Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences via a global sensitivity analysis (GSA). However, these codes can be time consuming which prevents a GSA based on the classical Sobol' indices, requiring too many simulations. This is especially true as the number of inputs is important. To address this limitation, we consider recent advances in dependence measures, focusing on the distance correlation and the Hilbert-Schmidt independence criterion (HSIC). Our objective is to study these indices and use them for a screening purpose.Numerical tests reveal some differences between dependence measures and classical Sobol' indices, and preliminary answers to "What sensitivity indices to what situation?" are derived. Then, two approaches are proposed to use the dependence measures for a screening purpose. The first one directly uses these indices with independence tests; asymptotic tests and their spectral extensions exist and are detailed. For a higher accuracy in presence of small samples, we propose a nonasymptotic version based on bootstrap sampling. The second approach is based on a linear model associating two simulations, which explains their output difference as a weighed sum of their input differences. From this, a bootstrap method is proposed for the selection of the influential inputs. We also propose a heuristic approach for the calibration of the HSIC Lasso method. Numerical experiments are performed and show the potential of these approaches for screening when many inputs are not influential.

Data assimilation is widely used to improve flood forecasting capability, especially through parameter inference requiring statistical information on the uncertain input parameters (upstream discharge, friction coefficient) as well as on the variability of the water level and its sensitivity with respect to the inputs. For particle filter or ensemble Kalman filter, stochastically estimating probability density function and covariance matrices from a Monte Carlo random sampling requires a large ensemble of model evaluations, limiting their use in real-time application. To tackle this issue, fast surrogate models based on Polynomial Chaos and Gaussian Process can be used to represent the spatially distributed water level in place of solving the shallow water equations. This study investigates the use of these surrogates to estimate probability density functions and covariance matrices at a reduced computational cost and without the loss of accuracy, in the perspective of ensemble-based data assimilation. This study focuses on 1-D steady state flow simulated with MASCARET over the Garonne River (SouthWest France). Results show that both surrogates feature similar performance to the Monte-Carlo random sampling, but for a much smaller computational budget; a few MASCARET simulations (on the order of 10-100) are sufficient to accurately retrieve covariance matrices and probability density functions all along the river, even where the flow dynamic is more complex due to heterogeneous bathymetry.