Assessing the impact of uncertainty on flood risk estimates with reliability analysis using 1-D and 2-D hydraulic models

摘要

This paper addresses the use of reliability techniques such as Rosenblueth'sPoint-Estimate Method (PEM) as a practical alternative to more precise MonteCarlo approaches to get estimates of the mean and variance of uncertainflood parameters water depth and velocity. These parameters define the floodseverity, which is a concept used for decision-making in the context offlood risk assessment. The method proposed is particularly useful when thedegree of complexity of the hydraulic models makes Monte Carlo inapplicablein terms of computing time, but when a measure of the variability of theseparameters is still needed. The capacity of PEM, which is a special case ofnumerical quadrature based on orthogonal polynomials, to evaluate the firsttwo moments of performance functions such as the water depth and velocity isdemonstrated in the case of a single river reach using a 1-D HEC-RAS model.It is shown that in some cases, using a simple variable transformation,statistical distributions of both water depth and velocity approximate thelognormal. As this distribution is fully defined by its mean and variance,PEM can be used to define the full probability distribution function ofthese flood parameters and so allowing for probability estimations of floodseverity. Then, an application of the method to the same river reach using a2-D Shallow Water Equations (SWE) model is performed. Flood maps of mean andstandard deviation of water depth and velocity are obtained, and uncertaintyin the extension of flooded areas with different severity levels isassessed. It is recognized, though, that whenever application of Monte Carlomethod is practically feasible, it is a preferred approach.