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.

Copula-Based Drought Monitoring and Assessment According to Zonal and Meridional Temperature Gradients

Drought is one of the most severe natural disasters. However, many of its characteristic variables have complex nonlinear relationships. Therefore, it is difficult to construct effective drought assessment models. In this study, we analyzed regional drought characteristics in China to identify their relationship with changes in meridional and zonal temperature gradients. Drought duration and severity were extracted according to standardized precipitation evapotranspiration index (SPEI) drought grades. Trends in drought duration and severity were detected by the Mann-Kendall test for the period of 1979–2019; they showed that both parameters had been steadily increasing during that time. Nevertheless, the increasing trend in drought severity was particularly significant for northwest and southwest China. A composite analysis confirmed the relationships between drought characteristics and temperature gradients. The northwest areas were relatively less affected by temperature gradients, as they are landlocked, remote from the ocean, and only slightly influenced by the land–ocean thermal contrast (LOC) and the meridional temperature gradient (MTG). The impacts of LOC and MTG on drought duration and severity were positive in the southwest region of China but negative in the northeast. As there was a strong correlation between drought duration and severity, we constructed a 2D copula function model of these parameters. The Gaussian, HuslerReiss, and Frank copula functions were the most appropriate distributions for the northeast, northwest, and southwest regions, respectively. As drought processes are highly complex, the present study explored the internal connections between drought duration and severity and their responses to meteorological conditions. In this manner, an accurate method of predicting future drought events was developed.

The Spatial-Temporal Variation Characteristics of Natural Vegetation Drought in the Yangtze River Source Region, China

In the context of climate change, ecosystem in Yangtze River Source Region (YRSR) is under threat from severe droughts. This study introduced a new natural vegetation drought index, standardized supply-demand water index (SSDI), and identified natural vegetation drought events and parameters (e.g., duration, severity, peak, and coverage area) based on run theory. Then the drought-prone regions were investigated via 2-dimensional joint copula. The results indicate that (1) compared with traditional meteorological drought index, the SSDI is reliable and can reflect the comprehensive characteristics of the ecological drought information more easily and effectively; (2) the YRSR had witnessed the most severe drought episodes in the periods of late-1970s, mid-1980s, and mid-1990s, but the SSDI showed a wetting trend since the mid-2000s. Additionally, droughts in the Southern YRSR were relatively more severe with longer drought duration; (3) in most areas of Togton River Basin and Dam River Basin, the severe ecological drought events occurred more frequently; (4) drought duration and severity in the YRSR were more susceptible to temperature when the temperature rise was above 1.0 °C. The average drought duration and severity increased by 20.7% and 32.6% with a temperature rise of 1 °C. Investigating and evaluating drought characteristics, causes, and drought index effectiveness provide essential information for balanced water resource allocation, utilization, and drought prevention. Understanding these spatial-temporal characteristics of drought and return period was useful for drought risk assessment and sustainable development of water resources.

Drought Risk Analysis in the Eastern Cape Province of South Africa: The Copula Lens

This research study was carried out to investigate the characteristics of drought based on the joint distribution of two dependent variables, the duration and severity, in the Eastern Cape Province, South Africa. The drought variables were computed from the Standardized Precipitation Index for 6- and 12-month accumulation period (hereafter SPI-6 and SPI-12) time series calculated from the monthly rainfall data spanning the last five decades. In this context, the characteristics of climatological drought duration and severity were based on multivariate copula analysis. Five copula functions (from the Archimedean and Elliptical families) were selected and fitted to the drought duration and severity series in order to assess the dependency measure of the two variables. In addition, Joe and Gaussian copula functions were considered and fitted to the drought duration and severity to assess the joint return periods for the dual and cooperative cases. The results indicate that the dependency measure of drought duration and severity are best described by Tawn copula families. The dependence structure results suggest that the study area exhibited low probability of drought duration and high probability of drought severity. Furthermore, the multivariate return period for the dual case is found to be always longer across all the selected univariate return periods. Based on multivariate analysis, the study area (particularly Buffalo City, OR Tambo and Alfred Zoo regions) is determined to have higher/lower risks in terms of the conjunctive/cooperative multivariate drought risk (copula) probability index. The results of the present study could contribute towards policy and decision making through e.g., formulation of the forward-looking contingent plans for sustainable management of water resources and the consequent applications in the preparedness for and adaptation to the drought risks in the water-linked sectors of the economy.

Analysis and Application of Drought Characteristics Based on Theory of Runs and Copulas in Yunnan, Southwest China

Drought is a complex natural disaster phenomenon. It is of great significance to analyze the occurrence and development of drought events for drought prevention. In this study, two drought characteristic variables (the drought duration and severity) were extracted by using the Theory of Runs based on four drought indexes (i.e., the percentage of precipitation anomaly, the standardized precipitation index, the standardized precipitation evapotranspiration index and the improved comprehensive meteorological drought index). The joint distribution model of drought characteristic variables was built based on four types of Archimedean copulas. The joint cumulative probability and the joint return period of drought events were analyzed and the relationship between the drought characteristics and the actual crop drought reduction area was also studied. The results showed that: (1) The area of the slight drought and the extreme drought were both the zonal increasing distribution from northeast to southwest in Yunnan Province from 1960 to 2015. The area of the high frequency middle drought was mainly distributed in Huize and Zhanyi in Northeast Yunnan, Kunming in Central Yunnan and some areas of Southwest Yunnan, whereas the severe drought was mainly occurred in Deqin, Gongshan and Zhongdian in Northwest Yunnan; (2) The drought duration and severity were fitted the Weibull and Gamma distribution, respectively and the Frank copula function was the optimal joint distribution function. The Drought events were mostly short duration and high severity, long duration and low severity and short duration and low severity. The joint cumulative probability and joint return period were increased with the increase of drought duration and severity; (3) The error range between the theoretical return period and the actual was 0.1–0.4 a. The year of the agricultural disaster can be accurately reflected by the combined return period in Yunnan Province. The research can provide guidelines for the agricultural management in the drought area.

Copula-Based Multivariate Frequency Analysis of the 2012–2018 Drought in Northeast Brazil

The 2012–2018 drought was such an extreme event in the drought-prone area of Northeast Brazil that it triggered a discussion about proactive drought management. This paper aims at understanding the causes and consequences of this event and analyzes its frequency. A consecutive sequence of sea surface temperature anomalies in the Pacific and Atlantic Oceans, at both the decadal and interannual scales, led to this severe and persistent drought. Drought duration and severity were analyzed using run theory at the hydrographic region scale as decision-makers understand impact analysis better at this scale. Copula functions were used to properly model drought joint characteristics as they presented different marginal distributions and an asymmetric behavior. The 2012–2018 drought in Ceará State had the highest mean bivariate return period ever recorded, estimated at 240 years. Considering drought duration and severity simultaneously at the level of the hydrographic regions improves risk assessment. This result advances our understanding of exceptional events. In this sense, the present work proposes the use of this analysis as a tool for proactive drought planning.

Identification of the Space-Time Variability of Hydrological Drought in the Arid Region of Northwestern China

Drought monitoring is crucial to water resource management and strategic planning. Thus, the objective of this study is to identify the space-time variability of hydrological drought across the broad arid region of northwestern China. Seven distributions were applied to fitting monthly streamflow records of 16 gauging stations from 10 rivers. Finally, the general logistic distribution was selected as the most appropriate one to compute the Standardized Streamflow Index (SSI). The severity and duration of hydrological droughts were also captured from the SSI series. Moreover, we investigate the relationship between hydrological drought (SSI) and meteorological drought (Standardized Precipitation-Evapotranspiration Index (SPEI)) at different time scales. The results show that drought duration and severity decreased over time in the Aibihu, Irtysh, Kaidu, Aksu, Yarkand, Hoton, Shule, Heihe (upstream), and Shiyang Rivers. However, the Tarim (upstream) and Heihe (middle stream) Rivers showed increasing drought duration and severity and this can be attributed to recent decades human activities. Furthermore, two correlation coefficient patterns between SSI and SPEI were found for the rivers of interest, an “increasing-decreasing” pattern for the Irtysh, Heihe, and Shiyang Rivers, where the precipitation is the main runoff supply, and an “increasing-stable” pattern for Aibihu and the Kaidu, Aksu, Yarkand, Hotan, and Shule Rivers, where glacier melt water provided a relatively high supply of runoff. Our findings are a contribution towards implementing effective water resources evaluation and planning in this arid region.