Design Flood Values Research Articles

Robustness of design flood estimates under nonstationary conditions: parameter sensitivity perspective

The changing frequency of flooding in global watersheds, driven by various human and natural factors like land use/cover changes and global warming, necessitates innovative approaches in flood frequency analysis and risk assessment. Nonetheless, the reliability of nonstationary frequency analysis models remains a concern given challenges in accurately measuring the uncertainty introduced by these methods and the impact on design flood values. In this study, deviation-based differential sensitivity indices, including single-parameter (SDDSI) and entire-parameter (EDDSI) measures were developed to assess the influence of parameter uncertainty in nonstationary models using Bayesian statistics and "equivalent reliability" nonstationary design. The Weihe River, the largest tributary of the Yellow River which is experiencing both climate change and heavy impact of human activities, is chosen to be the study area to investigate the impact of precipitation change and land use change on nonstationary flood frequency. Results show that in the One-At-A-Time (OAT) sensitivity analysis under a small uncertainty scenario (SUS) for parameter inputs, the shape parameter stands out as the most influential factor (SDDSI_SUS = 0.347) affecting the 100-year design flood in the Stationary Generalized Extreme Value (SGEV) model. For the Non-Stationary GEV (NGEV) models, the influence of this parameter is less pronounced, with SDDSI_SUS values of 0.095 and 0.093 for the SSP126 and SSP585 scenarios, respectively. Instead, attention turns to the regression coefficient of the grassland area, associated with the GEV scale parameter. In global sensitivity analysis under the posterior uncertainty scenario (PUS) for parameter inputs, the EDDSI_PUS values for SGEV, NGEV_SSP126, and NGEV_SSP585 models were 0.52, 1.41, and 1.30, respectively, inferring heightened sensitivity of NGEV models to perturbations from entire parameters. It is anticipated that incorporating additional evidence, such as historical flood data, is essential for accurate nonstationary hydrological design to mitigating the influence of parameter uncertainty. The sensitivity indices in this study provide significant insights for assessing the robustness of nonstationary hydrological design in flood risk management and applications.

Recalculating Design Flood Values under Nonstationary Conditions in the Yalong River Basin, China

Recalculating Design Flood Values under Nonstationary Conditions in the Yalong River Basin, China

Hydrological models and datasets to support flood flow estimation at river-bridge intersections

A working group on the "Hydraulic Compatibility of Bridges" (sites.google.com/view/gii-ponti) has been recently established in the hydraulic engineering academic community aiming at reviewing methodologies, studying good practices, and suggesting guidelines for assessing the bridge hydraulic compatibility. In this initiative, a subgroup is focusing on the hydrological aspects as in Italy there are not standard procedures to estimate design flood values requested by the Italian technical standards of constructions (NTC 2018) over the whole country as, for example, in the UK where the Flood Estimation Handbook provides standard data and methods. Some models are available at the regional scale but are often based on not up-to-date data; moreover, while in large rivers flood discharge values, defined according to the European Flood Directive have been computed and mapped, in small river catchments they are not available.In this context, the unit of Politecnico di Torino working on hydrology is going to release some country-wide hydrological datasets, including all the available official information on discharge and rainfall extremes updated to recent years, that can be used as a common reference for bridge analyses. These include high-resolution maps of extreme precipitation statistics, a database of flood flow extremes recorded at more than 600 river sections, and a catalogue of river catchments characteristics (morphology, climate, land use, etc).Nation-wide datasets can support the application of standardized hydrological analyses, needed for flood hazard assessment, especially in small basins. Operational products will be made available within the PNRR RETURN project in order to be easily available and referable for any hydrological analysis in Italy.

Flexible and consistent Flood–Duration–Frequency modeling: A Bayesian approach

Design flood values give estimates of flood magnitude within a given return period and are essential to making adaptive decisions around land use planning, infrastructure design, and disaster mitigation. Many hydrologic applications where flood retention is important, e.g. floodplain management and reservoir design, need design flood values for different durations. Flood–Duration–Frequency (QDF) models extend the standard statistical flood frequency analysis framework to multiple flood durations and are analogous to intensity–duration–frequency models for precipitation. Implementations of QDF models commonly assume simple scaling, where only the magnitude of the index flood is assumed to change with duration, despite empirical analyses showing a more complex dependence structure. We propose a multiscaling extension to existing QDF models where the magnitude of the index flood and the slope of the growth curve may scale independently with duration. In an application to 12 locations in Norway, we assess how three different QDF models capture relationships between floods of different duration. Incorporating duration dependency independently in both the index flood and the growth curve (extended QDF model) improves modeling of both short-duration events and events with long return periods. This model extension further expands the models’ ability to simultaneously model a wide range of durations. As measured by the integrated quadratic distance, the extended QDF model performs better than the original QDF model in 83% of the out of sample subdaily durations studied. Additionally, we find that the choice of durations used to fit QDF models is a highly influential aspect of the modeling process.

Bivariate Nonstationary Extreme Flood Risk Estimation Using Mixture Distribution and Copula Function for the Longmen Reservoir, North China

Recently, the homogenous flood generating mechanism assumption has become questionable due to changes in the underlying surface. In addition, flood is a multifaced natural phenomenon and should be characterized by both peak discharge and flood volume, especially for flood protection structures. Hence, in this study, data relating to the 55-year reservoir inflow, annual maximum flood peak (AMFP), and annual maximum flood volume (AMFV) for the Longmen Reservoir in North China have been utilized. The 1-day AMFV exhibits a significant correlation with AMFP. The extreme flood peak-volume pairs are then used to detect the heterogeneity and to perform nonstationary flood risk assessment using mixture distribution as the univariate marginal distribution. Moreover, a copula-based bivariate nonstationary flood frequency analysis is developed to investigate environmental effects on the dependence of flood peak and volume. The results indicate that the univariate nonstationary return period is between the joint OR and the AND return periods. The conditional probabilities of 1-day AMFV, when AMFP exceeds a certain threshold, are likely to be high, and the design flood values estimated by joint distribution are larger than the ones in the univariate nonstationary context. This study can provide useful information for engineers and decision-makers to improve reservoir flood control operations.

Flood frequency analysis using generalized distributions and entropy-based model selection method

Flood frequency analysis (FFA) is used for estimating the return period of a design flood. Fundamental to FFA is the selection of a frequency distribution fitted to the data set, where an inappropriate choice of a distribution can lead to significant error and bias in the design flood estimate. The usual criteria for selecting a distribution are Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE), although these criteria have limitations. This paper performed FFA using three main steps. First, five generalized distributions were considered as candidate distributions for FFA; second, the principle of maximum entropy (POME) and the method of maximum likelihood (MLE) were used for parameter estimation; and third a new model selection criterion based on the value of entropy was proposed to choose the best-fitted distribution. Monte Carlo simulation was carried out to test this entropy-based method for four sample sizes equal to 50, 200, 1000, and 10000, and simulation was repeated 1000 times for each sample size. Then, the probability that a given method identified the correct distribution was determined. The probabilities affected by the sample size, skewness, and shape of the probability density function (PDF) were assessed. Using Qing River basin, China, as a case study, the design flood values were calculated and compared. Results of simulation showed that the proposed method was better than other methods for the following cases: (a) the sample size of data set X is small; (b) the skewness coefficient CS>0; and (c) the shape of PDFs is bell-shaped.

Non-Stationary Flood Frequency Analysis Using Cubic B-Spline-Based GAMLSS Model

Under changing environments, the most widely used non-stationary flood frequency analysis (NFFA) method is the generalized additive models for location, scale and shape (GAMLSS) model. However, the model structure of the GAMLSS model is relatively complex due to the large number of statistical parameters, and the relationship between statistical parameters and covariates is assumed to be unchanged in future, which may be unreasonable. In recent years, nonparametric methods have received increasing attention in the field of NFFA. Among them, the linear quantile regression (QR-L) model and the non-linear quantile regression model of cubic B-spline (QR-CB) have been introduced into NFFA studies because they do not need to determine statistical parameters and consider the relationship between statistical parameters and covariates. However, these two quantile regression models have difficulties in estimating non-stationary design flood, since the trend of the established model must be extrapolated infinitely to estimate design flood. Besides, the number of available observations becomes scarcer when estimating design values corresponding to higher return periods, leading to unreasonable and inaccurate design values. In this study, we attempt to propose a cubic B-spline-based GAMLSS model (GAMLSS-CB) for NFFA. In the GAMLSS-CB model, the relationship between statistical parameters and covariates is fitted by the cubic B-spline under the GAMLSS model framework. We also compare the performance of different non-stationary models, namely the QR-L, QR-CB, and GAMLSS-CB models. Finally, based on the optimal non-stationary model, the non-stationary design flood values are estimated using the average design life level method (ADLL). The annual maximum flood series of four stations in the Weihe River basin and the Pearl River basin are taken as examples. The results show that the GAMLSS-CB model displays the best model performance compared with the QR-L and QR-CB models. Moreover, it is feasible to estimate design flood values based on the GAMLSS-CB model using the ADLL method, while the estimation of design flood based on the quantile regression model requires further studies.

Improved Mixed Distribution Model Considering Historical Extraordinary Floods under Changing Environment

Historical extraordinary floods are an important factor in non-stationary flood frequency analysis and they may occur at any time, regardless of whether the environment is changing or not. Based on mixed distribution (MD) modeling, this paper proposed an improved mixed distribution (IMD) model to consider the discontinuity and non-stationarity of flood samples simultaneously, which adds historical extraordinary floods in both sub-series divided by a change point. As a case study, the annual maximum peak discharge and volume series of Ankang hydrological station, located in the upper Hanjiang River Basin of China, were selected to identify non-stationarity by using the variation diagnosis system. MD and IMD were used to fit the flood characteristic series and a genetic algorithm was employed to estimate the optimal parameters. Compared with the design flood values fitted by the stationary Pearson type-III distribution, the results computed by IMD decreased at low return periods and increased at high return periods, with the difference varying from −6.67% to 7.19%. The results highlighted that although the design flood values of IMD are slightly larger than those of MD with different return periods, IMD provided a better result than MD. IMD provides a new perspective for non-stationary flood frequency analysis.

Design Flood Estimation Methods for Cascade Reservoirs Based on Copulas

Reservoirs operation alters the natural flow regime at downstream site and thus has a great impact on the design flood values. The general framework of flood regional composition and Equivalent Frequency Regional Composition (EFRC) method are currently used to calculate design floods at downstream site while considering the impact of the upstream reservoirs. However, this EFRC method deems perfect correlation between peak floods that occurred at one sub-basin and downstream site, which implicitly assumes that the rainfall and the land surface process are uniformly distributed for various sub-basins. In this study, the Conditional Expectation Regional Composition (CERC) method and Most Likely Regional Composition (MLRC) method based on copula function are proposed and developed under the flood regional composition framework. The proposed methods (i.e., CERC and MLRC) are tested and compared with the EFRC method in the Shuibuya-Geheyan-Gaobazhou cascade reservoirs located at Qingjiang River basin, a tributary of Yangtze River in China. Design flood values of the Gaobazhou reservoir site are estimated under the impact of upstream cascade reservoirs, respectively. Results show that design peak discharges at the Gaobazhou dam site have been significantly reduced due to the impact of upstream reservoir regulation. The EFRC method, not taking the actual dependence of floods occurred at various sub-basins into account; as a consequence, it yields an under-or overestimation of the risk that is associated with a given event in hydrological design. The proposed methods with stronger statistical basis can better capture the actual spatial correlation of flood events occurred at various sub-basins, and the estimated design flood values are more reasonable than the currently used EFRC method. The MLRC method is recommended for design flood estimation in the cascade reservoirs since its composition is unique and easy to implement.

Incorporation of “Risk Factor” in Design Flood Review of Existing Dams

At present there are about 4877 completed large dams in India. More than 75% of Indian dams are at least two decades old and for these dams the original design floods call for revisions. Examination of revised design flood studies carried out for a set of 118 dams under ‘Dam Rehabilitation and Improvement Project (DRIP)’ reveal that the design flood values have increased substantially with trends indicating that percentage increases in the revised design flood values are greater for lower dams and also for older dams. Paper illustrates that the upward revision in the design flood estimate of existing dam in no way leads to amplification of the actual risk associated with that dam, and it only underlines the gap between the acceptable risk level and existing risk level. The paper shows that flood related risk mitigation of existing dams is a challenging task often facing constraints of technical and economical viabilities. With the substantial data set of design flood revisions of DRIP dams, the paper brings out the skew observed in distribution of revised design floods on account of present-day norms related to computation of design floods, as contained in the Indian Standard IS: 11223 – 1985 (reaffirmed 1995). Paper also proposes amendments in this Standard in respect of existing large dams with an alternative recourse of formulating a new Standard for revision of design floods incorporating the risk factor associated with these large dam structures.

Generalized Beta Distribution of the Second Kind for Flood Frequency Analysis

Estimation of flood magnitude for a given recurrence interval T (T-year flood) at a specific location is needed for design of hydraulic and civil infrastructure facilities. A key step in the estimation or flood frequency analysis (FFA) is the selection of a suitable distribution. More than one distribution is often found to be adequate for FFA on a given watershed and choosing the best one is often less than objective. In this study, the generalized beta distribution of the second kind (GB2) was introduced for FFA. The principle of maximum entropy (POME) method was proposed to estimate the GB2 parameters. The performance of GB2 distribution was evaluated using flood data from gauging stations on the Colorado River, USA. Frequency estimates from the GB2 distribution were also compared with those of commonly used distributions. Also, the evolution of frequency distribution along the stream from upstream to downstream was investigated. It concludes that the GB2 is appealing for FFA, since it has four parameters and includes some well-known distributions. Results of case study demonstrate that the parameters estimated by POME method are found reasonable. According to the RMSD and AIC values, the performance of the GB2 distribution is better than that of the widely used distributions in hydrology. When using different distributions for FFA, significant different design flood values are obtained. For a given return period, the design flood value of the downstream gauging stations is larger than that of the upstream gauging station. In addition, there is an evolution of distribution. Along the Yampa River, the distribution for FFA changes from the four-parameter GB2 distribution to the three-parameter Burr XII distribution.

Process-based design flood estimation in ungauged basins by conditioning model parameters on regional hydrological signatures

The use of rainfall–runoff models constitutes an alternative to statistical approaches (such as at-site or regional flood frequency analysis) for design flood estimation and represents an answer to the increasing need for synthetic design hydrographs associated with a specific return period. Nevertheless, the lack of streamflow observations and the consequent high uncertainty associated with parameters estimation usually pose serious limitations to the use of process-based approaches in ungauged catchments, which in contrast represent the majority in practical applications. This work presents a Bayesian procedure that, for a predefined rainfall–runoff model, allows for the assessment of posterior parameters distribution, using limited and uncertain information available about the response of ungauged catchments, i.e. the regionalized first three L-moments of annual streamflow maxima. The methodology is tested for a catchment located in southern Italy and used within a Monte Carlo scheme to obtain design flood values and simulation uncertainty bands through both event-based and continuous simulation approaches. The obtained results highlight the relevant reduction in uncertainty bands associated with simulated peak discharges compared to those obtained considering a prior uniform distribution for model parameters. A direct impact of uncertainty in regional estimates of hydrological signatures on posterior parameters distribution is also evident. For the selected case study, continuous simulation, generally, better matches the estimates of the statistical flood frequency analysis.

Potential changes in inflow design flood under future climate projections for Darbandikhan Dam

Summary Insignificant changes in the future system might be assumed due to the impacts of climate changes. Temperature changes and anticipated precipitation suggest possible changes in floods. Extreme events will have bigger impacts on sectors with direct connections to climate, such as water sector; there is great belief that climate changes have the potential to critically affect water management systems. This study investigated how future climate change might affect the Inflow Design Flood (IDF) of Darbandikhan Dam. The study uses the projected downscaled daily inflow from Global Climate Models (GCMs) in comparative to the historical peak inflows. Flood frequency analysis based on historical data, both observed and statistically downscaled, was used to obtain the new design flood values. Analysis of the future projections of flood frequency analysis (FFA) reveals a general tendency toward changes in the magnitude of IDF.

丹江口水库洪水资源调控技术研究

丹江口水库既是汉江中下游地区的控制性防洪工程，又是南水北调中线工程的水源地，承担着防洪、供水、发电、航运等重要功能。本文把资料系列延长至2014年并进行设计洪水复核，开展汛期分期、运行水位动态控制和提前蓄水研究。结果表明：在不降低防洪标准的前提下，利用1~5 d预见期信息，夏汛期(6月21日至8月20日)和秋汛期(9月1日到10月10日)的运行水位分别在160.0~162.9 m和163.5~ 165.7 m区间浮动，年均可增加蓄水量31.6~49.98亿m³，或增加发电量9.96~100.21 M kW•h；汛末提前蓄水时间为9月15日，蓄水水位上限值为166 m，与原设计方案相比，水库蓄满年份从4年增加到12年，年均多蓄水8.98亿m³。 The Danjiangkou Reservoir is both a key flood control project for the middle and lower reaches of the Han River and water source of the South-to-North Water Diversion Project in China. It is a multi-purpose reservoir, including flood control, water supply, hydropower generation, navigation, etc. The hydrological data series were extended to 2014 and the design flood values were rechecked. The flood seasonal identification, dynamic control of water levels during flood season and early refill of reservoir were studied. Results show that with 1 - 5 d forecasting information, dynamic control bounds of water level during summer flood season (Jun. 21 - Aug. 20) and autumn flood season (Sep. 1 - Oct. 10) are 160.0 - 162.9 m and 163.5 - 165.7 m respectively without decreasing flood protection standards, which can increase 3.16 - 4.998 billion m³ storage water or 9.96 - 100.21 MkW•h hydropower generation annually. It is also shown that reservoir’s early refill starts on Sep. 15 with the maximum water level limited to 166 m during September; the full storage rate can increase from 4 years to 12 years, and the storage water increases 0.898 billion m³ annually.

Reservoir Flood Routing Considering the Non-Stationarity of Flood Series in North China

Owing to the increasing anthropogenic activities, flood frequency analysis and flood control scheduling of reservoir become more and more complicated because of the non-stationarity of flood series. This paper aims to assess the effects that non-stationary flood series, which is affected by land use change of Daqing River Basin (in North China), has induced on the reservoir flood routing. And the analysis has been carried out in Xidayang Reservoir, which is located in south branch of Daqing River Basin of North China. In this paper, the annual maximum peak discharge series and the annual maximum flood volume (1-day, 3-day and 6-day) series of Xidayang Reservoir were selected to detect their variation using three steps change point diagnosis. Mixed distribution was employed to fit the non-stationary flood series, estimating parameters by simulated annealing algorithm. The results indicate that (1) mixed distribution provided a more appropriate and superior fit than conventional distribution (P3 distribution) to non-stationary flood series, (2) design flood values estimated by mixed distribution reduced by 0.03 %–20.24 % with different return periods compared with the results computed by conventional P3 distribution, and (3) through reservoir flood routing, the maximum water level and maximum discharge with various return periods considering the series’ non-stationarity also showed a decrease by up to 0.56 m and 81.68 % respectively compared with the results regardless of the series’ non-stationarity. These results provide a significant theoretical basis for flood control and water resources management in Daqing River Basin.

基于Copula函数的梯级水库设计洪水地区 组成研究

目前工程设计中常用的同频率地区组成带有一定的人为性，统计理论基础不足。利用Copula函数推导了两种考虑空间相关性的梯级水库设计洪水地区组成，即条件期望组成和最可能组成。以清江流域为例，对三种地区组成进行比较研究，分析了上游水布垭-隔河岩梯级水库的调蓄对高坝洲断面设计洪水的影响。结果表明：同频率组成计算的设计结果系统偏小，可能会增加设计断面的防洪风险。基于Copula函数的两种组成充分考虑了各分区洪水的随机性和空间相关性，设计成果比较合理。受上游梯级水库调蓄的影响，高坝洲断面千年一遇设计洪水的削峰率为40%左右。 The equivalent frequency regional composition method is widely used in practice. However, this method is based on artificial hypothesis and lacks the statistical basis. Two statistical composition methods, i.e. the conditional expectation method and the most likely method are proposed and derived based on Copula function. The Qingjiang cascade reservoirs are selected as the case study and the impact of Shuibuya-Geheyan cascade reservoirs regulation on the design flood of Gaobazhou dam site is analyzed. It is demonstrated that the results of equivalent frequency method are systematically smaller than those of the two proposed methods, which may lead to increasing the hydrological estimation risk. The proposed methods with strong statistical basis can capture the spatial correlation of flood events for each contributing watershed area, and the estimated design flood values are more reasonable than those of the equivalent frequency method. The 1000-year design peak discharge at Gaobazhou dam site has been cut about 40% due to the regulation of upstream cascade reservoirs.

Design soil moisture estimation by comparing continuous and storm‐based rainfall‐runoff modeling

In recent years local, national, and international authorities have showed an increasing awareness of flood and inundation hazard, likely due to the large floods which occurred in the past years in many regions of the world. In this context, the estimation of the design flood values to be adopted for flood risk assessment or floodplain management represents a crucial factor. In the case of ungauged or scarcely gauged catchments where a sufficiently long discharge time series is missing, a relevant uncertainty is involved in the flood frequency analysis and a possible solution to reduce this uncertainty is the application of continuous simulation (CS) approaches. Because of the complex structure of this type of approaches and pursuing the parameters parsimony criteria, in the hydrological practice the approaches based on the design storm (DS) estimation are more widely known and applied, mainly for their simplicity. However, one major limit of the DS method is the choice of the “design soil moisture” conditions, representing a critical parameter for assessing the initial wetness of the basin. To that end, this study of investigating six subcatchments of the upper Tiber River basin (Central Italy), with drainage area ranging from 13 to 284 km2, proposes a procedure based on the application of the CS approach as a tool to define the design soil moisture to be afterwards incorporated into the more simple DS method. For each catchment, the procedure consists of (1) stochastic generation of long synthetic rainfall and temperature series starting from observed hourly data; (2) application of a lumped continuous rainfall‐runoff model to generate synthetic discharge series and, hence, to obtain the corresponding flood frequency curves; (3) estimation of the design soil moisture, for each return period, by varying in the DS approach the initial wetness conditions of the catchment so that the peak discharge estimated by the DS method matches the one given by the synthetic flood frequency curve. Moreover, in order to apply the more simple DS approach avoiding the use of the CS one, a preliminary analysis to regionalize the design soil moisture as a function of the geo‐morphological characteristics and the return period is also shown.

Estimation of log-normal quantiles: Monte Carlo results and first-order approximations

Monte Carlo estimates of the average bias and root mean square error achieved with different quantile estimation procedures for the three-parameter log-normal distribution allow a comparison of the methods' performance. The maximum likelihood method, method of moments, and two quantile-lower-bound estimators in combination with two moments in real or in log space were considered. The maximum likelihood method and Stedinger's quantile-lower-bound methods provide more accurate estimators of the 1 and 10 percentiles of the distribution. No method was best for estimating the 99 and 99.8 percentiles. First-order approximations provide reasonable estimates of the estimators' sampling variance in most cases. All quantile estimators of the 99 or 99.8 percentiles of a flood-flow distribution were shown to yield design flood values which will be exceeded with probabilities substantially in excess of 1% and 0.2%, respectively.

Design events with specified flood risk

A maximum likelihood or method of moments estimate of the 99 percentile of a flood flow distribution is the traditional choice for the 100‐year design flood event in flood plain planning. Because such estimates ignore the small‐sample properties of quantile estimators, the resulting design event values will be exceeded with a probability in excess of that intended. For a sample size of 16 the estimated 100‐year flood is, in expectation, the 50‐year flood. Bayesian and classical statistical approaches can be used to develop design flood values which, given available hydrologic information, will (on average) be exceeded with the specified 1% design probability. Bias in estimates of expected flood damages and procedures for using regional information at gauged and ungauged sites are discussed.