Application of variational calculus to parameter estimation in a real hydrological system

Abstract

This paper presents an estimation study based on calculus of variations for parameters in a real hydrological system, namely Tondi-Kiboro catchment, in Niger. The considered dynamical representation for this system is first given, from the well-known Saint-Venant equations under some simplifying assumptions. A cost function is then defined based on the gap between measured and predicted water discharges at the real sensor position, and the calculus of variations along with the first order optimality condition are used to find the gradients of Lagrangian objective functional with respect to the parameters to be estimated. Depending on the infiltration model used in the system model, two applications of this adjoint-based approach are finally presented: the first one only estimates the friction coefficient, with the assumption that infiltration is described by the physical so-called Green-Ampt model, while the second one additionally estimates the parameters of an alternative infiltration representation called Horton model. Some simulation-based validation and robustness discussion concludes the paper.