For subcritical flow, a specified discharge or water-surface elevation time series or a tabular relation between discharge and water-surface elevation (single-valued rating curve) can be used as the downstream boundary condition.
Another downstream boundary condition can be a computed loop-rating curve based on the Manning equation, i.e.,
The loop is produced by using the friction slope (Sf) rather than the channel bottom slope (So) in the Manning equation. The friction slope exceeds the bottom slope during the rising limb of the hydrograph while the reverse is true for the recession limb. The friction slope (Sf) is approximated by using Eq. (30) where L and Wf are assumed to be zero while sm and /? are assumed to be unity (Fread, 1985, 1988, 1992), i.e., s/K = (qjn - Qfl)/(gAJNAtJ) - [(&/AyN - (&/AyN_x]/(gAi Axn_x)
The loop-rating boundary equation allows the unsteady wave to pass the downstream boundary with minimal disturbance by the boundary itself, which is desirable when the routing is terminated at an arbitrary location along the channel/floodplain and not at a location of actual flow control such as a dam or waterfall, or where the flow is affected by downstream backwater conditions produced by tidal action, reservoirs, or tributary inflow.
When the downstream boundary is a stage/discharge relation (rating curve), the flow at the boundary should not be otherwise affected by flow conditions farther downstream. Although there are often some minor effects due to the presence of cross-sectional irregularities downstream of the chosen boundary location, these usually can be neglected unless the irregularity is so pronounced as to cause significant backwater or drawdown effects. Reservoirs, major tributaries, or tidal effects located below the downstream boundary, which cause backwater effects at the boundary, should be avoided. When either of these situations is unavoidable, the routing reach should be extended downstream to the dam in the case of the reservoir or to a location downstream of where the major tributary enters. Sometimes the routing reach may be shortened by moving the downstream boundary to a location farther upstream where backwater effects are negligible.
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