Theory

The DBC is inserted between two identical cross-sections that are separated by a small distance (HEC-RAS creates the identical cross-section automatically). Given the small distance, the DBC assumes that the stage and flow at the two cross-sections should be the same; hence, if the upstream cross-section is number j , then

1)	$\begin{array}{l}\begin{matrix} Z^n_j = Z^n_{j+1} \\ Q^n_j = Q^n_{j+1} \end{matrix}\end{array}$

in which Z is the stage and Q is the flow.

When optimizing stage, the river reach is effectively broken into two routing reaches. The stage hydrograph is used as the new downstream boundary for the upstream reach and the stage hydrograph is used as the new upstream boundary for the downstream reach; cross-sections j and j+1 are the downstream and upstream boundaries respectively.

When optimizing flow, the flow hydrograph is applied as the upstream boundary at cross-section j+1 and serves as the upstream boundary of the downstream reach. The stage hydrograph is still applied at cross-section j and serves as the downstream boundary of the upstream reach.

After running the model, the flow at j is the routed flow from upstream. Since the ungaged inflow is unknown and not entered, the flow at j is missing the ungaged inflow. For the downstream reach, the flow at j+1 contains the ungaged inflow. If the flow at j+1 is computed from a stage boundary condition, the flow is generated by the hydrodynamics and the geometry of the reach downstream. The ungaged inflow is the difference between the flow hydrographs at j and the flow at j+1,

2)	$\begin{array}{l}\displaystyle Q^l_U = Q^n_{j+1} - Q^n_j\end{array}$

in which is the ungaged inflow for iteration 1.

The ungaged inflow enters between the upstream boundary of the upstream reach and cross-section j, the downstream boundary. To use the ungaged inflow in a model, the program lags the flow backward in time and inserts it in the model as point and/or uniform lateral inflow(s). Point inflow occurs at known ungaged tributaries and the remainder is uniform inflow. The user can delineate any number of point inflows and uniform lateral inflows. The distribution of flow between the inflows must be specified (often this is based on drainage area) and the user must also enter the lag time for each inflow.

The DBC is best used at principal gage locations where the stage or flow records are the most accurate. Generally, these locations are the USGS (U. S. Geological Survey) gaging stations. If a reach includes k interior gages, inserting DBC at each of the gages creates k routing reaches. For example, for the Missouri River between Rulo, Nebraska and St. Charles, Missouri, DBC's are inserted at the USGS gages at St. Joseph, Kansas City, Waverly, Boonville, and Hermann, breaking the model into five routing reaches. Ungaged inflow cannot be optimized between Hermann and St. Charles because St. Charles is a stage gage in the backwater of the Mississippi River.