Abstract. This paper addresses the use of reliability techniques such as Rosenblueth's Point-Estimate Method (PEM) as a practical alternative to more precise Monte Carlo approaches to get estimates of the mean and variance of uncertain flood parameters water depth and velocity. These parameters define the flood severity, which is a concept used for decision-making in the context of flood risk assessment. The method proposed is particularly useful when the degree of complexity of the hydraulic models makes Monte Carlo inapplicable in terms of computing time, but when a measure of the variability of these parameters is still needed. The capacity of PEM, which is a special case of numerical quadrature based on orthogonal polynomials, to evaluate the first two moments of performance functions such as the water depth and velocity is demonstrated 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 the lognormal. As this distribution is fully defined by its mean and variance, PEM can be used to define the full probability distribution function of these flood parameters and so allowing for probability estimations of flood severity. Then, an application of the method to the same river reach using a 2-D Shallow Water Equations (SWE) model is performed. Flood maps of mean and standard deviation of water depth and velocity are obtained, and uncertainty in the extension of flooded areas with different severity levels is assessed. It is recognized, though, that whenever application of Monte Carlo method is practically feasible, it is a preferred approach.

Abstract:The use of high resolution ground-based light detection and ranging (LiDAR) datasets provides spatial density and vertical precision for obtaining highly accurate Digital Surface Models (DSMs). As a result, the reliability of flood damage analysis has improved significantly, owing to the increased accuracy of hydrodynamic models. In addition, considerable error reduction has been achieved in the estimation of first floor elevation, which is a critical parameter for determining structural and content damages in buildings. However, as with any discrete measurement technique, LiDAR data contain object space ambiguities, especially in urban areas where the presence of buildings and the floodplain gives rise to a highly complex landscape that is largely corrected by using ancillary information based on the addition of breaklines to a triangulated irregular network (TIN). The present study provides a methodological approach for assessing uncertainty regarding first floor elevation. This is based on: (i) generation an urban TIN from LiDAR data with a density of 0.5 points¨m´2, complemented with the river bathymetry obtained from a field survey with a density of 0.3 points¨m´2. The TIN was subsequently improved by adding breaklines and was finally transformed to a raster with a spatial resolution of 2 m; (ii) implementation of a two-dimensional (2D) hydrodynamic model based on the 500-year flood return period. The high resolution DSM obtained in the previous step, facilitated addressing the modelling, since it represented suitable urban features influencing hydraulics (e.g., streets and buildings); and (iii) determination of first floor elevation uncertainty within the 500-year flood zone by performing Monte Carlo simulations based on geostatistics and 1997 control elevation points in order to assess error. Deviations in first floor elevation (average: 0.56 m and standard deviation: 0.33 m) show that this parameter has to be neatly characterized in order to obtain reliable assessments of flood damage assessments and implement realistic risk management.

This paper addresses the use of reliability techniques such as Rosenblueth's Point-Estimate Method (PEM) as a practical alternative to more precise Monte Carlo approaches to get estimates of the mean and variance of uncertain flood parameters water depth and velocity. These parameters define the flood severity, which is a concept used for decision-making in the context of flood risk assessment. The method proposed is particularly useful when the degree of complexity of the hydraulic models makes Monte Carlo inapplicable in terms of computing time, but when a measure of the variability of these parameters is still needed. The capacity of PEM, which is a special case of numerical quadrature based on orthogonal polynomials, to evaluate the first two moments of performance functions such as the water depth and velocity is demonstrated 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 the lognormal. As this distribution is fully defined by its mean and variance, PEM can be used to define the full probability distribution function of these flood parameters and so allowing for probability estimations of flood severity. Then, an application of the method to the same river reach using a 2-D Shallow Water Equations (SWE) model is performed. Flood maps of mean and standard deviation of water depth and velocity are obtained, and uncertainty in the extension of flooded areas with different severity levels is assessed. It is recognized, though, that whenever application of Monte Carlo method is practically feasible, it is a preferred approach