Probabilistic interval estimation of design floods under non-stationary conditions by an integrated approach

Quantifying the uncertainty of non-stationary flood frequency analysis is very crucial and beneficial for planning and design of water engineering projects, which is fundamentally challenging especially in the presence of high climate variability and reservoir regulation. This study proposed an integrated approach that combined the Generalized Additive Model for Location, Scale and Shape parameters (GAMLSS) method, the Copula function and the Bayesian Uncertainty Processor (BUP) technique to make reliable probabilistic interval estimations of design floods. The reliability and applicability of the proposed approach were assessed by flood datasets collected from two hydrological monitoring stations located in the Hanjiang River of China. The precipitation and the reservoir index were selected as the explanatory variables for modeling the time-varying parameters of marginal and joint distributions using long-term (1954–2018) observed datasets. First, the GAMLSS method was employed to model and fit the time-varying characteristics of parameters in marginal and joint distributions. Second, the Copula function was employed to execute the point estimations of non-stationary design floods. Finally, the BUP technique was employed to perform the interval estimations of design floods based on the point estimations obtained from the Copula function. The results demonstrated that the proposed approach can provide reliable probabilistic interval estimations of design floods meanwhile reducing the uncertainty of non-stationary flood frequency analysis. Consequently, the integrated approach is a promising way to offer an indication on how design values can be estimated in a high-dimensional problem.

Design flood estimation for global river networks based on machine learning models

Design flood estimation is a fundamental task in hydrology. In this research, we propose a machine-learning-based approach to estimate design floods globally. This approach involves three stages: (i) estimating at-site flood frequency curves for global gauging stations using the Anderson–Darling test and a Bayesian Markov chain Monte Carlo (MCMC) method; (ii) clustering these stations into subgroups using a K-means model based on 12 globally available catchment descriptors; and (iii) developing a regression model in each subgroup for regional design flood estimation using the same descriptors. A total of 11 793 stations globally were selected for model development, and three widely used regression models were compared for design flood estimation. The results showed that (1) the proposed approach achieved the highest accuracy for design flood estimation when using all 12 descriptors for clustering; and the performance of the regression was improved by considering more descriptors during training and validation; (2) a support vector machine regression provided the highest prediction performance amongst all regression models tested, with a root mean square normalised error of 0.708 for 100-year return period flood estimation; (3) 100-year design floods in tropical, arid, temperate, cold and polar climate zones could be reliably estimated (i.e. <±25 % error), with relative mean bias (RBIAS) values of −0.199, −0.233, −0.169, 0.179 and −0.091 respectively; (4) the machine-learning-based approach developed in this paper showed considerable improvement over the index-flood-based method introduced by Smith et al. (2015, https://doi.org/10.1002/2014WR015814) for design flood estimation at global scales; and (5) the average RBIAS in estimation is less than 18 % for 10-, 20-, 50- and 100-year design floods. We conclude that the proposed approach is a valid method to estimate design floods anywhere on the global river network, improving our prediction of the flood hazard, especially in ungauged areas.

Climate change adjustments in engineering design standards: European perspective

The European Commission Flood Risk Directive review shows that while many nations have embraced the concepts of flood risk management, there is still quite more to do in delineating risk–cost-effective measures and developing cost estimates and financing of those measures. Not mentioned are the necessary changes to existing design standards and protocols which will have to change in order to properly encompass climate change and variability, with associated uncertainties. Adjustments in engineering design standards and changes in hazards are examined, based on trend detection in observational records and projections for the future. Issues of urban and transport (motorways and railways) drainage design are also examined. Furthermore, risk reduction strategies are discussed. Finally, a way of accounting for non-stationarity in determining design precipitation and design floods is tackled. Climate change adjustments in engineering design standards, such as design precipitation and design floods, are reviewed via examples from Europe.

Flood frequency from maximum daily vs. instantaneous peak flows

&lt;p&gt;Flood frequency analysis (FFA) has long been the standard procedure for obtaining design floods for all kinds of purposes. Ideally, the data at the basis of the statistical operations have a high temporal resolution, in order to facilitate a full account of the observed flood peaks and hence a precise model fitting and flood quantile estimation.&lt;/p&gt;&lt;p&gt;Unfortunately, high-resolution flows are rarely disposable. Often, average daily flows pose the only available/sufficiently long base for flood frequency analysis. This averaging naturally causes a significant smoothing of the flood wave, such that the &amp;#8220;instantaneous&amp;#8221; peak can no longer be observed. As a possible consequence, design floods derived from these data may be severely underrated.&lt;/p&gt;&lt;p&gt;How strongly the original peaks are flattened and how this influences the design flood estimation depends on a variety of factors and varies from gauge to gauge. In this study we are looking at a range of errors arising from the use of daily instead of instantaneous flow data. These include differences in the observed individual flood peaks and mean annual maximum floods, as well as the estimated distribution parameters and flood quantiles. The aim is to identify catchment specific factors that influence the magnitude of these errors, and ultimately to provide a means for error assessment on the mere basis of local hydrological conditions, specifically where no high-resolution data is available.&lt;/p&gt;&lt;p&gt;The analyses are carried out on an all-German dataset of discharge gauges, for which high-resolution data is available for at least 30 years. The classical FFA approach of fitting distributions to annual maximum series is utilized for error assessment. For identification of influencing factors, both the discharge series themselves and a catalogue of climatic and physiographic catchment descriptors are screened.&lt;/p&gt;

Uncertainty Based Design Floods

Many statistical distributions approximate well the frequent values of the maximum discharges, but have a very large spread for medium or rare probabilities of exceedance. This scattering defines a range of uncertainty of maximum discharges outside the measured values. Based on the upper (U) and lower (L) values of the uncertainty interval, a maximum discharge flood (MDF) and a maximum volume flood (MVF) are defined for each probability of exceedance. This approach is in agreement with the bivariate analysis, the contour lines for a certain probability of exceedance putting into evidence an infinity of couples (maximum discharge, flood volume). If the most critical combinations are selected, the MDF and MVF are derived. Apart from maximum discharge and flood volume, the shape of the design flood, characterized by the time to peak and the total duration, is also important. The easiest way to obtain the design flood is to use an analytical curve that passes through the characteristic points of the flood. Another possibility, which was largely developed in this paper, is to normalize the floods, then to define clusters of floods with similar shapes, and to obtain an average dimensionless flood for each class. Finally, a family of design floods with different shapes, but characterized by the same parameters for each probability of exceedance, are derived. The use of these floods in the design or operation of hydrotechnical works or in the delineation of flooded areas is presented at the end.