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.
Highlights
Hydraulic models provide essential hydraulic parameters for informed flood risk management, such as water depths, velocities, and timing of inundation
The sensitivity indices for each input variable were computed for the considered output model variable, the water depths in this case, predicted over the study domain
The water depth information under the surface was obtained by subtracting the local elevation of the ground
Summary
Hydraulic models provide essential hydraulic parameters for informed flood risk management, such as water depths, velocities, and timing of inundation. A spatially distributed sensitivity analysis (SA) is generally applied to investigate the relative influence of the input variables (individual or in combination) and their impacts on the model outputs [9,10] Methods such as the Monte Carlo analysis have been applied successfully in a wide range of studies, like flood inundation modelling [11,12]. SA evaluates model performance, varying one input parameter at a time, while the global methods consider the whole variation range of the main input parameters to assess their contribution to the uncertainty. They are not limited to linear models with inputs that have uncertainties of different orders of magnitude. The sensitivity analysis was conducted using a steady-state application of the Richelieu River hydraulic model
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