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Long-Range Persistence of Elevation and Relief Values Along the Continental Divide in the Conterminous U.S.
RICE-SNOW, Scott (email@example.com), Ball State University, Department of Geology, Muncie, IN 47306; RUSSELL, Joshua, Rocky Mountain Consultants, 825 Delaware Avenue, Suite 500, Longmont, CO 80501
Key Words: drainage divides, hausdorff dimension, self-affinity, R/S analysis
We have collected a variety of elevation and relief statistics for 336 points (measurement stations) spaced at 10-km linear intervals along the U.S. Continental Divide extending from the Mexican to the Canadian border. The information was derived from 1:100,000 topographic quadrangles, with vertical resolution on the order of map contour intervals (20-50 m). These statistics can be treated as sequential data sets and tested for self-affine characteristics by rescaled range (R/S) analysis. Results show a good fit to the self-affine model for all measures tested, with sample intervals of 5 to 336 stations. For the smallest intervals available (3-5 stations) there is a somewhat lower plot slope, corresponding to higher fractal dimension (D) value. This drift at small intervals is notably opposite in sense to the "initial transients" in time-series examples given by Mandelbrot and Wallis.
Elevation data series for the Continental Divide crest yield very uniform, low, D values in the approximate range 1.02-1.04. This indicates a very high degree of persistence in values, with consistent self-affine character bridging the scales of mountain range segments, entire ranges, and full physiographic provinces. The minor variations in results for different statistics indicate slightly higher persistence for minimum Divide elevation within a 5-km radius of station, than for station point elevation or maximum Divide elevation within 5 km.
Various local relief statistics also show significant long-range persistence along the Divide, though with D values higher than obtained for elevation series. Among the statistics, relatively low fractal dimension values (approx. 1.05) indicate very high along-divide persistence for overall relief measures, including relief from Divide station to lowest point within a 10-km radius, and maximum relief available within 5 km. The least persistence (D range 1.12-1.18) is indicated for more subtle relief along the Divide crest within 5 km of station, and relief in the immediate vicinity of the Divide, from station to lowest point within 1-km radius.
Unlike Continental Divide elevation series and associated overall relief measures, the more subtle Divide relief statistics, with their reduced degree of long-range persistence, show little systematic variation from one physiographic province to another. This suggests that divide-crest and very local divide-area relief characteristics are largely independent of regional geologic and climatic controls.