Influences of different surveying and mapping methods on fractal characteristics of gully-head shoulder lines

Abstract

Accurate quantification of gully shoulder lines (gully borderlines) will help better understand gully formation and evolution. Surveying and mapping are the most important ways to obtain precise morphology. To evaluate the influences of different steps of surveying and of curve-fitting methods of mapping on the morphology of the shoulder line characterized by fractal dimensions, 13 shoulder lines at gully heads were surveyed using a total station and then mapped with different methods of curve fitting, with the fractal dimensions calculated by maps compared with those measured in the field. Fractal dimensions by field measurement ranged from 1.185 to 1.456. Compared with field measurements, the average absolute errors of polygonal line, quadratic B-spline, and arc-fitting methods are 0.045, 0.040, and 0.046, respectively; the average relative errors are 3.48, 3.13, and 3.59%. Therefore, the quadratic B-spline method has a higher accuracy. The standard error of the fractal dimension tends to be larger as average step length increases. The error is ~5% when the step length is 0.7 m, which is advisable for field surveying. This study will help promote the efficiency of field surveying and mapping, and thus promote the accuracy and credibility of gully morphology.