Analyzing the duration frequency and severity of drought using copula function in the Yazd city

Duration and severity are the two main variables used in drought analysis. The copula functions are appropriate for multivariate drought analysis, as it lacks the limitations of the classical multivariate distribution function. This study investigated the bivariate frequency analysis of drought duration and severity of Yazd city in Iran synoptic station during 1953–2013. To this end, first, the drought duration and severity variables were derived from the 6-month Standardized Precipitation Index. Then, considering the distribution functions, the gamma distribution function was selected for analyzing the severity and the exponential distribution function was selected for analyzing the duration and then the Clayton copula function was selected out of the three copula functions as the most appropriate one. After conducting bivariate frequency analysis, the joint seasonal and conjunctive return period and conditional return period curves were plotted. The current study well signified that multivariate analyses could present better interpretations of the reality; for example, as it was identified in conditional return period curves of the drought, for every constant duration, the amount of the return period changed as the severity changed. On the contrary, in analyzing the univariate of duration, no effects of severity were observed.

Fuzzy-probabilistic modeling the flood characteristics using bivariate frequency analysis and α-cut decomposition

Water allocation in agricultural lands, optimal design of hydraulic structures and climatic phenomena are the events in water management science that face hydrological uncertainties. The purpose of this study is to estimate the characteristics of surface runoff based on probabilistic and fuzzy analysis. Separation and generation of basic hydrological information, probabilistic modeling, fuzzy analysis, and optimization to achieve the solution were the main steps of the decision-making problem. Long-term hydrological data of the study area were collected, analyzed and used as a basis for the simulation model. In this study, a copula-based stochastic method was developed to deal with uncertainties related to rainfall and runoff characteristics as well as to address the nonlinear dependence between multiple random variables. The relationship between rainfall variables and flood characteristics was formulated through fuzzy set theory. The feasible domain of the fuzzy problem was searched using the non-dominated sorting genetic algorithm to find the optimal extreme points. The obtained solutions were used as a fuzzy response to calculate the flood of the Baghmalek plain in Khuzestan province in southwestern Iran. The results showed that the maximum model error occurred in predicting rainfall depth and flood volume, and the maximum rainfall rate and runoff flow could be calculated more accurately. Moreover, the developed fuzzy-probabilistic model was able to predict more than 90% of flood events within the defined fuzzy range.

Hydrological drought risk recurrence under climate change in the karst area of Northwestern Algeria

This study aims to estimate hydrological drought risk using probabilistic analysis of bivariate drought characteristics to assess both past and future drought severity and duration in three basins located in the widest karst massif of northern Algeria. The procedures entail: (1) identification of extent of meteorological drought that could trigger corresponding hydrological drought through their characteristics; (2) assessment of future risk of extreme drought according to two emission scenarios of the representative concentration pathway (RCP 4.5 and 8.5); and (3) estimation of drought return periods using bivariate frequency analysis and investigation of their future change rates under climate change. Hydrological droughts were computed by using the bias-corrected future climate projections from nine global climate models downscaled using the Rossby Centre Regional Climate model (RCA4), and GR2M hydrological model. The analysis revealed a connection between meteorological and hydrological drought occurrences and the response time depended on the memory effect of the considered basin. We also found strong consensus between past drought event return periods, determined by bivariate frequency analysis, and those determined by climate models under RCP8.5 scenario. Finally, in regards to drought return periods (10, 50 and 100 years), the risk of extreme drought recurrence in the future has been projected to be larger than the reference period.

Hydrologic Risk Assessment of Future Extreme Drought in South Korea Using Bivariate Frequency Analysis

Recently, climate change has increased the frequency of extreme weather events. In South Korea, extreme droughts are frequent and cause serious damage. To identify the risk of extreme drought, we need to calculate the hydrologic risk using probabilistic analysis methods. In particular, future hydrologic risk of extreme drought should be compared to that of the control period. Therefore, this study quantitatively assessed the future hydrologic risk of extreme drought in South Korea according to climate change scenarios based on the representative concentration pathway (RCP) 8.5. A threshold level method was applied to observation-based rainfall data and climate change scenario-based future rainfall data to identify drought events and extract drought characteristics. A bivariate frequency analysis was then performed to estimate the return period considering both duration and severity. The estimated return periods were used to calculate and compare hydrologic risks between the control period and the future. Results indicate that the average duration of drought events for the future was similar with that for the control period, however, the average severity increased in most future scenarios. In addition, there was decreased risk of maximum drought events in the Yeongsan River basin in the future, while there was increased risk in the Nakdong River basin. The median of risk of extreme drought in the future was calculated to be larger than that of the maximum drought in the control period.

Vulnerability Assessment of Dam Water Supply Capacity Based on Bivariate Frequency Analysis Using Copula

The vulnerability of the water supply capacity of a dam is defined as the expected deficit volume from a typical water deficit event. In this study, a water deficit event was assumed to be a rectangle composed of the deficit duration and deficit intensity whose occurrence probability was then estimated by the bivariate frequency analysis based on the copula method. This approach is different from the conventional one based on the assumption of the same occurrence probability for all events. This proposed method was applied to the Namgang dam in Korea as an example and the resulting estimate of the vulnerability was compared with the conventional method. First, the ‘OR’ concept was found to be better than the ‘AND’ concept in the calculation of the occurrence probability. Additionally, based on the consideration of multicollinearity, it could be concluded that the occurrence probability should be estimated by considering the water deficit intensity and duration. For the Namgang dam, the vulnerability was determined to be 9.11 × 106 m3, which is about 3% of the total storage capacity. This estimated vulnerability is also about 70% of the amount estimated by applying the conventional method with the same occurrence probability for all water deficit events.