Uncertainty quantification and global sensitivity analysis with dependent inputs parameters: Application to a basic 2D-hydraulic model

International audienceHydraulic models used to evaluate the flooding risk, include many uncertainties related to the model parameters in particular (e.g. hydrograph parameters, roughness coefficient). Uncertainty Quantification (UQ) and Global Sensitivity Analysis (GSA) allow to quantify these uncertainties and to identify the most influent model inputs as the non-influent ones, in order to rank parameters. To use traditional methods of UQ and GSA, the model inputs must be independent and most of the time, this is not the case. Therefore, this research aims to show that the dependence between hydraulic model inputs should not be neglected in UQ and GSA studies. In order to illustrate this, we used a very simple hydraulic model used as “validation case” in the open-source TELEMAC-2D hydrodynamic model. This case represents a hypothetical linear river protected by a dyke and a floodplain area. In addition, a breach of variable size can occur in the dyke center, depending on the flood parameters. The study methodology is completed following these steps: the uncertain model inputs (hydrograph parameters, roughness coefficient and breach parameters) and the outputs of interest (water level in some points of the floodplain area) are identified. Then, the margins of all inputs are defined through a statistical analysis using real dataset. The dependence structure between inputs is figured using copulas. As UQ and GSA require a large number of simulations, kriging metamodels are built to increase the number of experiences in a short time period. Finally, the UQ and GSA are achieved considering dependent inputs on one hand and independent inputs on the other hand. Regarding the UQ results, the outputs distribution is not the same if the inputs are considered dependent or not, whereas regarding the GSA results, there are more influent parameters if the inputs are considered to be dependent than if there are not. Some parameters, usually considered non-influent in the hypothesis of independent inputs, have in fact, a real impact on the outputs. Even if the differences are not substantial for this simplified case, these results suggest that it could be interesting to take into account the dependencies between model inputs for “real” application involving large scale 2D numerical models