A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence

Abstract

Seasonal design floods which consider information on seasonal variation are very important for reservoir operation and management. The seasonal design flood method currently used in China is based on seasonal maximum (SM) samples and assumes that the seasonal design frequency is equal to the annual design frequency. Since the return period associated with annual maximum floods is taken as the standard in China, the current seasonal design flood cannot satisfy flood prevention standards. A new seasonal design flood method, which considers dates of flood occurrence and magnitudes of the peaks (runoff), was proposed and established based on copula function. The mixed von Mises distribution was selected as marginal distribution of flood occurrence dates. The Pearson Type III and exponential distributions were selected as the marginal distribution of flood magnitude for annual maximum flood series and peak-over-threshold samples, respectively. The proposed method was applied at the Geheyan Reservoir, China, and then compared with the currently used seasonal design flood methods. The case study results show that the proposed method can satisfy the flood prevention standard, and provide more information about the flood occurrence probabilities in each sub-season. The results of economic analysis show that the proposed design flood method can enhance the floodwater utilization rate and give economic benefits without lowering the annual flood protection standard.

Citation Chen, L., Guo, S. L., Yan, B. W., Liu, P. & Fang, B. (2010) A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence. Hydrol. Sci. J. 55(8), 1264–1280.     

Non-identical models for seasonal flood frequency analysis

Abstract

The aim is to build a seasonal flood frequency analysis model and estimate seasonal design floods. The importance of seasonal flood frequency analysis and the advantages of considering seasonal design floods in the derivation of reservoir planning and operating rules are discussed, recognising that seasonal flood frequency models have been in use for over 30 years. A set of non-identical models with non-constant parameters is proposed and developed to describe flows that reflect seasonal flood variation. The peak-over-threshold (POT) sampling method was used, as it is considered to provide significantly more information on flood seasonality than annual maximum (AM) sampling and has better performance in flood seasonality estimation. The number of exceedences is assumed to follow the Poisson distribution (Po), while the peak exceedences are described by the exponential (Ex) and generalized Pareto (GP) distributions and a combination of both, resulting in three models, viz. Po-Ex, Po-GP and Po-Ex/GP. Their performances are analysed and compared. The Geheyan and the Baiyunshan reservoirs were chosen for the case study. The application and statistical experiment results show that each model has its merits and that the Po-Ex/GP model performs best. Use of the Po-Ex/GP model is recommended in seasonal flood frequency analysis for the purpose of deriving reservoir operation rules.     

Cautionary note on multicomponent flood distributions for annual maxima

Multicomponent probability distributions such as the two‐component Gumbel distribution are sometimes applied to annual flood maxima when individual floods are seen as belonging to different classes, depending on physical processes or time of year. However, hydrological inconsistencies may arise if only nonclassified annual maxima are available to estimate the component distribution parameters. In particular, an unconstrained best fit to annual flood maxima may yield some component distributions with a high probability of simulating floods with negative discharge. In such situations, multicomponent distributions cannot be justified as an improved approximation to a local physical reality of mixed flood types, even though a good data fit is achieved. This effect usefully illustrates that a good match to data is no guarantee against degeneracy of hydrological models. Copyright © 2016 John Wiley & Sons, Ltd.     

Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River

As an alternative to the commonly used univariate flood frequency analysis, copula frequency analysis can be used. In this study, 58 flood events at the Litija gauging station on the Sava River in Slovenia were analysed, selected based on annual maximum discharge values. Corresponding hydrograph volumes and durations were considered. Different bivariate copulas from three families were applied and compared using different statistical, graphical and upper tail dependence tests. The parameters of the copulas were estimated using the method of moments with the inversion of Kendall's tau. The Gumbel–Hougaard copula was selected as the most appropriate for the pair of peak discharge and hydrograph volume (Q‐V). The same copula was also selected for the pair hydrograph volume and duration (V‐D), and the Student‐t copula was selected for the pair of peak discharge and hydrograph duration (Q‐D). The differences among most of the applied copulas were not significant. Different primary, secondary and conditional return periods were calculated and compared, and some relationships among them were obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust flood statistics: comparison of peak over threshold approaches based on monthly maxima and TL-moments

ABSTRACT

Flood quantile estimation based on partial duration series (peak over threshold, POT) represents a noteworthy alternative to the classical annual maximum approach since it enlarges the available information spectrum. Here the POT approach is discussed with reference to its benefits in increasing the robustness of flood quantile estimations. The classical POT approach is based on a Poisson distribution for the annual number of exceedences, although this can be questionable in some cases. Therefore, the Poisson distribution is compared with two other distributions (binomial and Gumbel-Schelling). The results show that only rarely is there a difference from the Poisson distribution. In the second part we investigate the robustness of flood quantiles derived from different approaches in the sense of their temporal stability against the occurrence of extreme events. Besides the classical approach using annual maxima series (AMS) with the generalized extreme value distribution and different parameter estimation methods, two different applications of POT are tested. Both are based on monthly maxima above a threshold, but one also uses trimmed L-moments (TL-moments). It is shown how quantile estimations based on this “robust” POT approach (rPOT) become more robust than AMS-based methods, even in the case of occasional extraordinary extreme events.

Editor M.C. Acreman Associate editor A. Viglione     

Estimation of the annual maximum distribution from samples of maxima in separate seasons

Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.     

Unbiased estimation of flood risk with the GEV distribution

Conventional flood frequency analysis is concerned with providing an unbiased estimate of the magnitude of the design flow exceeded with the probabilityp, but sampling uncertainties imply that such estimates will, on average, be exceeded more frequently. An alternative approach is therefore, to derive an estimator which gives an unbiased estimate of flow risk: the difference between the two magnitudes reflects uncertainties in parameter estimation. An empirical procedure has been developed to estimate the mean true exceedance probabilities of conventional estimates made using a GEV distribution fitted by probability weighted moments, and adjustment factors have been determined to enable the estimation of flood magnitudes exceeded with, on average, the desired probability.     

Data‐based analysis of bivariate copula tail dependence for drought duration and severity

In recent decades, copula functions have been applied in bivariate drought duration and severity frequency analysis. Among several potential copulas, Clayton has been mostly used in drought analysis. In this research, we studied the influence of the tail shape of various copula functions (i.e. Gumbel, Frank, Clayton and Gaussian) on drought bivariate frequency analysis. The appropriateness of Clayton copula for the characterization of drought characteristics is also investigated. Drought data are extracted from standardized precipitation index time series for four stations in Canada (La Tuque and Grande Prairie) and Iran (Anzali and Zahedan). Both duration and severity data sets are positively skewed. Different marginal distributions were first fitted to drought duration and severity data. The gamma and exponential distributions were selected for drought duration and severity, respectively, according to the positive skewness and Kolmogorov–Smirnov test. The results of copula modelling show that the Clayton copula function is not an appropriate choice for the used data sets in the current study and does not give more drought risk information than an independent model for which the duration and severity dependence is not significant. The reason is that the dependence of two variables in the upper tail of Clayton copula is very weak and similar to the independent case, whereas the observed data in the transformed domain of cumulative density function show high association in the upper tail. Instead, the Frank and Gumbel copula functions show better performance than Clayton function for drought bivariate frequency analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Pooled flood frequency analysis: a comparison based on peaks-over-threshold and annual maximum series

Despite some theoretical advantages of peaks-over-threshold (POT) series over annual maximum (AMAX) series, some practical aspects of flood frequency analysis using AMAX or POT series are still subject to debate. Only minor attention has been given to the POT method in the context of pooled frequency analysis. The objective of this research is to develop a framework to promote the implementation of pooled frequency modelling based on POT series. The framework benefits from a semi-automated threshold selection method. This study introduces a formalized and effective approach to construct homogeneous pooling groups. The proposed framework also offers means to compare the performance of pooled flood estimation based on AMAX or POT series. An application of the framework is presented for a large collection of Canadian catchments. The proposed POT pooling technique generally improved flood quantile estimation in comparison to the AMAX pooling scheme, and achieved smaller uncertainty associated with the quantile estimates.     

Development of design flood hydrographs using probability density functions

Probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQ_P) and error of time to peak (ET_P) were computed. The best‐fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20‐, 50‐, 100‐ and 200‐year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20‐, 50‐, 100‐ and 200‐year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormal‐produced peak discharge was very close to the estimated design discharge in case of 20‐year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50‐, 100‐ and 200‐year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50‐, 100‐ and 200‐year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma. Copyright © 2009 John Wiley & Sons, Ltd.     

An improved nonstationary model for flood frequency analysis and its implication for the Three Gorges Dam,China

This study proposes an improved nonstationary model for flood frequency analysis by investigating the relationship between flood peak and flood volume, using the Three Gorges Dam (TGD), China, for verification. First, the generalized additive model for location, scale and shape (GAMLSS) is used as the prior distribution. Then, under Bayesian theory, the prior distribution is updated using the conditional distribution, which is derived from the copula function. The results show that the improvement of the proposed model is significant compared with the GAMLSS-based prior distribution. Meanwhile, selection of a suitable prior distribution has a significant effect on the results of the improvement. For applications to the TGD, the nonstationary model can obviously increase the engineering management benefits and reduce the perceived risks of large floods. This study provides guidance for the dynamic management of hydraulic engineering under nonstationary conditions.     

Comparison between the peaks-over-threshold method and the annual maximum method for flood frequency analysis

Abstract

Flood frequency analysis can be made by using two types of flood peak series, i.e. the annual maximum (AM) and peaks-over-threshold (POT) series. This study presents a comparison of the results of both methods for data from the Litija 1 gauging station on the Sava River in Slovenia. Six commonly used distribution functions and three different parameter estimation techniques were considered in the AM analyses. The results showed a better performance for the method of L-moments (ML) when compared with the conventional moments and maximum likelihood estimation. The combination of the ML and the log-Pearson type 3 distribution gave the best results of all the considered AM cases. The POT method gave better results than the AM method. The binomial distribution did not offer any noticeable improvement over the Poisson distribution for modelling the annual number of exceedences above the threshold.

Editor D. Koutsoyiannis

Citation Bezak, N., Brilly, M., and ?raj, M., 2014. Comparison between the peaks-over-threshold method and the annual maximum method for flood frequency analysis. Hydrological Sciences Journal, 59 (5), 959–977.     

An analysis of change in alpine annual maximum discharges: implications for the selection of design discharges

The paper presents an analysis of 17 long annual maximum series (AMS) of flood flows for Swiss Alpine basins, aimed at checking the presence of changes in the frequency regime of annual maxima. We apply Pettitt's change point test, the nonparametric sign test and Sen's test on trends. We also apply a parametric goodness‐of‐fit test for assessing the suitability of distributions estimated on the basis of annual maxima collected up to a certain year for describing the frequency regime of later observations. For a number of series the tests yield consistent indications for significant changes in the frequency regime of annual maxima and increasing trends in the intensity of annual maximum discharges. In most cases, these changes cannot be explained by anthropogenic causes only (e.g. streamflow regulation, construction of dams). Instead, we observe a statistically significant relationship between the year of change and the elevation of the catchment outlet. This evidence is consistent with the findings of recent studies that explain increasing discharges in alpine catchments with an increase in the temperature controlling the portion of mountain catchments above the freezing point. Finally, we analyse the differences in return periods (RPs) estimated for a given flood flow on the basis of recent and past observations. For a large number of the study AMS, we observe that, on average, the 100‐year flood for past observations corresponds to a RP of approximately 10 to 30 years on the basis of more recent observation. From a complementary perspective, we also notice that estimated RP‐year flood (i.e. flood quantile (FQ) associated with RP) increases on average by approximately 20% for the study area, irrespectively of the RP. Practical implications of the observed changes are illustrated and discussed in the paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Copula‐based flood frequency (COFF) analysis at the confluences of river systems

Many civil infrastructures are located near the confluence of two streams, where they may be subject to inundation by high flows from either stream or both. These infrastructures, such as highway bridges, are designed to meet specified performance objectives for floods of a specified return period (e.g. the 100 year flood). Because the flooding of structures on one stream can be affected by high flows on the other stream, it is important to know the relationship between the coincident exceedence probabilities on the confluent stream pair in many hydrological engineering practices. Currently, the National Flood Frequency Program (NFF), which was developed by the US Geological Survey (USGS) and based on regional analysis, is probably the most popular model for ungauged site flood estimation and could be employed to estimate flood probabilities at the confluence points. The need for improved infrastructure design at such sites has motivated a renewed interest in the development of more rigorous joint probability distributions of the coincident flows. To accomplish this, a practical procedure is needed to determine the crucial bivariate distributions of design flows at stream confluences. In the past, the copula method provided a way to construct multivariate distribution functions. This paper aims to develop the Copula‐based Flood Frequency (COFF) method at the confluence points with any type of marginal distributions via the use of Archimedean copulas and dependent parameters. The practical implementation was assessed and tested against the standard NFF approach by a case study in Iowa's Des Moines River. Monte Carlo simulations proved the success of the generalized copula‐based joint distribution algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Implications of heterogeneous flood‐frequency distributions on traditional stream‐discharge prediction techniques

Traditional flood‐frequency analysis involves the assumption of homogeneity of the flood distribution. However, floods are often generated by heterogeneous distributions composed of a mixture of two or more populations. Differences between the populations may be the result of a number of factors, including seasonal variations in the flood‐producing mechanisms, changes in weather patterns resulting from low‐frequency climate shifts and/or El Niño/La Nina oscillations, changes in channel routing owing to the dominance of within‐channel or floodplain flow, and basin variability resulting from changes in antecedent soil moisture. Not recognizing these physical processes in conventional flood‐frequency analysis probably is the main reason that many frequency distributions do not provide an acceptable fit to flood data. In this paper, we use long‐term hydroclimatic records from the Gila River basin of south‐east and central Arizona in the USA to explore the extent and significance of mixed populations. First, we discuss the probable causes of heterogeneity in the frequency distribution of annual flood and present evidence of its occurrence. Second, we investigate the implications of using various popular homogeneous distributions for predicting peak flows for basins that exhibit mixed population characteristics. Third, we demonstrate how alternative frequency models that explicitly account for floods generated by a mixture of two or more populations are both hydrologically and statistically more appropriate. We illustrate how the selection of the most plausible distribution for flood‐frequency analysis also should be based on hydrological reasoning as opposed to the sole application of the traditional statistical goodness‐of‐fit tests. Copyright © 2002 John Wiley & Sons, Ltd.     

Assessment of past flood changes across Europe based on flood-generating processes

ABSTRACT

A rainfall–runoff model was employed to identify four major flood-generating processes corresponding to flood events identified from daily discharge data from 614 stations across Europe in the period 1961–2010: long-rain, short-rain, snowmelt, and rain-on-dry-soil flood events. Trend analyses were performed on the frequency of occurrence of each of the flood types continentally and in five geographical regions of Europe. Continentally, the annual frequency of flood events did not show a significant change over the investigation period. However, the frequency of both winter and summer long-rain events increased significantly, while that of summer snowmelt events decreased significantly. Regionally, the frequency of winter short and long-rain events increased significantly in Western Europe, while the frequency of summer snowmelt and short-rain events decreased in Northern Europe. The frequency of summer snowmelt events in Eastern Europe and winter short-rain events in Southern Europe showed a declining trend.     

Frequency analysis of nonstationary annual maximum flood series using the time‐varying two‐component mixture distributions

The most popular practice for analysing nonstationarity of flood series is to use a fixed single‐type probability distribution incorporated with the time‐varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time‐varying under changing environments. To allow the investigation of this complex nature, the time‐varying two‐component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series of two stations in the Weihe River basin, with the model parameters calibrated by the meta‐heuristic maximum likelihood method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single‐type distributions, stationary mixture distributions and time‐varying single‐type distributions. The results highlighted the advantages of TTMD with physically‐based covariates for both stations. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonstationarity-based evaluation of flood risk in the Pearl River basin: changing patterns,causes and implications

Nonstationary GEV-CDN models considering time as a covariate are built for evaluating the flood risk and failure risk of the major flood-control infrastructure in the Pearl River basin, China. The results indicate: (1) increasing peak flood flow is observed in the mainstream of the West River and North River basins and decreasing peak flood flow is observed in the East River basin; in particular, increasing peak flood flow is detected in the mainstream of the lower Pearl River basin and also in the Pearl River Delta region, the most densely populated region of the Pearl River basin; (2) differences in return periods analysed under stationarity and nonstationarity assumptions are found mainly for floods with return periods longer than 50 years; and (3) the failure risks of flood-control infrastructure based on failure risk analysis are higher under the nonstationarity assumption than under the stationarity assumption. The flood-control infrastructure is at higher risk of flood and failure under the influence of climate change and human activities in the middle and lower parts of Pearl River basin.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR G. Thirel