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 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 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.

scholarly journals Bivariate Hydrologic Risk Assessment of Flood Episodes using the Notation of Failure Probability

2020 ◽  
Vol 6 (10) ◽  
pp. 2002-2023
Author(s):  
Shahid Latif ◽  
Firuza Mustafa
Keyword(s):  
Failure Probability ◽  
Goodness Of Fit ◽  
Peak Flow ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Distribution Analysis ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Flood Peak ◽  
Flood Volume

Floods are becoming the most severe and challenging hydrologic issue at the Kelantan River basin in Malaysia. Flood episodes are usually thoroughly characterized by flood peak discharge flow, volume and duration series. This study incorporated the copula-based methodology in deriving the joint distribution analysis of the annual flood characteristics and the failure probability for assessing the bivariate hydrologic risk. Both the Archimedean and Gaussian copula family were introduced and tested as possible candidate functions. The copula dependence parameters are estimated using the method-of-moment estimation procedure. The Gaussian copula was recognized as the best-fitted distribution for capturing the dependence structure of the flood peak-volume and peak-duration pairs based on goodness-of-fit test statistics and was further employed to derive the joint return periods. The bivariate hydrologic risks of flood peak flow and volume pair, and flood peak flow and duration pair in different return periods (i.e., 5, 10, 20, 50 and 100 years) were estimated and revealed that the risk statistics incrementally increase in the service lifetime and, at the same instant, incrementally decrease in return periods. In addition, we found that ignoring the mutual dependency can underestimate the failure probabilities where the univariate events produced a lower failure probability than the bivariate events. Similarly, the variations in bivariate hydrologic risk with the changes of flood peak in the different synthetic flood volume and duration series (i.e., 5, 10, 20, 50 and 100 years return periods) under different service lifetimes are demonstrated. Investigation revealed that the value of bivariate hydrologic risk statistics incrementally increases over the project lifetime (i.e., 30, 50, and 100 years) service time, and at the same time, it incrementally decreases in the return period of flood volume and duration. Overall, this study could provide a basis for making an appropriate flood defence plan and long-lasting infrastructure designs. Doi: 10.28991/cej-2020-03091599 Full Text: PDF

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 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.

Exploring frequency analysis alternatives on instantaneous peak flow, in the context of flood plain delineation in Southern Québec, Canada.

2021 ◽  
Author(s):  
Simon Ricard ◽  
Alexis Bédard-Therrien ◽  
Annie-Claude ACP Parent ◽  
Brian Morse ◽  
François Anctil
Keyword(s):  
Frequency Analysis ◽  
Peak Flow ◽  
Flood Plain ◽  
Flood Frequency ◽  
Regional Frequency Analysis ◽  
Flood Frequency Analysis ◽  
Flow Data ◽  
Specific Context ◽  
Pros And Cons ◽  
Regional Frequency

A flood frequency analysis is conducted using instantaneous peak flow data over a hydrologic sub-region of southern Québec following three distinct methodological frameworks. First, the analysis is conducted locally using available instantaneous peak flow data. Second, the analysis is conducted locally using daily peak flow data processed in order to consider the peak flow effect. Third, a regional frequency analysis is conducted pooling all available instantaneous peak flow data over the study area. Results reveal a notable diversity in the resulting recurrence peak flow estimates and related uncertainties from one analysis to another. Expert judgement appears essential to arbitrate which alternative should be operated considering a specific context of application for flood plain delineation. Pros and cons for each approach are discussed. We finally encourage the use of a diversity of approaches in order to provide a robust assessment of uncertainty affecting peak flow estimates.

scholarly journals Modeling the spatial dependence of floods using the Fisher copula

2019 ◽  
Vol 23 (1) ◽  
pp. 107-124 ◽  
Author(s):  
Manuela I. Brunner ◽  
Reinhard Furrer ◽  
Anne-Catherine Favre
Keyword(s):  
Frequency Analysis ◽  
Spatial Dependence ◽  
Regional Scale ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Flood Event ◽  
Dependence Structure ◽  
Suitable Model ◽  
Flood Events ◽  
Extreme Flood

Abstract. Floods often affect not only a single location, but also a whole region. Flood frequency analysis should therefore be undertaken at a regional scale which requires the considerations of the dependence of events at different locations. This dependence is often neglected even though its consideration is essential to derive reliable flood estimates. A model used in regional multivariate frequency analysis should ideally consider the dependence of events at multiple sites which might show dependence in the lower and/or upper tail of the distribution. We here seek to propose a simple model that on the one hand considers this dependence with respect to the network structure of the region and on the other hand allows for the simulation of stochastic event sets at both gauged and ungauged locations. The new Fisher copula model is used for representing the spatial dependence of flood events in the nested Thur catchment in Switzerland. Flood event samples generated for the gauged stations using the Fisher copula are compared to samples generated by other dependence models allowing for modeling of multivariate data including elliptical copulas, R-vine copulas, and max-stable models. The comparison of the dependence structures of the generated samples shows that the Fisher copula is a suitable model for capturing the spatial dependence in the data. We therefore use the copula in a way such that it can be used in an interpolation context to simulate event sets comprising gauged and ungauged locations. The spatial event sets generated using the Fisher copula well capture the general dependence structure in the data and the upper tail dependence, which is of particular interest when looking at extreme flood events and when extrapolating to higher return periods. The Fisher copula was for a medium-sized catchment found to be a suitable model for the stochastic simulation of flood event sets at multiple gauged and ungauged locations.

scholarly journals Assessing the Impacts of Univariate and Bivariate Flood Frequency Approaches to Flood Risk Accounting for Reservoir Operation

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 475 ◽  
Author(s):  
Ting Zhou ◽  
Zhiyong Liu ◽  
Juliang Jin ◽  
Hongxiang Hu
Keyword(s):  
Risk Assessment ◽  
Frequency Analysis ◽  
Flood Risk ◽  
Reservoir Operation ◽  
Integrated Approach ◽  
Flood Frequency ◽  
Central China ◽  
Flood Frequency Analysis ◽  
Flood Peak ◽  
Flood Risks

Flood frequency analysis plays a fundamental role in dam planning, reservoir operation, and risk assessment. However, conventional univariate flood frequency analysis carried out by flood peak inflow or volume does not account for the dependence between flood properties. In this paper, we proposed an integrated approach to estimate reservoir risk by combining the copula-based bivariate flood frequency (peak and volume) and reservoir routing. Through investigating the chain reaction of “flood frequency—reservoir operation-flood risk”, this paper demonstrated how to simulate flood hydrographs using different frequency definitions (copula “Or” and “And” scenario), and how these definitions affect flood risks. The approach was applied to the Meishan reservoir in central China. A set of flood hydrographs with 0.01 frequency under copula “Or” and “And” definitions were constructed, respectively. Upstream and downstream flood risks incorporating reservoir operation were calculated for each scenario. Comparisons between flood risks from univariate and bivariate flood frequency analysis showed that bivariate flood frequency analysis produced less diversity in the results, and thus the results are more reliable in risk assessment. More importantly, the peak-volume combinations in a bivariate approach can be adjusted according to certain prediction accuracy, providing a flexible estimation of real-time flood risk under different prediction accuracies and safety requirements.

scholarly journals Probabilistic Flood Hazard Maps from Monte Carlo Derived Peak Flow Values—An Application to Flood Risk Management in Zamora City (Spain)

2021 ◽  
Vol 11 (14) ◽  
pp. 6629
Author(s):  
Julio Garrote ◽  
Evelyng Peña ◽  
Andrés Díez-Herrero
Keyword(s):  
Risk Management ◽  
Monte Carlo ◽  
Frequency Analysis ◽  
Peak Flow ◽  
Flood Hazard ◽  
Flood Risk Management ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Hazard Maps ◽  
Flood Hazard Maps

All flood hazard and risk assessment suffer from a certain degree of uncertainty due to multiple factors, such as flood frequency analysis, hydrodynamic model calibration, or flood damage (magnitude–damage functions) models. The uncertainty linked to the flood frequency analysis is one of the most important factors (previous and present estimation point to 40%). Flood frequency analysis uncertainty has been approached from different points of view, such as the application of complex statistical models, the regionalization processes of peak flows, or the inclusion of non-systematic data. Here, we present an achievable approach to defining the uncertainty linked to flood frequency analysis by using the Monte Carlo method. Using the city of Zamora as the study site, the uncertainty is delimited by confidence intervals of a peak flow quantile of a 500-year return period. Probabilistic maps are derived from hydrodynamic results, and further analysis include flood hazard maps for human loss of stability and vehicle damage. Although the effect of this uncertainty is conditioned by the shape of the terrain, the results obtained may allow managers to achieve more consistent land-use planning. All those Zamora city results point out the probable underestimation of flood hazard (the higher hazard areas increase around 20%) and risk when the uncertainty analysis is not considered, thus limiting the efficiency of flood risk management tasks.

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