Drought is an insidious natural hazard that has damaging and costly impacts on agriculture, water resources, ecology, and society [1
]. Due to global climate change and rapid socio-economic development, drought disasters have occurred more frequently and extensively in recent decades [3
]. Drought is commonly defined as below-normal water availability [4
] and can be subdivided into different types of drought related to the variables of the hydrological cycle, precipitation (meteorological drought), soil moisture (agricultural drought), and streamflow (hydrological drought) [5
Hydrological drought is defined as a significant shortage of availability of water in all its forms appearing in the land phase of the hydrological cycle (e.g., streamflow, groundwater level and lake level) [6
]. It is traditionally detected using field observations of streamflow, surface water and groundwater levels, thereby providing direct evidence of any below-normal water availability [6
]. Below-normal water availability in rivers, lakes and reservoirs can cause water scarcity in combination with water demand, threating water supply and associated food production [8
]. Thus, it is important to identify hydrological drought characteristics and assess the effects of hydrological drought quantitatively. The Standardized Streamflow Index (SSI), proposed by Shukla and Wood [9
], has been used as a useful index for characterizing hydrological drought. It is constructed using streamflow data based on the concept of the standardized precipitation index (SPI). Similar to SPI, with the advantages of computational simplicity, the SSI is capable of characterizing hydrological drought condition at different time scales [3
], and it enables the severity of hydrological drought in different locations to be compared independently of the local characteristics [11
]. In addition, the SSI is sensitive to the factors and assumptions that govern probabilistic hydrology, since it is a probability-based drought index [6
Generally, statistical inferences and statistical analyses for hydrologic time series have relied heavily on the assumption of stationarity in hydrology [12
]. Under the stationarity assumption, hydrological series keep their distributional properties invariant with time, implying lack of trends and shift [14
]. However, the stationarity assumption has been widely questioned and should no longer serve as a central, default assumption, as a result of global climatic change and man-induced disturbance [15
]. In recent years, hydrological nonstationarity has drawn considerable attention [14
]. Coulibaly and Baldwin [18
] developed an optimal dynamic recurrent neural networks method to directly forecast hydrological series under nonstationarity conditions, and they found that neural networks are good alternatives for modeling the complex dynamics of the hydrological system. Villarini et al. [14
] modeled a long record of seasonal rainfall and temperature in a nonstationarity framework to characterize non-stationarities in hydro-climatic variables.
In the traditional calculation of SSI values, the streamflow sample series are firstly fitted to a suitable stationary probability distribution on the basis of stationarity assumption [11
]. This means that historical features of streamflow series can be used to derive SSI values in the future. However, changing environments (e.g., climate change and human activities) might alter the statistical characteristics of hydroclimate time series [19
], resulting in so-called nonstationarity. With respect to streamflow, there have been numerous studies on individual impacts of climate change (mainly changes in precipitation and temperature) and human activity (mainly water construction and building of dams) on it [20
], implying clear violations of the stationarity assumption. Ignoring the nonstationarity would therefore most likely diminish the availability and validity of traditional SSI in hydrological drought analysis and could lead to the underestimation or overestimation of the drought severity [21
]. Thus, it is essential to incorporate the nonstationarity of streamflow sample series in constructing an appropriate variant SSI (SSIvar
) under nonstationarity conditions, thereby providing significant information for evaluation and mitigation of risk of hydrological drought hazards and management of water resources. From this point of view, although some researchers have attempted to consider nonstationarity in developing drought index for drought monitoring, most research has only focused on mean time variance of precipitation time series for meteorological drought (e.g., [22
]). However, to date, relatively few studies have addressed the stationarity or nonstationarity of streamflow series for hydrological drought using a nonstationarity framework in different geographic regions considering both trends and change points in the parameters. This constituted the major motivation of this study.
Several methods have been proposed to model nonstationarity time series in the previous literature (e.g., [24
]), each having their own strengths and weakness. The Generalized Additive Models for Location, Scale and Shape (GAMLSS), proposed by Rigby and Stasinopoulos [26
], has recently gained popularity in modeling nonstationarity time series in hydrology [27
]. This model provides a high degree of flexibility in addressing nonstationarity probabilistic modeling. In GAMLSS, the assumption that the variable of interest follows a distribution from the exponential family is relaxed, allowing the use of more general distributions, such as highly skewed or kurtotic distributions, which may be more appropriate for modeling the record of interest. This makes it an appealing framework for nonstationarity modeling of hydrometeorological variables to improve the existing drought index.
In this study, the GAMLSS was used to model streamflow with nonstationarity distribution to construct a variant SSI index (SSIvar) in eight catchments in the eastern region of China. The main objectives of this study are: (1) to analyze whether streamflow series are stationary in the eastern region of China, and (2) to construct an appropriate variant SSI that accounts for the changes in the parameters of the selected distribution under nonstationarity conditions. The results of this study could provide important information for the management of water resources and evaluation of hydrological drought hazards under a changing environment.