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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.

Changes in annual maximum flood (AMF), which are usually detected using simple trend tests (e.g., Mann‐Kendall test (MKT)), are expected to change design‐flood estimates. We propose an alternate framework to detect significant changes in design‐flood between two periods and evaluate it for synthetically generated AMF from the Log‐Pearson Type‐3 (LP3) distribution due to changes in moments associated with flood distribution. Synthetic experiments show MKT does not consider changes in all three moments of the LP3 distribution and incorrectly detects changes in design‐flood. We applied the framework on 31 river basins spread across the United States. Statistically significant changes in design‐flood quantiles were observed even without a significant trend in AMF and basins with statistically significant trend did not necessarily exhibit statistically significant changes in design‐flood. We recommend application of the framework for evaluating changes in design‐flood estimates considering changes in all the moments as opposed to simple trend tests. Plain Language Summary Any statistically significant change in the design‐flood quantile between two periods needs to account for changes in moments (such as mean, variance, and skewness) of the underlying flood distribution. Simple trend tests cannot be relied upon to identify basins undergoing changes in their design‐flood as they fail to capture changes in all the relevant moments. The proposed framework investigates statistically significant changes in design‐flood by considering changes in all moments of the flood distribution. Key Points Design‐flood quantile estimation, a function of moments of flood variable, is vital for water infrastructure design Temporal trend tests do not account for changes in all moments associated with any flood distribution The proposed framework tests the hypothesis of statistically significant change in design‐flood quantiles between two periods

There is a need to estimate design floods for areal planning and the design of important infrastructure. A major challenge is the mismatch between the length of the flood records and needed return periods. A majority of flood time series are shorter than 50 years, and the required return periods might be 200, 500, or 1,000 years. Consequently, the estimation uncertainty is large. In this paper, we investigated how the use of historical information might improve design flood estimation. We used annual maximum data from four selected Norwegian catchments, and historical flood information to provide an indication of water levels for the largest floods in the last two to three hundred years. We assessed the added value of using historical information and demonstrated that both reliability and stability improves, especially for short record lengths and long return periods. In this study, we used information on water levels, which showed the stability of river profiles to be a major challenge.

The recurring flooding causes loss of life and damage to buildings and other structures, including bridges, sewerage systems, roadways and canals. It also frequently damages power transmission and sometimes power generation, which then has knock-on effects caused by the loss of power. The present study compares the relative performance of flood frequency methods to estimate design flood, using available data of 18 small catchments in the Mahanadi River basin (India). The primary objective of the referred approach was for design flood estimation at gauge sites; however, the main focus is referred to ungauged catchments by an interpolation method. In this regard, three interpolation methods are used: (1) inverse distance weighing method, (2) ordinary kriging and (3) area weighted method. As per the recent trends, flood frequency analysis methods are used specifically for two data types, i.e., at-site analysis and for regionalizing the available data within the homogeneous region. In this study, an attempt has been made to categorize the interpolation properties, where the first two approaches belong to site analysis and the third one uses the regional analysis. In the first approach, the output results in terms of flood quantiles are interpolated for the intermediate results, which is generally termed as direct interpolation of flood quantile, and the second approach uses the linear interpolating or L-moments in flood estimation. The above one refers to the interpolation of L-moments, while flood index is interpolated in the third approach, which is named as ‘flood index procedure.’ In the study, it was observed that the designed flood quantile results were better by using the flood index approach at lower return periods at 2 and 5 years, and the direct interpolation method gave a better estimation for higher return periods. Further, it was found that the difference in prediction error of direct interpolation of flood quantiles and the flood index procedure is negligible.

We compare statistical and hydrological methods to estimate design floods by proposing a framework that is based on assuming a synthetic scenario considered as ‘truth’ and use it as a benchmark for analysing results. To illustrate the framework, we used probability model selection and model averaging as statistical methods, while continuous simulations made with a simple and relatively complex 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 fewer 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.

Estimating peak river discharge, a critical issue in engineering hydrology, is essential for designing and managing hydraulic infrastructure such as dams and bridges. In the UK, practitioners typically apply the Flood Estimation Handbook (FEH) statistical method which estimates the design flood as the product of a relatively frequent flow estimate (the index flood, IF) and a regional growth factor. For gauged catchments the IF is estimated from observations. For ungauged catchments it is computed through a multiple regression model. While the FEH IF method provides peak flow estimates that are statistically robust, it does not readily take into account catchment heterogeneity or effect of environmental change on river flows. This study presents a new methodology to estimate the IF at national scale using continuous simulation from a physically based hydrological model (Grid-to-Grid). The methodology is tested across Great Britain and compares well with IF estimates at 550 gauging stations (R2 = 0.91). The promising results for Great Britain support the aspiration that continuous simulation from large-scale hydrological models coupled with increasing availability of global weather and climate products, could be used to estimate design floods in regions with limited gauge data or affected by environmental change.

The estimation of design flood is mainly focused on the peak flow and the volume, ignoring the underlying surface factor and flood rising and falling process. Three basic conceptual hydrological models, XAJ, TANK and SCS, are selected and applied for design flood estimation in two small-scale basins of northern China. Model parameter calibration is based on both the optimization algorithm SCE-UA and artificial adjusting, by using a combined objecting function of flood peak, volume and process. Each model singles out a set of optimal parameters as input to simulate the design flood process. The simulation results are compared with original engineering design standards and instantaneous unit hydrograph method. The results show that the XAJ model has the best performance in simulating the 100-year design flood in study basins. The SCS model also gives acceptable results, but the TANK model on the other hand in an underestimated flood peak with a prolonged recession period, which is not likely to be applicable. This study is to test the applicability of the conceptual hydrological models in simulating the design flood process in small-scale watersheds and should be a supplement to the traditional methods and further deliberation to a ungauged basin. Starting from the most basic models with simple structures, it is hoped that the methodology can be transferred to more complicated and physically based models with more realistic description of the rainfall-runoff transformation mechanism and dynamic mechanism for climate change.

Internationally, the occurrence and frequency of floods, along with the uncertainty involved in the estimation thereof, contribute to the practitioners' dilemma to make a single, justifiable decision when various design flood estimation methods are used. This article presents the further development of a Design Flood Estimation Tool (DFET) using Microsoft Visual Basic for Applications to assess the performance of event‐based design flood estimation methods in 48 gauged catchments in South Africa. The improved DFET proved to be an easy‐to‐use software tool for the rapid estimation and assessment of at‐site design floods in both gauged and ungauged catchments. In using a ranking‐based selection procedure, the Soil Conservation Service, Alternative Rational and Catchment Parameter methods provided the best estimates of the at‐site probabilistic flood peaks, while the Standard Design Flood method proved to be the least appropriate. Since the accuracy and uncertainty associated with each design flood method's key input parameters are unknown when applied in ungauged catchments, the incorporation of an ensemble event approach as part of the DFET calculation routines, is recommended. This will ensure that the key input parameters from an expected range of values are used to achieve probability neutrality between input rainfall and estimated runoff.

Floods are one of the major climate-related hazards and cause casualties and substantial damage. Accurate and timely flood forecasting and design flood estimation are important to protect lives and property. The Distance Distribution Dynamic (DDD) is a parsimonious rainfall-runoff model which is being used for flood forecasting at the Norwegian flood forecasting service. The model, like many other models, underestimates floods in many cases. To improve the flood peak prediction, we propose a dynamic river network method into the model. The method is applied for 15 catchments in Norway and tested on 91 flood peaks. The performance of DDD in terms of KGE and BIAS is identical with and without dynamic river network, but the relative error (RE) and mean absolute relative error (MARE) of the simulated flood peaks are improved significantly with the method. The 0.75 and 0.25 quantiles of the RE are reduced from 41% to 23% and from 22% to 1%, respectively. The MARE is reduced from 32.9% to 15.7%. The study results also show that the critical support area is smaller in steep and bare mountain catchments than flat and forested catchments.

Hydrological models are developed for different purposes including flood forecasting, design flood estimation, water resources assessment, and impact study of climate change and land use change, etc. In this study, applicability and uncertainty of two deterministic lumped models, the Xinanjiang (XAJ) model and the Hydrologiska Byråns Vattenbalansavdelning (HBV) model, in design flood estimation are evaluated in a data rich catchment in southern China. Uncertainties of the estimated design flood caused by model equifinality and calibration data period are then assessed using the generalized likelihood uncertainty estimation (GLUE) framework. The results show that: (1) the XAJ model is likely to overestimate the design flood while HBV model underestimates the design flood; (2) the model parameter equifinality has significant impact on the design flood estimation results; (3) with the same length of calibration period, the results of design flood estimation are significantly influenced by which period of the data is used for model calibration; and (4) 15–20 years of calibration data are suggested to be necessary and sufficient for calibrating the two models in the study area.