River hydraulic models are used to assess the environmental risk associated to floodingand consequently inform decision support systems for civil security needs. These numericalmodels are generally based on a deterministic approach based on resolving the partial differentialequations. However, these models are subject to various types of uncertainties in theirinput. Knowledge of the type and magnitude of these uncertainties is crucial for a meaningfulinterpretation of the model results. Uncertainty quantification (UQ) framework aims to probabilizethe uncertainties in the input, propagate them through the numerical model and quantifytheir impact on the simulated quantity of interest, here, water level field discretized over an unstructuredfinite element mesh over the Garonne River (South-West France) between Tonneinsand La R´eole simulated with a numerical solver, TELEMAC-2D. The computational cost of thesensitivity analysis with the classical Monte Carlo approach is reduced using a surrogate modelinstead 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 andfriction coefficients. The quality of the surrogate was assessed on a validation set, with smallroot mean square error and a predictive coefficient equal to 1. Sobolâ sensitivity indices arecomputed and enhance the high impact of the input discharge on the water level variation.