Differential dynamic programming for estuarine management

This study is divided into two phases. In Phase I, a differential dynamic programming (DDP) method is modified and applied to solve both linear and nonlinear estuarine management problems to determine the optimal amount of freshwater inflows into bays and estuaries to maximize fishery harvests. Fishery harvests are expressed in regression equations as functions of freshwater inflows. The optimization problem is posed as a discrete-time optimal control problem in which salinity represents the state variable and freshwater inflow represents the control variable. Both linear and nonlinear regression equations that relate salinity to freshwater inflow are used as the transition equations. The bound constraints for the control and state variables are incorporated into the objective function using a penalty function method to convert the problem into an unconstrained formulation. Three penalty functions are selected to compare the effects of different penalty functions on the convergence rate of the DDP procedure. For linear transition equation, two methods are explored to guarantee quadratic convergence of the DDP procedure. One is using a quadratic function to approximate the original objective function and the other is using an adaptive shift procedure. For nonlinear transition equation, a constant shift procedure is used to guarantee the quadratic convergence of the DDP procedure. The DDP method is applied to the Lavaca-Tres Palacios Estuary in Texas and the results are compared with those of using other nonlinear programming solver. The results indicate that the DDP method converges with fewer iterations than nonlinear programming method.; In Phase II, a hydrodynamic-salinity transport model HYD-SAL is used as a transition equation. HYD-SAL is a two-dimensional finite difference model used to simulate the flow circulation and temporal and spatial salinity pattern in the bay system. Because HYD-SAL consists of four partial differential equations and the control variables freshwater inflows are parts of the boundary conditions of HYD-SAL, it is difficult to find the derivatives of HYD-SAL analytically. Finite difference method must be used to obtain the derivatives of HYD-SAL with respect to freshwater inflow. Number of calls to HYD-SA1 and CPU time will increase dramatically. A successive approximation linear quadratic regulator (SALQR) is adopted to solve the computational complexity of the derivatives of the HYD-SAL. The SALQR method is applied to the Lavaca-Tres Palacios Estuary in Texas and the results are compared with those of Phase I. The model developed in Phase II is advanced over the models developed in Phase I, because the new model has the capability of incorporating other important factors affecting the salinity in the bay system. The computer model developed can provide a useful tool for decision makers to quantitatively analyze various water management strategies.