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.

Identification of suitable copulas for bivariate frequency analysis of flood peak and flood volume data

2011 ◽  
Vol 42 (2-3) ◽  
pp. 193-216 ◽  
Author(s):  
Hemant Chowdhary ◽  
Luis A. Escobar ◽  
Vijay P. Singh
Keyword(s):  
Frequency Analysis ◽  
Goodness Of Fit ◽  
Peak Flow ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Dependence Structure ◽  
Volume Data ◽  
Data Set ◽  
Flood Peak ◽  
Goodness Of Fit Tests

Multivariate flood frequency analysis, involving flood peak flow, volume and duration, has been traditionally accomplished by employing available functional bivariate and multivariate frequency distributions that have a restriction on the marginals to be from the same family of distributions. The copula concept overcomes this restriction by allowing a combination of arbitrarily chosen marginal types. It also provides a wider choice of admissible dependence structure as compared to the conventional approach. The availability of a vast variety of copula types makes the selection of an appropriate copula family for different hydrological applications a non-trivial task. Graphical and analytic goodness-of-fit tests for testing the suitability of copulas are beginning to evolve and are being developed; there is limited experience of their usage at present, especially in the hydrological field. This paper provides a step-wise procedure for copula selection and illustrates its application to bivariate flood frequency analysis, involving flood peak flow and volume data. Several graphical procedures, tail dependence characteristics, and formal goodness-of-fit tests involving a parametric bootstrap-based technique are considered while investigating the relative applicability of six copula families. The Clayton copula has been identified as a valid model for the particular flood peak flow and volume data set considered in the study.

scholarly journals At Site Flood Frequency Analysis of Baitarani River at Champua Watershed, Odisha

2019 ◽  
pp. 54-64
Author(s):  
Rebati Sinam
Keyword(s):  
Frequency Analysis ◽  
Return Period ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Gumbel Distribution ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Floodplain Management ◽  
Chi Squared ◽  
Anderson Darling

For any development of hydraulic structures and dam modelling, flood frequency analysis is an effective tool to determine the appropriate measures and strategy. Flood frequency analysis has been conventionally used in hydraulic engineering and floodplain management. The present study is an attempt to estimate the expected flood using two probability distributions: Gumbel distribution and Log Pearson III distribution at Champua watershed, Upper Baitarani River Basin, Odisha. The analysis is based on annual maximum flood time series from 1991 to 2018 (28 years) obtained from Water Resources Information System at the Champua gauging station. Three Goodness of fit methods namely Kolmogorov Smirnov, Anderson Darling and Chi Squared tests are used to choose the better model. From the analysis, expected flood for return period 2, 10, 25, 50, 100 and 1000 years are calculated. Gumbel give an expected flood 521.72 cumecs while Log Pearson III give an expected flood of 493.17 cumecs for 2 years return period. It is observed that Gumbel estimated a higher values for all the said return period except for 1000 years where Log Pearson III predicted a much higher values. Goodness of test show inconsistent results. While Chi-squared test indicate Gumbel Method as the better model, the other two tests show that Log Pearson III is the better fitting model for the given dataset. Therefore, Log Pearson III is chosen as the best model. However, the results from both the distributions can be referred for storm management.

Nonstationary Flood Frequency Analysis for Annual Flood Peak and Volume Series in Both Univariate and Bivariate Domain

2018 ◽  
Vol 32 (13) ◽  
pp. 4239-4252 ◽  
Author(s):  
Jianzhu Li ◽  
Yuming Lei ◽  
Senming Tan ◽  
Colin D. Bell ◽  
Bernard A. Engel ◽  
...  
Keyword(s):  
Frequency Analysis ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Flood Peak

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 Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Changjiang Xu ◽  
Jiabo Yin ◽  
Shenglian Guo ◽  
Zhangjun Liu ◽  
Xingjun Hong
Keyword(s):  
Joint Probability ◽  
Flood Frequency ◽  
Peak Discharge ◽  
Flood Frequency Analysis ◽  
Design Flood ◽  
Copula Functions ◽  
Danjiangkou Reservoir ◽  
Flood Peak ◽  
Flood Hydrograph

Design flood hydrograph (DFH) for a dam is the flood of suitable probability and magnitude adopted to ensure safety of the dam in accordance with appropriate design standards. Estimated quantiles of peak discharge and flood volumes are necessary for deriving the DFH, which are mutually correlated and need to be described by multivariate analysis methods. The joint probability distributions of peak discharge and flood volumes were established using copula functions. Then the general formulae of conditional most likely composition (CMLC) and conditional expectation composition (CEC) methods that consider the inherent relationship between flood peak and volumes were derived for estimating DFH. The Danjiangkou reservoir in Hanjiang basin was selected as a case study. The design values of flood volumes and 90% confidence intervals with different peak discharges were estimated by the proposed methods. The performance of CMLC and CEC methods was also compared with conventional flood frequency analysis, and the results show that CMLC method performs best for both bivariate and trivariate distributions which has the smallest relative error and root mean square error. The proposed CMLC method has strong statistical basis with unique design flood composition scheme and provides an alternative way for deriving DFH.

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.

scholarly journals Flood frequency analysis using mean daily flows vs. instantaneous peak flows

2021 ◽  
Author(s):  
Anne Bartens ◽  
Uwe Haberlandt
Keyword(s):  
Frequency Analysis ◽  
Linear Models ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Estimation Methods ◽  
Entire Study ◽  
Flood Peak ◽  
Flood Dynamics ◽  
Event Based ◽  
Available Information

Abstract. In many cases flood frequency analysis needs to be carried out on mean daily flow (MDF) series without any available information on the instantaneous peak flow (IPF). We analyze the error of using MDFs instead of IPFs for flood quantile estimation on a German dataset and assess spatial patterns and factors that influence the deviation of MDF floods from their IPF counterparts. The main dependence could be found for catchment area but also gauge elevation appeared to have some influence. Based on the findings we propose simple linear models to correct both MDF flood peaks of individual flood events and overall MDF flood statistics. Key predictor in the models is the event-based ratio of flood peak and flood volume obtained directly from the daily flow records. This correction approach requires a minimum of data input, is easily applied, valid for the entire study area and successfully estimates IPF peaks and flood statistics. The models perform particularly well in smaller catchments, where other IPF estimation methods fall short. Still, the limit of the approach is reached for catchment sizes below 100 km2, where the hydrograph information from the daily series is no longer capable of approximating instantaneous flood dynamics.

scholarly journals Selecting the best probability distribution for at-site flood frequency analysis; a study of Torne River

2019 ◽  
Vol 1 (12) ◽  
Author(s):  
Mahmood Ul Hassan ◽  
Omar Hayat ◽  
Zahra Noreen
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Goodness Of Fit ◽  
Direct Method ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Goodness Of Fit Tests ◽  
Pearson Type

AbstractAt-site flood frequency analysis is a direct method of estimation of flood frequency at a particular site. The appropriate selection of probability distribution and a parameter estimation method are important for at-site flood frequency analysis. Generalized extreme value, three-parameter log-normal, generalized logistic, Pearson type-III and Gumbel distributions have been considered to describe the annual maximum steam flow at five gauging sites of Torne River in Sweden. To estimate the parameters of distributions, maximum likelihood estimation and L-moments methods are used. The performance of these distributions is assessed based on goodness-of-fit tests and accuracy measures. At most sites, the best-fitted distributions are with LM estimation method. Finally, the most suitable distribution at each site is used to predict the maximum flood magnitude for different return periods.

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