Rationalizing the Differences Among Hydraulic Relationships Using a Process‐Based Model

Abstract

An ancient Chinese proverb states: "Don't push the river, it flows by itself." Scientists and engineers have long struggled to fully translate the second part of the proverb into a mathematical description. Leopold and Maddock (1953) linked the time-varying measurements of instantaneous river width B, depth H and velocity U at a gauging station to the corresponding discharge Q using simple power functions, and termed such empirical relationships as at-a-station hydraulic geometry (denoted as "AHG" hereafter). At the same time, the authors created downstream hydraulic geometry (denoted as "DHG" hereafter) to describe the hydraulic relations with bankfull (or mean annual) B, H, U, and Q downstream along a river. The fundamental difference between these two relationships is that AHG deals with temporal variability while DHG focuses on spatial variability. In addition, the mean annual or bankfull parameters used in DHG generally have a longer returning period than the time-varying parameters of AHG. Despite their conceptual difference, both AHG and DHG were expressed by the same well-known functional forms:

Hydraulic Geometry and Theory of Equilibrium Water Depth of Branching River

“…Based on the theories of minimum energy dissipation theory of fluid movement and river morphodynamics, Yang [33] analyzed the relationship between river island shape coefficient and flow and sediment dynamics under stable equilibrium conditions. Some researchers proposed two different forms of power law, hydropower station hydraulic geometry (AHG) and downstream hydraulic geometry (DHG), and derived the theoretical expressions of AHG and DHG [34][35][36]. Tran used a process-based morphodynamic model to simulate the evolution of tidal inlets towards equilibrium when subjected to a range of tide and wave conditions.…”