Regional bivariate modeling of droughts using L-comoments and copulas

Abdi, Amin; Hassanzadeh, Yousef; Talatahari, Siamak; Ahmad, Fadzil; Mirabbasi, Rasoul

doi:10.1007/s00477-016-1222-x

Cited by 31 publications

(12 citation statements)

References 59 publications

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“…In this study, SPEI at the 6-month timescale, denoted by SPEI-6 is estimated for each station and seven regions. SPEI-6 is most useful for describing the shallow soil moisture available to crops (Reddy and Singh, 2014;Abdi et al 2016).…”

Section: Drought Indices and Drought Identificationmentioning

confidence: 99%

“…The Kolmogorov-Smirnov (KS) and Anderson-darling (AD) tests are employed as a goodness-of-fit test, and the principle that the threshold value should be as small as possible to preserve the largest sample is employed (Shiau and Modarres, 2009;Song and Singh, 2010;Abdi et al 2016). The fitted distributions of Di are compared against the empirical nonexceedance probabilities estimated utilizing Gringorten's plotting position function as follows (Gringorten, 1963;Cunnane, 1978;Song and Singh, 2010):…”

Section: Marginal Distribution Of Drought Variablementioning

confidence: 99%

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Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions

Ayantobo

Song

2018

Water Resour Manage

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In drought frequency analysis, as the number of drought variables increases, the joint behavior between these variables needs to be studied. Therefore, this study aims to develop a flexible four-variate joint distribution function of the regional stochastic nature of drought. Using run theory, drought duration, severity, peak, and inter-arrival time were abstracted from the Standardized Precipitation Evapotranspiration Index (SPEI) aggregated at six months, observed in mainland China between 1961 and 2013. As these drought variables showed significant dependence properties and followed different marginal distributions, we employed and compared six four-variate symmetric and asymmetric Archimedean copulas (i.e., Frank, Clayton, Gumbel-Hougaard). The best-fitting model for each region was carefully selected using RMSE, AIC, and BIAS goodness-of-fit tests. Results revealed that the empirical and theoretical probabilities of the symmetric Clayton in regions NE (Northeast), CS (Central and Southern China), EMC (Entire China), and symmetric Frank in regions NC (North China), SC (South China), IM (Inner Mongolia), NW (Northwest), TP (Tibet Plateau) agreed well. Symmetric Frank copula was considered the best-fit for station-based drought analysis in EMC. Based on these copulas, the drought probabilities and return periods for the occurrence of drought events over the next 5, 10, 20, 50, and 100 years in each region were hereby comprehensively explained, and the results shown here could be helpful in the appraisal of the adequacies of water supply systems under drought conditions in all regions. This study showed that a four-variate copula approach is a vital tool for probabilistic interpretation of hydrological and meteorological data in the different climatic region of mainland China.

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Section: Drought Indices and Drought Identificationmentioning

confidence: 99%

Section: Marginal Distribution Of Drought Variablementioning

confidence: 99%

Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions

Ayantobo

Song

2018

Water Resour Manage

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“…To this end, the following evaluation indices are employed:

Efficiency coefficient : E C = 1 - \frac{\sum_{i = 1}^{N} {(y_{i} - {\hat{y}}_{i})}^{2}}{\sum_{i = 1}^{N} {(y_{i} - \overset{true¯}{y})}^{2}}

Relative root - mean - square error : R R M S E = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(\frac{y_{i} - {\hat{y}}_{i}}{y_{i}})}^{2}}

Relative bias : R B I A S = \frac{1}{N} \sum_{i = 1}^{N} true(\frac{y_{i} - {\overset{y}{true}}_{i}}{y_{i}} true)

where

y_{i}

denotes the local estimated quantile at the site i and

{\overset{y}{true}}_{i}

is the regional estimated one. N is the total number of sites [ Hassanzadeh et al ., ; Abdi et al ., ].…”

Section: Applications and Numerical Implementationsmentioning

confidence: 99%

Fully nonlinear statistical and machine‐learning approaches for hydrological frequency estimation at ungauged sites

Ouali

Chebana

Ouarda³

2017

J Adv Model Earth Syst

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The high complexity of hydrological systems has long been recognized. Despite the increasing number of statistical techniques that aim to estimate hydrological quantiles at ungauged sites, few approaches were designed to account for the possible nonlinear connections between hydrological variables and catchments characteristics. Recently, a number of nonlinear machine‐learning tools have received attention in regional frequency analysis (RFA) applications especially for estimation purposes. In this paper, the aim is to study nonlinearity‐related aspects in the RFA of hydrological variables using statistical and machine‐learning approaches. To this end, a variety of combinations of linear and nonlinear approaches are considered in the main RFA steps (delineation and estimation). Artificial neural networks (ANNs) and generalized additive models (GAMs) are combined to a nonlinear ANN‐based canonical correlation analysis (NLCCA) procedure to ensure an appropriate nonlinear modeling of the complex processes involved. A comparison is carried out between classical linear combinations (CCAs combined with linear regression (LR) model), semilinear combinations (e.g., NLCCA with LR) and fully nonlinear combinations (e.g., NLCCA with GAM). The considered models are applied to three different data sets located in North America. Results indicate that fully nonlinear models (in both RFA steps) are the most appropriate since they provide best performances and a more realistic description of the physical processes involved, even though they are relatively more complex than linear ones. On the other hand, semilinear models which consider nonlinearity either in the delineation or estimation steps showed little improvement over linear models. The linear approaches provided the lowest performances.

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“…Generally, RFA involves two main steps: (1) the formation and identification of homogeneous regions and (2) the estimation of extreme events. Attention has been given to index‐flood based multivariate RFA recently mainly in the work of Chebana and Ouarda (, 2009), Chebana et al (), Ben Aissia et al (), Abdi et al (), Requena et al () and Masselot et al (). The index‐flood based regional approach assumes that the region is homogeneous, which means that all sites within a region have identical frequency distributions apart from a site‐specific scale factor.…”

Section: Introductionmentioning

confidence: 99%

“…Generally, RFA involves two main steps: (1) the formation and identification of homogeneous regions and (2) the estimation of extreme events. Attention has been given to index-flood based multivariate RFA recently mainly in the work of Ouarda (2007, 2009), ), Ben Aissia et al (2015, Abdi et al (2016), Requena et al (2016) and Masselot * Correspondence: T. Šimková, Studentská 14022, Liberec 1, 46117, Czech Republic. E-mail: tereza.simkova@tul.cz et al (2016).…”

Section: Introductionmentioning

confidence: 99%

L‐moment homogeneity test in trivariate regional frequency analysis of extreme precipitation events

Šimková

2017

Meteorological Applications

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Identification of homogeneous regions is a key task in regional frequency analysis to obtain accurate estimates of a given event. Homogeneity testing based on multivariate L-moments has recently been proposed and all studies dealing with application of the methodology using real-world data still focus on the bivariate case. The practical aspects of the trivariate homogeneity tests for maximum annual 1, 3 and 7 day precipitation totals measured at stations in the Czech Republic are investigated. A trivariate model of the precipitation amounts for simulating synthetic homogeneous regions in parametric testing was determined by goodness-of-fit tests based on the Cramér-von Mises and Vuong statistics and Akaike and Bayesian information criteria while considering selected trivariate exchangeable Archimedean, fully nested Archimedean and mixed C-vine copulas in the copula model test space. Each of the regions into which the area of the Czech Republic is divided meets the homogeneity condition when using both the parametric and non-parametric L-moment homogeneity tests and considering three mixed C-vine copula models given by the bivariate Gumbel copula for two unconditional pair-copulas and normal, Frank or Plackett copula families for the conditional pair-copula for simulating synthetic homogeneous regions.

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Regional bivariate modeling of droughts using L-comoments and copulas

Cited by 31 publications

References 59 publications

Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions

Multivariate Drought Frequency Analysis using Four-Variate Symmetric and Asymmetric Archimedean Copula Functions

Fully nonlinear statistical and machine‐learning approaches for hydrological frequency estimation at ungauged sites

L‐moment homogeneity test in trivariate regional frequency analysis of extreme precipitation events

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