A direct analysis of flood interval probability using approximately 100-year streamflow datasets

ABSTRACT

Series of observed flood intervals, defined as the time intervals between successive flood peaks over a threshold, were extracted directly from 11 approximately 100-year streamflow datasets from Queensland, Australia. A range of discharge thresholds were analysed that correspond to return periods of approximately 3.7 months to 6.3 years. Flood interval histograms at South East Queensland gauges were consistently unimodal whereas those of the North and Central Queensland sites were often multimodal. The exponential probability distribution (pd) is often used to describe interval exceedence probabilities, but fitting utilizing the Anderson-Darling statistic found little evidence that it is the most suitable. The fatigue life pd dominated sub-year return periods (<1 year), often transitioning to a log Pearson 3 pd at above-year return periods. Fatigue life pd is used in analysis of the lifetime to structural failure when a threshold is exceeded, and this paper demonstrates its relevance also to the elapsed time between above-threshold floods. At most sites, the interval medians were substantially less than the means for sub-year return periods. Statistically the median is a better measure of the central tendency of skewed distributions but the mean is generally used in practice to describe the classical concept of flood return period.

Editor Z.W. Kundzewicz; Associate editor I. Nalbantis     

Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis / Modèles d’extrêmes utilisant le système Burr XII étendu à trois paramètres et application à l’analyse fréquentielle des crues

Abstract

Abstract A new theoretically-based distribution in frequency analysis is proposed. The extended three-parameter Burr XII distribution includes the generalized Pareto distribution, which is used to model the exceedences over threshold; log-logistic distribution, which is also advocated in flood frequency analysis; and Weibull distribution, which is a part of the generalized extreme value distribution used to model annual maxima as special cases. The extended Burr distribution is flexible to approximate extreme value distribution. Note that both the generalized Pareto and generalized extreme value distributions are limiting results in modelling the exceedences over threshold and block extremes, respectively. From a modelling perspective, generalization might be necessary in order to obtain a better fit. The extended three-parameter Burr XII distribution is therefore a meaningful candidate distribution in the frequency analysis. Maximum likelihood estimation for this distribution is investigated in the paper. The use of the extended three-parameter Burr XII distribution is demonstrated using data from China.     

Ground motion prediction equations derived from the Italian strong motion database

We present a set of ground motion prediction equations (GMPEs) derived for the geometrical mean of the horizontal components and the vertical, considering the latest release of the strong motion database for Italy. The regressions are performed over the magnitude range 4?C6.9 and considering distances up to 200?km. The equations are derived for peak ground acceleration (PGA), peak ground velocity (PGV) and 5%-damped spectral acceleration at periods between 0.04 and 2?s. The total standard deviation (sigma) varies between 0.34 and 0.38?log₁₀ unit, confirming the large variability of ground shaking parameters when regional data sets containing small to moderate magnitude events (M?<?6) are used. The between-stations variability provides the largest values for periods shorter than 0.2?s while, for longer periods, the between-events and between-stations distributions of error provide similar contribution to the total variability.     

Laboratory examination of linearity in rainfall–runoff relationships

ABSTRACT

Certain rainfall–runoff models, e.g. the unit hydrograph, assume linear relationships between the variables. These are proportionality of runoff discharges to (net) rainfall depth and linear summations of discharges resulting from (net) rainfalls during different time intervals or over different sectors of a watershed. This study examines the validity of these assumptions by use of an extensive two-dimensional laboratory experimentation. The results indicate that proportionality would be found under high rainfall intensity through a long duration. Spatial summations would more likely yield correct discharges in cases where rainfall duration is equal to, or is longer than, the time of concentration. Temporal summations may yield correct discharges when rainfall duration is longer than one half of the time of concentration. Here, the time of concentration is determined at the beginning of gradual approach of the discharge towards the equilibrium state.     

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     

Modelling the influence of hydrogeological parameters on low flow in hilly and mountainous regions of Serbia / Modélisation de l'influence de paramètres hydrogéologiques sur les basses eaux dans des régions de collines et de montagnes de Serbie

Abstract

During dry weather periods of the year with long rainless intervals, streams slacken to what is generally termed “low flow”. This work presents an analysis of the influence of hydrogeology on low flows, using multiple linear regression, in natural medium and small streams in hilly and mountainous regions of Serbia. The study cases encompass 61 gauged catchments south of the rivers Sava and Danube. Characteristic relevant minimum mean 30-day flows of 80- or 95-percentile exceedence (Q _80%, Q _95%) are taken as dependent variables. Independent variables are the observable hydrogeological quantities: catchment area upstream of a gauging station; surface area of a hydrogeological soil category in a catchment; number of perennial springs of minimum flow higher than or equal to 1 L/s in a gauged catchment; number of perennial springs, each of minimum flow higher than or equal to 1 L/s, in a given hydrogeological soil category of the catchment; cumulative perennial spring flow of minimum single flow higher than or equal to 1 L/s in a catchment; and cumulative perennial spring flow of minimum single flow higher than or equal to 1 L/s in a hydrogeological soil category of a catchment. Through multiple linear regression between the characteristic relevant low flow and the hydrogeological elements, 16 models are developed and analysed, each based on a different combination of hydrogeological elements and characteristic low flow. The regional relationships developed for the minimum mean 30-day flows of 80- and 95-percentile exceedences are evaluated. The statistical tests of the representation quality of each multiple regression relationship show that the models justify the use of hydrogeological elements.     

Frequency analysis of climate extreme events in Zanjan, Iran

In this study, generalized extreme value distribution (GEV) and generalized Pareto distribution (GPD) were fitted to the maximum and minimum temperature, maximum wind speed, and maximum precipitation series of Zanjan. Maximum (minimum) daily and absolute annual observations of Zanjan station from 1961 to 2011 were used. The parameters of the distributions were estimated using the maximum likelihood estimation method. Quantiles corresponding to 2, 5, 10, 25, 50, and 100 years return periods were calculated. It was found that both candidate distributions fitted to extreme events series, were statistically reasonable. Most of the observations from 1961 to 2011 were found to fall within 1–10 years return period. Low extremal index (θ) values were found for excess maximum and minimum temperatures over a high threshold, indicating the occurrence of consecutively high peaks. For the purpose of filtering the dependent observations to obtain a set of approximately independent threshold excesses, a declustering method was performed, which separated the excesses into clusters, then the de-clustered peaks were fitted to the GPD. In both models, values of the shape parameters of extreme precipitation and extreme wind speed were close to zero. The shape parameter was less negative in the GPD than the GEV. This leads to significantly lower return period estimates for high extremes with the GPD model.     

A physically based distribution function for low flow

Abstract

An attempt is made to incorporate the physical mechanism in a distribution function of low flow in terms of baseflow recession. The derived distribution function contains four parameters of which two are determined from a traditional recession analysis of low flow periods. The other two are derived from a statistical analysis of the maximum length of “dry weather” periods when precipitation is less than an assumed threshold value. The distribution function with the same parameters can be applied to calculate mean low flow for different durations. It is applied and tested for summer low flow in southern and western Norway.     

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.     

Inter-catchment comparison of flow regime between the Hailiutu and Huangfuchuan rivers in the semi-arid Erdos Plateau,Northwest China

Abstract

Two river catchments, the Huangfuchuan and the Hailiutu, located in the same climate zone in the Erdos Plateau, China, have distinctly different flow regimes. This study systematically compared differences between the flow regimes of these two catchments using several statistical methods, and analysed the possible causes. The variations in yearly, monthly and daily mean discharges were found to be much greater in the Huangfuchuan catchment than in the Hailiutu catchment. Preliminary analysis indicated that these differences are not caused by changes in climate, but are instead attributable to differences in geology, geomorphology, hydrological processes and human interventions. In the Hailiutu catchment, the dominant groundwater contribution maintains stationary daily and monthly river discharges, while shifts in yearly mean discharges were closely associated with the expansion or reduction of crop area. In the Huangfuchuan catchment, the dominant direct rainfall–runoff process generates flashier daily and monthly river discharges, while the decrease of yearly mean discharges is caused mainly by the construction of check dams. These findings have significant implications for water resource management and the implementation of proper soil and water conservation measures in the middle reach of the Yellow River Basin of China.

Editor Z.W. Kundzewicz; Associate editor Y. Gyasi-Agyei     

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.     

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.     

Reconstruction of the rainy season precipitation in central Jordan

Abstract

Concurrent reconstructions of October—April precipitation at Madaba and Rabba gauging sites in central Jordan back to the year 1777 using a multivariate regression model are presented. The reconstruction model was calibrated using concurrent precipitation and tree-ring data for the period 1953–1981 The regression equation is significant (p < 0.05), while reconstructions account for 53% and 48% (adjusted for lost degrees of freedom) of the total variability of the precipitation at the Madaba and Rabba sites, respectively. The validation statistic obtained indicates the existence of worthwhile information in the reconstructions. A threshold of 1 standard deviation below the mean is used to define extremely dry years. The concurrent analysis of the reconstructed precipitation at both sites indicates the occurrence of 24 regional extremely dry periods of between 1 and 2 years' duration. Dry periods of more than 2 years' duration rarely occur. This study indicates the occurrence of noticeable extremely dry individual years: 1800, 1827, 1895 and 1933. The estimated mean recurrence times of extreme droughts are 9.3 and 51.3 years for droughts of 1-year and 2-years duration, respectively.     

The effects of climate variability on discharge as dependent on catchment characteristics in the Upper Loire basin,France

Abstract

The effects of climatically deviating periods of at least four years on discharge were investigated employing flow duration curves in the Upper Loire basin, France. The periods were determined using the standardized cumulative yearly deviation from the mean precipitation for ten climate stations. Flow duration curves from 27 catchments were determined and parameterized for each period. Results show that the effect of precipitation on discharge is more pronounced than the effect of temperature. They also show that the parameter values that determine the flow duration curve differ significantly between dry and wet periods. Furthermore the effect of drought on discharge is larger than the effect of wetness. Catchments with a high variability of discharge are more sensitive to changes of precipitation than catchments with a low variability of discharge.     

Characteristics of the response of isothermal atmospheres with nonlinear waves

Abstract

We have studied the behavior of nonlinear waves in isothermal atmospheres using an improved beam scheme method. It is shown that although the magnitude of the mass leakage due to side beams is significant, nevertheless in a motion close to hydrostatic equilibrium it can be suppressed, if special density distributions and/or suitable mesh intervals are selected. We adopt as the parameters for our model of the atmospheres M=1 M[odot], R=50 R[odot] and T=4864 K. The time variation of the physical quantities in each cell is found for several oscillation periods. The critical frequency for the model atmosphere in the case of waves with a weak nonlinearity seems to be consistent with that in the linear theory.     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi     

Types of probability distributions in the evaluation of extreme floods

The development of an optimal scheme for evaluation of maximal water discharges is discussed, including adequate probability distribution laws, an effective procedure for their approximation based on observational data, and reliable goodness-of-fit tests for analytical and empirical distributions. One-dimensional probability distribution laws are systematized. Promising distributions were identified, including generalized distribution of extreme values, lognormal distribution, Pearson type V power distribution, and GPD, for evaluating maximal discharges. The available methods for approximating analytical curves, including the up-to-date method of L-moments are considered. Parameter estimation algorithm based on L-moment method for Pearson type III distribution is considered. Pearson type III distribution, lognormal distribution, GEV, and GPD are compared in the approximation of maximal water discharges in rivers of Austria, Siberia, Far East, and the Hawaiian Islands.     

A study on hydrological series of the Niger River

Abstract

The Hubert segmentation procedure has been applied to historical series of annual average discharges of the Niger River at Koulikoro (Mali), Niamey (Niger) and Lokoja (Nigeria) stations. The breaks, especially those identified at Koulikoro and Niamey, match well with those identified in the Senegal River series at Bakel using the same procedure. Lokoja departs from this regional pattern, as it shows in the late 1980s a return to wetter conditions much earlier than the other three stations. The magnitudes of the variation of the inter-annual means between the alternating wet and dry periods are significant and similar. These results seem to suggest that phenomena causing non-stationarity in hydrological series can have a sub-continental impact or, in contrast, may be more limited in their spatial coverage.

Editor Z.W. Kundzewicz; Associate editor H. Aksoy

Citation Abrate, T., Hubert, P., and Sighomnou, D., 2013. A study on hydrological series of the Niger River. Hydrological Sciences Journal, 58 (2), 271–279.     

Regional frequency analyses of successive-duration annual maximum rainfalls by L-moments method

ABSTRACT

The index flood method of the regional L-moments approach is adapted to annual maximum rainfall (AMR) series of successively increasing durations from 5 minutes to 24 hours. In Turkey, there are 14 such AMRs having standard durations of 5, 10, 15, 30, 60, 120, 180, 240, 300, 360, 480, 720, 1080 and 1440 min. The parameters of the probability distributions found suitable for these AMR series in a homogeneous region need to be adjusted so that their quantile functions will not cross each other over the entire range of probabilities. This adjustment is done so as to make (1) the derivative of the quantile function with respect to the Gumbel reduced variate of a longer-duration AMR be greater than or equal to that of the shorter-duration AMR, and (2) the quantile of a longer-duration AMR be greater than that of the shorter-duration AMR, both to be satisfied for any specific probability. Accordingly, the parameters of a probability distribution fitted to some AMR series must either increase or decrease or be constant with respect to increasing rainstorm duration; and the parameters of different distributions fitted to two sequential AMR series must be interrelated. The index flood method by the L-moments approach modified in such manner for successive-duration AMR series is applied to the Inland Anatolia region of Turkey using data recorded at 31 rain-gauging stations with recording lengths from 31 to 66 years.

EDITOR Z.W. Kundzewicz; ASSOCIATE EDITOR A. Viglione     

An investigation of seismicity for the Central Anatolia region,Turkey

The aim of this study is to investigate the seismicity of Central Anatolia, within the area restricted to coordinates 30–35° longitude and 38–41° latitude, by determining the “a” and “b” parameters in a Gutenberg–Richter magnitude–frequency relationship using data from earthquakes of moment magnitude (Mw)?≥?4.0 that occurred between 1900 and 2010. Based on these parameters and a Poisson model, we aim to predict the probability of other earthquakes of different magnitudes and return periods (recurrence intervals). To achieve this, the study area is divided into six seismogenic zones, using spatial distributions of earthquakes greater than Mw?≥?4.0 with active faults. For each seismogenic zone, the a and b parameters in the Gutenberg–Richter magnitude–frequency relationship were calculated by the least squares method. The probability of occurrence and return periods of various magnitude earthquakes were calculated from these statistics using the Poisson method.