Hydrology An Introduction

Streamflow routing describes the motion of a flood wave in a well-defined open channel. Two extreme types of large waves can be discerned, depending on the main factors controlling the momentum budget in the shallow-water equations. An abrupt wave, a surge or moving hydraulic jump occurs when the inertia and hydrostatic pressure gradient terms are predominant and the friction and gravity terms can be neglected; such types of waves have caused disastrous floods. The monoclinal rising wave occurs in the opposite situation, when friction and slope terms predominate compared to the dynamic terms. Most flood waves are intermediate and their analysis requires, beside the continuity equation, inclusion of the complete momentum equation. Yet, in practice excellent results have been obtained with lumped kinematic methods, among which the well-known Muskingum method, which uses only the continuity equation without explicit momentum conservation considerations. A kinematic approach normally leaves the shape of the flood wave unchanged. However, numerical diffusion due to the discretization of the continuity equation in finite increments allows the description of the changing shape of the wave.