Hydrological consistency between the upstream and downstream estimates of Q1000 flood on the upper Rhine River, using historical series in Basel (1808-2017) and Maxau (1815-2018)

2021 ◽  
Author(s):  
Michel Lang ◽  
Benjamin Renard ◽  
Jérôme Le Coz
Keyword(s):  
Return Period ◽  
Shape Parameter ◽  
Extreme Values ◽  
Flood Frequency ◽  
Alternative Methods ◽  
Flood Frequency Analysis ◽  
Rhine River ◽  
Gev Distribution ◽  
Historical Series ◽  
Upper Rhine

<div> <p>Estimation of extreme design floods with a short series of a few decades remains challenging because the statistical extrapolation of observed floods to extreme floods induces great uncertainties. Several alternative methods take advantage of the use of additional information: regional methods (e.g. the index flood method), Monte Carlo rainfall-runoff simulation methods, or specific statistical methods adapted to historical series. Here we present a flood frequency analysis on the upper Rhine River, using long historical series in Basel (1808-2017) and Maxau (1815-2018). We used a Bayesian framework to fit the parameters of the GEV distribution. Each value of the annual maximum discharge has uncertainties, which vary from ± 5-7% for the last decades to ± 22-42% for the oldest period depending on the station. At the local scale, without prior assumption on the three parameters of a GEV distribution, we found that the credibility intervals of the Basel and Maxau flood distributions are consistent. However, beyond a 1000-year return period, flood quantiles are incoherent with Q(Maxau) < Q(Basel) although Maxau (50 000 km<sup>2</sup>) is located downstream of Basel (36 000 km<sup>2</sup>). The floods at Basel are almost Gumbel distributed (shape parameter k = 0.066), whereas the floods at Maxau are Weibull distributed (shape parameter k = 0.219) with an asymptotic maximum value. Assuming that the shape parameter k has a certain regional consistency, we have performed a second iteration, with a prior interval [-0.1; +0.4] on k. The width of this interval corresponds to the union of the posterior distribution of k parameter of each local distribution: [-0.1; +0.2] at Basel and [0.0; +0.4] at Maxau. The second version of each distribution is almost the same up to a return period of 100 years, but there is no more crossing for extreme values. Using the predictive distribution with a regional prior on the shape parameter of the GEV distribution, the result is hydrologically consistent from upstream to downstream.</p> </div>

scholarly journals Hydro-meteorological characteristics and occurrence probability of extreme flood events in Moroccan High Atlas

2020 ◽  
Vol 11 (S1) ◽  
pp. 310-321 ◽  
Author(s):  
Mohamed El Mehdi Saidi ◽  
Tarik Saouabe ◽  
Abdelhafid El Alaoui El Fels ◽  
El Mahdi El Khalki ◽  
Abdessamad Hadri
Keyword(s):  
Return Period ◽  
Peak Flow ◽  
Extreme Event ◽  
Rare Event ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
High Atlas ◽  
Flood Water ◽  
Extreme Flood ◽  
Water Volumes

Abstract Flood frequency analysis could be a tool to help decision-makers to size hydraulic structures. To this end, this article aims to compare two analysis methods to see how rare an extreme hydrometeorological event is, and what could be its return period. This event caused many deadly floods in southwestern Morocco. It was the result of unusual atmospheric conditions, characterized by a very low atmospheric pressure off the Moroccan coast and the passage of the jet stream further south. Assessment of frequency and return period of this extreme event is performed in a High Atlas watershed (the Ghdat Wadi) using historical floods. We took into account, on the one hand, flood peak flows and, on the other hand, flood water volumes. Statistically, both parameters are better adjusted respectively to Gamma and Log Normal distributions. However, the peak flow approach underestimates the return period of long-duration hydrographs that do not have a high peak flow, like the 2014 event. The latter is indeed better evaluated, as a rare event, by taking into account the flood water volumes. Therefore, this parameter should not be omitted in the calculation of flood probabilities for watershed management and the sizing of flood protection infrastructure.

scholarly journals Flood frequency analysis for annual maximum streamflow using a non-stationary GEV model

2019 ◽  
Vol 79 ◽  
pp. 03022
Author(s):  
Shangwen Jiang ◽  
Ling Kang
Keyword(s):  
Frequency Analysis ◽  
Return Period ◽  
Yangtze River ◽  
Flood Frequency ◽  
Additive Models ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
The Yangtze River ◽  
Stationary Model ◽  
Risk Of Failure

Under changing environment, the streamflow series in the Yangtze River have undergone great changes and it has raised widespread concerns. In this study, the annual maximum flow (AMF) series at the Yichang station were used for flood frequency analysis, in which a time varying model was constructed to account for non-stationarity. The generalized extreme value (GEV) distribution was adopted to fit the AMF series, and the Generalized Additive Models for Location, Scale and Shape (GAMLSS) framework was applied for parameter estimation. The non-stationary return period and risk of failure were calculated and compared for flood risk assessment between stationary and non-stationary models. The results demonstrated that the flow regime at the Yichang station has changed over time and a decreasing trend was detected in the AMF series. The design flood peak given a return period decreased in the non-stationary model, and the risk of failure is also smaller given a design life, which indicated a safer flood condition in the future compared with the stationary model. The conclusions in this study may contribute to long-term decision making in the Yangtze River basin under non-stationary conditions.

scholarly journals A Bayesian Hierarchical Model for the Spatial Analysis of Carbon Monoxide Pollution Extremes in Mexico City

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
José del Carmen Jiménez-Hernández ◽  
Marisol López-Cerino ◽  
Alejandro Ivan Aguirre-Salado
Keyword(s):  
Air Pollution ◽  
Carbon Monoxide ◽  
Mexico City ◽  
Metropolitan Area ◽  
Return Period ◽  
Extreme Values ◽  
Spatial Behavior ◽  
Gev Distribution ◽  
Bayesian Hierarchical ◽  
One Year

Air pollution by carbon monoxide is a serious problem that affects many cities around the world, and the theory of extreme values has played a crucial role in the study of this issue. In this paper, we proposed a Bayesian hierarchical spatial model of extreme values to evaluate the risk of extreme events of air pollution due to carbon monoxide in the metropolitan area of Mexico City. Spatial trends are modeled through of a Gaussian process for the generalized extreme value (GEV) distribution parameters, and prediction maps are produced for each of these. The results show a marginal spatial behavior for the location, scale, and shape parameters of GEV distribution, which indicate the existence of local variations that would not be possible to model using only stationary models. A return map of the maximum concentrations with a return period of one year is obtained. We found that the return levels for a one-year return period of CO concentration above 8 ppm in the Metropolitan Area of the Valley of Mexico are concentrated in the central part of this region, and the areas with the lowest estimates are distributed in the periphery. In addition, a quantile-quantile (QQ) plot between the theoretical and empirical quantiles was provided, which showed a very good fit of data to the proposed model.

scholarly journals Flood Frequency Analysis at the Downstream of Sg. Perak River Basin using Annual Maximum Flow Discharge Data

2018 ◽  
Vol 7 (4.35) ◽  
pp. 709 ◽  
Author(s):  
Munir Snu ◽  
Sidek L.M ◽  
Haron Sh ◽  
Noh Ns.M ◽  
Basri H ◽  
...  
Keyword(s):  
Probability Distribution ◽  
River Basin ◽  
Frequency Analysis ◽  
Return Period ◽  
Maximum Flow ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Discharge Data ◽  
Flow Discharge

The recent flood event occurred in 2014 had caused disaster in Perak and Sungai Perak is the main river of Perak which is a major natural drainage system within the state. The aim of this paper is to determine the expected discharge to return period downstream for Sg. Perak River Basin in Perak by using annual maximum flow data. Flood frequency analysis is a technique to assume the flow values corresponding to specific return periods or probabilities along the river at a different site. The method involves the observed annual maximum flow discharge data to calculate statistical information such as standard deviations, mean, sum, skewness and recurrence intervals. The flood frequency analysis for Sg. Perak River Basin was used Log Pearson Type-III probability distribution method. The annual maximum peak flow series data varying over period 1961 to 2016. The probability distribution function was applied to return periods (T) where T values are 2years, 5years, 10years, 25years, 50years, and 100years generally used in flood forecasting. Flood frequency curves are plotted after the choosing the best fits probability distribution for annual peak maximum data. The results for flood frequency analysis shows that Sg. Perak at Jambatan Iskandar much higher inflow discharge  which is 3714.45m3/s at the 100years return period compare to Sg. Plus at Kg Lintang and Sg. Kinta at Weir G. With this, the 100years peak flow at Sg Perak river mouth is estimated to be in the range of 4,000 m3/s. Overall, the analysis relates the expected flow discharge to return period for all tributaries of Sg. Perak River Basin.

Assessment of overtopping reliability and benefits of a flood detention dam

2008 ◽  
Vol 35 (10) ◽  
pp. 1177-1182 ◽  
Author(s):  
A. Melih Yanmaz ◽  
M. Engin Gunindi
Keyword(s):  
Return Period ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Site Specific ◽  
Joint Return ◽  
Dam Site ◽  
Bivariate Gamma Distribution ◽  
Project Characteristics ◽  
Joint Return Period

There is a growing tendency to assess safety levels of existing dams and to design new dams using probabilistic approaches according to project characteristics and site-specific conditions. This study is a probabilistic assessment of the overtopping reliability of a dam, which will be designed for flood detention purpose, and will compute the benefits that can be gained as a result of the implementation of this dam. In a case study, a bivariate flood frequency analysis was carried out using a five-parameter bivariate gamma distribution. A family of joint return period curves relating the runoff peak discharges to the runoff volumes at the dam site was derived. A number of hydrographs were also obtained under a joint return period of 100 years to observe the variation of overtopping tendency. The maximum reservoir elevation and overtopping reliability were determined by performing a probabilistic reservoir routing based on Monte Carlo simulations.

scholarly journals Comparison Between Bivariate and Trivariate Flood Frequency Analysis Using the Archimedean Copula Functions, A Case Study of the Karun River in Iran

2021 ◽  
Author(s):  
Mohamad Haytham Klaho ◽  
Hamid R. Safavi ◽  
Mohamad H. Golmohammadi ◽  
Maamoun Alkntar
Keyword(s):  
Frequency Analysis ◽  
Return Period ◽  
Goodness Of Fit ◽  
Flood Frequency ◽  
Archimedean Copula ◽  
Flood Frequency Analysis ◽  
Cumulative Probability ◽  
Copula Functions ◽  
Flood Peak ◽  
Multiple Variables

Abstract Historically, severe floods have caused great human and financial losses. Therefore, the flood frequency analysis based on the flood multiple variables including flood peak, volume and duration poses more motivation for hydrologists to study. In this paper, the bivariate and trivariate flood frequency analysis and modeling using Archimedean copula functions is focused. For this purpose, the annual flood data over a 55-year historical period recorded at the Dez Dam hydrometric station were used. The results showed that based on goodness of fit criteria, the Frank function built upon the couple of the flood peak-volume and the couple of the flood peak-duration as well as the Clayton function built upon the flood volume-duration were identified to be the best copula families to be adopted. The trivariate analysis was conducted and the Clayton family was chosen as the best copula function. Thereafter, the common and conditional cumulative probability distribution functions were built and analyzed to determine the periodic "and", "or" and "conditional" bivariate and trivariate flood return periods. The results suggest that the bivariate conditional return period obtained for short-term periods is more reliable than the trivariate conditional return period. Additionally, the trivariate conditional return period calculated for long-term periods is more reliable than the bivariate conditional return period.

scholarly journals Flood frequency analysis supported by the largest historical flood

2014 ◽  
Vol 14 (6) ◽  
pp. 1543-1551 ◽  
Author(s):  
W. G. Strupczewski ◽  
K. Kochanek ◽  
E. Bogdanowicz
Keyword(s):  
Return Period ◽  
Historical Record ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Historical Period ◽  
Time Period ◽  
Extreme Flood ◽  
Discrete Uniform Distribution ◽  
L Value ◽  
Discrete Uniform

Abstract. The use of non-systematic flood data for statistical purposes depends on the reliability of the assessment of both flood magnitudes and their return period. The earliest known extreme flood year is usually the beginning of the historical record. Even if one properly assesses the magnitudes of historic floods, the problem of their return periods remains unsolved. The matter at hand is that only the largest flood (XM) is known during whole historical period and its occurrence marks the beginning of the historical period and defines its length (L). It is common practice to use the earliest known flood year as the beginning of the record. It means that the L value selected is an empirical estimate of the lower bound on the effective historical length M. The estimation of the return period of XM based on its occurrence (L), i.e. ^M = L, gives a severe upward bias. The problem arises that to estimate the time period (M) representative of the largest observed flood XM. From the discrete uniform distribution with support 1, 2, ... , M of the probability of the L position of XM, one gets ^L = M/2. Therefore ^M = 2L has been taken as the return period of XM and as the effective historical record length as well this time. As in the systematic period (N) all its elements are smaller than XM, one can get ^M = 2t( L+N). The efficiency of using the largest historical flood (XM) for large quantile estimation (i.e. one with return period T = 100 years) has been assessed using the maximum likelihood (ML) method with various length of systematic record (N) and various estimates of the historical period length ^M comparing accuracy with the case when systematic records alone (N) are used only. The simulation procedure used for the purpose incorporates N systematic record and the largest historic flood (XMi) in the period M, which appeared in the Li year of the historical period. The simulation results for selected two-parameter distributions, values of their parameters, different N and M values are presented in terms of bias and root mean square error RMSEs of the quantile of interest are more widely discussed.

Flood Frequency Analysis of the Mahi Basin by Using Log Pearson Type III Probability Distribution

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Uttam Pawar ◽  
Pramodkumar Hire
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Return Period ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Series Data ◽  
Period Range ◽  
Type Iii ◽  
Pearson Type ◽  
Data Points

Flood frequency analysis is one of the techniques of examination of peak stream flow frequency and magnitude in the field of flood hydrology, flood geomorphology and hydraulic engineering. In the present study, Log Pearson Type III (LP-III) probability distribution has applied for flood series data of four sites on the Mahi River namely Mataji, Paderdi Badi, Wanakbori and Khanpur and of three sites on its tributaries such as Anas at Chakaliya, Som at Rangeli and Jakham at Dhariawad. The annual maximum series data for the record length of 26-51 years have been used for the present study. The time series plots of the data indicate that two largest ever recorded floods were observed in the year 1973 and 2006 on the Mahi River. The estimated discharges of 100 year return period range between 3676 m3/s and 47632 m3/s. The return period of the largest ever recorded flood on the Mahi River at Wankbori (40663 m3/s) is 127-yr. The recurrence interval of mean annual discharges (Qm) is between 2.73-yr and 3.95-yr, whereas, the return period of large floods (Qlf) range from 6.24-yr to 9.33-yr. The magnitude-frequency analysis curves represent the reliable estimates of the high floods. The fitted lines are fairly close to the most of the data points. Therefore, it can be reliably and conveniently used to read the recurrence intervals for a given magnitude and vice versa.

Application of Gumbel’s Distribution Method for Flood Frequency Analysis of Lower Ganga Basin (Farakka Barrage Station), West Bengal, India

2021 ◽  
pp. 51-58
Author(s):  
Kajal Kumar Mandal ◽  
K. Dharanirajan ◽  
Sabyasachi Sarkar
Keyword(s):  
Frequency Analysis ◽  
Return Period ◽  
Flood Hazard ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Ganga Basin ◽  
Distribution Method ◽  
Discharge Data ◽  
Gumbel’S Distribution ◽  
Farakka Barrage

The analysis of flood frequency will depend on the historical peak discharge data for at least 10 years. This study has taken into account peak annual maximum discharge data for 72 years (1949 to 2020). The discharge data was collected from the Farakka Barrage Gauging station (24°48'15.10" N and 87°55'52.70" E) situated in the upper part of lower Ganga basin. The flood frequency analysis of the lower Ganga basin’s upper portions has been carried out using Gumbel’s frequency distribution method. Gumbel’s method (XT) is a prediction analysing statistical approach. The discharge data was tabulated in descending order and rank has been assigned based on the discharge volume. The return period was calculated based on Weibull’s formula (P) for this analysis. The flood frequency data was plotted on a graph where X-axis shows the return period and the Yaxis is the discharge value. The R2 value of this graph is 0.9998 which describe Gumbel’s distribution method is best for the flood frequency analysis. The flood frequency analysis is an essential step to assess the flood hazard.

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