Estimation of optimal parameters for a surface hydrology model

The estimation of infiltration, roughness, and rainfall intensity parameters in a surface flow model is studied. The problem is formulated as an optimal control problem in which the parameters to be estimated are viewed as controls in the surface flow model and a fit-to-data functional is viewed as a control functional. The control system is obtained as the approximation of the distributed model by means of finite elements in the spatial domain and finite differences in the time domain. The leap-frog and implicit differences are used for the time differencing approximations. The resulting minimization problem is solved by a descent method, The adjoint equations are introduced in the context of a general method to calculate efficiently the derivatives of the functional. The adjoint equations are developed for the continuous as well as the finite difference equations. A numerical example is presented. This example illustrates the effect of the accuracy of prior rainfall intensity information on the estimates of roughness and infiltration parameters.