Storage routing models applicable to reservoirs, which have essentially level water-surface profiles, can be developed by assuming X to be zero in Eq. (5), i.e., storage is dependent only on outflow. Expressing the term AS/At in Eq. (4) as the product of reservoir surface area (Sa), which is a known function of water-surface elevation (h ) and the change of h over a j At time step, i.e.,
Now denoting O (outflow) as Q (discharge), the following reservoir routing model (Fread, 1977) is obtained:
0.5(1J + V'+I) - 0.5(QJ + QJ+1) - 0.5(S^ + SJ+l)(hj+l - hJ)/Atj = 0 (7)
The inflows (/) at times j and j + 1 are known from the specified inflow hydrograph; the outflow (QJ) at time j can be computed from the known water-surface elevation (hJ) and an appropriate spillway discharge equation. The surface area (Sj) can be determined from the known value of hJ. The unknowns in the equation consist of hJ+x, QJ+1, and S I+1 ; the latter two are known nonlinear functions of hj+i. Hence, Eq. (7) can be solved for hj+1 by an iterative method such as Newton-Raphson, i.e.,
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