard Standards? Figure 3 shows the SNV comparison for the elevation and slope maps. The red areas indicate locations where the map values are at dramatically different positions on the standard normal curve; blue tones indicate fairly similar positioning; and gray is where the points are at the same position. The median of the absolute difference is 52, indicating that half of the map area has differences of about half a standard deviation or less. In practice, SNV comparison maps can be generated for the same variables at different locations or different variables at the same location. Because the standard normal curve is a “standard,” the color ramp can be fixed, and the spatial pattern and overall similarities/differ- ences among apples, oranges, peaches, pears and pomegranates can be compared. All that’s Mobility/GPS Special Issue Figure 3. The absolute difference between SNV-normalized maps generates a consistent scale of similarity that can be extended to different map variables and geographic locations. Figure 2. Normalizing maps by the standard normal variable (SNV) provides a foothold for comparing seemingly incomparable things. required is grid-based quantitative mapped data (no qualitative vector maps allowed). Author’s Note: For more information on map normalization and comparison, see the online book, Beyond Mapping III, posted at www.innovativegis.com, Topic 18, Understanding Grid-based Data, and Topic 16, Characterizing Patterns and Relationships. A P R I L 2 O 1 1 / W W W . G E O P L A C E . C O M 11