Issue link: https://read.dmtmag.com/i/27856
I really got was “dropping the ball.” In looking back, I now realize that an “additive factor table” could have been a key to the solution. The table in Figure 2 shows the “costs/payments” of downhill, across and uphill movements. For this simplified example, imagine a money-exchange booth at each grid location—the toll or payout is dependent on the direction of the wave front with respect to the surface’s orientation. If you started somewhere with a $10 bag of money, depending on your movement path and surface configuration, you would collect a dollar for going straight downhill (+1.0), but lose a dollar for going straight uphill (-1.0). The table summarizes the cost/payout for all the movement directions under various terrain condi- tions. For example, a northeast step is highlighted (direction = 2) that corresponds to a southwest terrain orientation (aspect = 6), so the movement would be straight uphill and cost a dollar. The effective net accumulation from a given starter cell to every other location is the arithmetic sum of costs/payments encountered—the current amount in the bag at a location is the net accumula- tion; stop when the bag is empty ($0). In the real world, the costs/payments would be coefficients of exacting equations to determine the depletions/addi- tions at each step. Steep Costs Figure 3 extends the consideration of dynamic move- ment through a “multiplicative factor table” based on two criteria: terrain aspect and steepness. All trekkers know that hiking up, down or across slope are radi- cally different endeavors, especially on steep slopes. Most hiking-time solutions, however, simply assign a “typical cost” (friction) that assumes “the steeper the terrain, the slower one goes” regardless of the direction of travel. But that’s not always true; it’s about as easy to negotiate across a steep slope as to traverse a gentle uphill slope. The table in Figure 3 identifies the multiplicative weights for each uphill, downhill or across movement based on terrain aspect. For example, as a wave front considers stepping into a new location, it checks its movement direction (NE = 2) and the aspect of the cell (SW = 6), identifies the appropriate multiplicative weight in the table (2,6 position = 2.5), then checks the “typical” steepness impedance (steep = 4.0) and multiplies them together for an overall friction value (2.5 * 4.0 = 10.0). If movement was northeast on a gentle slope, the overall friction value would be just 1.1. In effect, moving uphill on steep slopes is consid- ered nearly 10 times more difficult than traversing across a gentle slope—that makes a lot of sense. Figure 3. Directional effects of movement with respect to slope/aspect variations can be accounted for “on the fly.” Figure 2. Accumulation and momentum can be used to account for dynamic changes in the nature of intervening conditions and assumptions about movement in geographic space. But few map-analysis packages handle any of the “dynamic movement” considerations (gravity model, stepped-accumulation, back-link, guiding surface and dynamic impedance)—that doesn’t make sense. Author’s Note: For more information on effective-distance procedures (static and dynamic), see www.innovativegis.com/ basis/MapAnalysis/Topic25/Topic25.htm, online book Beyond Mapping III, Topic 25, “Calculating Effective Distance and Con- nectivity.” Instructors can use the online-course readings, lecture and exercise for Week 4, “Calculating Effective Distance,” at www.innovativegis.com/basis/Courses/GMcourse10. M A R C H 2 O 1 1 / W W W . G E O P L A C E . C O M 11