Basic Concepts and Equations

This is the simplest of the routing models in HEC-HMS. Using the Lag model, the outflow hydrograph is simply the inflow hydrograph, but with all ordinates translated (lagged in time) by a specified duration. The flows are not attenuated, so the shape is not changed. 

This method does not include any representation of attenuation or diffusion processes.  Consequently, it is best suited to short stream segments with a predicable travel time that doesn't vary with changing conditions.

Mathematically, the downstream ordinates are computed by:

1) O_{t}=\left\{\begin{array}{cc}I_{t} & t<\operatorname{lag} \\ I_{t+\ lag} & t \geq \operatorname{lag}\end{array}\right\}

where O_t = outflow hydrograph ordinate at time t; I_t = inflow hydrograph ordinate at time t; and lag = time by which the inflow ordinates are to be lagged.

The lag model is a special case of other models, as its results can be duplicated if parameters of those other models are carefully chosen. For example, if X = 0.50 and K = \Delta t in the Muskingum model, the computed outflow hydrograph will equal the inflow hydrograph lagged by K.

Required Parameters

The parameters that are required to utilize this method within HEC-HMS are the initial condition and a lag time [minutes].  Two options for specifying the initial condition are included: outflow equals inflow and specified discharge [ft3/sec or m3/sec].  The first option assumes that the initial outflow is the same as the initial inflow to the reach from the upstream elements which is equivalent to the assumption of a steady-state initial condition.  The second option is most appropriate when there is observed streamflow data at the end of the reach.  Lag time is the amount of time that the inflow hydrograph will be translated.

A tutorial describing an example application of this channel routing method, including parameter estimation and calibration, can be found here: Applying the Lag Routing Method.