Polynomial Surrogates for Open-Channel Flows in Random Steady State

Nabil El Moçayd (1) , Sophie Ricci (1) , Nicole Goutal (2) , Mélanie C. Rochoux , Sébastien Boyaval (2) , Cédric Goeury (3, 2) , Didier Lucor (4) , Olivier Thual (5, 1)

1 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
2 Saint-Venant - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics
3 EDF R&D LNHE - Laboratoire National d’Hydraulique et Environnement
4 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur
5 IMFT - Institut de mécanique des fluides de Toulouse

Assessing epistemic uncertainties is considered as a milestone for improving numerical predictions of a dynamical system. In hydrodynamics, uncertainties in input parameters translate into uncertainties in simulated water levels through the shallow water equations. We investigate the ability of generalized polynomial chaos (gPC) surrogate to evaluate the probabilistic features of water level simulated by a 1-D hydraulic model (MASCARET) with the same accuracy as a classical Monte Carlo method but at a reduced computational cost. This study highlights that the water level probability density function and covariance matrix are better estimated with the polynomial surrogate model than with a Monte Carlo approach on the forward model given a limited budget of MASCARET evaluations. The gPC-surrogate performance is first assessed on an idealized channel with uniform geometry and then applied on the more realistic case of the Garonne River (France) for which a global sensitivity analysis using sparse least-angle regression was performed to reduce the size of the stochastic problem. For both cases, Galerkin projection approximation coupled to Gaussian quadrature that involves a limited number of forward model evaluations is compared with least-square regression for computing the coefficients when the surrogate is parameterized with respect to the local friction coefficient and the upstream discharge. The results showed that a gPC-surrogate with total polynomial degree equal to 6 requiring 49 forward model evaluations is sufficient to represent the water level distribution (in the sense of the ℓ2 norm), the probability density function and the water level covariance matrix for further use in the framework of data assimilation. In locations where the flow dynamics is more complex due to bathymetry, a higher polynomial degree is needed to retrieve the water level distribution. The use of a surrogate is thus a promising strategy for uncertainty quantification studies in open-channel flows and should be extended to unsteady flows. It also paves the way toward cost-effective ensemble-based data assimilation for flood forecasting and water resource management.

Mots clés: Uncertainty quantification; Surrogate model; Polynomial chaos expansion; Sensitivity analysis; Covariance matrix; Hydraulic modeling

Domaines: Sciences de l'ingénieur [physics]; Génie civil; Sciences de l'environnement; Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Mécanique des fluides [physics.class-ph]

Nabil El Moçayd, Sophie Ricci, Nicole Goutal, Mélanie C. Rochoux, Sébastien Boyaval, et al.. Polynomial Surrogates for Open-Channel Flows in Random Steady State. Environmental Modeling & Assessment, 2017, ⟨10.1007/s10666-017-9582-2⟩. ⟨hal-01763259⟩