Upstream Boundary Conditions

Upstream boundary conditions are required at the upstream end of all reaches that are not connected to other reaches or storage areas. An upstream boundary condition is applied as a flow hydrograph of discharge versus time. The equation of a flow hydrograph for reach m is:

1)	$\begin{array}{l}\displaystyle \displaystyle \Delta Q_k^{n+1} = Q_k^n - Q_k\end{array}$

where $\begin{array}{l}k\end{array}$ is the upstream node of reach m. The finite difference form of (1) is:

2)	$\begin{array}{l}\displaystyle MUQ_m \Delta dQ_K = MUB_m\end{array}$

Symbol	Description
$\begin{array}{l}MUQ_m\end{array}$	1
$\begin{array}{l}MUB_m\end{array}$	$\begin{array}{l}Q_1^{n+1} - Q_1^n\end{array}$

Typical flow split and combination.