Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey

Tosunoğlu, Fatih; Can, İbrahim

doi:10.1007/s11069-016-2253-9

Cited by 77 publications

(31 citation statements)

References 61 publications

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“…Ganguli and Reddy [25] used a bivariate copula to assess the drought risk in Gujarat, India, adopting a normal kernel, quadratic kernel, gamma, lognormal, exponential, Gumbel and Weibull distributions to fit the drought duration and severity; these indicated that the exponential and normal kernel distributions respectively produced the best fit for drought duration and severity. Similar analyses can be found in [19] and [23]. Hence, a large amount of contrast analysis must be conducted to select an optimal distribution and, in some cases, two or more distributions fit the data well.…”

Section: Introductionmentioning

confidence: 72%

“…Since most studies in the literature have shown [18,19,22,23] that the Archimedean copulas are the most widely used for drought analysis, they were also used in this study to build a correspondence between the drought variables. Due to the limited number of samples, however, Equation (18) was used only to select the optimal copula function; it was not used to calculate the empirical interval probability and return period.…”

Section: Drought Characteristic and Distribution Testmentioning

confidence: 99%

“…Then, from the copula function, the correspondence between drought duration and severity is obtained and the joint probability and return time is calculated. As shown in the literature [17][18][19][20][21][22][23][24][25], conventional probability analysis focuses on joint cumulative probability and conditional probability. The interval probability was the main focus of the present study, since it provides a better understanding of drought details and is also suitable for comparing conventional and entropy methods.…”

Section: Interval Probabilitymentioning

confidence: 99%

“…The detailed theoretical background and descriptions for the use of copulas can be acquired from the books of Joe [15] and Nelsen [16]. Some recent works include, for example, Shiau [17] who constructed a joint drought duration and severity distribution using bivariate copulas in southern Taiwan; Zhang [18] employed a copula function to analyze drought risk, indicating a high risk in central and north-western Yunnan Province; and Tosunoglu and Can [19] used a two-dimensional copula function to analyze meteorological droughts in Turkey. Similar analyses can be found in [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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An Entropy-Based Investigation into Bivariate Drought Analysis in China

Zuo

Hou

Jia

2017

Water

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Abstract:Because of the high correlation between random variables of drought duration and severity, their joint distribution is difficult to obtain by traditional mathematical methods. However, the copula method has proved to be a useful tool for analyzing the frequency of drought duration and severity. Most studies have used different marginal distribution functions to fit the drought duration and severity distributions. This requires a great deal of contrast analysis, and sometimes two or more distributions fit the data well. Based on entropy theory, however, a unified probability distribution function is derived which reduces complex contrast analysis and improves the filtering distribution function. Based on monthly precipitation data at 162 stations in China for 1961-2015, the monthly standardized precipitation index was calculated and used to extract drought duration and severity. Then the entropy distribution was used to fit the distributions of drought duration and severity, and to establish the correspondence between them. The probabilities of the interval and return periods were then determined using the copula method. An analysis of the discrepancy between the conventional and entropy-based methods indicated that the entropy distribution showed a better fit than conventional methods for drought duration distribution, although no obvious difference was found in drought severity distribution. The entropy-based results were more consistent with the empirical data, whereas conventional methods showed apparent deviation in some drought types. Hence, the entropy-based method is proposed as an alternative method of deriving the marginal distributions of drought duration and severity, and for analyzing the interval probability and return period in China.

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Section: Introductionmentioning

confidence: 72%

Section: Drought Characteristic and Distribution Testmentioning

confidence: 99%

Section: Interval Probabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Entropy-Based Investigation into Bivariate Drought Analysis in China

Zuo

Hou

Jia

2017

Water

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“…Wu, Qing, Lu, et al () used copulas to simulate the joint distribution between drought duration and drought deficit and investigated the changes in hydrological drought frequency over the Xijiang River Basin in South China. Tosunoglu and Can () constructed the joint probability distributions of drought duration and severity series of Turkey using copulas.…”

Section: Introductionmentioning

confidence: 99%

Modelling bivariate extreme precipitation distribution for data‐scarce regions using Gumbel–Hougaard copula with maximum entropy estimation

Qian

Wang

Dang

et al. 2017

Hydrological Processes

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A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. This paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel-Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved to be generally reliable and robust by many simulations under three different situations. The Gumbel-Hougaard copula with MEE can also be applied to the bivariate frequency analysis of other extreme events in data-scarce regions.

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Joint probability risk modelling of storm surge and cyclone wind along the coast of Bay of Bengal using a statistical copula

Bushra

Trepanier

Rohli

2019

Intl Journal of Climatology

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High winds and storm surges associated with torrential rain from tropical cyclones (TCs) cause massive destruction to property and cost the lives of many people. The coastline of the Bay of Bengal (BoB) ranks as one of the most susceptible to storm surges in the world due to low-lying elevation and a high frequency of TC occurrence. This study uses data from 1885 to 2011 and a bivariate statistical copula to describe the relationship and dependency between empirical TC storm surge and reported wind speed before landfall at the BoB. Among the copulas and their families, an Archimedean, Gumbel copula with margins defined by the empirical distributions is specified as the most appropriate choice for the BoB. The model provides return periods for pairs of TC storm surge and 12-hr pre-landfall wind along the BoB coastline. On the shortest timescale, the BoB can expect a TC with 12-hr pre-landfall winds of at least 24 m/s and surge heights of at least 4.0 m, on average, once every 3.9 years. On the other hand, the long-term, worst case scenario suggests the BoB can expect 12-hr pre-landfall winds of 62 m/s and surge heights of at least 8.0 m, on average, once every 311.8 years. Using a copula to model the combined frequency of cyclone wind speeds along with storm surges along the BoB coastline increases the understanding of the dangerous TC characteristics in this region, which can reduce fatalities and monetary losses.

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Application of copulas for regional bivariate frequency analysis of meteorological droughts in Turkey

Cited by 77 publications

References 61 publications

An Entropy-Based Investigation into Bivariate Drought Analysis in China

An Entropy-Based Investigation into Bivariate Drought Analysis in China

Modelling bivariate extreme precipitation distribution for data‐scarce regions using Gumbel–Hougaard copula with maximum entropy estimation

Joint probability risk modelling of storm surge and cyclone wind along the coast of Bay of Bengal using a statistical copula

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