Analytical Solution for Level Pool Routing Equation Based on Various Inflow Hydrographs

Reservoir routing is one of the most important issues in reservoir management. Estimating outflow from a dam outlet, which is the target of reservoir routing, is significantly vital since unpredicted floods can bring about severe damages to infrastructures and human beings downstream of storage reservoirs. In essence, general analytical computation of storage and outflow may be impossible in practice and subsequently, application of numerical methods seems to be inevitable for reservoir routing. However, analytical relations for temporal variation of water storage in a typical reservoir for several cases of inflow hydrographs including triangular, abrupt wave, flood pulse and broad peak hydrographs are derived in this paper. . In these scenarios, an orifice was assumed for reservoir outlet. According to the literature, presented analytical solutions for the last three cases are proposed for the first time. The applicability of these analytical solutions is tested using four numerical examples while a robust numerical scheme, i.e., fourth-order Runge-Kutta, is also applied for solving these examples. The obtained results demonstrate that the recommended analytical solutions have a good agreement with the corresponding results of the utilized numerical scheme for all examples.