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GeoWorld December 2012

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barriers affecting movement. It has two unique characteristics: 1. It forms a bowl-like shape with the starting point (or points) having the lowest value of zero = 0 units away from the start. 2. It has continuously increasing travel-time values, re���ecting the relative ease of movement that warps the bowl, with areas of relatively rapid increases in travel time associated with areas of high relative barrier ���costs.��� Step by Step A stepped accumulation surface (top-center portion of Figure 2) shares these characteristics but is far more complex, as it re���ects the cumulative effects of different modes of travel and the impact of their changing relative and absolute barriers on movement. Note the dramatic ���ridge��� running NE/SW through the project area���s center as well as other morphological ups and downs in total combined travel time. In a sense, this wrinkling is analogous to a terrain surface, but the surface���s con���guration is the result of the relative ease of on- and off-road travel in cognitive space���not erosion, fracture, slippage and subsidence of dirt in real-world space. However, like a terrain surface, an ���aspect map��� of the accumulation surface captures its orientation information, identifying the direction of the ���best-path��� movement through every grid location. The enlarged portion in the ���gure���s top right shows that the travel direction through location 90, 32 in the analysis frame is from the south (octant 5). The ���gure���s lower portion identi���es that the terrain direction at the same location is oriented toward the southeast (octant 4). Hence, we know that the movement through the location is across slope at an oblique uphill angle. Know the Code Figure 3 depicts a simple technique for combining the travel and terrain-direction information. A two-digit code is generated by multiplying the ���Travel Direction��� map by 10 and adding it to the ���Terrain Direction��� map. For example, a ���11��� (one-one, not eleven) indicates that movement is toward the north on a north-facing slope, indicating an aligned downhill movement. A ���15��� indicates a northerly movement up a south-facing slope. The ���gure���s center inset isolates all locations that have ���aligned uphill movement��� (opposing alignment) in any of the cardinal directions indicated by two-digit codes of 15, 26, 37, 48, 51, 62, 73 and 84. Locations having ���aligned downhill movement��� are identi���ed by codes of 11, 22, 33, ���Figure 2. Maps of travel and terrain direction are characterized by the aspect (bearings) of their respective surfaces. ���Figure 3. A two-digit code is used to identify all combinations of travel and terrain directions. 44, 55, 66, 77 and 88. All other combinations indicate oblique or orthogonal cross-slope movements or locations occurring on ���at terrain without a dominant aspect. I realize the thought of ���an aspect map of an abstract surface,��� such as a stepped accumulation surface, might seem a bit uncomfortable and well beyond traditional mapping; however, it can provide very ���real��� and tremendously useful information. Characterizing directional movement is needed in backcountry emergency response, and it���s crucial in effective timber-harvest planning, wild���re-propagation modeling, pipeline routing and myriad other practical applications. Such out-ofthe-box spatial reasoning approaches are driving geotechnology to a whole new plane. Author���s Note: For detailed discussions characterizing 1) ���backcountry 911,��� see Topic 29, Spatial Modeling in Natural Resources, sections 4-6; and 2) ���stepped accumulation surfaces,��� see Topic 25, calculating Effective Distance and Connectivity, in the online book, Beyond Mapping III, at www.innovativegis.com/basis/MapAnalysis. D E C 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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