1. Introduction
According to the IPCC (Intergovernmental Panel on Climate Change) report, with climate change and human activities, climate extreme events such as droughts and floods are a significantly increasing trend [
1,
2,
3]. Drought is the below-average water storage conditions for a prolonged period in a given basin [
4,
5]. Droughts include meteorological droughts, hydrological droughts, agriculture droughts, and socio-economic droughts. Great importance is attached to hydrological drought due to its tremendous impact on human society [
6,
7]. In general, scholars usually focus on droughts that are related to economic losses and dramatic hazards. Severe droughts have occurred in seven major river basins of China in the past few decades [
8,
9,
10]. Due to global warming and intensifying human activities, hydrological drought events have significantly increased all over the world, which will pose a threat to ecosystems, agriculture development, and local socio-economic development [
11,
12,
13]. Hydrological drought events were characterized by duration, severity and drought area, and multi-dimensional hazardous phenomena [
14,
15]. If the individual drought characterization was analyzed, drought, in reality, cannot be revealed the serious consequence of drought in reality [
16,
17].
The Huai River Basin (HRB) plays an important role in agricultural development in China. The HRB provides 20% of the total agricultural products with 10% of the total cropland of China, feeding 20.4% of the total population [
18]. Therefore, agricultural development in the HRB is important to the food security of China. However, the basin is located in the transitional zone between humid and semi-humid climates. Increased drought frequency had affected agriculture development. Hence, a lot of researches focused on hydrological extremes in the HRB. Previous researches had concentrated on the spatiotemporal patterns of precipitation and streamflow extremes [
19], abrupt change of streamflow, long-term monotonic trend, related periodicity properties of streamflow variations, and so on [
18,
20].
Sun et al. (2018) showed that decreased streamflow could be observed in the HRB, with significantly decreased streamflow detected during April and May, which was likely the results of precipitation change and increased irrigation demand [
18]. Yan et al. (2014) analyzed the daily precipitation and showed that the precipitation of most months in drought years was reduced, therefore the relevant strategies (“annual basin-wide of long-term drought prevention”) should be carried out [
21]. Shi et al. (2014) showed that the reservoir regulations had apparently altered the monthly and seasonal streamflow in the upper HRB. The decreasing trend of the annual streamflow was found, and human activities were proven to be the dominant driving factor behind the decreasing annual streamflow [
22]. Wu et al. (2017) showed that seasonal alternation of droughts and flood events most probably occurred near the mainstream of the HRB, and drought and flood events were more likely to occur in summer-autumn than in spring-summer time intervals [
23]. Ji et al. (2017) analyzed the drought/flood disasters for the sudden alternations in the HRB [
24]. Wen et al. (2018) estimated soil moisture with various drought indices in the HRB of East China using the MODIS (Moderate Resolution Imaging Spectroradiometer) data [
25]. Geng et al. (2017) simulated maize yield losses caused by drought stress using the DSSAT-CERES-Maize (Decision Support System for Agrotechnology Transfer-Crop Environment Resource Syntheses- Maize) model and found a higher risk of high loss percentage in southern China, with a higher risk of low-mid loss percentage in northeastern China, and a higher risk of mid-high loss percentage in western China [
26].
However, most reports focused on the meteorological drought such as SPI (Standardized Precipitation Index), SPEI (Standardized Precipitation Evapotranspiration Index), and so on. Relatively few reports were available addressing the hydrological drought in the HRB. Hydrological droughts of the HRB are important for water resource and agricultural irrigation management. In this study, the daily streamflow at seven stations was collected, and hydrological droughts were identified using the run-length theory, and the AIC was accepted to evaluate the best fitting of the nine probability functions. The multivariate analysis methods, 26 copula functions, were used in this study with the aim of investigating joint probability behaviors of drought severity and drought duration. Therefore, the objectives of this study are to analyze the probability behaviors of hydrological droughts over the HRB. Then, the joint probability of drought severity and drought duration in the HRB were quantified using the best fitting Copula. Finally, possible reasons of hydrological droughts were discussed and explored.
2. Study Region and the Data
The HRB, one of the seven largest rivers in China, is located in the humid and semi-humid monsoon climate region of eastern China (
Figure 1). The HRB is also an important energy source and commodity grain base in China [
18,
27]. The population density of 662 persons per km
2 is the highest out of the seven largest rivers in China [
17]. Particularly, the precipitation period, influenced by the East Asian monsoon, is mainly between May and September in the HRB. The unique climate has caused natural disasters such as floods, waterlogging, and drought [
28,
29].
The daily streamflow series from 1964 to 2016 at seven hydrological stations (Xixian, Wangjiaba, Lutaizi, Bengbu, Bantai, Jiangjiaji, and Fuyang) were selected to identify hydrological drought events in the HRB (
Table 1). These data were obtained from the Water Resources Research Institute of Anhui Province and Huai River China. Land use data were sourced from Resources and Environmental Data Cloud Platform, Chinese Academy of Sciences (RESDC) [
30], and the dataset comprised a series of land use from 2000, 2005, and 2010–2015. The data were extracted from Landsat TM, ETM+, and OLI remote sensing images and generated through artificial visual interpretation with a spatial resolution of 1 km. Land use types included six primary types (cultivated land, forest, grassland, water bodies, artificial surfaces, and unused land) and 25 secondary types.
3. Methods
The identification of droughts is a prerequisite for drought character. Based on the daily streamflow, the drought event is mainly identified, which includes drought duration and drought severity, and the marginal distributions of drought duration and severity are subsequently evaluated, respectively. Finally, the joint probability of the two marginal distributions is constructed by the copula functions with the best performance.
3.1. Identification of a Drought Event
In this study, the duration and severity of hydrological droughts are defined by the threshold level method [
31], i.e., a hydrological drought is defined as a period during which flow is below the specified threshold level. The drought duration (
D) is the number of consecutive days for which streamflow is below the referenced discharge, and the drought severity (
S) is the cumulative deficit of streamflow for that duration. The drought severity is also called the total deficit or the negative run sum [
32]. When the threshold level is set to represent the boundary between normal and unusually low streamflow, it is chosen based on the characteristics of streamflow. In this case, low flow indices, such as percentiles from the flow duration curve (FDC), are frequently applied for both perennial and intermittent streams. For perennial streams, threshold levels between the 70-percentile flow (Q70) and the 95-percentile flow (Q95) from the FDC are frequently applied, which are the flows that are exceeded 70–95% of the time [
33]. In this study, the threshold level
Q0 was defined as the 75-percentile flow (Q75).
The threshold level method was developed for discharge series with a time resolution of one month or longer, but it has also been applied to daily discharge series [
32,
34]. When the temporal resolution is high in view of the droughts to be studied, a problem arises that has to be considered (see
Figure 2). During a prolonged dry period, it is often observed that the hydrological determinant exceeds the truncation level in a short period of time, thus we subdivided a large drought into a number of minor dry spells that are mutually dependent. Thus, a consistent definition of drought events should include some kind of pooling in order to define an independent sequence of droughts. Tallaksen et al. (1997) introduced an inter-event time and volume-based criterion for the pooling of mutually dependent droughts [
34]. The two dry spell periods with characteristics (
D1,
S1) and (
D2,
S2), respectively, are assumed to be mutually dependent, given:
- (a)
the inter-event time Ti is less than a critical value Tc;
- (b)
the ratio between the excess volume Ei and the preceding deficit volume is less than a critical value pc.
Then, the two dry spell periods are pooled into a single drought event with the characteristics as:
Statistical analysis of drought characteristics may be complicated by a large number of minor droughts that are usually present in the drought series. In this study, a more consistent approach, as suggested by Madsen and Rosbjerg (1995) was used [
35]. It is based on predefined percentages,
Rd and
Rs, of the mean values
E{
D} and
E{
S} of duration and severity, respectively, i.e., droughts with duration less than
Rd ×
E{
D} or severity less than
Rs ×
E{
S} are excluded. Tallaksen et al. (1997) and Zhang et al. (2013) recommend that
Rd =
Rs = 0.3 [
34,
36]. As with d
0, droughts with duration less than
Rd ×
E{
D} or severity less than
Rs ×
E{
S}, the drought day is still regarded as one drought event with
D = d
1 + d
2 + d
0.
3.2. Marginal Distribution
The probabilistic behavior of drought severity and drought duration are analyzed as follows: firstly, nine probability distribution functions, widely used in drought character analysis, are selected [
15,
27]; Secondly, nine probability distribution functions are fitted for the drought duration and drought characteristics in the HRB respectively. Meanwhile, parameters of nine probability distribution functions are estimated by the L-moment estimation [
37]; Thirdly, the AIC is used to select the appropriate marginal distribution. The smaller the value of AIC values, the better appropriate marginal distribution fitting; Finally, the appropriate marginal distribution that described the probabilistic characteristics of drought severity and drought duration is selected for seven stations based on AIC values.
3.3. Joint Probability Distribution
The copula function, commonly used in hydrology such as drought and flood, can couple two or three marginal distributions to the multivariate joint probability distribution [
28,
38]. In previous studies, Archimedean copula family includes a range of copula functions and are easy to be constructed, the copula family has been widely used to analyze the joint probabilistic behavior of hydrological extremes [
39,
40]. In this study, 26 copula functions were used to analyze the joint probabilistic behavior of hydrological drought. Sadegh et al. (2017) found that only the Tawn and Marshall–Olkin copulas can allow for characterizing the asymmetric dependence structure of precipitation and soil moisture [
41]. The Tawn copula performance is better than the Archimedean copula family. Therefore, in this study, we used 26 copula families to construct the joint distribution of drought severity and drought duration based on 26 copulas. Twenty-six copula families are selected and explained in detail in
Table 2. We have selected copula families with simple closed-form mathematical formulation, which is amenable for model inference.
The copula function is used to construct the drought probability model with the following formula:
where
Cθ(
S,
D) is the copula function combined with the drought severity
Fs(
s) and drought duration
FD(
d).
Two cases of drought risk probability should be calculated, as follows (Zhang et al. 2013):
3.4. Bayesian Analysis
The 26 Copula parameters can be estimated by Markov Chain Monte Carlo (MCMC) simulation within a Bayesian framework [
42,
43]. Bayesian analysis has been successfully employed in different fields [
43,
44,
45], including hydrology [
46,
47,
48], for model inference and uncertainty quantification purposes. Bayes’ theorem updates the prior probability (belief) of a certain hypothesis when new information is acquired. Bayes’ law conveniently attributes all modeling uncertainties to the parameters and estimates the posterior distribution of model parameters through
in which
and
signify prior and posterior distribution of parameters, respectively.
denotes likelihood function, and
is coined evidence. Evidence, being a constant value in each modeling practice, can be simply removed from the analysis if the main goal is to estimate the posterior distribution of parameters, and posterior parameter distributions can be estimated through
In the absence of useful information regarding the prior distribution of parameters, one may employ a flat uniform prior [
49]. Assuming error residuals are uncorrelated, homoscedastic, and Gaussian-distributed with mean zero, the likelihood function can be formulated as [
50]:
where
is an estimate of standard deviation of measurement error. For simplicity and numerical stability, this equation is usually logarithmically transformed to
Given the underlying assumptions about error residuals,
can be estimated as
We can, then, further simplify Equation (9) to
For comparison purposes, we can conveniently remove the constants and present log-likelihood function as,
Bayes’ Equation (7) is usually difficult, if not impossible, to solve analytical and numerical methods, such as MCMC simulation, are adopted to sample from the posterior distribution.
Further clarification is warranted here that we impose no assumption whatsoever on the posterior distribution of parameters. The aforementioned assumptions of “homoscedasticity, no correlation, and Gaussian distribution with mean zero” only apply to the distribution of error residuals which is used to construct the likelihood function that summarizes the distance between observations (empirical bivariate probability values) and model simulations (copula predicted bivariate probability values) into a single scalar.
Markov Chain Monte Carlo (MCMC) algorithms are a class of statistical methods to sample from high-dimensional complex distributions [
51]. The equilibrium state of MCMC, if the transition kernel warrants ergodicity, represents the target distribution. A newly developed hybrid evolution MCMC approach is employed adaptive proposal distributions to delineate the posterior parameter region in a Bayesian context.
Meanwhile, methods such as AIC is used to evaluate the performance of 26 copula models [
52,
53].
3.5. Goodness of Fit Measures
In this study, we use several goodness-of-fit measures to evaluate the performance of different copula models, including likelihood value, AIC, BIC (Bayesian Information Criterion), RMSE (Root mean square error), and NSE (Nash-Sutcliff Efficiency). A parameter set that provides the maximum likelihood minimizes the residuals between model simulations and observations. It, therefore, provides, in this sense, the best fit to the observed data.
Higher model complexity (more degrees of freedom) provides the advantage of greater model flexibility and hence usually results in a better fit to the observed data. However, this might stimulate over conditioning of the model. AIC, in contrast to the ad hoc likelihood value, takes into account both the complexity of the model and minimization of error residuals and provides a more robust measure of the quality of model predictions. AIC avoids the problem of over conditioning by adding a penalty term based on the number of parameters. AIC is formulated as [
52,
53]
in which
Q is the number of parameters of the statistical model and
l is the log-likelihood value of the best parameter set (Equation (7)). This equation can be simplified to
given the Gaussian assumption of error residuals,
, and a constant
CS. A lower AIC value associates with a better model fit.
5. Discussions and Conclusions
The frequency of hydrological droughts in the upper HRB is higher than that in the middle HRB. While the duration of the hydrological drought is in reverse spatial pattern. Zhang et al. (2011) showed that the rainfall-runoff relationship was significant in both highly-regulated rivers and less-regulated rivers [
29]. The runoff of the Huai River basin is mainly from rainfall. Therefore, runoff is mainly influenced by precipitation in the HRB [
55,
56]. Xia et al. (2019) showed that the drought severity in the southwest is higher than that in other regions, and meteorological drought has a decreasing trend in the southwest of HRB [
57]. Therefore, the decrease of precipitation and the increase of drought intensity lead to the high frequency of hydrologic drought.
Figure 1 shows the spatial distribution of irrigated areas in the HRB. There are irrigated areas with the area (2230 km
2) in the upper reaches of HRB, which is lower than the irrigated area (2.2 × 10
4 km
2) in the middle reaches of HRB. However, hydrological droughts occurred frequently in winter and spring in HRB, with more than a quarter of the drought events occurring in these seasons. Water conservancy projects such as reservoirs in irrigated area can store water from October to March. Crop irrigation can consume a lot of water resources in spring, although water conservancy projects can effectively reduce the occurrence of hydrologic droughts. Hydrology stations such as Lutaizi and Bengbu have a large drainage area in the middle reaches of HRB. Water conservancy projects can be more effective in reducing drought duration in small drainage areas than that in large drainage areas.
The correlation coefficient between drought duration and drought intensity is the minimum in the Shiguan River. This is because the Shiguan river is located in the Pishihang irrigation district, one of the three largest irrigation districts in Chia. While water reservoirs were built across the HRB during late 1950s and early 1960s, the Xianghongdian, Mozitan, and Shishan water reservoirs were built during 1958, 1958, and 1962 respectively in the Shiguan River. These water reservoirs can help to decrease peak flood flow and increase low flow [
18]. Hence, irrigation districts and small drainage areas lead to the correlation coefficient minimum.
The frequency of droughts along the mainstream of the HRB is higher than the tributaries of the HRB. However, concurrence probability of droughts along the mainstream of the HRB is lower than the tributaries of the HRB. Compared to the mainstream of HRB, tributary of HRB, such as Hongru River, Shiguan River, and Shaying River, have small irrigation areas and small storage capacity. The drainage area of the Shiguan River on the south bank of HRB is the smallest among the tributaries and has a high proportion of irrigated area, so that the probability of joint return periods is the maximum in the tributaries of HRB. Furthermore, the drainage area with more irrigation area (2.2 × 10
4 km
2) is the largest in Bengbu station in the mainstream of HRB, the probability of joint return periods is the minimum, implying the probability of drought duration or drought severity is highest. Furthermore, the larger drainage area has more arable land for agriculture, people, and industry. However, water demand is significantly increasing due to the rapid development of agricultural irrigation and industry in the dry season. While the drainage area of Bantai in the Hongru river is larger than that in the Shiguan river, the irrigation area (635 km
2) in the Hongru river is less than the irrigation area (3867 km
2) in the Shiguan river [
58]. Therefore, because of agricultural irrigation, the probability of drought duration or drought severity is larger in the Jiangjiaji than that in the Bantai.
The days of hydrological drought in HRB accounted for 21.4% of the total days. The results indicated that precipitation could be detected with larger fluctuations in the last 50 years with intensifying precipitation processes [
18,
59,
60]. The precipitation amount from June to September accounts for 50–75% of the annual total precipitation amount [
61], which causes largely uneven annual distribution of runoff. The variation coefficient of streamflow ranges from 0.16 to 0.85, and the annual extremum ratio of the streamflow between 1.7 and 23.9 in the HRB [
18,
62]. Meanwhile, results showed that the HRB was characterized by the highest population density with the heavy responsibility of supplier of agricultural products. The crop areas during 1983–2014 increased from 16.4 × 10
4 to 19.2 × 10
4 km
2. Besides, there were more than 5700 water reservoirs built with a total water capacity of 2.72 × 10
10 m
3 [
62]. Human interferences on streamflow changes render hydrological processes larger fluctuations in both space and time [
18,
62]. Although runoff has a decreasing trend, drought duration is basically unchanged, and the drought intensity in middle HRB shows a decreasing trend, but the decreasing trend is not significant.
Notably, hydrological droughts occurred frequently during the period of 1975–1985, especially in winter and spring, with more than a quarter of the drought events occurring in these seasons. Droughts occurred frequently in the 1990s and early 21st century.
Figure 13 shows that drought-affected crop areas and drought-destroyed crop areas have a significantly increasing trend from 1981 to 2001. Especially, the drought-affected areas were 27.33 × 10
4 km
2 and 27.24 × 10
4 km
2 respectively, while the ratio of the disaster area to the drought-affected area was 67.7% and 63.4% in 1994 and 2001, respectively. The annual distribution of precipitation in the HRB is extremely uneven, with spring precipitation amount accounting for only 19% of the annual precipitation amount when the winter wheat demand peaks and is an important period of growth. Spring precipitation decreased significantly in the 1990s [
29,
56], which is largely the main reason for the drought-affected areas in the 1990s. However, the increasing trend of hydrological droughts had not cause drought-affected crop significantly increase area after 2010. The main reason is that the Chinese government required strengthening of the construction of water conservancy facilities. The drought resistance capacity of HRB has been significantly improved, effectively reducing the impact of hydrological drought on crops.
In summary, some interesting and important conclusions can be drawn as follows:
The frequency of hydrological droughts in the upper Huai River is more than in the middle of the Huai River Basin, while the duration of hydrological drought is just the opposite. The drought frequency and drought duration of the three major tributaries are between the upper and middle of the mainstream. What’s more, the drought frequency of the Shiguan River on the south bank is higher than that of the other two tributaries.
Generalized Pareto distribution is the right distribution function with the lowest of AIC in the study of drought duration over the Huai River Basin. The Generalized Extreme Value distribution satisfactorily described the probabilistic behavior of the drought severity. Joe copula and Tawn copula were the right choice and used in this current study. Given the return period of droughts less than 30 years, the day of drought duration in the upper Huai River is the maximum and is the minimum in the middle Huai river. However, the drought duration in Fuyang station is increasing based on the increase of the return period. The ratio of drought intensity to flow is negatively correlated with basin area.
The frequency of the Joint return period of drought severity and drought duration in the mainstream of the Huai River is higher than the tributary of the Huai River. The frequency of the concurrent return period of drought severity and drought duration in the mainstream of the Huai River is lower than that of the tributary of the Huai River Basin. The drought resistance capacity of HRB has been significantly improved, effectively reducing the impact of hydrological drought on crops after 2010.