Uncertainty quantification in a two-dimensional river hydraulic model

River hydraulic models are used to assess the environmental risk associated to flooding and consequently inform decision support systems for civil security needs. These numerical models are generally based on a deterministic approach based on resolving the partial differential equations. However, these models are subject to various types of uncertainties in their input. Knowledge of the type and magnitude of these uncertainties is crucial for a meaningful interpretation of the model results. Uncertainty quantification (UQ) framework aims to probabilize the uncertainties in the input, propagate them through the numerical model and quantify their impact on the simulated quantity of interest, here, water level field discretized over an unstructured finite element mesh over the Garonne River (South-West France) between Tonneins and La Reole simulated with a numerical solver, TELEMAC-2D. The computational cost of the sensitivity analysis with the classical Monte Carlo approach is reduced using a surrogate model instead of the numerical solver. The present study investigates one of the machine learning algorithms: A surrogate model based on Gaussian process. This latter was used to represent the spatially distributed water level with respect to uncertain stationary flow to the model and friction coefficients. The quality of the surrogate was assessed on a validation set, with small root mean square error and a predictive coefficient equal to 1. Sobol' sensitivity indices are computed and enhance the high impact of the input discharge on the water level variation.