Under the background of global climate change and local
anthropogenic activities, multiple driving forces have introduced various
nonstationary components into low-flow series. This has led to a high demand
on low-flow frequency analysis that considers nonstationary conditions for
modeling. In this study, through a nonstationary frequency analysis framework
with the generalized linear model (GLM) to consider time-varying distribution
parameters, the multiple explanatory variables were incorporated to explain
the variation in low-flow distribution parameters. These variables are
comprised of the three indices of human activities (HAs; i.e., population,
POP; irrigation area, IAR; and gross domestic product, GDP)
and the eight measuring indices of the climate and catchment conditions
(i.e., total precipitation

Low flow is defined as the flow of water in a stream during prolonged dry weather (WMO, 2009). Yu et al. (2014) quantitatively described a low-flow event as a segment of hydrograph during a period of dry weather with discharge values below a preset (relatively small) threshold. According to WMO (2009), annual minimum flows averaged over several days can be used to measure low flows. During low-flow periods, the magnitude of river flow will greatly restrict its various functions (e.g., providing water supply for production and living, diluting waste water, ensuring navigation, meeting ecological water requirement). Therefore, the investigation of the magnitude and frequency of low flows is of primary importance for engineering design and water resources management (Smakhtin, 2001). In recent years, low flows, as an important part of river flow regime, have been attracting an increasing attention of hydrologists and ecologists in the context of the significant impacts of climate change and human activities (HAs; Bradford and Heinonen, 2008; Du et al., 2015; Kam and Sheffield, 2015; Kormos et al., 2016; Liu et al., 2015; Sadri et al., 2016). In general, under the impact of a changing environment, combinations of multiple factors, such as precipitation change, temperature change, irrigation area (IAR) change and construction of reservoirs, can drive various patterns of streamflow changes (Liu et al., 2017; Tang et al., 2016). Unfortunately, when subjected to a variety of influencing forces, low flow is more vulnerable than high flow or mean flow. Therefore, it is a pretty important issue in hydrology to identify low-flow changes, track multiple driving factors and quantify their contributions from the perspective of hydrological frequency analysis.

In hydrological analysis and design, conventional frequency analysis estimates the statistics of a hydrological time series based on recorded data with the stationary hypothesis which means that this series is “free of trends, shifts or periodicity (cyclicity)” (Salas, 1993). However, global warming and human forces have changed climate and catchment conditions in some regions. Time-varying climate and catchment conditions (TCCCs) can affect all aspects of the flow regime, i.e., changing the frequency and magnitude of floods, altering flow seasonality and modifying the characteristics of low flows. The hypothesis of stationarity has been suspected (Milly et al., 2008). If this problematic method is still used, the frequency analysis may lead to high estimation error in hydrological design. Therefore, considerable literature has introduced the concept of hydrologic nonstationarity into analysis of various hydrological variables, such as annual runoff (Arora, 2002; Jiang et al., 2015a; Xiong et al., 2014; Yang and Yang, 2013), flood (Gilroy and Mccuen, 2012; Kwon et al., 2008; Yan et al., 2017; Zhang et al., 2015), low flow (Du et al., 2015; Jiang et al., 2015b; Liu et al., 2015), precipitation (Gu et al., 2017; Mondal and Mujumdar, 2015; Villarini et al., 2010) and so on. Compared with the literature on annual runoff, floods and precipitation, the literature on the nonstationary analysis of low flow is relatively limited.

Previous hydrological literature on frequency analysis of nonstationary hydrological series mainly focuses on two aspects: development of the nonstationary method and exploration of covariates reflecting changing environments. Strupczewski et al. (2001) presented the method of time-varying moment which assumes that the hydrological variable of interest obeys a certain distribution type, but its moments change over time. The method of time-varying moment was modified to be the method of time-varying parameter values for the distribution representative of hydrologic data (Richard et al., 2002). Villarini et al. (2009) presented this method using the generalized additive models for location, scale and shape parameters (GAMLSS; Rigby and Stasinopoulos, 2005), a flexible framework to assess nonstationary time series. The time-varying parameter method can be extended to the physical covariate analysis by replacing time with any other physical covariates (Jiang et al., 2015b; Kwon et al., 2008; López and Francés, 2013; Liu et al., 2015; Villarini and Strong, 2014). For example, Jiang et al. (2015b) used reservoir index as an explanatory variable based on the time-varying copula method for bivariate frequency analysis of nonstationary low-flow series in Hanjiang River, China. Du et al. (2015) took precipitation and air temperature as the explanatory variables to explain the inter-annual variability in low flows of the Weihe River, China (also known as the Wei He River). Liu et al. (2015) took the sea surface temperature in the Nino3 region, the Pacific Decadal Oscillation, the sunspot number (3 years ahead), the winter areal temperature and precipitation as the candidate explanatory variables to explain the inter-annual variability in low flows of Yichang station, China. Kam and Sheffield (2015) ascribed the increasing inter-annual variability of low flows over the eastern United States to the North Atlantic Oscillation and Pacific North America.

To our knowledge, compared with the nonstationary flood frequency analysis, the studies on the nonstationary frequency analysis of low-flow series are not very extensive because of incomplete knowledge of low-flow generation (Smakhtin, 2001). Most of these studies explain nonstationarity of low-flow series only by using climatic indicators or a single indicator of human activity. However, the indicators of catchment conditions (e.g., recession rate) related to physical hydrological processes have seldom been attached in nonstationary modeling of low-flow series. This lack of linking with hydrological processes makes it impossible to accurately quantify the contributions of influencing factors for the nonstationarity of low-flow series, and such a scientific demand for tracing the sources of nonstationarity of low-flow series and qualifying their contributions motivated the present study. The knowledge of low-flow generation has been increased by efforts of hydrologists, which can help develop physical covariates to address nonstationarity. Low flows generally originate from groundwater or other delayed outflows (Smakhtin, 2001; Tallaksen, 1995). Their generation relates to both an extended dry weather period (leading to a climatic water deficit) and complex hydrological processes which determine how these deficits propagate through the vegetation, soil and groundwater system to streamflow (WMO, 2009). Thus, not only climate condition drivers (e.g., potential evaporation exceeds precipitation), but also catchment condition drivers (e.g., the faster hydrologic response rate to precipitation) can cause low flows.

The significant factors such as precipitation, temperature,
evapotranspiration (EP), streamflow recession, large-scale teleconnections and
human forces may play important roles in influencing low-flow generation
(Botter et al., 2013; Giuntoli et al., 2013; Gottschalk et al., 2013; Kormos
et al., 2016; Sadri et al., 2016). Gottschalk et al. (2013) presented a
derived low-flow probability distribution function with climate and catchment
characteristics parameters (i.e., the mean length of dry spells

The goal of this study is to trace origins of nonstationarity in low flows
through developing a nonstationary low-flow frequency analysis framework with
the consideration of the time-varying climate and catchment conditions and human activity. In this framework, the climate and catchment
conditions are quantified using the eight indices, i.e., meteorological
variables (total precipitation

This paper is organized as follows. Section 2 describes the methods. The Weihe River basin and available data sets used in this study are described in Sect. 3, followed by a presentation of the results and discussion in Sect. 4. Section 5 summarizes the main conclusions.

The framework of nonstationary low-flow frequency analysis.

The flowchart of how to organize the nonstationary low-flow frequency analysis framework is shown in Fig. 1. The whole process is divided into three steps. The first step is the preliminary analysis, including the graphical presentation of both explanatory variables and low-flow series, the statistical test for nonstationarity, and the correlations between each explanatory variable and each low-flow series. The second step is the single covariate analysis for the most important explanatory variable. The third step is the multiple covariate analysis for the optimal combination. We use a low-flow frequency analysis model and stepwise regression method to accomplish the last two steps. In the following subsections, first, the low-flow frequency analysis model is constructed based on the nonstationary probability distributions method, in which distribution parameters serving as response variables can vary as functions of explanatory variables. Second, the distribution types used to build the nonstationary model are outlined. Then, the candidate explanatory variables related to the time-varying climate and catchment conditions and human activity are clarified. Finally, estimation of model parameters and selection of models are illustrated.

Generally, a nonstationary frequency analysis model can be established based
on the time-varying distribution parameters method (Du et al., 2015;
López and Francés, 2013; Liu et al., 2015; Richard et al., 2002;
Villarini and Strong, 2014). For the nonstationary probability distribution

In order to compare the nonstationary models constructed by various
combinations of explanatory variables, Eq. (2) is modified in this study
using the dimensionless method for the standard GLM parameters. The value of

The probability density functions and moments (the mean and variance) for the candidate distributions in this study.

We need to select the form of probability distribution

Description of the developed nonstationary models using time, TCCCs indices and/or HA indices as explanatory variables.

We look for variables

Annual mean frequency of precipitation events is defined as an index to
represent the intensity of precipitation recharge to the streamflow:

The ratio of annual potential evaporation to precipitation, commonly known as
the climate aridity index, has been used to assess the impacts of climate
change on annual runoff (Arora, 2002; Jiang et al., 2015a). The climate
aridity index largely reflects the climatic regimes in a region and
determines runoff rates (Arora, 2002). Therefore, we choose the annual
climate aridity index as a measure of time-varying climate and catchment
conditions and estimate its value in a whole region using

The base-flow index (BFI) is defined as the ratio of base flow to total flow. This index has been applied to quantify catchment conditions (e.g., soil, geology and storage-related descriptors) to explain hydrological drought severity (Van Loon and Laaha, 2015). We also choose annual base-flow index as a measure of TCCCs. BFI is estimated using a hydrograph separation procedure in the R package “lfstat” (Koffler and Laaha, 2013).

The recession constant is an important catchment characteristic index measuring the timescale of the hydrological response and reflecting water retention ability in the upstream catchment (Botter et al., 2013). Various estimation methods have been developed to extract recession segments and to parameterize characteristic recession behavior of a catchment (Hall, 1968; Sawaske and Freyberg, 2014; Tallaksen, 1995).

In this study, annual recession analysis (ARA) is performed to obtain the annual
streamflow recession constant (

In this study, the recession-related aridity index is defined as the ratio of
recession rate (

The model parameters including

Location, topography, hydro-meteorological stations and river systems of the Weihe River basin.

The summary of candidate explanatory variables and reason of selection.

The annual minimum low flows and fitted trend lines in both Huaxian (H) and Xianyang (X) gauging stations.

Model selection contains the selection of the type of probability
distribution and the selection of the explanatory variables to explain the
response variables (i.e., distribution parameters

The Weihe River, located in the southeast of the northwest Loess Plateau, is
the largest tributary of the Yellow River, China. The Weihe River has a
drainage area of 134 766 km

In the Weihe basin, the impacts of agricultural irrigation on runoff have
been found to be significant (Jiang et al., 2015a; Lin et al., 2012). Lin et
al. (2012) mentioned that the annual runoff of the Weihe River was
significantly affected by irrigation diversion of the Baoji Gorge irrigation
district. The irrigated area of the Baoji Gorge irrigation district increased over time
since the founding of P.R. China in 1949, and, due to one influential
irrigation system project in that area, it became more than twice as large
as the original irrigation area since 1971. Jiang et
al. (2015a) demonstrated that, in the Weihe basin, irrigated area, as
compared with the other indices, e.g., population, gross domestic product and
cultivated land area, was a more suitable human explanatory variable for
explaining the time-varying behavior of annual runoff. With the above
background, it is important to consider the effects of human activities that
mainly originate from irrigation diversion, especially for studying low-flow
series in this basin. The estimations of annual recession rate (

Frequency distributions (using the kernel density estimations) and time series processes of TCCCs variables in both Huaxian (H) and Xianyang (X) stations.

We used daily streamflow records (1954–2009) provided by the Hydrology Bureau
of the Yellow River Conservancy Commission from both Huaxian station (with a
drainage area of 106 500 km

We downloaded daily total precipitation and daily mean air temperature
records for 19 meteorological stations over the basin from the National
Climate Center of the China Meteorological Administration (source:

Human activity data (i.e., gross domestic product, population and irrigation
area) were taken from annals of statistics provided by the Shaanxi
Provincial Bureau of Statistics (

HA indices in both Huaxian (H) and Xianyang
(X).

The graphical representation and statistical test provide a preliminary analysis
for low-flow nonstationarity. The graphical representations of time-series
data help visualize the trends of related variables (i.e., low flow, TCCCs and
HA variables), the density distributions of TCCCs variables, and the
correlations between low-flow variables and these explanatory variables. In
Fig. 3, four annual minimum streamflow series (AM

Figure 4 shows the kernel density estimations and time processes of TCCCs
variables for both Huaxian (H) and Xianyang (X) stations. The results show
that these variables have different variation patterns. For example, the
mean frequency of precipitation events (

The results of trend test and change-point detection for both the four low-flow series and TCCCs variables in Huaxian and Xianyang.

Significance codes: 0 “***” 0.001 “**” 0.01 “*” 0.05 “

The Pearson correlation coefficients matrix between the annual minimum flow series and candidate explanatory variables in Huaxian (H) and Xianyang (X) stations; the darker color intensity represents a higher level of correlation (blue indicates positive correlation and red indicates negative correlations).

Comparisons among M0, M1 and M2 based on the AIC values for the
four observed low-flow series in Huaxian (H) at

The significance of trends in the four annual minimum streamflow series and
TCCCs variables is tested by the Mann–Kendall trend test (Kendall, 1975;
Mann, 1945; Yue et al., 2002), and the change points in these series are
detected by Pettitt's test (Pettitt, 1979). The results in Table 4 show
that, in both Huaxian and Xianyang stations, the decreasing trends in all the
four low-flow series (AM

A preliminary attribution analysis is performed using the Pearson correlation
matrix to investigate the relations between the annual minimum series and
eight candidate explanatory variables. Figure 6 indicates that there are
significant linear correlations between the four minimum low-flow series
(AM

Figure 7 presents the AIC values of the four types of models (M0, M1, M2a and
M2b) fitted for the low-flow series (AM

Performance assessments of GA_M2 for AM

Figure 8 shows the diagnostic assessment of the GA_M2 model
(with the optimal explanatory variable) for AM

Comparisons of performance of stationary model (M0), time
covariate model (M1) and physical covariate models (M2a, M2b, M3, M4, M5 and
M6 with their corresponding optimal explanatory variables) for AM

Figure 9 shows the AIC values of the stationary model (M0), time covariate model
(M1) and physical covariate models (M2a, M2b, M3, M4, M5 and M6) for AM

The summary of frequency analysis using GA distribution for AM

Performance assessments of GA_M6 for AM

Contribution of selected explanatory variables to

A summary of frequency analysis based on nonstationary GA distribution
AM

The diagnostic assessment of the GA_M6 model for AM

Figure 11 presents the contribution of each selected explanatory variable to

The impacts of both human activities and climate change on low flows of the study area led to time-varying climate and catchment conditions. Nonstationary modeling for annual low-flow series using TCCCs variables and/or HA variables as explanatory variables is clearly different from either the stationary model (M0) or the time covariate model (M1). The result demonstrates that considering multiple drivers (e.g., the variability in catchment conditions), especially in such an artificially influenced river, is necessary for nonstationary modeling of annual low-flow series.

In this study area, nonstationary modeling considering TCCCs is supported by
the following facts and findings. For human activities, an important
milestone representative is the completion and operation of the irrigation
system on the plateau in the Baoji Gorge irrigation district since 1971 (Sect. 3.1).
Figure 5c shows the change in irrigation area in this basin. And the
change-point detection test in Sect. 4.1 shows that significant change
points of low-flow series occur exactly at around 1971. This result
demonstrates that changes in AM

There is an increasing need to develop an effective nonstationary low-flow
frequency model to deal with nonstationarities caused by climate change and
time-varying anthropogenic activities. In this study, time-varying climate
and catchment conditions in the Weihe River basin were measured by
annual time series of the eight indices, i.e., total precipitation (

The data used in this paper can be requested by contacting the corresponding author Lihua Xiong at xionglh@whu.edu.cn.

The authors declare that they have no conflict of interest.

The study was financially supported by the National Natural Science Foundation of China (NSFC grants 51525902 and 51479139) and projects from State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University. We greatly appreciate the editor and three reviewers for their insightful comments and constructive suggestions that helped us to improve the manuscript. Edited by: Fuqiang Tian Reviewed by: Xiaohong Chen, Dengfeng Liu, and one anonymous referee