On downstream hydraulic geometry and optimal energy expenditure: case study of the Ashley and Taieri Rivers

The downstream distribution of channel geometry and of the rate of energy expenditure per unit channel area Pa are analyzed on extensive datasets from the Ashley and Taieri Rivers in New Zealand. We investigate whether the rivers conform to local optimality, by which Pa tends to be constant throughout the network. We look at energy expenditure from two perspectives. (1) In the context of downstream hydraulic geometry (DHG) relations, we derive equations for the general unconstrained optimal combination of the DHG exponents b and f under local optimality, and compare these with data-derived exponents from the Ashley and Taieri Rivers. (2) Treating Pa as a random variable, we examine the downstream scaling of moments of Pa. Results suggest that E(Pa) is constant in the higher order stream network in both basins. The scaling of Var(Pa) with discharge illustrates that basin and channel heterogeneity play an important role in understanding the spatial distribution of energy expenditure and its variability in river systems.