This study compares model averaging and model selection methods to estimate design floods, while accounting for the observation error that is typically associated with annual maximum flow data. Model selection refers to methods where a single distribution function is chosen based on prior knowledge or by means of selection criteria. Model averaging refers to methods where the results of multiple distribution functions are combined. Numerical experiments were carried out by generating synthetic data using the Wakeby distribution function as the parent distribution. For this study, comparisons were made in terms of relative error and root mean square error (RMSE) referring to the 1-in-100 year flood. The experiments show that model averaging and model selection methods lead to similar results, especially when short samples are drawn from a highly asymmetric parent. Also, taking an arithmetic average of all design flood estimates gives estimated variances similar to those obtained with more complex weighted model averaging.

The design of flood defence structures requires the estimation of flood water levels corresponding to a given probability of exceedance, or return period. In river flood management, this estimation is often done by statistically analysing the frequency of flood discharge peaks. This typically requires three main steps. First, direct measurements of annual maximum water levels at a river cross-section are converted into annual maximum flows by using a rating curve. Second, a probability distribution function is fitted to these annual maximum flows to derive the design peak flow corresponding to a given return period. Third, the design peak flow is used as input to a hydraulic model to derive the corresponding design flood level. Each of these three steps is associated with significant uncertainty that affects the accuracy of estimated design flood levels. Here, we propose a simulation framework to compare this common approach (based on the frequency analysis of annual maximum flows) with an alternative approach based on the frequency analysis of annual maximum water levels. The rationale behind this study is that high water levels are directly measured, and they often come along with less uncertainty than river flows. While this alternative approach is common for storm surge and coastal flooding, the potential of this approach in the context of river flooding has not been sufficiently explored. Our framework is based on the generation of synthetic data to perform a numerical experiment and compare the accuracy and precision of estimated design flood levels based on either annual maximum river flows (common approach) or annual maximum water levels (alternative approach).

We compare statistical and hydrological methods to estimate design floods by proposing a framework based on virtual reality. To illustrate the framework, we used probability model selection and model averaging as statistical methods, while continuous simulations made with a simple or a perfect rainfall-runoff model are used as hydrological methods. The results of our numerical exercise show that design floods estimated by using a simple rainfall-runoff model have small parameter uncertainty and limited errors, even for high return periods. Statistical methods perform better than the linear reservoir model in terms of median errors for high return periods, but their uncertainty (i.e. variance of the error) is larger. Moreover, selecting the best fitting probability distribution is associated with numerous outliers. On the contrary, using multiple probability distributions, regardless of their capability in fitting the data, leads to significantly less outliers, while keeping a similar accuracy. Thus, we find that, among the statistical methods, model averaging is a better option than model selection. Our results also show the relevance of the precautionary principle in design flood estimation, and thus help develop general recommendations for practitioners and experts involved in flood risk reduction.

This study aims at comparing model averaging to model selection techniques in design flood estimation. Model selection refers to the selection of  a single best distribution function by means of a suitable selection criterion, such as, Akaike Information Criterion (AIC). Model averaging refers to the modelling approach where the estimates from a number of probability models are combined together as a weighted average. We investigated two methods of model averaging. First, weighted model averaging (WMA) were differential weights are assigned to estimates based on different distribution functions with the distribution when the best fit having the highest weight. Second, equal weighting or model mean (MM) which is similar to taking the arithmetic mean of design flood estimates from all the distributions considered. MS and MA (which includes WMA and MM) were implemented using an exceptionally long time series of annual maximum flows recorded at the Tiber River in Rome, Italy.  For this study, comparisons we refer to the 1-in-100 year flood, i.e. the quantile of annual maximum flows corresponding to a 1% exceedance probability, widely used as a reference in flood risk management. The results suggest that MA performs better than MS. Specifically, MM performs better that WMA even though the latter can be judged as to be consistent with logical reasoning.