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Flood frequency analysis should consider small and frequent floods. Despite the complexities in partial duration series implementation, it can give a better flood estimation in a way that it does not exclude any significant high flow events, even if it is not the highest event of the year. This study employs the streamflow data recorded at Kajang station, Sungai Langat, Malaysia over a 36-year period spanning from 1978 to 2013. The paper attempts to conduct flood frequency analysis using two approaches, annual maximum and partial duration series. The optimal threshold value is selected to be 48.7 m3/s, where the dispersion index stabilizes at around 1, DI = 1 . The results have shown that generalized extreme value (GEV) distribution describes the annual maximum data while the lognormal (LN3) and generalized Pareto (GPA) distribution is chosen as the best fit distribution at Kajang station for a partial duration series. There is a slight difference between estimated streamflow magnitude when using GPA and LN3 for selected return periods, while a considerable difference was observed when using annual maximum at a higher return period. As a conclusion, PDS gives more relevant magnitude estimation rather than AMS. Flood frequency plays an important role in understanding the nature and magnitude of high flow, which in turn can assist relevant agencies in the design of hydrological structures and reduce flood impacts.

The nonstationary hydrologic processes due to climate variability and intensification of human activities are challenging and questionable for researchers. This study investigates nonstationary partial duration series (PDS) records for the period 1971–2017 at 14 hydrological stations across the Gorganrood River Basin, Iran. The Gorganrood Basin is very diverse in terms of climate such as humid, semihumid, Mediterranean, semiarid, and arid climates. Change points are analyzed using the Pettitt technique. Trends of PDS are detected using the Mann–Kendall method. The nonstationarity of the PDS series is examined by generalized additive models for location, scale, and shape (GAMLSS). Results indicate that abrupt changes are significant for the PDS series in the Gorganrood River Basin. Change points have a considerable effect on trend detection, and these may be attributed to the fact that an abrupt increase or decrease in mean values affects trend changes. In addition, the GAMLSS results showed that the most suitable performance distribution was LNO distribution and then RGE distribution in the Gorganrood River Basin. On other hand, the GAMLSS model and the Pettitt test have good capability in detecting stationary and nonstationary PDS series.

Keith Beven was amongst the first to propose and demonstrate a combination of conceptual rainfall–runoff modelling and stochastically generated rainfall data in what is known as the ‘continuous simulation’ approach for flood frequency analysis. The motivations included the potential to establish better links with physical processes and to avoid restrictive assumptions inherent in existing methods applied in design flood studies. Subsequently, attempts have been made to establish continuous simulation as a routine method for flood frequency analysis, particularly in the UK. The approach has not been adopted universally, but numerous studies have benefitted from applications of continuous simulation methods. This paper asks whether industry has yet realized the vision of the pioneering research by Beven and others. It reviews the generic methodology and illustrates applications of the original vision for a more physically realistic approach to flood frequency analysis through a set of practical case studies, highlighting why continuous simulation was useful and appropriate in each case. The case studies illustrate how continuous simulation has helped to offer users of flood frequency analysis more confidence about model results by avoiding (or exposing) bad assumptions relating to catchment heterogeneity, inappropriateness of assumptions made in (UK) industry‐standard design event flood estimation methods, and the representation of engineered or natural dynamic controls on flood flows. By implementing the vision for physically realistic analysis of flood frequency through continuous simulation, each of these examples illustrates how more relevant and improved information was provided for flood risk decision‐making than would have been possible using standard methods. They further demonstrate that integrating engineered infrastructure into flood frequency analysis and assessment of environmental change are also significant motivations for adopting the continuous simulation approach in practice. Copyright © 2016 John Wiley & Sons, Ltd.

Flood frequency analysis estimates reliable design flood, which is critical for the safety of any hydraulic, hydrologic construction and management. The overall objective of this study is to perform flood frequency analysis for Seonath and Hasdeo river basins of Chhattisgarh state, India. In this study, homogeneous regions are delineated by Ward cluster analysis. Cluster variables are L-moment ratios of annual maximum events and catchment characters. Index flood is performed for parametric quantile estimation of flood events. L-moments are employed in regionalization, frequency distribution selection, and distribution parameter estimation. Locally weighted polynomial model (Locfit) is performed for at-site frequency analysis. Flood quantiles are estimated for regions and at sites. In regional flood frequency analysis, regionalisation based on annual maximum flood series shows better flood quantiles than regionalisation based on site characteristics. It reveals that geophysical homogeneity does not mean hydrologic homogeneity. Regional formulae for annual mean discharge are formulated based on catchment character for estimation of flood quantiles for ungauged catchments.KeywordsFlood frequency analysisCluster analysisL-momentsIndex floodLocfit

Flood frequency analysis is used by water resources professionals to estimate the probability of exceedence associated with a flood of a given magnitude. The estimation of flood frequencies is important because they are used in the planning and design of hydraulic structures, in flood-plain management, and in reservoir operation. The index flood method is commonly used to develop a flood frequency curve that relates flood magnitude to flood rarity. This method involves scaling a dimensionless flood frequency curve by the index flood. The index flood is a middle-sized flood for which the mean or median of the flood data series is typically used. When the catchment of interest is ungauged, statistical models, such as multiple regression, are often used to relate the index flood to catchment descriptors. In this study six different parameter estimation techniques and three regionalization techniques are compared in terms of ability to predict the index flood for an ungauged catchment. A case study employing a split-sample experiment with data from catchments in Ontario, Canada, was used to evaluate the approaches. The models were assessed using three performance indices to evaluate the capability to predict the index flood for 20 stations. The dimensionless nonlinear model outperformed all of the other parameter estimation techniques for each of the three indices selected. The performance was improved through the use of geostatistical residual mapping, however, the improvement was small. The residual mapping was found to greatly improve the estimates obtained using ordinary least-squares regression.Key words: index flood, flood frequency analysis, regression, residual mapping, geostatistics.

Abstract. Flood frequency analysis (FFA) entails the estimation of the upper tail of a probability density function (PDF) of annual peak flows obtained from either the annual maximum series or partial duration series. In hydrological practice, the properties of various methods of upper quantiles estimation are identified with the case of known population distribution function. In reality, the assumed hypothetical model differs from the true one and one cannot assess the magnitude of error caused by model misspecification in respect to any estimated statistics. The opinion about the accuracy of the methods of upper quantiles estimation formed from the case of known population distribution function is upheld. The above-mentioned issue is the subject of the paper. The accuracy of large quantile assessments obtained from the four estimation methods is compared to two-parameter log-normal and log-Gumbel distributions and their three-parameter counterparts, i.e., three-parameter log-normal and GEV distributions. The cases of true and false hypothetical models are considered. The accuracy of flood quantile estimates depends on the sample size, the distribution type (both true and hypothetical), and strongly depends on the estimation method. In particular, the maximum likelihood method loses its advantageous properties in case of model misspecification.

Nonstationary flood and low flow frequency analysis in the upper reaches of Huaihe River Basin, China, using climatic variables and reservoir index as covariates

<p>The Glomma river is the largest in Norway and repeated destructive floods continue to represent a major climate hazard. Area planning and dam safety assessment in Norway, including the large catchment that feeds Glomma, are based on estimates of design flood sizes from 200 to 1000 years return periods despite the fact that most streamflow time series are ≤50 years. Consequently, design flood estimates are subject to sample uncertainty. Other data than streamflow measurements such as historical data and lake sediment cores can be employed not only to increase knowledge about floods, but also to reduce uncertainty in design flood estimates. By merging different data sources, it is possible to reduce the uncertainty associated with flood frequency analysis. The primary objective of this study is to combine systematic- historical and paleo-information in a methodological effort to improve flood frequency analysis.</p><p>We approach this ambition by (i) compiling historical flood data from the existing literature, (ii) presenting  high resolution XRF, MS and CT scanning data from a sediment core covering the last 10 000 years, and (iii) combining flood data from systematic streamflow measurements, historical sources and lacustrine sediment cores for estimating design floods and assessing non-stationarities in flood frequency.</p><p>Based on the lake sediments from Lake Flyginsjøen, which faithfully records flood events in Glomma, we can estimate flood frequency in a moving window of 50 years. Whenever the discharge is sufficient the floodwater crosses a local threshold and suspended sediments are deposited in the lake, providing information about how flood frequency has changed over the last 10 00 years. </p><p>The lake sediment data shows that past flood frequency is non-stationarity on different time scales. Periods with increased flood activity corresponds broadly to similar timeseries from eastern Norway and also in the Alps on centennial time scales. The flood frequency shows significant non-stationarities within periods with increased flood activity as was the case for the 18th century. The lake data indicates that the major historical flood in 1789 is the largest on record for the last 10 000 years at this site.</p><p>The results show that estimation of flood quantiles can benefit from the inclusion of historical and paleodata. The paleodata were in particular useful for evaluating how the flood information in historical data represent flood frequency on longer time scales. Using the frequency of floods obtained from the paleo-flood record resulted in minor changes in design flood estimates.   <br><br>This study has shown that the potential advantage of including paleoflood data and we suggest that paleodata has a high potential for detecting links between climate and flood frequency. The data presented here can be used alone, or in combination with paleoflood data from other locations in Norway and Europe, to assess and better understand the potential links between changes in climate and the corresponding changes in flood frequency.</p>

Flood frequency analysis is crucial for understanding flood risks in specific regions. This study applied the Gumbel Distribution Method to analyze flood frequency using river discharge data from the Kadamaian and Wariu Rivers in Kota Belud, Sabah, Malaysia. The analysis involved data collection, parameter estimation, goodness-of-fit testing, and determination of annual recurrence intervals (ARIs). The study found that the ARIs for the Kadamaian and Wariu Rivers are 50 years and 30 years, respectively, highlighting the need for targeted flood mitigation strategies in these areas. These findings emphasize the higher flood risk in the Kadamaian River basin, necessitating more robust flood control measures compared to the Wariu River basin. The Gumbel distribution provided accurate flood frequency estimations validated by the Kolmogorov-Smirnov test and correlation coefficient (R2). The calculated ARIs offer valuable insights for flood hazard assessment and contingency planning. These findings underscore the importance of accurate flood frequency analysis in enhancing flood mitigation strategies and disaster preparedness. It is recommended that local authorities incorporate these results into flood management and urban planning initiatives.

Different flood-generating mechanisms are responsible for high flows in different catchments. This mixture of generating mechanisms could violate the homogeneity assumption of the extreme value distribution used often in flood frequency analysis. Thus, this study aims to classify flood samples into homogenous process-based groups and estimate the flood quantiles for different return periods. Furthermore, this study also deals with the sample inadequacy in the flood classification by pooling ensemble reforecast datasets based on the UNprecedented Simulated Extreme ENsemble (UNSEEN) approach. The Dresden gauge in the Elbe River is selected as the study site. Daily discharge data are extracted from the GRDC, and flood events are separated based on our proposed ‘Peak-identification flood separation algorithm’, which follows four steps: 1. Identification of peaks, i.e., points with a higher streamflow value than its prior and next values, 2. Pruning based on 90th percentile threshold value, 3. Application of independence criterion, 4. Identification of flood starting and ending position. After flood separation, hydrograph features-based flood grouping and ensemble data pooling are performed. We observe the difference in the distribution characteristics of the observed in comparison to the pooled datasets. A relative difference of 0.25 (cumecs/cumecs) is noticed for the 100-year return level between observed and pooled data. As our key contribution, we address the sample mixing problem using the flood classification technique and establish the importance of data pooling.

To obtain the flooding frequency distribution for an urban watershed, different methods based on simulations of synthetic rainfall events were compared with an empirical analysis of the flooding data and with the results of long‐term simulations. A copula‐based multivariate statistical analysis of the main hydrological variables was proposed to generate synthetic hyetographs. Two different approaches were adopted to assess a temporal pattern to the synthetic rainfall: one analyses all available historical rainfall patterns, and another adopts the cluster analysis in three different variants to reduce the computational effort of the analysis.To test the methodology reliability, the analysis was carried out for a real urban watershed. To carry out the flooding frequency analysis, all generated synthetic hyetographs were used as input of a dual drainage mathematical model of the analysed drainage system. Results showed that the method based on the analysis of all historical rainfall patterns was efficient in the estimation of flooding frequency, especially for higher return periods and approximately halved the computational costs of ordinary long‐term analysis. Regarding clustering approaches, although attractive for their computational efficiency, their adoption must be carefully evaluated because it could neglect relevant information and result in a less accurate flood frequency analysis.

The higher-order linear moments (LH-moments) method is one of the most commonly used methods for estimating the parameters of probability distributions in flood frequency analysis without sample censoring. This article presents the relationships necessary to estimate the parameters for eight probability distributions used in flood frequency analysis. Eight probability distributions of three parameters using first- and second-order LH-moments are presented, namely the Pearson V distribution, the CHI distribution, the inverse CHI distribution, the Wilson–Hilferty distribution, the Pseudo-Weibull distribution, the Log-normal distribution, the generalized Pareto Type I distribution and the Fréchet distribution. The exact and approximate relations for parameter estimation are presented, as are the exact and approximate relations for estimating the frequency factor specific to each method. In addition, the exact and approximate relationships of variation in the LH-skewness–LH-kurtosis are presented, as is the variation diagram of these statistical indicators. To numerically represent the analyzed distributions, a flood frequency analysis case study using the annual maximum series was carried out for the Prigor River. The analysis is presented compared to the linear moments (L-moments) method, which is the method that is intended to be used in the development of a new norm in Romania for determining the maximum flows. For the Prigor River, the most fit distributions are the Pseudo-Weibull and the generalized Pareto Type I for the linear moments method and the CHI and the Wilson–Hilferty distributions for the first higher-order linear moments method. The performance was evaluated using linear and higher-order linear moment values and diagrams.

We present an extension to Jaynes’ maximum entropy principle that incorporates latent variables. The principle oflatent maximum entropywe propose is different from both Jaynes’ maximum entropy principle and maximum likelihood estimation, but can yield better estimates in the presence of hidden variables and limited training data. We first show that solving for a latent maximum entropy model poses a hard nonlinear constrained optimization problem in general. However, we then show that feasible solutions to this problem can be obtained efficiently for the special case of log-linear models---which forms the basis for an efficient approximation to the latent maximum entropy principle. We derive an algorithm that combines expectation-maximization with iterative scaling to produce feasible log-linear solutions. This algorithm can be interpreted as an alternating minimization algorithm in the information divergence, and reveals an intimate connection between the latent maximum entropy and maximum likelihood principles. To select a final model, we generate a series of feasible candidates, calculate the entropy of each, and choose the model that attains the highest entropy. Our experimental results show that estimation based on the latent maximum entropy principle generally gives better results than maximum likelihood when estimating latent variable models on small observed data samples.

Both flood magnitude and frequency might change under the changing environment. In this study, a procedure combining statistical methods, flood frequency analysis and attribution analysis was proposed to investigate the response of floods to urbanization and precipitation change in the Qinhuai River Basin, an urbanized basin located in Southeast China, over the period from 1986 to 2013. The Mann–Kendall test was employed to detect the gradual trend of the annual maximum streamflow and the peaks over threshold series. The frequency analysis was applied to estimate the changes in the magnitude and frequency of floods between the baseline period (1986–2001) and urbanization period (2002–2013). An attribution analysis was proposed to separate the effects of precipitation change and urbanization on flood sizes between the two periods. Results showed that: (1) there are significant increasing trends in medium and small flood series according to the Mann–Kendall test; (2) the mean and threshold values of flood series in the urbanization period were larger than those in the baseline period, while the standard deviation, coefficient of variation and coefficient of skewness of flood series were both higher during the baseline period than those during the urbanization period; (3) the flood magnitude was higher during the urbanization period than that during the baseline period at the same return period. The relative changes in magnitude were larger for small floods than for big floods from the baseline period to the urbanization period; (4) the contributions of urbanization on floods appeared to amplify with the decreasing return period, while the effects of precipitation diminish. The procedure presented in this study could be useful to detect the changes of floods in the changing environment and conduct the attribution analysis of flood series. The findings of this study are beneficial to further understanding interactions between flood behavior and the drivers, thereby improving flood management in urbanized basins.

A Bayesian copula-based nonstationary framework for compound flood risk assessment along US coastlines