GeoWorld November 2012

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crookedness. For example, the largest diversion ratio for the road network is 5.4—a crow-walking distance nearly five and a half times that of crow-flying distance. The average ratio for the entire network is 2.21, indicating a lot of overall diversion from straight-line connection throughout the set of roads. Summaries for specific path segments are easily isolated from the overall diversion ratio map—compute once, summarize many. For example, the U.S. Forest Service could calculate a diversion ratio map for each national forest's road system and then simply "pluck off" crookedness information for portions as needed in harvest or emergency-response planning. Now for Something Different The deviation index in Figure 3 takes an entirely different view of crookedness. It compares the deviation from a straight line connecting a path's endpoints for each location along the actual route. The result measures the route's "deflection" as the perpendicular distance from the centerline. If a route is perfectly straight, it will align with the centerline and contain no deflections (all deviation values = 0). Larger deviation values along a route indicate an increasingly non-straight path. The left side of Figure 3 shows the centerline proximity for two paths. Note the small deviation values (green tones) for Path1, confirming that it's generally close to the centerline. It's much straighter than Path2, which has a lot of deviation values greater than 30 cells away (red tones). The average deflection (overall deviation index) is just 3.9 cells for Path1 and 26.0 cells for Path2. But crookedness seems more than just longer diverted routing or deviation from a centerline. It could be that a path simply makes a big swing away from the crow's beeline flight—a smooth curve and not a crooked, sinuous path. Nor is the essence of crookedness simply counting the number of times that a path crosses its direct route. Both paths in the examples cross the centerline just once, but they're obviously very different patterns. Another technique might track the above/below or left/right deflections from the centerline. The sign of the arithmetic sum would note which side contains the most deflections. The magnitude of the sum would report how off-center (unbalanced) a route is. Or perhaps a roving-window technique could be used to summarize the deflection angles as the window is moved along a route. The bottom line (pun intended) is that spatial analysis is still in its infancy. Although nonspatial math/stat procedures are well developed and understood, quantitative analysis of mapped data is fertile Government Special Issue Figure 2. A diversion ratio map identifies the comparison of path vs. straight-line distances for every location along a route. Figure 3. A deviation index identifies the deflection from a path's centerline for every location along a route. turf for aspiring minds. Are any bright and inquiring grad students out there up to the challenge? Author's Note: For a related discussion characterizing the configuration of landscape features, see the online book, Beyond Mapping I, Topic 5: Assessing Variability, Shape and Pattern of Map Features, at BeyondMapping_I/Topic5. N O V E M B E R 2 O 1 2 / W W W . G E O P L A C E . C O M 11

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