Optimization modeling for sedimentation in alluvial rivers

Mathematical models are developed for determining optimum reservoir releases in order to minimize the aggradation and degradation in downstream river reaches. The physical system is composed of a reservoir-river interaction in which the releases from the reservoir comprise the inflows for the downstream river reach. A finite-difference scheme of sediment routing is adopted to determine the changes of bed profile along the river. The nonlinear programming problem is solved using a nonlinear programming solver, a dynamic programming (DP) procedure, and a differential dynamic programming (DDP) procedure. Four sediment transport functions have been used in order to evaluate and test the validity of the formulation. Chance-constrained formulations are also presented to consider the uncertainties of sediment transport parameters used in the modeling. A rectangular channel is used for the purpose of illustrating the procedure, which is a preliminary step toward the application of the methodology to a large existing system.