Adjoint-method-based estimation of Manning roughness coefficient in an overland flow model

An optimal estimation approach for distributed Manning roughness coefficient in an overland flow based on the adjoint method is here proposed. Through some appropriate assumptions and simplifications, the governing equation describing the system is derived from the first continuity equation of the well-known one-dimensional Saint-Venant equations. In this equation, the empirical Manning parameter is considered to be unknown and can be estimated through a new parameter called K which is approximated by a Radial Basis Function Network (RBFN) with specified weighting factors. Estimation of distributed Manning coefficient can be reduced to estimation of weighting factors of RBFN. Infiltration process is also taken account in this work via the so-called Green-Ampt model. For the optimization, the adjoint model is obtained by means of a variational approach. Because of their non-linearity and complexity, the system and adjoint equations are numerically solved by using nonlinear implicit Preissmann schemes. Using steepest decent method and backtracking line search method, the cost functional is optimized in order to estimate the mentioned weighting factors from a set of lumped observation values. Finally, the method is illustrated on a simulated example with a simple overland flow and infiltration over a variable rainfall period.