The steps in sequential optimization follows:

  1. An observed stage hydrograph and a flow hydrographs (if optimizing to flow) are applied at the at the first DBC station. No observed hydrographs are applied at downstream stations.
  2. The model is run.
  3. Ungaged inflow is calculated for the first reach using equation 2.
  4. The program reruns the model and ungaged inflow for the first reach is corrected using equation 3.
  5. If the flow hydrographs at cross-sections j and j+1 have converged go to step 7.
  6. Go to step 4.
  7. Move to the next downstream DBC station. Remove observed hydrographs at all upstream DBC stations. Apply a stage hydrograph and a flow hydrograph (if optimizing to flow) to the DBC station. No observed hydrographs are applied to downstream stations.
  8. The program reruns the model.
  9. Ungaged inflow is calculated for the first reach using equation 2.
  10. The program reruns the model and ungaged inflow for the first reach is corrected using equation 3.
  11. If the flow hydrographs at cross-sections j and j+1 have converged go to step 13.
  12. Go to step 10.
  13. If the last DBC, the iteration is complete. Otherwise go to step 7.

The time interval for the ungaged inflow is based on the Hydrograph Output Interval (see the HEC-RAS Unsteady Flow Analysis editor). For instance, if the Hydrograph Output Interval is one hour, then the ungaged inflow will be computed as a series of hourly flows. The final ungaged inflow hydrograph will also be output to the DSS file at this same time interval. When determining the ungaged inflow, the program will average the flow over the given time interval. For hourly data, for example, the program will average the ungaged inflow for a half hour before and a half hour after the specified time—the 1:00 inflow is the average of the ungaged flow from 12:30 to 1:30.

Short time intervals may, in some instances, cause spikes and dips in the resulting hydrograph. For instance, a one hour time interval might bounce between a high and low flow value. In order to smooth this out, the user can set a time frame to average the flows over (i.e., smoothing window). For example, the user could choose a three hour smoothing window to go along with the one hour hydrograph interval. In this case, the flows will be computed each hour, but each computed flow will be the flow that is averaged from one and a half hours before the specified time until one and a half hours after the specified time.

The user can also enter a minimum and maximum ungaged inflow. This will put limits on the ungaged inflow and may be needed for stability and/or to maintain hydrologically reasonable answers.

The flow tolerance convergence is based on an average least squared difference. For each time step of the unsteady flow model, there is a difference between the computed flow and the known (observed) flow at the gage. This flow difference for each time step is squared and then summed for all of the time steps. The sum is then divided by the number of time steps and, finally, the square root is taken in order to determine an average flow difference over the entire simulation. The unknown inflow is considered to have converged if this flow difference is within the tolerance specified by the user.