Identification of Manning's roughness coefficients in shallow water flows

A numerical method based on optimal control theories for identifying Manning's roughness coefficients (Manning's n) in modeling of shallow water flows is presented. The coefficients are difficult to be determined especially when the spatial variation is significant, and are usually estimated empirically. The present methodology is applied to determine the optimal values of the spatially distributed parameters, which give least overall discrepancies between simulations and measurements. Through a series of systematic studies to identify the n values in both a hypothetical open channel and a natural stream stretch, several identification procedures based on unconstrained and constrained minimizations are analyzed. It is found that the limited-memory quasi-Newton method has the advantages of higher rate of convergence, numerical stability and computational efficiency. Although the identification of Manning's n is chosen as an example, the identification methods can be applied to numerical simulations of various flow problems.