Optimal state estimation in an overland flow model using the adjoint method

In this paper, an optimal estimation method for initial conditions in an overland flow based on the adjoint method is presented. This system is described by an infinite dimensional model given by the first continuity equation of the well-known one-dimensional Saint-Venant equations. Infiltration process is also taken account in this work by using the so-called Green-Ampt model. The adjoint model is obtained by means of a variational approach. Both the system and adjoint equations are numerically solved by using the nonlinear implicit Preissmann scheme. From the combination between the steepest descent method and a line search method, the cost functional is optimized in order to estimate the mentioned initial conditions from a set of lumped observation values. Finally, a simulation example with a simple overland flow and infiltration in a variable rainfall period is presented in order to demonstrate the effectiveness of this solution.