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This study analyzed extreme precipitation events, using daily rainfall data for 1966–2015. A Mann–Kendall trend test was used to evaluate trends in extreme precipitation, copula functions were applied to compute the joint return periods of extreme events, and univariate and bivariate distributions were used to determine risk. The results showed that the decrease in consecutive wet days (CWD) was significant in the west and the northwest of Iran, while the consecutive dry days (CDD) index was increasing therein. The precipitation on more than the 90th percentile (P90) very wet days and annual number of days with precipitation less than the 90th percentile threshold (D90) indices followed similar patterns, with no significant trend in most parts of Iran, but at several stations in the north, west, and northwest, their decline was extreme. Furthermore, the increase of D10 (annual number of days with precipitation less than the 90th percentile threshold) and P10 (total precipitation of D10 of a year) was extreme in the wet regions of Iran, including the north, west, and northwest areas, and also part of the center. More than 50 percent of Iran experienced a low risk level, with a return period of extreme events (CWD, CDD) of more than 27.5 years, and the joint return periods of (D10, D90), (P10, P90), and (D10, P10) pairs were less than 100 years in most regions of Iran. Due to the increasing number of dry days in the north, west, and northwest of Iran, the drought risk increased. Based on the changes in extreme precipitation indices in recent years, the findings of this study will be useful for copula-based frequency analysis under a changing environment at regional and global scales. [ABSTRACT FROM AUTHOR]

Drought severity, duration and magnitude are important for evaluating the drought condition. This study developed multivariate (Joint Deficit Index) JDI and then used bivariate and trivariate copulas to assess hydrological drought risk in the Karkheh River basin in the west of Iran, since there exists a significant dependency between severity (S), duration (D), and magnitude (M). The JDI was constructed by implementing Kendall's empirical copula on (SRImod1,..., SRImod12) at 18 stations in the river basin. The generalized gamma (severity), the Pareto (duration), and the log-normal (magnitude) were identified as the best marginal distributions for drought characteristics. The Gaussian, Student's t, Joe and Clayton were found to be the best bivariate copulas for S and D, S and M, and D and M, respectively. The trivariate Clayton copula was the best copula function of the (S–D–M) variable. Results of fitting were analyzed based on several statistical diagnostic tests and graphs. Further analysis was implemented based on multivariate and conditional return periods. The multivariate return periods of "AND" and "OR" cases were obtained and the spatial graphs of drought risks were constructed. Results showed that the return periods of the "AND" cases were greater than the return periods of the "OR" cases. In the other words, the whole of the sub-basin is in the high risk situation (R > 0.9) when R (OR) S–D, S–M, D–M, S–D–M, in the low risk situation (R = 0.38) when R (AND) S–D, S–M, D–M and in the moderate risk situation (0.48 < R < 0.68) when (OR) S–D–M. This study revealed that separate evaluation of return periods in "OR" and "AND" cases may result in under-dimension or over-dimension. Hence, the return periods of "AND" and "OR" cases should be considered simultaneously. Further investigation showed that multivariate return periods were important in the management of drought condition and decisions. [ABSTRACT FROM AUTHOR]

This study investigated droughts in arid and semi-arid regions in Iran using long historical data from 25 stations. These stations were clustered into three homogeneous regions using a fuzzy clustering method. The severity and duration were extracted using the Standardized Precipitation Index-12, and the dependence structure between drought severity and duration was evaluated using Pearson's, Spearman's ranked, and Kendal's tau correlation coefficients. The best marginal distributions of severity and duration were selected using graphical and theoretical goodness-of-fit criteria. Results showed that the generalized logistic (GLO) model satisfactorily fitted drought duration in regions I and III, while the Wakeby distribution fitted better in region II. For drought severity, the best fitted model was the GLO model in region I, the generalized extreme value (GEV) model in region III, and the Wakeby model in region II. Furthermore, the Gumbel copula in region I and the Gaussian copulas in regions II and III were able to model the dependence between drought variables well. Also, stochastic simulation of bivariate drought using selected copulas showed that the behavior of bivariate drought changed when the degree of correlation between variables was considered. The copula method was used to obtain bivariate and conditional return periods. The bivariate analysis of drought risk indicated that coastal and internal regions of Iran were more risky than semi-arid and arid regions. The results of this study would be useful for water resource management and risk analysis at the regional scale. [ABSTRACT FROM AUTHOR]

Copula functions are widely used to derive multivariate probability distributions in hydrometeorology. One of the key steps in the copula method is the derivation of marginal distributions of individual variables which can be accomplished using the principle of maximum entropy where the distribution parameters are estimated from the specified constraints. This study, investigated two drought variables (severity and duration) by coupling the principle of maximum entropy with parametric and empirical copulas. So, homogeneous climatic zones were first identified by applying the fuzzy clustering method to data from 39 synoptic stations in Iran and then drought severity and duration were determined with the standardized precipitation index. These two variables were scaled and their marginal probability distribution functions were derived using the principle of maximum entropy as well as empirically. Then, the joint probability distribution of drought severity and duration was determined using maximum entropy-copula, and parametric and empirical copulas. Thereafter, bivariate conditional return periods were determined for each homogeneous region. Results showed that 1) univariate and bivariate distributions can be obtained by maximizing entropy; 2) the dependence structure via Spearman's rho, which directly affects the Lagrange parameters of entropy copula, was a controlling factor to optimize the objective function; 3) for a given set of constraints, the maximum entropy copula is independent of the types of marginals; 4)The entropy-entropy copula (with entropy marginals) is considered a better method than alternatives, because it has a similar result to the parametric methods while it only needs to fit a single model. • A Maximum entropy copula method is developed for bivariate drought analysis at homogenous regions of Iran. • The integration of maximum entropy and copula provides a useful method for modeling the dependence structure. • Conditional return period graphs are generated for four homogenous regions using severity and duration drought. • Conditional return period in region I, are significantly greater than other regions. [ABSTRACT FROM AUTHOR]

The copula functions are frequently used by researchers for modeling dependence structure among the correlated attributes in many areas. The copulas are widely used for the analysis of drought frequency, drought characteristics, drought coincidence risk, uncertainty, and drought forecasting. In this research, we have compared two indices of drought assessment, including SPI‐12 and copula‐based joint deficit index (JDI). In this regard, the drought characteristics, including the severity, duration, and drought frequency have been studied in 25 synoptic stations of Iran during the 1968–2014. The results showed that, unlike JDI, the SPI‐12 is not able to estimate the drought peak during the critical and extreme condition. Although JDI has identified a severe and extreme drought during the pervasive drought, the SPI‐12 estimated a normal condition. The results show that JDI accurately estimates the drought frequency, but the SPI‐12 provided an unexpected estimation is some stations. In addition, the MannKendal trend test for drought characteristics represents that JDI accurately estimates the expected trend (an increasing trend) whereas the SPI‐12 exhibits no significant trend in most stations. Finally, JDI provides a comprehensive assessment of drought for decision‐makers and natural managers. Recommendations for Resource Managers: Through this research, two well‐known indices in drought analysis, including copula‐based joint deficit drought index (JDI) and the SPI‐12 were applied and compared for drought assessment in the arid and semi‐arid regions of Iran. Also, the spatial distributions of drought characteristics (severity, duration, and frequency) have been assessed using the Mann–Kendal approach. This conclusion has four implications for resource managers: ●A joint deficit index (JDI) is defined based on copula functions. This approach provides a probability‐based description of the overall drought status.●The JDI is not only able to reflect the beginning and ending times of drought, but also provides the possibility of monthly drought assessment.●Multivariate analysis of drought characteristics (severity, duration, and frequency) provides an accurate understanding of drought status in arid and semi‐arid regions in Iran.●The results of the meteorological drought analysis using JDI show that this method is a useful tool for managers and decision‐makers to assess the drought conditions in arid and semi‐arid regions. [ABSTRACT FROM AUTHOR]

Drought is multivariate, yet several univariate and bivariate indices have been proposed for the evaluation of drought characteristics. However, limited attention has been paid to the mechanisms and performance of these drought indices. This study considered canonical correlation analysis (CCA), principal component analysis (PCA), and copula-based method to construct three composite hydro-meteorological indices, namely, JDHMI-CCA, JDHMI-PCA, and JDHMI-Copula. The main elements of these indices are rainfall and runoff for which historical data for the period of 1986–2016 at a 12-month time scale were collected for Kol-Mehran and Bandar-Sedij basins, Iran. Results demonstrated that the pattern of composite indices reflected the comprehensive moisture status well and was not affected by a single element. Analysis indicated that although the composite, univariate, and multivariate indices followed similar patterns in various parts but the behavior of runoff was the main source of inconsistency in the study region. While PCA and CCA ignored or assigned smaller weights to runoff, the copula method used the information of runoff in constructing the copula-based index. This study investigated the mechanisms of linear and non-linear methods in assessing the drought condition. The methods had a significant effect on the construction of composite indices which can provide useful information for drought monitoring. • Three composite drought indices were constructed based on linear and non-linear methods. • Performances of JDHMI-Copula, JDHMI-PCA and JDHMI-CCA for multivariate drought characterization were assessed. • The linear and non-linear methods had performed differently in estimating the drought situation. • Runoff was the main factor for inconsistency between composite drought indices. [ABSTRACT FROM AUTHOR]