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

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 Joint Modeling of Precipitation and Temperature Using Copula Theory for Current and Future Prediction under Climate Change Scenarios in Arid Lands (Case Study, Kerman Province, Iran)

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
T. Mesbahzadeh ◽  
M. M. Miglietta ◽  
M. Mirakbari ◽  
F. Soleimani Sardoo ◽  
M. Abdolhoseini
Keyword(s):  
Climate Change ◽  
Goodness Of Fit ◽  
Joint Modeling ◽  
Copula Function ◽  
Gaussian Copula ◽  
Climate Change Scenarios ◽  
Climatic Parameters ◽  
Goodness Of Fit Test ◽  
Copula Theory ◽  
Precipitation And Temperature

Precipitation and temperature are very important climatic parameters as their changes may affect life conditions. Therefore, predicting temporal trends of precipitation and temperature is very useful for societal and urban planning. In this research, in order to study the future trends in precipitation and temperature, we have applied scenarios of the fifth assessment report of IPCC. The results suggest that both parameters will be increasing in the studied area (Iran) in future. Since there is interdependence between these two climatic parameters, the independent analysis of the two fields will generate errors in the interpretation of model simulations. Therefore, in this study, copula theory was used for joint modeling of precipitation and temperature under climate change scenarios. By the joint distribution, we can find the structure of interdependence of precipitation and temperature in current and future under climate change conditions, which can assist in the risk assessment of extreme hydrological and meteorological events. Based on the results of goodness of fit test, the Frank copula function was selected for modeling of recorded and constructed data under RCP2.6 scenario and the Gaussian copula function was used for joint modeling of the constructed data under the RCP4.5 and RCP8.5 scenarios.

scholarly journals Drought Risk Analysis in the Eastern Cape Province of South Africa: The Copula Lens

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1938 ◽  
Author(s):  
Christina M. Botai ◽  
Joel O. Botai ◽  
Abiodun M. Adeola ◽  
Jaco P. de Wit ◽  
Katlego P. Ncongwane ◽  
...  
Keyword(s):  
South Africa ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Drought Risk ◽  
Eastern Cape Province ◽  
Return Periods ◽  
Eastern Cape ◽  
Copula Functions ◽  
Drought Duration ◽  
Drought Duration And Severity

This research study was carried out to investigate the characteristics of drought based on the joint distribution of two dependent variables, the duration and severity, in the Eastern Cape Province, South Africa. The drought variables were computed from the Standardized Precipitation Index for 6- and 12-month accumulation period (hereafter SPI-6 and SPI-12) time series calculated from the monthly rainfall data spanning the last five decades. In this context, the characteristics of climatological drought duration and severity were based on multivariate copula analysis. Five copula functions (from the Archimedean and Elliptical families) were selected and fitted to the drought duration and severity series in order to assess the dependency measure of the two variables. In addition, Joe and Gaussian copula functions were considered and fitted to the drought duration and severity to assess the joint return periods for the dual and cooperative cases. The results indicate that the dependency measure of drought duration and severity are best described by Tawn copula families. The dependence structure results suggest that the study area exhibited low probability of drought duration and high probability of drought severity. Furthermore, the multivariate return period for the dual case is found to be always longer across all the selected univariate return periods. Based on multivariate analysis, the study area (particularly Buffalo City, OR Tambo and Alfred Zoo regions) is determined to have higher/lower risks in terms of the conjunctive/cooperative multivariate drought risk (copula) probability index. The results of the present study could contribute towards policy and decision making through e.g., formulation of the forward-looking contingent plans for sustainable management of water resources and the consequent applications in the preparedness for and adaptation to the drought risks in the water-linked sectors of the economy.

scholarly journals The Effect of Sample Size on Bivariate Rainfall Frequency Analysis of Extreme Precipitation

Proceedings ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 19 ◽  
Author(s):  
Nikoletta Stamatatou ◽  
Lampros Vasiliades ◽  
Athanasios Loukas
Keyword(s):  
Sample Size ◽  
Frequency Analysis ◽  
Extreme Precipitation ◽  
Goodness Of Fit ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Rainfall Frequency ◽  
Rainfall Frequency Analysis ◽  
Pseudo Likelihood Estimation

The objective of this study is to compare univariate and joint bivariate return periods of extreme precipitation that all rely on different probability concepts in selected meteorological stations in Cyprus. Pairs of maximum rainfall depths with corresponding durations are estimated and compared using annual maximum series (AMS) for the complete period of the analysis and 30-year subsets for selected data periods. Marginal distributions of extreme precipitation are examined and used for the estimation of typical design periods. The dependence between extreme rainfall and duration is then assessed by an exploratory data analysis using K-plots and Chi-plots and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical, and Extreme Value families are fitted using a pseudo-likelihood estimation method, evaluated according to the corrected Akaike Information Criterion and verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic. The selected copula functions and the corresponding conditional and joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results highlight the effect of sample size on univariate and bivariate rainfall frequency analysis for hydraulic engineering design practices.

scholarly journals Run Theory and Copula-Based Drought Risk Analysis for Songnen Grassland in Northeastern China

2019 ◽  
Vol 11 (21) ◽  
pp. 6032 ◽  
Author(s):  
Wu ◽  
Zhang ◽  
Bao ◽  
Guo
Keyword(s):  
Risk Analysis ◽  
Goodness Of Fit ◽  
Distribution Functions ◽  
Drought Severity ◽  
Dependence Structure ◽  
Drought Risk ◽  
Drought Event ◽  
Return Periods ◽  
Copula Functions ◽  
Run Theory

Droughts are among the more costly natural hazards, and drought risk analysis has become urgent for the proper planning and management of water resources in grassland ecosystems. We chose Songnen grassland as a case study, used a standardized precipitation evapotranspiration index (SPEI) to model drought characteristics, employed run theory to define the drought event, and chose copula functions to construct the joint distribution for drought variables. We applied two kinds of return periods to conduct a drought risk assessment. After evaluating and comparing several distribution functions, drought severity (DS) was best described by the generalized extreme value (GEV) distribution, whereas drought duration (DD) was best fitted by gamma distribution. The root mean square error (RMSE) and Akaike Information Criterion (AIC) goodness-of-fit measures to evaluate their performance, the best-performing copula is Frank copula to model the joint dependence structure for each drought variables. The results of the secondary return periods indicate that a higher risk of droughts occurs in Keshan county, Longjiang county, Qiqiha’er city, Taonan city, and Baicheng city. Furthermore, a relatively lower risk of drought was found in Bei’an city, Mingquan county, Qinggang county, and qian’an county, and also in the Changling county and Shuangliao city. According to the calculation of the secondary return periods, which considered all possible scenarios in our study, we found that the secondary return period may be the best indicator for evaluating grassland ecosystem drought risk management.

scholarly journals Bivariate Flood Frequency Analysis Using Copulas

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 635 ◽  
Author(s):  
Nikoletta Stamatatou ◽  
Lampros Vasiliades ◽  
Athanasios Loukas
Keyword(s):  
Return Period ◽  
Goodness Of Fit ◽  
Univariate Analysis ◽  
Flood Frequency ◽  
Peak Discharge ◽  
Flood Frequency Analysis ◽  
Hydraulic Structures ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Pseudo Likelihood Estimation

Flood frequency estimation for the design of hydraulic structures is usually performed as a univariate analysis of flood event magnitudes. However, recent studies show that for accurate return period estimation of the flood events, the dependence and the correlation pattern among flood attribute characteristics, such as peak discharge, volume and duration should be taken into account in a multivariate framework. The primary goal of this study is to compare univariate and joint bivariate return periods of floods that all rely on different probability concepts in Yermasoyia watershed, Cyprus. Pairs of peak discharge with corresponding flood volumes are estimated and compared using annual maximum series (AMS) and peaks over threshold (POT) approaches. The Lyne-Hollick recursive digital filter is applied to separate baseflow from quick flow and to subsequently estimate flood volumes from the quick flow timeseries. Marginal distributions of flood peaks and volumes are examined and used for the estimation of typical design periods. The dependence between peak discharges and volumes is then assessed by an exploratory data analysis using K-plots and Chi-plots, and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical and Extreme Value families are fitted using a pseudo-likelihood estimation method, verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic and evaluated according to the corrected Akaike Information Criterion. The selected copula functions and the corresponding joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results indicate the importance of the bivariate analysis in the estimation of design return period of the hydraulic structures.

scholarly journals The nexus between black and digital gold: evidence from US markets

2021 ◽  
Author(s):  
Toan Luu Duc Huynh ◽  
Rizwan Ahmed ◽  
Muhammad Ali Nasir ◽  
Muhammad Shahbaz ◽  
Ngoc Quang Anh Huynh
Keyword(s):  
Goodness Of Fit ◽  
Tail Dependence ◽  
Oil Prices ◽  
Likelihood Estimation ◽  
Dependence Structure ◽  
Goodness Of Fit Test ◽  
Left Tail ◽  
Stationary Bootstrap ◽  
The Us ◽  
Pseudo Likelihood Estimation

AbstractIn the context of the debate on cryptocurrencies as the ‘digital gold’, this study explores the nexus between the Bitcoin and US oil returns by employing a rich set of parametric and non-parametric approaches. We examine the dependence structure of the US oil market and Bitcoin through Clayton copulas, normal copulas, and Gumbel copulas. Copulas help us to test the volatility of these dependence structures through left-tailed, right-tailed or normal distributions. We collected daily data from 5 February 2014 to 24 January 2019 on Bitcoin prices and oil prices. The data on bitcoin prices were extracted from coinmarketcap.com. The US oil prices were collected from the Federal Reserve Economic Data source. Maximum pseudo-likelihood estimation was applied to the dataset and showed that the US oil returns and Bitcoin are highly vulnerable to tail risks. The multiplier bootstrap-based goodness-of-fit test as well as Kendal plots also suggest left-tail dependence, and this adds to the robustness of the results. The stationary bootstrap test for the partial cross-quantilogram indicates which quantile in the left tail has a statistically significant relationship between Bitcoin and US oil returns. The study has crucial implications in terms of portfolio diversification using cryptocurrencies and oil-based hedging instruments.

scholarly journals Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

2016 ◽  
Vol 2 (12) ◽  
pp. 646-655 ◽  
Author(s):  
O.A Agbede ◽  
Oluwatobi Aiyelokun
Keyword(s):  
Probability Distribution ◽  
Stochastic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Flood Management ◽  
Return Periods ◽  
Probability Models ◽  
Goodness Of Fit Test ◽  
Southwest Nigeria ◽  
Anderson Darling

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model  generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

scholarly journals Modeling of short duration extreme rainfall events over Lower Yamuna Catchment

MAUSAM ◽  
2022 ◽  
Vol 63 (3) ◽  
pp. 391-400
Author(s):  
MEHFOOZ ALI ◽  
SURINDER KAUR ◽  
S.B. TYAGI ◽  
U.P. SINGH
Keyword(s):  
Short Duration ◽  
Goodness Of Fit ◽  
Extreme Rainfall ◽  
Return Periods ◽  
Goodness Of Fit Test ◽  
Extreme Rainfall Events ◽  
Rainfall Events ◽  
Kolmogorov Smirnov ◽  
Level Of Significance ◽  
Made In

Short duration rainfall estimates and their intensities for different return periods are required for many purposes such as for designing flood for hydraulic structures, urban flooding etc. An attempt has been made in this paper to Model extreme rainfall events of Short Duration over Lower Yamuna Catchment. Annual extreme rainfall series and their intensities were analysed using EVI distribution for rainstorms of short duration of 5, 10, 15, 30, 45 & 60 minutes and various return periods have been computed. The Self recording rainguage (SRRGs) data for the period 1988-2009 over the Lower Yamuna Catchment (LYC) have been used in this study. It has been found that EVI distribution fits well, tested by Kolmogorov-Smirnov goodness of fit test at 5 % level of significance for each of the station.

scholarly journals Determination of the flood volume by the aspects of peak flow and flood hydrograph at the level of the city of Biskra, Wadi Biskra watershed, Algeria.

2021 ◽  
Author(s):  
amel Boumessenegh ◽  
hadda dridi
Keyword(s):  
Peak Flow ◽  
Daily Rainfall ◽  
Maximum Flow ◽  
Return Periods ◽  
Empirical Methods ◽  
Flood Volume ◽  
Flood Hydrograph ◽  
Intensity Duration Frequency ◽  
The City

Abstract The peak flow of a flood can be determined by several empirical methods. Among these methods, the Gradex method is used in this work to estimate the project flood and the volumes corresponding to the flows. This approach has made it possible to recognize the flow of different frequencies by aspects of the peak flow and the flood hydrograph. The study was based on the maximum annual daily rainfall for a long series of observations (47 years), and on the intensity-duration-frequency (IDF) curves of the four rainfall stations Biskra, T'kout, Djemoura, and El kantara; located in the watershed of Oued Biskra. The application of the Gradex method has allowed to approach the maximum flow of floods at the level of the outlet which is located at the entrance of the city of Biskra; for the rare frequency of occurrence (return periods ranging from 10 to 1000 years).

Sign in / Sign up

Export Citation Format

Share Document