A Fractal Concept used in Time of Concentration Estimates

Abstract

In present hydrologic practice, it is generally recognized that the shallow overland sheet flow through the upper portions of a watershed is very slow, and that runoff gradually accelerates as it concentrates into gullies and, finally, streams. In this paper, the fractal concept is applied by testing whether a watershed's stream-and-swale system branches in a characteristic pattern that repeats itself into successively finer but similar segments. Commonly used geometric, geomorphologic, hydraulic, and hydrologic equations are combined to reduce the number of parameters. Kinematic wave equations are then developed for the runoff movement in the channels, and integrated to obtain an equation for the time of concentration.