Identification of Manning's roughness coefficients in channel network using adjoint analysis

In this paper, a numerical method based on optimal control theories and adjoint analysis for identifying Manning's roughness coefficients in the full nonlinear de Saint Venant equations is presented. In order to make the parameter identification applicable to most natural river flows, special attention to a complex channel network is paid. The adjoint equations of the one-dimensional (1D) full nonlinear de Saint Venant equations in a channel network are obtained by means of variational approaches. To solve the adjoint equations in a channel network with confluences, the internal boundary conditions for confluences in the channel network are also derived from variational approaches and specified at the nodal points of confluences. In the present identification approach, one set of distributed parameters with spatial variation along river reaches can be identified, which insures the minimum simulation error along the whole channel network. By imposing the internal boundary conditions on confluences, the optimal estimations of the distributed roughness coefficients in unsteady channel network flows are achieved. In addition, the Limited-Memory Quasi-Newton (LMQN) method is utilized for enhancement of effectiveness of identification procedure. The bound constraints for Manning's roughness coefficients are taken into account. The constraints are capable of preserving the physical meaning of the estimated parameters throughout the identification process. This identification approach can be applied to estimate the spatial distribution of Manning's roughness coefficients in natural channel network flows.