Calibration and Control for Estuary System under Uncertainty

A comprehensive stochastic management methodology is developed for a distributed-parameter estuary system (DPES) which is described by partial differential equations (PDEs). The proposed stochastic management methodology consists of uncertainty-based calibration (i.e. parameter estimation under uncertainty) and uncertainty-based control (i.e. determination of optimal freshwater inflows into the estuary under uncertainty). The technique for uncertainty-based calibration is based on Gauss-Newton minimization method and uncertainty analysis method such as Rosenblueth's point estimate method or Harr's point estimate method. The uncertainty-based calibration technique is used to estimate the optimal parameters such as Manning's roughness coefficient and dispersion coefficient in the PDEs while considering the uncertainties in the boundary conditions or initial conditions for the PDEs. The technique for uncertainty-based control is based on a real-time control method which is discrete-time stochastic linear quadratic feedback control. Real-time control is achieved by feedback control which uses salinities at test stations in the estuary as the state vector and controlled freshwater inflows as the control vector. The feedback control law determines the real-time control vector using observed states in a manner that best approximates desired states and controls (freshwater inflows). This new methodology for real-time control has been applied to the Lavaca-Tres Palacios Estuary in Texas for purposes of testing and illustration.