Coupled 1D-river and 2D-overland flow model to simulate the rainfall-runoff process in watersheds

Abstract

A modeling system integrating river and watershed, capable of simulating overland flow and surface runoff in natural streams, is proposed. This model is based on the coupling of two models: a 2D-model for the flow in the plain and a 1D- model for the river flow. It constitutes a possible alternative to conceptual models with lockers, which are based on a coarse partition of watershed tanks communicating with each other by transfer laws. The 2D model is based here on the kinematic wave approximation constructed from 2D equations of Barre Saint-Venant. To better determine the state of flow, an optimization procedure is then implemented to identify the boundary conditions upstream (unknown incoming flow) for the real watershed Hirson (France). In the present work, we tested algorithms without gradient calculation (Simplex), algorithms with gradient calculation (SQP: Sequential Quadratic Programming, BFG: Broyden-Fletcher-Goldfarb-Shanno) and probabilistic CMAES type algorithms (Covariance Matrix Adaptation Evolution Strategy). The numerical solutions were compared with success, first with analytical solutions and then with numerical solutions found in the international literature. The results show that the CMAES algorithm is more relevant for identifying unknown flows in the case of a real watershed.