New Sensitivity Indices of a 2D Flood Inundation Model Using Gauss Quadrature Sampling

Abstract

A new method for sensitivity analysis of water depths is presented based on a two-dimensional hydraulic model as a convenient and cost-effective alternative to Monte Carlo simulations. The method involves perturbation of the probability distribution of input variables. A relative sensitivity index is calculated for each variable, using the Gauss quadrature sampling, thus limiting the number of runs of the hydraulic model. The variable-related highest variation of the expected water depths is considered to be the most influential. The proposed method proved particularly efficient, requiring less information to describe model inputs and fewer model executions to calculate the sensitivity index. It was tested over a 45 km long reach of the Richelieu River, Canada. A 2D hydraulic model was used to solve the shallow water equations (SWE). Three input variables were considered: Flow rate, Manning’s coefficient, and topography of a shoal within the considered reach. Four flow scenarios were simulated with discharge rates of 759, 824, 936, and 1113 m 3 / s . The results show that the predicted water depths were most sensitive to the topography of the shoal, whereas the sensitivity indices of Manning’s coefficient and the flow rate were comparatively lower. These results are important for making better hydraulic models, taking into account the sensitivity analysis.

Keywords

• flood mapping
• Gauss quadrature sampling
• Monte Carlo
• shallow water equations
• hydraulic modelling