Optimal control of salinity in the Sacramento-San Joaquin Delta (California)

This dissertation applies optimal control techniques to minimize the water cost of meeting a salinity regulation in an estuary. The Sacramento-San Joaquin Delta in California is channel network that is vulnerable to salinity intrusion from the ocean. Water quality in the delta is regulated for human and ecological uses.; The minimum water cost compliance problem is posed as an optimal control problem. The controls are upstream inflow and pumping, and the cost is the sum over time of upstream releases minus water recovered at the pumps. The physical system is described by one-dimensional conservation equations for mass, momentum and salinity transport. The salinity regulation appears as a state constraint. The controls must be bound or regularized in order to obtain a solution that has practical merit.; The control problem is formulated continuous time and then discretized and solved numerically. Continuous and discrete adjoint methods and a discrete sensitivity method are described for obtaining analytically the reduced gradient of the objective with respect to control. Five solution techniques are compared on a simplified problem on a single channel with one upstream inflow and one midstream pump. Three use non-linear programming solvers (TRICE, GENCAN, L-BFGS-B) with a penalty function appropriate for continuous state constraints to enforce the salinity regulation. The other two include sequential linear programming with an merit function and a first order algorithm with a min-max merit function based on the currently most-violated constraint.; The successive linear programming algorithm is applied in the Delta on a historical compliance problem using a one-dimensional model and a parameterized control. Optimization is compared to trial-and-error analysis of water cost. Appropriate time granularity of the controls is investigated, and it is shown that much of the potential improvement can be achieved with coarse steps. Initial conditions are shown to be a major source of error, and an optimization-based method is described for obtaining improved initial conditions by assimilating field data.