Law of Stream Relief in Horton's Stream Morphological System

Within a river basin, the streams can be classified by the Horton-Strahler stream order system. In 1945, Horton introduced the law of stream lengths and the law of stream slopes and found the average stream lengths and slopes as semilogarithmic functions of the stream order. In this study, paralleling Horton's development, the law of stream relief is proposed and the average stream relief is found also to be a semilog function of the stream order. Results from numerical analysis indicate that the riverbed profile can be described by a semilog equation expressing stream relief as a function of stream length. The F value in the stream relief equation may be considered as an indicator of the riverbed profile properties; however, more investigations are needed before any conclusive statements can be made.