These are carried out over a series of time steps, with the information obtained from solving equations at one time step being used as an input to the next step.
In reservoirs, the information needed is:
- a relationship between storage and outflow, usually as a storage-elevation relation (derived from the reservoir topography) and an outflow-elevation relationship (derived from weir and orifice relationships),
- an inflow hydrograph,
- a starting condition, often an empty reservoir.
For catchment routing, one procedure is to treat the catchment and its internal stream system as a storage. This can be linear, with the relationship: Storage, S = k.Q, where k is a constant with units of time, and Q is the outflow or discharge rate.
It can also be a non-linear function, of the form, S = k.Qm where k and m are constants. m is 1 for a linear model. In most non-linear storage routing models, m is in the range 0.65 to 0.85. These methods require an iterative solution at each time step.
For stream channels, routing can be undertaken by methods such as the Muskingum Method, lag and route methods, Muskingum-Cunge routing and hydraulic routing using methods such as kinematic wave calculations. DRAINS employs the latter in RAFTS-style stream routing reaches, following a method described in Chapter 9 of Open Channel Hydraulics by F.M. Henderson (Macmillan, 1966).