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.
Highlights
Flood inundation models numerically transform discharge rates into predictions of water depth, flow velocity, etc. [1]
The objective of this paper is to demonstrate the applicability of the point estimate method (PEM) for computing of the mean and standard deviation of the simulated water depths
To investigate the effect of topography uncertainty on model predictions, a standard deviation related to each grid cell was generated by kriging the digital elevation models (DEM) used as the mean value
Summary
Flood inundation models numerically transform discharge rates into predictions of water depth, flow velocity, etc. [1]. The contribution of the three most commonly considered potential sources of uncertainty by flood inundation models is analyzed: discharge rate, Manning’s coefficient and topography Each of these input variables and parameters is subject to measurement, modelling errors and/or sampling errors [17,18]. The uncertainty of any model output (water surface elevations and inundation extent) is obtained by combining the standard deviation of the following variables: discharge rate, Manning’s coefficient and topography [46,47]. The uncertainty proposed involved the following steps: for (i) define the probability the hydraulic model analysis based onmethod these input parameters (recalculate the model each sampled input); distribution for each of the input variables: X (flow rate),. General procedure for uncertainty analysis based on point estimate method (PEM) simulations
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