Optimal control of flood diversion in watershed using nonlinear optimization

Abstract This study aims to develop a simulation-based optimization model applicable to mitigate hazardous floods in storm events in a watershed which consists of a complex channel network and irregular topography. A well-established model, CCHE1D, is used as the simulation model to predict water stages and discharges of unsteady flood flows in a channel network, in which irregular (i.e. non-rectangular and non-prismatic) cross-sections are taken into account. Based on the variational principle, the adjoint equations are derived from the nonlinear hydrodynamic equations of CCHE1D, which are to establish a unique relationship between flood control variables and hydrodynamic variables. The internal conditions at the confluence in channel network for solving the adjoint equations in a watershed are obtained. An implicit numerical scheme (i.e. Preissman’s scheme) is implemented for discretizing and solving the adjoint equations with the derived internal conditions and boundary conditions. The applicability of this integrated optimization model is demonstrated by searching for the optimal diversion hydrographs for withdrawing flood waters through a single floodgate and multiple floodgates into detention basins. Numerical optimization results show that this integrated model is efficient and robust. It is found that the single-floodgate control leads to an unfavorable speed-up in river flow which may create extra erosions in the channel bed; and multiple-floodgates diversion control diverts less flood waters, therefore can be a cost-effective control action. This simulation-based optimization model is capable of determining the optimal schedules of diversion discharge, optimal floodgate locations, minimum capacities of flood water detention basins in rivers and watersheds.

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