Hydrological Drought Regimes of the Huai River Basin, China: Probabilistic Behavior, Causes and Implications

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Article Hydrological Drought Regimes of the Huai River Basin, China: Probabilistic Behavior, Causes and Implications

Peng Sun 1,2 , Qiang Zhang 3,4,5,*, Rui Yao 6,7,* and Qingzhi Wen 2,6

1 Anhui Province Key Laboratory of Water Conservancy and Water Resources, Anhui and Huaihe River Institute of Hydraulic Research, Bengbu 233000, China; [email protected] 2 School of Geography and Tourism, Anhui Normal University, Wuhu 241002, China; [email protected] 3 Key Laboratory of Environmental Change and Natural Hazard, Ministry of Education, Beijing Normal University, Beijing 100875, China 4 State Key Laboratory of Surface Process and Ecology Resource, Beijing Normal University, Beijing 100875, China 5 Faculty of Geographical Science, Academy of Disaster Reduction and Emergency Management, Beijing Normal University, Beijing 100875, China 6 Key Laboratory of Virtual Geographic Environment for the Ministry of Education, Nanjing Normal University, Nanjing 210023, China 7 State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China * Correspondence: [email protected] (Q.Z.); [email protected] (R.Y.)

Received: 28 August 2019; Accepted: 9 November 2019; Published: 14 November 2019

Abstract: Hydrological droughts were characterized using the run-length theory and the AIC (Akaike information criterion) techniques were accepted to evaluate the modeling performance of nine probability functions. In addition, the copula functions were used to describe joint probability behaviors of drought duration and drought severity for the major tributaries of the Huai River Basin (HRB) which is located in the transitional zone between humid and semi-humid climates. The results indicated that: (1) the frequency of hydrological droughts in the upper HRB is higher than that in the central HRB, while the duration of the hydrological drought is in reverse spatial pattern. The drought frequency across the Shiguan River along the south bank of the HRB is higher than the other two tributaries; (2) generalized Pareto distribution is the appropriate distribution function with the best performance in modelling the drought duration over the HRB; while the Generalized Extreme Value (GEV) distribution can effectively describe the probabilistic properties of the drought severity. Joe copula and Tawn copula functions are the best choices and were used in this study. Given return periods of droughts of <30 years, the droughts in the upper HRB are the longest, and the shortest are in the central HRB; (3) the frequency of droughts along the mainstream of the HRB is higher than tributaries of the HRB. However, concurrence probability of droughts along the mainstream of the HRB is lower than the tributaries of the HRB. The drought resistance capacity of HRB has been significantly improved, effectively reducing the impact of hydrological drought on crops after 2010.

Keywords: hydrological drought; probabilistic behavior; copula; Huai river basin

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 [1–3]. Drought is the below-average water storage conditions for a prolonged period in a

Water 2019, 11, 2390; doi:10.3390/w11112390 www.mdpi.com/journal/water Water 2019, 11, 2390 2 of 20 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 [8–10]. 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 [11–13]. 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. Water 2019, 11, 2390 3 of 20 Water 2019, 11, x 3 of 22

2.2. Study Region and the Data TheThe HRB,HRB, oneone ofof thethe sevenseven largestlargest riversrivers inin China,China, isis locatedlocated inin thethe humidhumid andand semi-humidsemi-humid monsoonmonsoon climate region region of of eastern eastern China China (Figure (Figure 1).1). The The HRB HRB is isalso also an animportant important energy energy source source and andcommodity commodity grain grain base basein China in China [18,27]. [18 The,27]. population The population density density of 662 ofpersons 662 persons per km per2 is the km 2highestis the highestout of the out seven of the largest seven largestrivers in rivers China in [17]. China Particularly, [17]. Particularly, the precipitation the precipitation period, period, influenced inﬂuenced by the byEast the Asian East Asianmonsoon, monsoon, is mainly is mainly between between May and May September and September in the in HRB. the HRB. The Theunique unique climate climate has hascaused caused natural natural disasters disasters such such as flood as ﬂoods,s, waterlogging, waterlogging, and and drought drought [28,29]. [28,29 ].

FigureFigure 1.1. Locations of the hydrological stationsstations andand irrigationirrigation area.area.

TheThe dailydaily streamflowstreamflow seriesseries fromfrom 19641964 to 2016 at seven hydrological stations (Xixian, Wangjiaba, Lutaizi,Lutaizi, Bengbu,Bengbu, Bantai,Bantai, Jiangjiaji,Jiangjiaji, andand Fuyang)Fuyang) werewere selectedselected toto identify hydrological droughtdrought eventsevents inin thethe HRBHRB (Table(Table1 1).). These These data data werewere obtained obtained from from the the WaterWater Resources Resources Research Research Institute Institute of of Anhui Anhui ProvinceProvince andand Huai Huai River River China. China. Land Land use use data data were were sourced sourced from from Resources Resources and Environmentaland Environmental Data CloudData Cloud Platform, Platform, Chinese Chinese Academy Academy of Sciences of Sciences (RESDC) (RESDC) [30], [30], and and the datasetthe dataset comprised comprised a series a series of landof land use use from from 2000, 2000, 2005, 2005, and and 2010–2015. 2010–2015. The The data data were were extracted extracted from from Landsat Landsat TM, ETMTM, +ETM+,, and OLIand remoteOLI remote sensing sensing images images and generated and generated through through artificial artificial visual interpretation visual interpretation with a spatial with resolution a spatial ofresolution 1 km. Land of 1 use km. types Land included use types six included primary typessix primary (cultivated types land, (cultivated forest, grassland, land, forest, water grassland, bodies, artificialwater bodies, surfaces, artificial and unused surfaces, land) and andunused 25 secondary land) and types. 25 secondary types.

TableTable 1.1. InformationInformation ofof hydrologicalhydrological stationstation inin HuaiHuai RiverRiver Basin.Basin.

Basin Area Length Slope of Runoﬀ RunoffRuno ﬀ River Station Basin Area Length Slope of Runoff River Station (km2) (km) River (%) (108 m3) DepthDepth (mm) (km2) (km) River (%) (108 m3) Upper Xixian 10,190 250 4.9 62.2(mm) 60.8 Upper Xixian 10,190 250 4.9 62.2 60.8 Main Upper Wangjiaba 30,630 364 0.35 99.8 32.5 stream MainMiddle Upper LutaiziWangjiaba 88,630 30,630 529 364 0.3 0.35 99.8 250 32.5 28.2 streamMiddle Middle BengbuLutaizi 121,330 88,630 651 529 0.3 0.3 250 299 28.2 24.6 Middle Bengbu 121,330 651 0.3 299 24.6 HongruHongru BantaiBantai 11,663 11,663 240 240 1 1 28.1 28.1 24.0 24.0 TributaryTributaryShiguan Shiguan Jiangjiaji Jiangjiaji 5930 5930 172 172 9.2 9.2 31.5 31.5 53.1 53.1 ShayingShaying Fuyang Fuyang 35,250 35,250 490 490 0.03 0.03 55.6 55.6 15.7 15.7

Water 2019, 11, 2390 4 of 20

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 Figure2). 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:

Dpool = Di + Di+1 + Ti (1)

S = S + S + E (2) pool i i 1 − i 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 R E{D} or severity less than Rs E{S} are excluded. Tallaksen et al. (1997) and d × × Zhang et al. (2013) recommend that Rd = Rs = 0.3 [34,36]. As with d0, droughts with duration less than R E{D} or severity less than Rs E{S}, the drought day is still regarded as one drought event with d × × D = d1 + d2 + d0. Water 2019, 11, 2390 5 of 20 Water 2019, 11, x 5 of 22 /s) 3 Discharge (m

Figure 2. DefinitionDeﬁnition of drought ev eventsents using run theory.

3.2. MarginalStatistical Distribution analysis of drought characteristics may be complicated by a large number of minor droughtsThe probabilistic that are usually behavior present of drought in the drought severity series. and drought In this durationstudy, a aremore analyzed consistent as follows: approach, firstly, as ninesuggested probability by Madsen distribution and Rosbjerg functions, (1995) widely was used used in [35]. drought It is characterbased onanalysis, predefined are percentages, selected [15,27 R];d Secondly,and Rs, of ninethe mean probability values distributionE{D} and E{S} functions of duration are and fitted severity, for the resp droughtectively, duration i.e., droughts and drought with characteristicsduration less than in theRd × HRB E{D} respectively. or severity less Meanwhile, than Rs × E{S} parameters are excluded. of nine Tallaksen probability et al. distribution (1997) and functionsZhang et al. are (2013) estimated recommend by the that L-moment Rd = Rs = estimation0.3 [34,36]. As [37 ];with Thirdly, d0, droughts the AIC with is usedduration to select less than the appropriateRd × E{D} or marginalseverity less distribution. than Rs × The E{S} smaller, the drought the value day of is AIC still values, regard theed betteras one appropriate drought event marginal with distributionD = d1 + d2 + d fitting;0. Finally, the appropriate marginal distribution that described the probabilistic characteristics of drought severity and drought duration is selected for seven stations based on AIC3.2. Marginal values. Distribution The probabilistic behavior of drought severity and drought duration are analyzed as follows: 3.3. Joint Probability Distribution firstly, nine probability distribution functions, widely used in drought character analysis, are selected [15,27];The Secondly, copula function, nine probability commonly distributi used in hydrologyon functions such are as fitted drought for the and drought flood, can duration couple twoand ordrought three marginalcharacteristics distributions in the to HRB the multivariaterespectively. joint Meanwhile, probability parameters distribution of [28 nine,38]. Inprobability previous studies,distribution Archimedean functions copula are estimated family includes by the aL-moment range of copula estimation functions [37]; and Thirdly, are easy the to AIC be constructed, is used to theselect copula the appropriate family has been marginal widely distribution. used to analyze The thesmaller joint probabilisticthe value of behaviorAIC values, of hydrological the better extremesappropriate [39 ,40marginal]. In this study,distribution 26 copula fitting; functions Finally, were the used appr to analyzeopriate the marginal joint probabilistic distribution behavior that ofdescribed hydrological the probabilistic drought. Sadegh characteristics et al. (2017) of found drough thatt severity only the Tawnand drought and Marshall–Olkin duration is selected copulas canfor allowseven forstations characterizing based on AIC the asymmetric values. dependence structure of precipitation and soil moisture [41]. The Tawn copula performance is better than the Archimedean copula family. Therefore, in this study, we3.3. usedJoint 26Probability copula families Distribution 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 Table2. We have The copula function, commonly used in hydrology such as drought and flood, can couple two selected copula families with simple closed-form mathematical formulation, which is amenable for or three marginal distributions to the multivariate joint probability distribution [28,38]. In previous model inference. studies, Archimedean copula family includes a range of copula functions and are easy to be The copula function is used to construct the drought probability model with the following formula: 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 P(S s, D d) = Cθ(Fs(s), FD(d)) (3) 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 where Cθ(S, D) is the copula function combined with the drought severity Fs(s) and drought duration precipitation and soil moisture [41]. The Tawn copula performance is better than the Archimedean FD(d). copulaTwo family. cases Therefore, of drought in risk this probability study, we shouldused 26 be copula calculated, families as followsto construct (Zhang theet joint al. 2013):distribution of droughtCase 1: severity “and ( )”: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,P(S >whichs D is> amenabled) = 1 F fors(s )modelFD( dinference.) + C (Fs (s), FD(d)) (4) ∩ − − θ The copula function is used to construct the drought probability model with the following formula:Case 2: “or ( )”: ∪ P(S > s D > d) = 1 Cθ(Fs(s), FD(d)) (5) P(S≤≤=∪ s,D d ) C−θ (F (s),F (d )) (3) sD Water 2019, 11, 2390 6 of 20

Table 2. Copula families and their closed-form mathematical description.

Name Mathematical Descriptiona Parameter Range

1(µ) 1(ν) 2 2 R φ− R φ− 2θxy x y Gaussian 1 exp − − dxdyb θ [ 1, 1] √ 2 2(1 θ2) −∞ −∞ 2π 1 θ − ∈ − − (θ2+2) 1 ( ) 1 ( ) Γ 2 2 (θ2+2)/2 R tθ− µ R tθ− ν 2 x 2θ xy+y t 2 2 + − 1 θ [ 1, 1] and θ [0, ] q 1 θ dxdy 1 2 −∞ −∞ Γ(θ /2)πθ 1 θ2 2 ∈ − ∈ ∞ 2 2 − 1 1/θ Clayton max µ θ + ν θ 1, 0 − θ [ 1, ] 0 − − − ∈ − ∞ | (exp( θµ) 1)(exp( θν)) Frank 1 ln + − − − θ R 0 θ 1 exp( θ) 1 − − − ∈ \ h i1/θ Gumbel exp ( ln(µ))θ + ( ln(ν))θ θ [1, ) − − − ∈ ∞ Independence µν µν Ali-Mikhail-Haq (AMH) 1 θ(1 µ)(1 ν) θ [ 1, 1) − − − ∈ − h i1/θ Joe 1 (1 µ)θ + (1 ν)θ (1 µ)θ(1 ν)θ θ [1, ) − − − − − − ∈ ∞ Farlie-Gumbel-Morgenstern µν[1+θ(1 µ)(1 ν)] θ (0, ), θ (1, ) (FGM) − − 1 ∈ ∞ 2 ∈ ∞ Gumbel-Barnett µ + ν 1 + (1 µ)(1 ν)exp[ θln(1 µ)ln(1 ν)] θ [0, 1] − − − − − − ∈ q 1+(θ 1)(µ+ν) [1+(θ 1)(µ+ν)]2 4θ(θ 1)µν Plackett − − − − − θ (0, ) 2(θ 1) ∈ ∞ − θ (1 θ) Cuadras-Auge [min(µ, ν)] (µν) − θ [0, 1] ∈  1 θ 1 θ 1  1 θ 1− θ 1 θ i f  µ 1+−θ µ − ν − ν − , µ ν Raftery − 1 θ − 1 ≤ θ [0, 1)  1 θ −  ν − ν 1 θ µ 1 θ µ 1 θ , i f ν µ ∈ − 1+θ − − − − ≤ ( (1 θ)µν + θmin(µ, ν), i f θ (0, ) − ∈ ∞ Shih-Louis (1 + θ)µν + θ(µ + ν 1)Ψ(µ + ν 1) i f θ ( , 0] − − ∈ −∞ Ψ(a) = 1 i f a 0 and Ψ(a) = 0 i f a < 0 ≥ [u + θ(1 u)]v, i f v u and θ [0, 1] − ≤ ∈ [v + θ(1 v)]u, i f u v and θ [0, 1] Linear-Spearman − ≤ ∈ θ [ 1, 1] (1 + θ)uv, i f u + v < 1 and θ [ 1, 0] ∈ − ∈ − uv + θ(1 u)(1 v), i f u + v 1 and θ [ 1, 0] − − ≥ ∈ − Cubic uv[1 + θ(u 1)(1 v)(2u 1)(2v 1)] θ [ 1, 2] − − − − ∈ − h 1/θ 1/θ i θ Burr u + v 1 + (1 u)− + (1 v)− 1 − θ (0, ) − − − − ∈ ∞ [exp( θu) 1][exp( θv) 1] Nelsen 1 + − − − − θ (0, ) −θ log 1 exp( θ) 1 − − ∈ ∞ n θ θo 1/θ Galambos uv exp ( ln(u))− + ( ln(v))− − θ [0, ) − − ∈ ∞ h 2 i Marshall-Olkin min u(1 θ1)v, uv(1 θ ) θ , θ [0, ) − − 1 2 ∈ ∞ n θ θ o1/θ2 Fischer-Hinzmann θ [min(u, v)] 2 + (1 θ )[uv] 2 θ1 [0, 1), θ2 R 1 − 1 ∈ ∈  " #1/θ   θ θ 1/θ2 1   θ1 2 θ1 2  Roch-Alegre exp1 (((1 ln(u)) 1) + ((1 ln(v)) 1) ) + 1  θ1 [0, ), θ2 [1, ]  − − − − −  ∈ ∞ ∈ ∞

h 1/θ 1/θ iθ1 Fischer-Kock uv 1 + θ (1 u 1 )(1 v 1 ) θ1 [1, ), θ2 [ 1, 1] 2 − − ∈ ∞ ∈ − 1/θ ( 1/θ )− 1 θ2 θ2 2 BB1 1 + u θ1 1 + v θ1 1 θ1 (1, ), θ2 (1, ) − − − − ∈ ∞ ∈ ∞ ( ) 1/θ 1/θ1 θ1 θ1 θ1θ2 θ1θ2 2 BB5 exp ( ln(u)) + ( ln(v)) (( ln))− + ( ln (v)− )− θ1 [1, ), θ2 (0, ) − − − − − − ∈ ∞ ∈ ∞ h i1/θ (1 θ ) (1 θ ) θ3 θ3 3 Tawn exp (ln(u 1 )) + (ln(v 2 )) ( θ ln(u)) + ( θ ln(v)) θ1, θ2 [0, 1], θ3 [1, ] − − − − 1 − 2 ∈ ∈ ∞

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 [43–45], including hydrology [46–48], 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 Water 2019, 11, 2390 7 of 20

p(θ)p Y˜ θ p θ Y˜ = | (6) p Y˜ in which p(θ) and p θ Y˜ signify prior and posterior distribution of parameters, respectively. p Y˜ θ R | v θ Y˜ denotes likelihood function, and p Y˜ p Y˜ θ dθ is coined evidence. Evidence, being a e | 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 p θ Y˜ p(θ)p Y˜ θ (7) ∝ | 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]:

Yn 1 1 2 2 v θ Y˜ = exp σ˜ [y˜i yi(θ)] (8) √ 2 −2 − i=1 2πσ˜ where σ˜ is an estimate of standard deviation of measurement error. For simplicity and numerical stability, this equation is usually logarithmically transformed to

2 Xn n 1 2 l θ Y˜ = ln(2π) σ˜ − [y˜i yi(θ)] (9) 2 − 2 − i=1

Given the underlying assumptions about error residuals, σ˜ can be estimated as

n P 2 [y˜i yi(θ)] i=1 − σ˜ 2 = (10) n We can, then, further simplify Equation (9) to

n P 2 [y˜i yi(θ)] n n n i=1 − l θ Y˜ = ln(2π) ln (11) − 2 − 2 − 2 n For comparison purposes, we can conveniently remove the constants and present log-likelihood function as,  n   P 2   [y˜i yi(θ)]  n  i=1 −  l θ Y˜ ˜ ln  (12)   − − 2  n    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 Water 2019, 11, 2390 8 of 20 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]

AIC = 2Q 2l (13) − 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

 n   P 2   [y˜ y(θ)]   i=1 −  AIC = 2Q + n ln  2CS (14)    n  −  

n P 2 [y˜i yi(θ)] 2 i=1 − given the Gaussian assumption of error residuals, σ˜ = n , and a constant CS. A lower AIC value associates with a better model ﬁt.

4. Results

4.1. Basic Statistical Properties of the Hydrological Drought It can be observed from Table3 that the frequency of drought (about 190) in the upper Huai River is higher than that in the middle Huai River (about 154). However, drought duration (about 22 days) in the upper Huai River is shorter than that in the middle Huai River (about 28 days) which lead to the maximum duration of drought in the upper reaches (198 days) far less than that in the middle reaches (246 days). The frequency of drought in the Shiguanhe River is the largest across the three tributaries. Table3 shows significant relations between drought severity and drought duration in the Huai River. The absolute Pearson-statistics of drought severity and drought duration in the Huai River are observed >0.67 and the p-values are far <0.05, which indicates that there are significant statistical correlations between drought severity and drought duration. However, the correlation coefficient of D and S is the lowest in the Shiguan River. Pishihang irrigation district, with a total designed irrigation area of 7987 square kilometers, is one of the three largest irrigation districts in China. The drought duration of normal dry years cannot lead to high drought intensity, which is caused by the significant increase in irrigation of rivers, lakes, and large reservoirs. This is the main reason for the low correlation coefficient between drought severity and drought duration in Jiangjiaji station. The drought duration in the Huai River basin has no significant trends, and the drought intensity in the middle Huai River has a predominantly decreasing tendency, but the decreasing trend is not significant at the 5% level. Water 2019, 11, x 11 of 22

correlations between drought severity and drought duration. However, the correlation coefficient of D and S is the lowest in the Shiguan River. Pishihang irrigation district, with a total designed irrigation area of 7987 square kilometers, is one of the three largest irrigation districts in China. The drought duration of normal dry years cannot lead to high drought intensity, which is caused by the significant increase in irrigation of rivers, lakes, and large reservoirs. This is the main reason for the low correlation coefficient between drought severity and drought duration in Jiangjiaji station. The

Waterdrought2019, 11duration, 2390 in the Huai River basin has no significant trends, and the drought intensity 9in of the 20 middle Huai River has a predominantly decreasing tendency, but the decreasing trend is not significant at the 5% level. Table 3. Basic drought statistical properties of drought-duration (D) and drought-severity (S) at the sevenTable stations 3. Basic ofdrought the Huaihe statistical River properti Basin. es of drought-duration (D) and drought-severity (S) at the seven stations of the Huaihe River Basin. Stations Times D Maximum D S Correlation of D and S Trend of D Trend of S XixianStations 191 Times 22 D Maximum 189 D 323 S Correlation 0.92 of D and S Trend 0.01of D Trend of 0.3 S WangjiabaXixian 190191 2222 207 189 702 323 0.92 0.84 0.01 0.01 0.3 0.50 LutaiziWangjiaba 165 190 2622 245 207 2095 702 0.84 0.83 0.010.03 0.50 1.49 − − BengbuLutaizi 143165 2926 247245 22682095 0.83 0.90 −0.03 0.00 −1.49 1.17 − BantaiBengbu 172143 2429 197247 1102268 0.90 0.89 0.00 0.01 −1.17 0.08 JiangjiajiBantai 178172 2324 242 197 94 110 0.89 0.67 0.01 0.00 0.08 0.03 FuyangJiangjiaji 159178 2523 250 242 228 94 0.67 0.80 0.000.04 0.03 0.13 Fuyang 159 25 250 228 0.80 −0.04− −0.13−

TheThe resultsresults ofof droughtdrought durationduration are are shown shown in in FigureFigure3 .3. The The bar bar represents represents the the drought drought event event and and thethe length length of of the the bar bar indicates indicates the the drought drought duration. duration. While While the the Y-axis Y-axis represents represents the beginningthe beginning and endand ofend the of drought. the drought. The hydrologicalThe hydrological drought drought occurred occurred mostly mostly in the in 1st–150ththe 1st–150th day day and and 270th–365th 270th–365th day day of aof year a year in the in the Huai Huai River River basin. basin. That That means means that that drought drought appeared appeared mainly mainly from from October October to May. to May. The jointingThe jointing and heading and heading stage ofstage winter of wheatwinter iswheat during is Aprilduring and April May and in the May Huai in Riverthe Huai basin. River Therefore, basin. theTherefore, water requirements the water requirements of winter wheat of winter are mostly wheat during are mostly April andduring May; April irrigation and May; of winter irrigation wheat of inwinter spring wheat consumed in spring large consumed amounts oflarge water amounts resources. of water While resources. drought occurringWhile drought in spring occurring is one ofin thespring major is naturalone of disasters,the major thenatural proportion disasters, of water the proportion resources andof water precipitation resources during and March–Juneprecipitation isduring less than March–June water supply is less andthan demandwater supply contradictory and demand is increasingly contradictory prominent is increasingly [18]. prominent Hydrological [18]. droughtHydrological also shows drought obvious also decadalshows obvious changes, decadal the duration changes, of drought the duration from 1975 of drought to 1985 isfrom the longest,1975 to accounting1985 is the longest, for a quarter accounting of the for total a quarter duration of the of drought. total duration In addition, of drought. in the In 1990saddition, and in early the 1990s 21st century,and early a drought21st century, occurred a drought frequently. occurred What’s freque more,ntly. drought What’s duration more, drought accurately duration reﬂects accurately historical drought,reflects historical such as 1973, drought, 1978, such 1992, as 1994, 1973, and 1978, so 1992, on. 1994, and so on.

Figure 3. Hydrological drought duration in the Huai River Basin.

China’s urbanization level increased steadily after 2000 [54], while the level of rural development showed a declining trend at ﬁrst and then a rising trend. Therefore, Table4 and Figure4 show the variation of land-use of the Huai River Basin from 2000 to 2015. Land cover change analysis between the periods of 1995 and 2015 has shown that the artiﬁcial surfaces area has increased from 11.73% to 12.91%, grassland from 3.20% to 3.24%, and water bodies from 2.71% to 2.89%, while forest area has Water 2019, 11, x 12 of 22

Figure 3. Hydrological drought duration in the Huai River Basin.

China’s urbanization level increased steadily after 2000 [54], while the level of rural development showed a declining trend at first and then a rising trend. Therefore, Table 4 and Figure 4 show the variation of land-use of the Huai River Basin from 2000 to 2015. Land cover change analysis between Waterthe periods2019, 11, 2390of 1995 and 2015 has shown that the artificial surfaces area has increased from 11.73%10 of 20to 12.91%, grassland from 3.20% to 3.24%, and water bodies from 2.71% to 2.89%, while forest area has decreaseddecreased fromfrom 10.86%10.86% toto 10.83%,10.83%, andand croplandcropland fromfrom 71.43%71.43% toto 70.14%.70.14%. TheThe areaarea ofof grasslandgrassland andand forestlandforestland had had little little change change in in HRB. HRB. However, However, from from 2000 2000 to to 2015, 2015, this this can can be be most most obviously obviously observed observed in 2 farmland,in farmland, with with 1400 1400 km km2 of of farmland farmland converted converted Forestland Forestland and and Artificial Artificial surfaces surfaces (accounting(accounting forfor 1.1%1.1% totaltotal HRBHRB basin basin area), area), mainly mainly transforming transforming to artificial to artificial surfaces surfaces (urban, industrial(urban, industrial land, and residentialland, and land).residential Fuyang land). station, Fuyang belonging station, to belonging the Shaying to river, the Shaying has the maximumriver, has farmlandthe maximum transforming farmland to artificialtransforming surfaces to artificial (Figure 4surfaces), This may(Figure be 4), the This cause may of be drought the cause duration of drought increasing duration in theincreasing Shaying in 2 river.the Shaying The area river. of farmland The area transformedof farmland totransformed forestland isto maximumforestland (56is maximum km2), but the(56 km area), of but forestland the area 2 transformedof forestland to transformed artificial surfaces to artificial is minimum surfaces (55 kmis minimum2) from 2005 (55 to km 2010.) from Therefore, 2005 to drought 2010. Therefore, duration fromdrought 2005 duration to 2010 isfrom far 2005 less thanto 2010 that is fromfar less 2010 than to that 2015. from 2010 to 2015.

TableTable 4.4. DynamicDynamic variationvariation ofof land-useland-use ofof thethe HuaiHuai RiverRiver BasinBasin fromfrom2000 2000to to 2015 2015 (km (km22).).

Land LandUse Change Use Change 2000–2005 2000–2005 2005–2010 2005–2010 2010–20152010–2015 2000–20152000–2015 Grassland-Farmland 29 26 7 60 Grassland-Farmland 29 26 7 60 Paddy field-Dry farm 14 0 0 14 Paddy field-Dry farm 14 0 0 14 Dry farm-PaddyDry farm-Paddy field field0 016 16 1818 34 34 Farmland-ForestlandFarmland-Forestland 41 41 56 56 10 10 106 106 ForestForest land-Artificial land-Artificial surfaces surfaces 133 133 55 55 84 84 268 268 Farmland-ArtificialFarmland-Artificial surfaces surfaces 39 39 284 284 636 636 1294 1294

Figure 4. Spatial transformation variation map of land-use type of the Huai River Basin.

4.2. Probability of Hydrological Drought in HRB The parameters of the nine probability distributions were estimated by the L-moment technique and Optimal ﬁtting of probability distributions were selected with the NLogL (Negative of the log WaterWater 20192019,, 1111,, xx 1313 ofof 2222

FigureFigure 4.4. SpatialSpatial transformationtransformation variationvariation mapmap ofof land-useland-use typetype ofof thethe HuaiHuai RiverRiver Basin.Basin.

4.2.4.2. ProbabilityProbability ofof HydrologicalHydrological DroughtDrought inin HRBHRB Water 2019, 11, 2390 11 of 20 TheThe parametersparameters ofof thethe ninenine probabilityprobability distributionsdistributions werewere estimatedestimated byby thethe L-momentL-moment techniquetechnique andand OptimalOptimal fittingfitting ofof probabilityprobability distributionsdistributions werewere selectedselected withwith thethe NLogLNLogL (Negative(Negative ofof thethe loglog likelihood),likelihood), BIC,BIC, AIC,AIC, AIC, andand and AICcAICc AICc (AIC(AIC (AIC withwith with aa a correctioncorrection correction forfor for finitefinite ﬁnite samplesample sample sizes)sizes) sizes) (( FigureFigure ( Figure 5;5;5 ; Figure Figure Figure6 6).6).). TheThe result result ofof the the best best distribution distribution with with NLogL, NLogL, BIC, BIC, AIC, AIC, and and AICc AICc is is the the same same in in seven seven hydrological hydrological stations.stations. ForFor For example,example, thethe valuevalue of of goodness-of-ﬁtgoodness-of-fitgoodness-of-fit based based onon AICAICAIC forforfor nineninenine probabilityprobabilityprobability distributiondistributiondistribution functionsfunctions in in XixianXixian stationstation areare GeneralizedGeneralizedGeneralized ParetoPareParetoto <<< GeneralizedGeneralized ExtremeExtreme ValueValue <<< LoglogisticLoglogistic << LognormalLognormal << GammaGammaGamma << < WeibullWeibullWeibull <<

FigureFigure 5.5. TheTheThe valuevalue value ofof goodness-of-fitgoodness-of-fit goodness-of-ﬁt basedbased onon AIC AIC fo forforr nine nine probabilityprobability distributiondistribution functionsfunctions describingdescribing the the statistical statistical propertiesproperties ofof drought-durationdroudrought-durationght-duration inin thethe HuaiheHuaihe riverriverriver basin.basin.basin.

Figure 6. The value of goodness-of-ﬁt based on AIC for nine probability distribution functions describing the statistical properties of drought-severity in Huaihe river basin. Water 2019, 11, x 14 of 22 Water 2019, 11, x 14 of 22

Figure 6. The value of goodness-of-fit based on AIC for nine probability distribution functions Water Figure2019, 11 ,6. 2390 The value of goodness-of-fit based on AIC for nine probability distribution functions12 of 20 describing the statistical properties of drought-severity in Huaihe river basin. describing the statistical properties of drought-severity in Huaihe river basin.

FigureFiguresss 77 andand8 8also also demonstrates demonstrates the thethe ideal idealideal performance performance performance of of of Generalized Generalized Generalized Extreme Extreme Extreme Value ValueValue and andand Generalized Pareto Pareto distribution distribution in in terms terms of of descri descriptionption of of probability probability properties properties of of drought drought severity severity and drought duration. Although Although the the lognormal lognormal and and loglogistic loglogistic distribution distribution functions functions could could give give a description of the probabilistic behavior of the drought severity and drought duration. It should also be n notedoted that Generalized Pareto Pareto (GP) (GP) and Generalized Extreme Extreme Value Value ( (GEV)(GEV) had three parameters and we wererere widely widely usedused inin hydrometeorologicalhydrometeorological extremeextremeextreme value valuevalue analysis analysisanalysis [ [17]17[17]]... AsAsAs a aa result resultresult ofofof this,this,this, thethe GP GP and GEV GEV distribution distribution were were usually usually considered considered as as appropriate appropriate distribution distributionribution in in hydrological hydrological hydrological drought drought character analysis. analysis. Table Table 55 listslists lists thethe the estimatedestimated estimated GPGP GP andand and GEVGEV GEV distrdistr distributionibutionibution parameters.parameters. parameters.

Figure 7. Frequency distribution of drought severity. Figure 7. FrequencyFrequency distribution of drought severity severity..

Figure 8. Frequency distribution of drought duration. Figure 8. Frequency distribution of drought duration duration..

Table 65. and Parameters Figure9 estimated show the by drought L-Moment duration for the inGeneralized a di fferent Pareto return and period the Generalized which is calculatedExtreme by Table 5. Parameters estimated by L-Moment for the Generalized Pareto and the Generalized Extreme GeneralizedValue functions Pareto. in It terms can be of seen drought in Figure duration3, and and Tables drought4 and severity.5 that the drought duration is changing Value functions in terms of drought duration and drought severity. with different return periods in the middle reaches and tributary of the HRB. Drought duration has no Drought Duration Drought Severity significant differences for return periodsDrought of Duration<10 years. DroughtDrought duration Severity of return periods <30 years Stations Generalized Pareto Generalized Extreme Value is the longest in the middleStations reaches Generalized of the HBR Pareto and isGeneralized the shortest Extreme in the Value upper reaches of the HRB. k    However, the trends of drought durationk at seven  stations are significantly different due to the increase Xixian 0.48 8.44 7.00 −0.55 3.42 15.56 in the return period. ForXixian example, 0.48 Fuyang, 8.44 a tributary7.00 −0.55 of the north3.42 bank15.56 of the Huai River, has an Wangjiaba 0.57 7.85 7.00 −0.62 9.71 34.73 Wangjiaba 0.57 7.85 7.00 −0.62 9.71 34.73 obviously increasing trend.Lutaizi The change0.79 of7.12 drought 7.00 severity−0.57 is similar25.08 to drought89.98 duration. (Figures5 Lutaizi 0.79 7.12 7.00 −0.57 25.08 89.98 and9). Bengbu 0.60 10.49 7.00 −0.44 28.82 77.89 Bengbu 0.60 10.49 7.00 −0.44 28.82 77.89 Water 2019, 11, 2390 13 of 20

Water 2019, 11, x 15 of 22

Table 5. Parameters estimated by L-Moment for the Generalized Pareto and the Generalized Extreme Bantai 0.61 8.00 7.00 −0.50 1.61 4.76 Value functions in terms of drought duration and drought severity. Jiangjiaji 0.51 8.62 7.00 −0.55 1.75 4.57 Fuyang Drought 0.79 6.46 Duration 7.00 −0.39 Drought3.85 Severity 9.47 Table 6 and Figure 9 show the drought duration in a different return period which is calculated Stations Generalized Pareto Generalized Extreme Value by Generalized Pareto. It can be seen in Figure 3, and Tables 4 and 5 that the drought duration is k k changing with different return periods inσ the middle θ reaches and tributaryσ of µthe HRB. Drought Xixian 0.48 8.44 7.00 0.55 3.42 15.56 duration has no significant differences for return periods −of <10 years. Drought duration of return Wangjiaba 0.57 7.85 7.00 0.62 9.71 34.73 periods <30 years is the longest in the middle reaches of the− HBR and is the shortest in the upper Lutaizi 0.79 7.12 7.00 0.57 25.08 89.98 − reaches of the HRB.Bengbu However, 0.60 the trends 10.49 of drou 7.00ght duration0.44 at seven 28.82 stations 77.89 are significantly − different due to theBantai increase in 0.61the return 8.00 period. 7.00For example,0.50 Fuyang, 1.61 a tributary 4.76 of the north bank − of the Huai River,Jiangjiaji has an obviousl 0.51y increasing 8.62 trend. 7.00 The change0.55 of 1.75drought severity 4.57 is similar to − Fuyang 0.79 6.46 7.00 0.39 3.85 9.47 drought duration. (Figures 5 and 9). −

Figure 9.9.Return Return periods periods of droughtof drought duration duration (A) and (A drought-severity) and drought-severity (B). XX: Xixian;(B). XX: WJB: Xixian; Wangjiaba; WJB: LTZ:Wangjiaba; Lutaizi; LTZ: BB: Bengbu;Lutaizi; BB: BT: Bengbu; Bantai; JJJ: BT: Jiangjiaji; Bantai; JJJ: FY: Jiangjiaji; Fuyang. FY: Fuyang. Table 6. Return periods of drought duration. Table 6. Return periods of drought duration. Return Period Xixian Wangjiaba Lutaizi Bengbu Bantai Jiangjiaji Fuyang Return Period Xixian Wangjiaba Lutaizi Bengbu Bantai Jiangjiaji Fuyang 55 2727 2828 3838 35 35 29 29 29 2928 28 1010 4242 4444 5858 59 59 47 47 45 4549 49 2020 6363 6969 8181 94 94 76 76 68 6886 86 3030 7979 8989 9797 123 123 99 99 86 86119 119 5050 104104 121121 118118 171 171 137 137 115 115179 179 7070 124124 147147 134134 211 211 170 170 138 138233 233 100100 149149 182182 152152 264 264 213 213 168 168310 310

4.3. Joint Probabilistic Behaviors of Hydrological Droughts Across thethe HRBHRB The jointjoint distributionsdistributions of of drought drought severity severity and and drought drought duration duration at at all all the the stations stations are are calculated calculated by copulas.by copulas. In total,In total, the 26the candidate 26 candidate copulas copulas [41] were [41] usedwere forused the for joint the distribution joint distribution of drought of drought severity andseverity drought and durationdrought induration the HRB. in Thethe parametersHRB. The parameters of the 26 copula of the distributions 26 copula distributions were estimated were by theestimated Markov by Chain the Markov Monte CarloChain (MCMC)Monte Carlo simulation (MCMC) within simulation a Bayesian with framework.in a Bayesian It canframework. be seen inIt Figurecan be 10seen that in the Figure best copula10 that functionsthe best copula were selected functions using were the selected AIC. It isusing worthy the to AIC. note It that is worthy the Tawn to copulanote that shows the Tawn the maximum copula shows value the of AIC.maximum Therefore, value theof AIC. Twan Therefore, copula function the Twan was copula selected function as the appropriatewas selected copula as the appropriate for drought severitycopula for and drought drought severity duration and at drought the Wangjiaba, duration Bengbu, at the Wangjiaba, Bantai and JiangjiajiBengbu, Bantai stations. and Joe Jiangjiaji copula exhibitsstations. minimum Joe copula value exhibits of AIC minimum in Xixian, value Lutaizi, of AIC and in Fuyang.Xixian, Lutaizi, Table7 showsand Fuyang. the parameters Table 7 shows of Twan the and parameters Joe copulas of whichTwan and are theJoe appropriatecopulas which copulas are the across appropriate the HRB usingcopulas MCMC. across the HRB using MCMC. Water 2019, 11, 2390 14 of 20 WaterWater 2019 2019, 11, 11, x, x 1616 of of 22 22

Figure 10. The value of goodness-of ﬁt based on AIC in the Tarim River Basin. FigureFigure 10. 10. The The value value of of goodness goodness-of-of fit fit based based on on AIC AIC in in the the Tarim Tarim River River Basin Basin.. Table 7. Estimated parameters of the best copula function. TableTable 7. 7. E Estimatedstimated parameters parameters of of the the best best copula copula function function.. Station Copula Fuction θ1 θ2 θ3 Station Copula Fuction θ1 θ2 θ3 XixianStation Copula Joe Fuction 9.43θ1 θ2 — θ3 — Xixian Joe 9.43 — — WangjiabaXixian TawnJoe 9.43 0.90 — 1.00 — 6.85 Wangjiaba Tawn 0.90 1.00 6.85 LutaiziWangjiaba Tawn Joe 0.90 8.57 1.00 — 6.85 — Lutaizi Joe 8.57 — — BengbuLutaizi TawnJoe 8.57 0.85 — 1.00 — 4.51 Bengbu Tawn 0.85 1.00 4.51 BantaiBengbu TawnTawn 0.85 0.85 1.00 1.00 4.51 5.14 Bantai Tawn 0.85 1.00 5.14 JiangjiajiBantai TawnTawn 0.85 0.72 1.00 1.00 5.14 5.60 Jiangjiaji Tawn 0.72 1.00 5.60 FuyangJiangjiaji Tawn Joe 0.72 4.61 1.00 — 5.60 — FuyangFuyang JoeJoe 4.614.61 —— ——

TheThe best best marginal marginal distribution distribution functionsfunction functionss are are the the GeneralizedGeneralized Generalized ParetoPa Paretoreto and and GeneralizedGeneralized Generalized Extreme Extreme ValueValue functions,function functions,s, whilewhile while parametersparameters parameters were were estimatedestimated estimated by by the the L-momentL L-moment-moment technique technique (Table( Table(Table4 4). 4).). FigureFigure Figure 1111 11 showsshowshowss the the joint joint probabilistic probabilistic behavior behavior of of the the drought drough tseverity severity and and drought drought duration duration at at the the Wangjiaba Wangjiaba station.stationstation.. Th The Thee joint joint probabi probability probabilitylity of of drought droughts droughtss at at other other station stations stationss was was calculated calculated and and results results at at other other stationsstation stationss areare similarsimilar similar toto to the the the Wangjiaba Wan Wangjiabagjiaba station. station station. It. canIt It can can be be seenbe seen seen in Figurein in Figure Figure 11 that 11 11 that thethat probability the the probability probability was relativelywas was relatively relatively small whensmallsmall when long when drought long long drought drought duration duration duration with a with smallwith a a magnitudesmall small magnitude magnitude of drought of of drought drought severity severity severity occurred oc occurredcurred concurrently concurrently concurrently at one station.atat one one stati station. Theon probability. T Thehe probability probability is small is is whensmall small awhen when large a a magnitudelarge large magnitude magnitude of drought of of drought drought severity severity severity occurred occurred occurred and a and shortand a a durationshortshort duration duration at one at station,at one one statio station, however,n, h hoowever, thewever, probability the the probability probability is progressively is is progressivel progre higherssivelyy when higher higher the when droughtwhen the the durationdrought drought anddurationduration drought and and severitydrought drought both severity severity increased. both both incre increased.ased.

Figure 11. Cont. Water 2019, 11, x 17 of 22 WaterWater 20192019,, 1111,, 2390x 1715 of of 2022

FigureFigure 11. 11.Joe Joe Copula’s Copula’s JointJoint returnreturn periodperiod ( A)) and and the the current current return return period period (B (B) in) in Wangjiaba Wangjiaba station. station. Figure 11. Joe Copula’s Joint return period (A) and the current return period (B) in Wangjiaba station. Figure 12 shows concurrence return periods and joint return periods with different diﬀerent drought severityFigure and 12drought shows duration concurrence at hydrological return periods stations and in joint different diﬀerent return groups periods of returnwith different periods. It drought can be seenseverity that and concurrenceconcurrence drought duration returnreturn periods periods at hydrological were were larger larger stations than than the inthedesigned different designed returngroups return period of period return (Figure (Figure.12B), periods. 12B), It and can and the be thejointseen joint returnthat concurrencereturn periods periods is smallerreturn is smallerperiods than the thanwere designed largerthe de return thansigned the period return designed (Figure period return 12 A).(Figure.12A). period Changes (Figure.12B), in concurrenceChanges and in concurrencereturnthe joint periods return return and periods jointperiods return is and smaller periods joint returnthan of drought theperiods de severitysigned of drought andreturn drought severity period duration and (Figure.12A). drought in the duration mainstream Changes in the ofin mainstreamtheconcurrence HRB are largelyofreturn the HRB inperiods the are tributary andlargely joint ofin thereturn the HRB. tributary periods However, of of the drought the HRB. current severityHowever, return and periodthe drought current of drought duration return severity period in the ofandmainstream drought drought severity of duration the HRBand in droughtare the largely mainstream duration in the of intributary the the Huai mainstream of River the HRB. is of smaller the However, Huai than River thatthe is incurrent smaller the tributary return than thatperiod of the in theHuaiof drought tributary River severity (Figure of the 12and HuaiB). drought With River return duration (Figure.12B). periods in the of mainstreamWith<2 years, return the of periods concurrentthe Huai of River <2 occurrence years, is smaller the probability thanconcurrent that ofin occurrencehydrologicalthe tributary probability droughtsof the Huai of is higherhydrological River at (Figure.12B). the droughts Jiangjiaji andisWith higher Fuyang. return at the What’speriods Jiangjiaji more,of and<2 the Fuyang.years, joint the return What’s concurrent periods more, theofoccurrence droughts joint return probability in periods the tributary of droughtshydrological of the in Huai the droughts Rivertributary are is ofhigher shorter the Huai at than the River Jiangjiaji those are along shorter and theFuyang. than mainstream those What’s along ofmore, the mainstreamHuaithe joint River, return implyingof theperiods Huai a of lower River, droughts frequency implying in the ofa tributary lower hydrological frequency of the droughtsHuai of Riverhydrological at are the shorter Xixian, droughts than Wangjiaba, those at the along Lutaizi,Xixian, the Wangjiaba,andmainstream Bengbu Lutaizi, stationsof the Huai and when BengbuRiver, compared implying stations to other whena lower stations compared frequency (Figure to of 12other hydrologicalA). However,stations (Figure.12A). droughts the concurrence at theHowever, Xixian, return theperiodsWangjiaba, concurrence of droughts Lutaizi, return and at periods the Bengbu Bantai, of stations droughts Jiangjiaji, when at and the compared FuyangBantai, Jiangjiaji, station to other are andstations larger Fuyang in(Figure.12A). the station tributary are However, larger of HRB in thethanthe concurrencetributary that along of the returnHRB mainstream thanperiods that of along HRB,droughts implyingthe atmainstream the aBa lowerntai, ofJiangjiaji, frequency HRB, implyingand of hydrological Fuyang a lower station droughts frequency are larger in the ofin hydrologicalmainstreamthe tributary ofdroughts of HRB. HRB inthan the mainstreamthat along the of HRB.mainstream of HRB, implying a lower frequency of hydrological droughts in the mainstream of HRB.

Figure 12. DifferentDiﬀerent frequency combinations of drought du durationration and drought severity return period andFigure with 12. Joint Different return frequency period ( A combinations) and the current of drought return period duration (B). and 1: Xixian; Xixian; drought 2: 2: Wangjiaba;severity Wangjiaba; return 3: 3: Lutaizi; Lutaizi; period 4:and Bengbu; with Joint 5: Bantai; Bantai; return 6: 6: period Jiangjiaji; Jiangjiaji; (A) 7:and 7: Fuyang. Fuyang. the current return period (B). 1: Xixian; 2: Wangjiaba; 3: Lutaizi; 4: Bengbu; 5: Bantai; 6: Jiangjiaji; 7: Fuyang. 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 Water 2019, 11, 2390 16 of 20 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. Figure1 shows the spatial distribution of irrigated areas in the HRB. There are irrigated areas with the area (2230 km2) in the upper reaches of HRB, which is lower than the irrigated area (2.2 104 km2) 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 (2.2 104 km2) 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 km2) in the Hongru river is less than the irrigation area (3867 km2) 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 16.4 104 to × 19.2 104 km2. Besides, there were more than 5700 water reservoirs built with a total water capacity of × 2.72 1010 m3 [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. Water 2019, 11, x 19 of 22 Water 2019, 11, 2390 17 of 20 drought duration is basically unchanged, and the drought intensity in middle HRB shows a decreasing trend, but the decreasing trend is not significant. Notably, hydrologicalhydrological droughts droughts occurred occurred frequently frequently during during the the period period of of 1975–1985, 1975–1985, especially especially in winterin winter and and spring, spring, with with more more than athan quarter a quarter of the droughtof the drought events occurring events occurring in these seasons. in these Droughts seasons. occurredDroughts frequently occurred infrequently the 1990s andin the early 1990s 21st and century. early Figure 21st century.13 shows Figure that drought-a 13 showsffected that cropdrought- areas andaffected drought-destroyed crop areas and drought-destroyed crop areas have a significantly crop areas have increasing a significantly trend from increasing 1981 to 2001.trend Especially,from 1981 theto 2001. drought-a Especially,ffected the areas drought-affected were 27.33 10 areas4 km were2 and 27.33 27.24 × 10104 km4 km2 and2 respectively, 27.24 × 104 whilekm2 respectively, the ratio of × × thewhile disaster the ratio area of to the the disaster drought-a areaff toected the areadrought-affected was 67.7% and area 63.4% was in67.7% 1994 and and 63.4% 2001, respectively.in 1994 and 2001, The annualrespectively. distribution The annual of precipitation distribution in theof precipitation HRB is extremely in the uneven, HRB is with extremely spring precipitationuneven, with amount spring accountingprecipitation for amount only 19% accounting of the annual for only precipitation 19% of the amount annual whenprecipitation the winter amount wheat when demand the winter peaks andwheat is andemand important peaks period and of growth.is an important Spring precipitation period of decreasedgrowth. Spring significantly precipitation in the 1990s decreased [29,56], whichsignificantly is largely in the the 1990s main reason[29,56], for which the drought-ais largely fftheected main areas reason in the for 1990s. the drought-affected However, the increasing areas in trendthe 1990s. of hydrological However, the droughts increasing had nottrend cause of hydr drought-aologicalffected droughts crop had significantly not cause increase drought-affected area after 2010.crop significantly The main reason increase is that area the after Chinese 2010. governmentThe main reason required is that strengthening the Chinese ofgovernment the construction required of waterstrengthening conservancy of the facilities. construction The drought of water resistance conserva capacityncy facilities. of HRB The has drought been significantly resistance capacity improved, of eHRBffectively has been reducing significantly the impact improved of hydrological, effectively drought reducing on the crops. impact of hydrological drought on crops.

Figure 13. AffectedAﬀected area and disaster area of cropcrop from 1981 toto 20142014 inin thethe AnhuiAnhui province.province.

InIn summary,summary, somesome interestinginteresting andand importantimportant conclusionsconclusions cancan bebedrawn drawn as as follows: follows:

1.1. TheThe frequency ofof hydrologicalhydrological droughts droughts in in the the upper upper Huai Huai River River is moreis more than than in thein the middle middle of the of theHuai Huai River River Basin, Basin, while while the duration the duration of hydrological of hydrological drought drought is justthe is opposite.just the opposite. The drought The droughtfrequency frequency and drought and durationdrought ofduration the three of majorthe three tributaries major aretributaries between are the between upper and the middle upper andof the middle mainstream. of the mainstream. What’s more, What’s the drought more, the frequency drought of frequency the Shiguan of the River Shiguan on the River south on bank the southis higher bank than is higher that of than the other that of two the tributaries. other two tributaries. 2. GeneralizedGeneralized Pareto Pareto distribution distribution is is the right distribution function with the lowest of AIC in the studystudy ofof drought drought duration duration over over the Huaithe RiverHuai Basin.River TheBasin. Generalized The Generalized Extreme Value Extreme distribution Value distributionsatisfactorily satisfactorily described the described probabilistic the probabilistic behavior of behavior the drought of the severity. drought Joe severity. copula Joe and copula Tawn andcopula Tawn were copula the right were choice the right and choice used in and this used current in this study. current Given study. the return Given period the return of droughts period ofless droughts than 30 years,less than the 30 day years, of drought the day duration of drought in the duration upper Huai in the River upper is theHuai maximum River is andthe maximumis the minimum and is in the the minimum middle Huai in the river. middle However, Huai theriver. drought However, duration the drought in Fuyang duration station in is Fuyangincreasing station based is onincreasing the increase based of theon the return increase period. of Thethe return ratio of period. drought The intensity ratio of to drought flow is intensitynegatively to correlatedflow is negatively with basin correlated area. with basin area. 3. TheThe frequency of the Joint return period of drought severity and drought duration in the mainstreammainstream of thethe HuaiHuai RiverRiver is is higher higher than than the th tributarye tributary of of the the Huai Huai River. River. The The frequency frequency of the of theconcurrent concurrent return return period period of drought of drought severity severity and droughtand drought duration duration in the in mainstream the mainstream of the of Huai the HuaiRiver River is lower is lower than that than of that the tributaryof the tributary of the Huai of the River Huai Basin. River The Basin. drought The drought resistance resistance capacity capacityof HRB has of HRB been has significantly been signific improved,antly improved, effectively effectively reducing reducing the impact the of impact hydrological of hydrological drought droughton crops on after crops 2010. after 2010. Water 2019, 11, 2390 18 of 20

Author Contributions: P.S., Q.Z., R.Y. and Q.W. conceived and designed the experiments; P.S., Q.Z. and R.Y. performed the experiments; P.S., Q.Z. and R.Y. analyzed the data; P.S., Q.Z., R.Y., and Q.W. contributed analysis tools; P.S., Q.Z., R.Y. and Q.W. wrote the paper. Funding: This work is financially supported by China National Key R&D Program (Grant No.: 2019YFA0606900), the National Natural Science Foundation of China (No. 41601023, No. 41771536), National Science Foundation for Distinguished Young Scholars of China (Grant No.: 51425903), State Key Laboratory of Earth Surface Processes and Resource Ecology (Grant No. 2017-KF-04), Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and Hydropower Research) (Grant No. IWHR-SKL-201720) and Natural Science Foundation of Anhui province (Grant No.: 1808085QD117). Conflicts of Interest: The authors declare no conflict of interest.

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