Convex Routing

Convex routing is a hydrologic routing technique used to calculate the hydrograph at the downstream end of a link, given its value at the upstream end. It is used in all EPS runs of the GVF-convex solver.

The underlying logic in the convex routing method is that the routed outflow for a time step is based on the inflow and outflow for the previous time step. Each outflow ordinate is calculated as:

Where:

Ot +

= Outflow at time t +

t
= Current time (s, min)
t = Hydrologic time step (s, min)
c = Convex routing coefficient
It = Inflow at time t (l/s, gpm)
Ot = Outflow at time t (l/s, gpm)

The convex routing coefficient is essentially a ratio of the hydrologic time step and representative flow travel time through the pipe and is calculated as follows:

Where:

t = Hydrologic time step (s)
tt = Travel time (s)
V = Velocity established for representative flow. (m/s, ft/s)
L = Length of pipe (m, ft)

The velocity used to calculate the coefficient is either the normal velocity or full flow velocity generated for a user-specified percentage of the peak of the inflow hydrograph. In other words, if the percentage of the peak flow is greater than the capacity of the pipe then the full-flow velocity is used. If the percentage of the peak flow is less than the capacity the flow velocity for normal depth is used.

Note: You can specify the percentage of the peak flow, which is used to calculate the Convex Routing coefficient for each pipe by entering the value for the property Peak Flow Ratio % in the Calculation options when the GVF-convex solver is the active solver. The values typically range between 50% and 75%.

The higher the percentage of flow the faster the velocity used to calculate the convex routing coefficient, hence the closer the routed hydrograph will be to a pure translation of the inflow hydrograph.

The user-specified percentage can be modified in the calculation options. A typical value is around 75 % but can be modified for oddly shaped hydrographs with sharp uncharacteristic peaks or for calibration purposes.

In the case of negative sloping pipe, the convex routing coefficient can be very small and overestimate peak flow attenuation. In these pipes, there is usually very little peak attenuation. The user can provide a value for C for negative sloping pipe on the order of 0.3 to 0.5 to achieve more realistic results for this case. The value is entered in the property "Minimum convex C for negative conduit". The default value is zero.

Note: Known Flows are not routed. Known Flows override other known flows, and are not cumulative going downstream.