Assimilating Channel Lateral Inflow Hydrographs Using Adjoint State Method

Using de St. Venent Equation, this study derives the Adjoint State Equation and a time integral expression to compute the gradient of objective function with respect to the lateral hydrograph parameters. Efficiency in gradient computation is the key issue in assimilating observed stage data into routing model state variables during real-time flood forecasting. The objective function consists of the sum of simulation stage errors at gauging points and the temporal and spatial double integral of the conservation of mass and momentum equations each multiplied by an adjoint state variable. One major contribution of this study is to derive the boundary conditions of the Adjoint State Equations from the original physical problem and its initial and boundary conditions. The BFGS quasi-Newton algorithm in IMSL libraries is utilized for finding the new trial values in the iterative optimization procedure. The NewC scheme is adopted for modeling channel routing.

Four examples are designed to verify the methodology. The objective function values decreases to 10 to the -7th to -4th power meter square. It is believed that these values are related to the level of total numerical error during the simulation, adjoint state variable and gradient computation. Initial guesses of lateral inflow parameter values have an effect on he optimized result. When they are all greater or all smaller than their true values, the optimized results tend to better the mixed..This is due to the later has a stage error cancellation effect.