Calibration of Manning roughness coefficients in two-dimensional shallow water flows using optimal control theory

The optimal Manning roughness coefficients(n)control system of two-dimensional shallow water equations are first derived by using the optimal control theory for the partial differential equations. Then,the algorithm for automatically calibrating distributed n is implemented based on the framework of the unstructured finite volume methods. Considering the operational application,the n is not defined in each cell,but in each land cover block. Two conditions are investigated in our calibration experiments. One is the time-independent n identification for steady flows,and the other is the time-dependent n, which has fixed reference value and varies with water depth as given empiric relationship for unsteady flows. In both groups experiments,it is found that the n can be successfully calibrated using enough observations. Also,the functional relationship between referencen and water depth can be identified. But,the iteration number for the identification of the functional relationship increases largely because of larger freedom of control variables. Finally,the strategy for calibration are suggested in the modeling flood event,in which varied n is required to be considered.