Issue link: https://read.dmtmag.com/i/27856
A Dynamic Tune-Up for Distance Calculations BEYONDMAPPING L ast month’s “Beyond Mapping” column described three ways that a “starter value” can be used to extend traditional effective- BY JOSEPH BERRY distance calculations: 1) indicating movement weights (gravity model), 2) indicating a start- ing/continuing distance value (stepped- accumulation) and 3) a starter ID# for identifying which starter location is the closest (back-link). All three of these extensions dealt with differences in the nature of the movement itself as it ema- nates from a location. Two additional extensions for dynamic effective distance involve differences in the nature of the intervening conditions: 1) guiding surface redirection, and 2) dynamic impedance based on accumulation, momentum and direction. Follow the Guide Figure 1 identifies a “guiding surface” responding to whether a movement step is uphill, downhill or across based on the surface’s configuration. Inset a) on the figure’s left side shows a constrained proxim- ity surface that identifies locations that are up to 200 meters “downhill” from roads. The result forms a “variable-width buffer” around the roads that excludes uphill locations. The downhill locations within the buffer are assigned proximity values indicating how close each location is to the nearest road cell above it. Also note that the buffer is “clipped” by the ocean, so only on-island buffer distances are shown. Inset b) uses a different type Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at jkberry@du.edu. 10 of guiding surface: a tilted plane characterizing current flow from the southwest. In this case, downhill movement corresponds to “down- current” flows from the two adjacent watersheds. Although a simple tilted plane ignores the subtle twists and turns caused by winds and bathometry differences, it serves as a first-order current-movement characterization. A similar, yet more detailed, guiding surface is a barometric map derived from weather-station G E O W O R L D / M A R C H 2 O 1 1 Figure 1. A guiding surface can be used to direct or constrain movement within a project area. data. A “down-wind” map tracks the down-surface (barometric-gradient) movement from each project location to areas of lower atmospheric pressure. Similarly, “up-surface” movement from any location on a pollution-concentration surface can help identify the probable pathway flow from a pollution source (highest concentration). Dynamic Waves “Dynamic impedance” involves changes with respect to increasing distance (accumulation), net-movement force (momentum) and interactions between a move- ment path and its intervening conditions (direction). The top portion of Figure 2 outlines the use of an “additive factor equation” to dynamically slow down movement in a manner analogous to compound interest of a savings account. As a distance wave propagates from a starting location, the effective distance of each successive step is slightly more impeded, like a tired hiker’s pace decreasing with increasing distance—the last mile of a 20-mile trek seems a lot farther. The example shows the calculations for the 11th step of a southwest-moving wave front (orthogonal step type = 1.414) with a constant impedance (fric- tion = 1) and a 1 percent compounding impedance (rate = 0.01). The result is an accumulated hindrance effectively farther by about 25 meters (16.36 – 15.55 = 0.81 * 30-meter cell size). The bottom portion of Figure 2 shows the approach for assessing the net accumulation of movement (momentum). This brings back an old repressed memory of a lab exercise in a math/programming course I attempted more than 30 years ago. We were given a terrain-like surface and coef- ficients of movement (acceleration and deceleration) of a ball under various uphill and downhill situations. Our challenge was to determine the location to drop the ball so it would roll the farthest … the only thing