A Universal Form of Power Law Relationships for River and Stream Channels

Abstract

The description of the geomorphic characteristics in power law forms has been the subject of research, over the past 70 years, and has become the cornerstone of regime theory. However, just why power functions should represent such geomorphic relationships remains poorly understood. Hence, differences in the values of the regime exponents observed for different river systems remain largely unexplained. To address this issue, we derived generic forms of the power law relationships without postulating any power functions of the discharge. The theoretical approach accurately captures the systematic variations of the regime exponents shown by a number of large data sets from previous research. We also explain how frictional resistance is responsible for the systematic variability of regime exponents. Overall, our study provides a robust mechanism to describe the variations of the exponents, along with a deductive explanation of the power laws at the core of fluvial hydraulic geometry.