Quantifying the Relationship between Drought and Water Scarcity Using Copulas: Case Study of Beijing–Tianjin–Hebei Metropolitan Areas in China

Drought is a complex natural phenomenon that occurs throughout the world. Analyzing and grasping the occurrence and development of drought events is of great practical significance for preventing drought disasters. In this study, the Standardized Precipitation Evapotranspiration Index (SPEI) was adopted as a drought index to quantitatively analyze the temporal evolution, spatial distribution, and gridded trend characteristics of drought in the Yellow River basin (YRB) during 1961–2015. The duration and severity of drought events were extracted based on run theory, and the best-fitted Copula models were used to combine the drought duration and severity to analyze the drought return period. The results indicated that: (1) the drought showed a non-significant upward trend in the YRB from 1961 to 2015, and drought events became more serious after the 1990s; (2) the month and season with the most serious drought was June and summer, with an average SPEI value of −0.94 and −0.70; (3) the seasons with an increasing drought trend were spring, summer, and autumn; (4) the most serious drought lasted for 16 months in the YRB, with drought severity of 12.44 and drought return period of 115.18 years; and (5) Frank-copula was found to be the best-fitted one in the YRB. The research results can reveal the evolution characteristics of drought, and provide reference and basis for drought resistance and reduction in the YRB.

Section: Name Cumulative Distribution Function (Cdf)mentioning

confidence: 99%

Copula-Based Drought Analysis Using Standardized Precipitation Evapotranspiration Index: A Case Study in the Yellow River Basin, China

Wang

Yang

et al. 2019

“…Several methods have been proposed to investigate the bivariate characteristic of droughts, such as the product of the conditional distribution of drought severity for a given drought duration and the marginal distribution of drought duration to construct the joint distribution of drought duration and magnitude used by Salas et al [73] and González and Valdés [74], with complex mathematical derivation involved. Nevertheless, multivariate distributions using copulas, whose applications in hydrology have been increasing in recent years with several and different uses [67,[75][76][77][78][79][80], can overcome such issues.…”

Section: Bivariate Analysis Of Drought Duration and Magnitudementioning

confidence: 99%

Jointly Modeling Drought Characteristics with Smoothed Regionalized SPI Series for a Small Island

Espinosa

Portela

Filho

et al. 2019

The paper refers to a study on droughts in a small Portuguese Atlantic island, namely Madeira. The study aimed at addressing the problem of dependent drought events and at developing a copula-based bivariate cumulative distribution function for coupling drought duration and magnitude. The droughts were identified based on the Standardized Precipitation Index (SPI) computed at three and six-month timescales at 41 rain gauges distributed over the island and with rainfall data from January 1937 to December 2016. To remove the spurious and short duration-dependent droughts a moving average filter (MA) was used. The run theory was applied to the smoothed SPI series to extract the drought duration, magnitude, and interarrival time for each drought category. The smoothed series were also used to identify homogeneous regions based on principal components analysis (PCA). The study showed that MA is necessary for an improved probabilistic interpretation of drought analysis in Madeira. It also showed that despite the small area of the island, three distinct regions with different drought temporal patterns can be identified. The copulas approach proved that the return period of droughts events can differ significantly depending on the way the relationship between drought duration and magnitude is accounted for.

“…Major research results include: De Michele (2005) used the 2D copula function to calculate the designed flood yield of dams, and Salvadori (2006) used the 2D copula function to study the statistical characteristics of storms at sea [6,7]. De Michele (2013) and Linlin (2018) applied copula functions to analyze the drought frequency and its recurrence interval [8,9]. Razmkhah (2016) [10] and Yan (2018) [11] used the 2D copula function to study the relationship between precipitation and runoff.…”

Section: Introductionmentioning

confidence: 99%

Probability Analysis and Control of River Runoff–sediment Characteristics based on Pair-Copula Functions: The Case of the Weihe River and Jinghe River

You

Jiang

Liu

et al. 2019

Analyzing the encounter frequency of high–low runoff and sediment yield is important for the appropriate dispatching of runoff–sediment resources, as well as river regulation. However, there have been no reports on the utilization of the pair-copula function in analyzing the runoff–sediment characteristics from a probabilistic perspective and conducting probability control on the runoff–sediment yields of different hydrologic stations. This paper builds marginal distribution functions on the basis of kernel distribution theory. In addition, this paper builds the joint distribution functions through pair-copula functions in order to analyze the encounter probability and the compensation characteristics of high–low runoff and sediment at different stations on the Weihe River in China, as well as the origins of runoff–sediment, to conduct probability control of river runoff–sediment resource allocation. The results show that, in different periods, the synchronous probability of high–low runoff of the Weihe River’s Xianyang and Huaxian Stations, and the Jinghe River’s Zhangjiashan Station differ, while that of high–low sediment at the three stations changes little—remaining at around 54%. Therefore, the sediment and runoff of the Weihe River apparently have different origins. In years of high and low runoff, if the runoffs of the Xianyang and Zhangjiashan Stations can be kept within a certain range, then the runoff of the Huaxian Station will be in a particular range, at a certain probability. Sediment at the Huaxian Station can be controlled, in a similar way. These results are of great significance for the water and sediment management department of the Weihe river, in order to reasonably allocate water and sediment resources.