Scale-specific metrics for adaptive generalization and geomorphic classification of stream features

The Richardson plot has been used to illustrate fractal dimension of naturally occurring landscape features that are sensitive to changes in scale or resolution, such as coastlines and river channels. The Richardson method estimates the length of a path by traversing (i.e., “walking”) the path with a specific stride length. Fractal dimension is determined as the slope of the Richardson plot, which shows path length over a range of stride lengths graphed on log-log axes. This paper describes a variant of the Richardson plot referred to as the Scale-Specific Sinuosity (S³) plot. S³ is defined as negative one times the slope of the Richardson plot for a given stride length. A plot of S³ against stride length offers a frequency distribution whose area under the curve reflects total sinuosity, and whose points mark the amount of sinuosity contributed to the total sinuosity at each stride length. Mathematical relations of S³ with fractal dimension and sinuosity for linear features are described. The S³ metric is demonstrated and discussed for several linear stream features distributed over the conterminous United States. The S³ metric can help guide the preservation of stream feature sinuosity during cartographic generalization and may assist automated geomorphic classification of river systems.