9.18 Hydraulic Geometry: Empirical Investigations and Theoretical Approaches

Abstract

Hydraulic geometry equations relate the dimensions of the wetted channel to the stream discharge the channel conveys. One approach to hydraulic geometry considers temporal changes at a single location due to variations in discharge, and is referred to as at-a-station hydraulic geometry; another approach considers the spatial changes for a common discharge (such as the bankfull flow) and is referred to as downstream hydraulic geometry. Both are typically represented using empirically fitted power functions. In the first part of this chapter, the basic concepts are reviewed, and the physical basis for hydraulic geometry is presented. A set of reference equations describing the downstream scaling of Froude-similar channels is derived: they are exact power functions of the form P=κ1Q2/5, R=κ2Q2/5, and v=κ3Q1/5, where the coefficient values are determined by the channel shape, gradient, and a flow resistance parameter. A review of the literature indicates that although at-a-station relations have mostly been used to assess aquatic habitat, most of the research on downstream hydraulic geometry has focused on the factors determining the coefficients and exponents of the power functions or on the physical origin of the observed relations. Empirical studies of downstream relations have demonstrated that bankfull channel width generally increases at a rate slightly higher than suggested by Froude scaling, whereas channel depth typically increases at close to the rate associated with Froude scaling, but there are notable exceptions. Other key findings include identification of gradient, grain size, and riparian vegetation type as important variables influencing downstream hydraulic geometry. Progress has been made in understanding these empirical observations by developing theoretical models of hydraulic geometry; in particular, the incorporation of grain size and bank strength has advanced our understanding. Based on this review of the literature, the future research directions for at-a-station relations relate to improving their applicability to the practical problems for which they are commonly used, whereas those for downstream relations relate to improving our ability to model downstream hydraulic geometry and incorporating those relations in models of landscape evolution.