GeoWorld January 2013

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Optimal Path Density Isn't All that Dense (Conceptually) BEYONDMAPPING S everal previous "Beyond Mapping" columns addressed "Backcountry 911," which considers on- and off-road travel for emergency response (see GeoWorld, July-September 2010; "Author's Note," page 11). Recall that the approach uses a stepped-accumulation cost surface to estimate travel time by truck, then all-terrain vehicle (ATV) and finally hiking into areas too steep for ATVs. The result is a map surface (formally termed an accumulation surface) that identifies the minimum travel time to reach all accessible locations within a BY JOSEPH BERRY project area. It's created by employing the "splash algorithm" to simulate movement in an analogous manner to the concentric-wave pattern propagating out from a pebble tossed into a still pond. If the conditions are the same, the effect is directly comparable to the uniform set of ripples. However, as the wavefront encounters varying barriers to movement, the concentric rings are distorted as they bend and wiggle around the barriers to locate the shortest effective path. The conditions at each grid location are evaluated to determine whether movement is totally restricted (absolute barriers) or, if not, its relative difficulty (relative barrier). The end result is a map surface identifying the "shortest but not necessarily straight-line" distance from the starting location to all other locations in a project area. travel time to the farthest-away location (Emergency Location #1 = 96.0 minutes away). The quickest route is rarely a straight line a crow might fly, but bends and turns depending on the intervening conditions and how they affect travel. The optimal path (minimum accumulated travel-time route) from any location is identified as "the steepest downhill path over the accumulated travel-time surface." This pathway retraces the route that the wavefront took as it moved away from the starting location while minimizing travel time at each step. The small plots in the outer portion of Figure 1 identify the individual optimal paths from three emergency locations. The larger center plot combines the three routes to identify their convergence to shared pathways: gray = two paths, and black = all three paths. Access Corridors The left side of Figure 2 simulates a response to all accessible locations in the project area. The result is an "optimal path density" surface that "counts the number of optimal paths passing through each map location." This surface identifies major confluence areas, analogous to water running off a landscape and channeling into gullies of easiest flow. The lightcolored areas represent travel-time "ridges" that contain no or very few optimal paths. The emergencyresponse "gullies," shown as darker tones, represent off-road response corridors that service large portions of the backcountry. These "corridors of common access" are depicted as increasingly darker tones that switch to red Back at HQ Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at 10 The emergency-response surface shown in Figure 1 identifies the minimum travel time via a combination of truck, ATV and hiking from headquarters (HQ) to all other locations. Travel time increases with each wavefront step as a function of the relative difficulty of movement, which ultimately creates a warped bowl-like surface with the starting location at the bottom (HQ = 0.0 minutes away). The blue tones identify locations of very slow hiking conditions that result in the "mountain" of increasing G E O W O R L D / J A N U A R Y 2 O 1 3 Figure 1. Multiple optimal paths tend to converge to take advantage of "common access" routes over a travel-time surface. Imagery/LIDAR Special Issue

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