Data-based analysis of bivariate copula tail dependence for drought duration and severity

2012 ◽  
Vol 27 (10) ◽  
pp. 1454-1463 ◽  
Author(s):  
T. Lee ◽  
R. Modarres ◽  
T. B. M. J. Ouarda
Keyword(s):  
Tail Dependence ◽  
Drought Duration ◽  
Drought Duration And Severity ◽  
Bivariate Copula

Modeling drought duration and severity using two-dimensional copula

2021 ◽  
Vol 214 ◽  
pp. 105530
Author(s):  
Muhammad Asif Khan ◽  
Muhammad Faisal ◽  
Muhammad Zaffar Hashmi ◽  
Amna Nazeer ◽  
Zulfiqar Ali ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Drought Duration ◽  
Drought Duration And Severity

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.

Bivariate analysis of drought duration and severity for irrigation planning

2020 ◽  
Vol 229 ◽  
pp. 105926 ◽  
Author(s):  
L. Vergni ◽  
F. Todisco ◽  
B. Di Lena ◽  
F. Mannocchi
Keyword(s):  
Bivariate Analysis ◽  
Irrigation Planning ◽  
Drought Duration ◽  
Drought Duration And Severity

scholarly journals Identification of the Space-Time Variability of Hydrological Drought in the Arid Region of Northwestern China

Water ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 1051 ◽  
Author(s):  
Huaijun Wang ◽  
Zhongsheng Chen ◽  
Yaning Chen ◽  
Yingping Pan ◽  
Ru Feng
Keyword(s):  
Arid Region ◽  
Water Resource Management ◽  
Space Time ◽  
Hydrological Drought ◽  
Northwestern China ◽  
Logistic Distribution ◽  
Time Variability ◽  
Drought Duration ◽  
Monthly Streamflow ◽  
Drought Duration And Severity

Drought monitoring is crucial to water resource management and strategic planning. Thus, the objective of this study is to identify the space-time variability of hydrological drought across the broad arid region of northwestern China. Seven distributions were applied to fitting monthly streamflow records of 16 gauging stations from 10 rivers. Finally, the general logistic distribution was selected as the most appropriate one to compute the Standardized Streamflow Index (SSI). The severity and duration of hydrological droughts were also captured from the SSI series. Moreover, we investigate the relationship between hydrological drought (SSI) and meteorological drought (Standardized Precipitation-Evapotranspiration Index (SPEI)) at different time scales. The results show that drought duration and severity decreased over time in the Aibihu, Irtysh, Kaidu, Aksu, Yarkand, Hoton, Shule, Heihe (upstream), and Shiyang Rivers. However, the Tarim (upstream) and Heihe (middle stream) Rivers showed increasing drought duration and severity and this can be attributed to recent decades human activities. Furthermore, two correlation coefficient patterns between SSI and SPEI were found for the rivers of interest, an “increasing-decreasing” pattern for the Irtysh, Heihe, and Shiyang Rivers, where the precipitation is the main runoff supply, and an “increasing-stable” pattern for Aibihu and the Kaidu, Aksu, Yarkand, Hotan, and Shule Rivers, where glacier melt water provided a relatively high supply of runoff. Our findings are a contribution towards implementing effective water resources evaluation and planning in this arid region.

New approach in bivariate drought duration and severity analysis

2018 ◽  
Vol 559 ◽  
pp. 166-181 ◽  
Author(s):  
Majid Montaseri ◽  
Babak Amirataee ◽  
Hossein Rezaie
Keyword(s):  
Drought Duration ◽  
New Approach ◽  
Drought Duration And Severity

scholarly journals Analysis and Application of Drought Characteristics Based on Theory of Runs and Copulas in Yunnan, Southwest China

2020 ◽  
Vol 17 (13) ◽  
pp. 4654
Author(s):  
Liping Wang ◽  
Xingnan Zhang ◽  
Shufang Wang ◽  
Mohamed Khaled Salahou ◽  
Yuanhao Fang
Keyword(s):  
Short Duration ◽  
Return Period ◽  
Joint Distribution ◽  
Yunnan Province ◽  
Cumulative Probability ◽  
Drought Duration ◽  
Drought Characteristics ◽  
Joint Return ◽  
Drought Duration And Severity ◽  
Drought Characteristic

Drought is a complex natural disaster phenomenon. It is of great significance to analyze the occurrence and development of drought events for drought prevention. In this study, two drought characteristic variables (the drought duration and severity) were extracted by using the Theory of Runs based on four drought indexes (i.e., the percentage of precipitation anomaly, the standardized precipitation index, the standardized precipitation evapotranspiration index and the improved comprehensive meteorological drought index). The joint distribution model of drought characteristic variables was built based on four types of Archimedean copulas. The joint cumulative probability and the joint return period of drought events were analyzed and the relationship between the drought characteristics and the actual crop drought reduction area was also studied. The results showed that: (1) The area of the slight drought and the extreme drought were both the zonal increasing distribution from northeast to southwest in Yunnan Province from 1960 to 2015. The area of the high frequency middle drought was mainly distributed in Huize and Zhanyi in Northeast Yunnan, Kunming in Central Yunnan and some areas of Southwest Yunnan, whereas the severe drought was mainly occurred in Deqin, Gongshan and Zhongdian in Northwest Yunnan; (2) The drought duration and severity were fitted the Weibull and Gamma distribution, respectively and the Frank copula function was the optimal joint distribution function. The Drought events were mostly short duration and high severity, long duration and low severity and short duration and low severity. The joint cumulative probability and joint return period were increased with the increase of drought duration and severity; (3) The error range between the theoretical return period and the actual was 0.1–0.4 a. The year of the agricultural disaster can be accurately reflected by the combined return period in Yunnan Province. The research can provide guidelines for the agricultural management in the drought area.

scholarly journals New families of bivariate copulas via unit weibull distortion

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Fadal A.A. Aldhufairi ◽  
Jungsywan H. Sepanski
Keyword(s):  
Tail Dependence ◽  
Copula Function ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Density Distributions ◽  
New Family ◽  
Upper Tail Dependence ◽  
Bivariate Copula

Abstract This paper introduces a new family of bivariate copulas constructed using a unit Weibull distortion. Existing copulas play the role of the base or initial copulas that are transformed or distorted into a new family of copulas with additional parameters, allowing more flexibility and better fit to data. We present a general form for the new bivariate copula function and its conditional and density distributions. The tail behaviors are investigated and indicate the unit Weibull distortion may result in new copulas with upper tail dependence when the base copula has no upper tail dependence. The concordance ordering and Kendall’s tau are derived for the cases when the base copulas are Archimedean, such as the Clayton and Frank copulas. The Loss-ALEA data are analyzed to evaluate the performance of the proposed new families of copulas.

scholarly journals Trivariate copula to design coastal structures

2020 ◽  
Author(s):  
Olivier Orcel ◽  
Philippe Sergent ◽  
François Ropert
Keyword(s):  
Return Period ◽  
Tail Dependence ◽  
Structure Design ◽  
Likelihood Method ◽  
Dependence Structure ◽  
Practical Case ◽  
Coastal Structures ◽  
Copula Parameter ◽  
Bivariate Copula ◽  
Survival Copula

Abstract. Some coastal structures must be redesigned in the future due to rising sea levels caused by global warming. The design of structures subjected to the actions of waves requires an accurate estimate of the long return period of such parameters as wave height, wave period, storm surge and more specifically their joint exceedance probabilities. The Defra method that is currently used makes it possible to directly connect the joint exceedance probabilities to the product of the univariate probabilities by means of a simple factor. These schematic correlations do not, however, represent all the complexity of the reality and may lead to damaging errors in coastal structure design. The aim of this paper is therefore to remedy the lack of accuracy of these current approaches. To this end, we use copula theory with a copula function that aggregates joint distribution function to its univariate margins. We select a bivariate copula that is adapted to our application by the likelihood method with a copula parameter that is obtained by the error method. In order to integrate extreme events, we also resort to the notion of tail dependence. We can select the copulas with the same tail dependence as data. In the event of an opposite tail dependence structure, we resort to the survival copula. The tail dependence parameter makes it possible to estimate the optimal copula parameter. The most accurate copulas for our practical case with applications in Saint-Malo and Le Havre (France), are the Clayton normal copula and the Gumbel survival copula. The originality of this paper is the creation of a new and accurate trivariate copula. Firstly, we select the fittest bivariate copula with its parameter for the two most correlated univariate margins. Secondly, we build a trivariate function. For this purpose, we aggregate the bivariate function with the remaining univariate margin with its parameter. We show that this trivariate function satisfies the mathematical properties of the copula. We can finally represent joint trivariate exceedance probabilities for a return period of 10, 100 and 1000 years.

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