Meaning of flow routing

Flow routing is the mathematical procedure for finding the time and magnitude of a flood wave (the hydrograph) at a downstream point of a river or at the outlet of a reservoir, when the hydrograph at an upstream point (or the inflow to the reservoir) is known. As the flood moves through a reach or reservoir, storage changes its shape, so the outflow hydrograph differs from the inflow hydrograph.

Basis

Routing combines two relations:

• Continuity equation: $I - O = \dfrac{dS}{dt}$
• A storage relation: $S = f(I, O)$, for example $S = KO$ for a reservoir, or $S = K[xI + (1-x)O]$ for a river reach (Muskingum).

Effect of routing

 Q
 |      /\
 |     /  \     inflow
 |    /    \  __
 |   /   __/\/  \__   outflow
 |  /  _/         \__
 | /__/               \___
 +-------------------------> t
   lower, later, flatter peak

• Attenuation: the peak outflow is smaller than the peak inflow.
• Lag (translation): the peak outflow occurs later than the peak inflow.

Types

1. Reservoir (hydrologic storage) routing: outflow depends on storage only, e.g. Modified Puls (storage-indication) method.
2. Channel routing: storage depends on both inflow and outflow, e.g. Muskingum method.
3. Hydraulic routing: solves the Saint-Venant equations.

Uses

Flood forecasting, design of spillways and reservoir capacity, flood-control works, and flood-warning systems.