Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm

Song, Songbai; Singh, Vijay P.

doi:10.1007/s00477-010-0364-5

Cited by 157 publications

(74 citation statements)

References 68 publications

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“…A familiar approach to describing the relationships between drought characteristics is to use the multivariate joint distribution of these characteristics. Most such studies have focused on the relationship between drought duration and severity for meteorological and hydrological droughts separately (Shiau and Shen 2001, Kim et al 2003, Salas et al 2005, Mishra et al 2009, Serinaldi et al 2009, Cancelliere and Salas 2010, Song and Singh 2010a, 2010b. For example, Shiau and Shen (2001) formulated a methodology for frequency and risk analysis of hydrological droughts using streamflow, and obtained a theoretical derivation of the recurrence interval of hydrological droughts above a certain severity.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic analysis of hydrological drought characteristics using meteorological drought

Wong

Lanen

Torfs

2013

Hydrological Sciences Journal

112

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Droughts are an inevitable consequence of climate variability and are pervasive across many regions. Their effects can vary on an extensive scale, depending on the type of drought and people's vulnerability. Crucial characteristics of both hydrological (groundwater, streamflow) and meteorological (precipitation) droughts are related to their durations and severities, and these characteristics are typically correlated. While many studies have addressed the dependencies between these characteristics for either the meteorological or hydrological drought, the cross-dependence between meteorological and hydrological drought characteristics is barely investigated. The development of meteorological drought characteristics to hydrological drought characteristics is often hard to model and their connection is not definitively established. In order to better understand and explain this relationship, this study seeks to apply statistical tools and models. Drought characteristics data from areas in Europe with different climates are analysed. Two approaches of identifying related meteorological and hydrological drought are explored and compared. Classical linear correlation techniques do not provide promising results, indicating that any statistic of a hydrological drought is not a straightforward function of a preceding meteorological drought. Subsequently, the application of the concept of copulas to explore this dependence between meteorological and hydrological drought characteristics is investigated. The more comprehensive approach of copulas shows that the meteorological drought contains probability information of the successive hydrological drought.Key words hydrological drought; meteorological drought; cross-dependence; copula; correlation; bivariate distribution; forecasting Analyse probabiliste des caractéristiques de la sécheresse hydrologique utilisant la sécheresse météorologique Résumé Les sécheresses sont une conséquence inévitable de la variabilité du climat et sont omniprésentes dans de nombreuses régions. Leurs effets peuvent énormément varier, en fonction du type de la sécheresse et de la vulnérabilité des populations. Les caractéristiques essentielles des sécheresses hydrologiques (eaux souterraines, débits) et météorologiques (précipitations) sont liées à leur durée et à leur sévérité, et ces caractéristiques sont généralement corrélées. Alors que de nombreuses études ont porté sur les dépendances entre ces caractéristiques soit pour les sécheresses météorologiques soit pour les sécheresses hydrologiques, la dépendance croisée entre les caractéristiques des sécheresses météorologiques et hydrologiques a à peine été abordée. Le passage des caractéris-tiques des sécheresses météorologiques à celles des sécheresses hydrologiques est souvent difficile à modéliser et leur relation n'est pas définitivement établie. Afin de mieux comprendre et expliquer cette relation, cette étude vise à appliquer des outils statistiques et des modèles. Des données des caractéristiques de sécheresses provenant de régi...

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Section: Introductionmentioning

confidence: 99%

Probabilistic analysis of hydrological drought characteristics using meteorological drought

Wong

Lanen

Torfs

2013

Hydrological Sciences Journal

112

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“…The formulation of this bivariate Copula family is expressed in Equation (17) and its joint density function is shown in Equation (18) and (19).…”

Section: Frank Copulamentioning

confidence: 99%

“…Copula modeling was successfully enforced in other areas, particularly in survival analysis, actuarial science, and finance. In late times, the use of copulas has become popular for multivariate analysis in several fields, viz., in financial studies by ( [9] and [10]), in hydrology by ([11], [12], [13], [14], [15], [16] and [17]) and for drought analysis by ([18] and [19]). …”

Section: Introductionmentioning

confidence: 99%

Bivariate copulas functions for flood frequency analysis

Salleh

Yusof²,

Yusop³

2016

AIP Conference Proceedings

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Abstract.Bivariate flood frequency analysis offers improved understanding of the complex flood process and useful information in preparing flood mitigation measures. However, difficulties arise from limited bivariate distribution functions to jointly model major flood variables that are inter-correlated and each has different univariate marginal distribution. To overcome these difficulties, a Copula based methodology is presented in this study. Copula is functions that link univariate distribution functions to form bivariate distribution functions. Five Copula families namely Clayton, Gumbel, Frank, Gaussian and t Copulas were evaluated for modeling the joint dependence between peak flow-flood duration. The performance of four parameter estimation methods, namely inversion of Kendall's tau, inversion of Spearman's rho, maximum likelihood approach and inference function for margins for chosen copula's families are investigated. The analysis used 35 years hourly discharge data of Johor River from which the annual maximum were derived. Generalized Pareto and Generalized Extreme Value distribution were found to be the best to fit the flood variables based on the Kolmogorov-Smirnov goodness-of-fit test. Clayton Copula was chosen as the best fitted Copula function based on the Akaike Information Criterion goodness-of-fit test. It is found that, different methods of parameter estimation will give the same result on determining the best fit copula family. On performing a simulation based on a Cramer-von Mises as a test statistics to assess the performance of Copula distributions in modeling joint dependence structure of flood variables, it is found that Clayton Copula are well representing the flood variables. Thus, it is concluded that, the Clayton Copula based joint distribution function was found to be effective in preserving the dependency structure of flood variables. Thus, it is concluded that, the Clayton Copula based joint distribution function was found to be effective in preserving the dependency structure of flood variables.

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“…Since the introduction of Copulas in hydrological practice [see e.g., Salvadori et al, 2007, Ganguli and Reddy [2012], and also Mishra and Singh [2011] for a review. With the exception of Song and Singh [2010], these papers investigate the frequency of droughts by referring to meteorological droughts, as identified principally via the Standardized Precipitation Index. Instead, Song and Singh [2010] have addressed hydrological droughts with a trivariate analysis of duration, severity, and interarrival time, as identified by means of a threshold on the flow discharge.…”

Section: Introductionmentioning

confidence: 99%

“…With the exception of Song and Singh [2010], these papers investigate the frequency of droughts by referring to meteorological droughts, as identified principally via the Standardized Precipitation Index. Instead, Song and Singh [2010] have addressed hydrological droughts with a trivariate analysis of duration, severity, and interarrival time, as identified by means of a threshold on the flow discharge. A collection of recent papers dealing with different approaches to droughts can be found in VV.…”

Section: Introductionmentioning

confidence: 99%

Multivariate assessment of droughts: Frequency analysis and dynamic return period

et al. 2013

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[1] Droughts, like floods, are extreme expressions of the river flow dynamics. Here, droughts are intended as episodes during which the streamflow is below a given threshold, and are described as multivariate events characterized by two variables: average intensity and duration. In this work, we introduce the new concept of Dynamic Return Period, formulated using the theory of Copulas, and calculated via a Survival Kendall's approach. We show how it can be used (i) to monitor the temporal evolution of a drought event, and (ii) to perform real time assessment. In addition, a randomization strategy is introduced, in order to get rid of repeated measurements, which may adversely affect the statistical analysis of the available data, as well as the calculation of the return periods of interest: a practical example is shown, involving the fit of the drought duration distribution. The case study of the Po river basin (Northern Italy) is used as an illustration.

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Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm

Cited by 157 publications

References 68 publications

Probabilistic analysis of hydrological drought characteristics using meteorological drought

Probabilistic analysis of hydrological drought characteristics using meteorological drought

Bivariate copulas functions for flood frequency analysis

Multivariate assessment of droughts: Frequency analysis and dynamic return period

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