Uncertainty Analysis of a Two-Dimensional Hydraulic Model

Abstract

Abstract:A reliability approach referred to as the point estimate method (PEM) is presented to assess the uncertainty of a two-dimensional hydraulic model. PEM is a special case of numerical quadrature based on orthogonal polynomials, which evaluates the statistical moments of a performance function involving random variables. When applied to hydraulic problems, the variables are the inputs to the hydraulic model, and the first and second statistical moments refer to the mean and standard deviation of the model's output. In providing approximate estimates of the uncertainty, PEM appears considerably simpler and requires less information and fewer runs than standard Monte Carlo methods. An example of uncertainty assessment is shown for simulated water depths in a 46 km reach of the Richelieu River, Canada. The 2D hydraulic model, H2D2, was used to solve the shallow water equations. Standard deviations around the mean water depths were estimated by considering the uncertainties of three main input variables: flow rate, Manning's coefficient and topography. Results indicate that the mean standard deviation is <27 cm for the considered flow rates of 759, 824, 936, 1113 m 3 /s. Higher standard deviations were obtained upstream of the topographic shoal at the municipality of Saint-Jean-sur-Richelieu. The PEM method adds further value to the H2D2 model predictions as it indicates the magnitude and the spatial variation in uncertainties. The effort required to complete an uncertainty analysis using the PEM method is minimal and the resulting insight is meaningful. This knowledge should be incorporated into decision-making in the context of flood risk assessment.

Flood Mapping in a Complex Environment Using Bistatic TanDEM-X/TerraSAR-X InSAR Coherence

“…In fact, the model sensitivity to this parameter can be relatively limited [55] especially for 2D models. However, in this study, the friction coefficients were not calibrated but rather taken from the study of Oubennaceur et al [56] where a calibration was carried out over the same area of interest, but with another 2D hydraulic model. The availability of very high-resolution topographic and bathymetric data (see Section 2.2.2) enabled us to set up the flood model of Richelieu River at 6 m spatial resolution.…”

Sampling Methods for Metocean Data Aiming at Hydrodynamic Modeling of Estuarine and Coastal Areas

“…The uncertainty of modeling studies can be attributed to input variables and parameters and can arises from modeling errors as well as from the sampling and measurement processes [5].…”

Reducing uncertainties in flood inundation outputs of a two-dimensional hydrodynamic model by constraining roughness

“…Even though HD models are physically deterministic, they contain numerous uncertainties in model outputs (Bates et al, 2014;Beven et al, 2018). Information about the type and magnitude of these uncertainties is crucial for decisionmaking and for increasing confidence in model predictions (Oubennaceur et al, 2018). Despite uncertainties, decisionmaking in practice is based on first-hand data, expert judgement, and/or a calibrated model output (Henonin et al, 2013;Uusitalo et al, 2015).…”

“…The model structure, essentially either 1-D, 2-D, or hybrid 1-D-2-D HD code, is generally selected based on the purpose and scale of the modelling (Musall et al, 2011;Bach et al, 2014). In addition, there is no general agreement on the best approach to consider model structure uncertainty; hence, it is often neglected (Oubennaceur et al, 2018). In the case of hindcasting a flood event based on measured discharges or water levels as the input boundary conditions and a fineresolution elevation, roughness remains the main source of uncertainty in HD models; hence we focus this study on roughness uncertainty.…”