atmosphere

Article Regional Frequency Analysis of Precipitation Extremes and Its Spatio-Temporal Patterns in the Hanjiang River Basin,

Wenlong Hao 1 , Zhenchun Hao 1,*, Feifei Yuan 1 , Qin Ju 1 and Jie Hao 2

1 College of Hydrology and Water Resources, Hohai University, 210098, China; [email protected] (W.H.); [email protected] (F.Y.); [email protected] (Q.J.) 2 Materials and Structural Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210098, China; [email protected] * Correspondence: [email protected]

 Received: 12 February 2019; Accepted: 5 March 2019; Published: 9 March 2019 

Abstract: Extreme events such as rainstorms and floods are likely to increase in frequency due to the influence of global warming, which is expected to put considerable pressure on water resources. This paper presents a regional frequency analysis of precipitation extremes and its spatio-temporal pattern characteristics based on well-known index-flood L-moments methods and the application of advanced statistical tests and spatial analysis techniques. The results indicate the following conclusions. First, during the period between 1969 and 2015, the annual precipitation extremes at Fengjie station show a decreasing trend, but the station shows an increasing trend, and the other 24 stations have no significant trend at a 5% confidence level. Secondly, the Hanjiang River Basin can be categorized into three homogenous regions by hierarchical clustering analysis with the consideration of topography and mean precipitation in these areas. The GEV, GNO, GPA and P III distributions fit better for most of the basin and MARE values range from 3.19% to 6.41% demonstrating that the best-fit distributions for each homogenous region is adequate in predicting the quantiles estimates. Thirdly, quantile estimates are reliable enough when the return period is less than 100 years, however estimates for a higher return period (e.g., 1000 years) become unreliable. Further, the uncertainty of quantiles estimations is growing with the growing return periods and the estimates based on R95P series have a smaller uncertainty to describe the extreme precipitation in the Hanjiang river basin (HJRB). Furthermore, In the HJRB, most of the extreme precipitation events (more than 90%) occur during the rainy season between May and October, and more than 30% of these extreme events concentrate in July, which is mainly impacted by the sub-tropical monsoon climate. Finally, precipitation extremes are mainly concentrated in the areas of Du River, South River and Daba Mountain in region I and , Wuhan and Zhongxiang stations in region III, located in the upstream of Reservoir and Jianghan Plain respectively. There areas provide sufficient climate conditions (e.g., humidity and precipitation) responsible for the occurring floods and will increase the risk of natural hazards to these areas.

Keywords: extreme rainfall; regional frequency analysis; L-moments; Hanjiang river basin

1. Introduction Extreme climate events are expected to change in many regions due to the influence of global warming. Daily precipitation extremes do appear to be increasing in magnitude and frequency at a global or continental scale, in both dry and wet regions. This phenomena has a potential to trigger floods and droughts [1–3]. The Intergovernmental Panel on Climate Change (IPCC) special report on

Atmosphere 2019, 10, 130; doi:10.3390/atmos10030130 www.mdpi.com/journal/atmosphere Atmosphere 2019, 10, 130 2 of 25 managing the risks of extreme events and disasters to advance climate adaptation indicates that it is likely that the frequency of heavy precipitation or the proportion of total rainfall from heavy falls will increase in the twenty-first century in many areas of the world [4]. In China, there are the same variations. The average intensity and extreme precipitation values tend to increase, so does the extreme precipitation occurrence [5]. Heavy precipitation events present a challenge to public safety, life, and lead to huge economic loss and low food crop productivity [6]. Additionally, precipitation is a key component of the hydrological cycle and a primary input for hydrometeorological models [7]. Hence, extreme precipitation events have received an unprecedented level of attention in recent decades. The Hanjiang River Basin (HJRB), the largest drainage basin of the River, is the central hinge of economic joints between south and north, west and east of China due to the advantages of location and physical geographical environment [8]. The Danjiangkou Reservoir, located in the middle and upper reaches of Hanjiang River, is both a key flood control project for the middle and lower reaches of Hanjiang River and the water source for the middle line South-to-North water diversion project of China with its multiple purposes including flood control, water supply, hydropower generation, navigation, etc., which play an important role in the sustainable development of China [9]. However, frequent extreme precipitation events and floods in the Hanjiang River Basin lead to a considerable loss with respect to both the economy and human life. The continuous rainstorm during August 1981 caused a rare flood disaster in the Hanzhong area of HJRB [10]. On 30 July 1983, a catastrophic flood caused by regional heavy rain resulted in a devastating disaster to Ankang City [11]. During 5–7 July 1990, the regional heavy rain in the area of Hanzhong led to a flood disaster, which caused the economic loss about 400 million RMB [12]. There were different levels of floods caused by the rainstorms that occurred in the Hanjiang River Basin in 2003, 2005, 2007, 2010 and 2011 [13,14]. Considering the significance of water security in the HJRB, a large amount of research has been undertaken in order to improve regional water resource management for the basin. A lot of researchers analyzed all previous storm floods occurring in the Hanjiang River in detail, specifically in terms of the process and characteristics of precipitation and flooding [14–17]. To give an important technological support to flood control decision making and integrated water resource management for this basin, Guo and Zhang et al. designed and developed a GIS-based flood forecasting system for the Hanjiang River Basin [18,19]. Yin et al. analyzed the temporal and spatial changes of monthly/annual precipitation in the upper reaches of the Hanjiang River, and found that annual precipitation manifested a decreasing trend during the last 50 years on the whole, but the enhanced southeast monsoon possibly caused an increase in the occurrence of rainstorms and flooding in late July and August [11]. The impact of climate change on extreme events is a prevailing focus of research. Xu et al. predicted the runoff in the upper reaches of the Hanjiang River basin under A2 and B2 climate scenarios by coupling the GCM and HBV model and found that the floods will occur more frequently under both scenarios in these areas [20]. In order to reflect the true feature of extreme rainfall and floods, Chen et al. studied the joint distribution of the extreme rainfall and floods for the upper-middle reaches of the Hanjiang River based on the Copula function [21]. Xu et al. used the index-flood method to analyze the regional flood frequency upstream in the Hanjiang River and found that regional flood frequency analysis is an effective way to estimate flood quantiles and can satisfy engineering design requirements [22]. These studies were beneficial to understanding the behaviors of precipitation and flooding in the HJRB, but the investigation of regionalization of precipitation extremes and its spatial patterns in the HJRB is limited. Hosking and Wallis designed and developed the L-moments technique with the advantages of characterizing a wider range of distributions and more robustness with respect to outliers in data to undertake regional frequency analysis [23–25]. Regarding the advantages of this technique, a variety of L-moments based methods have been extensively employed in the regional frequency analysis of extreme precipitation and floods [22,26–30]. Although the L-moments method is being increasingly used in the regional frequency analysis, this technique has not acquired popularity in China because the Pearson-III distribution is still widely used as the official recommendation in hydrological frequency Atmosphere 2019, 10, 130 3 of 25 analysis [29]. Only a few reports concerning regional frequency analysis using the L-moments method can be found in China, especially in the HJRB. Chen et al. used the L-moments technique to do the regional low flow frequency analysis in the Dongjiang basin based on five frequency distributions and the results indicated that the LN3 distribution was identified as the most appropriate distribution for the area [31]. Yang et al. conducted regional frequency analysis using the well-known L-moments method to identify the spatial pattern of flooding and found that the flood frequency of the whole basin gradually decreases from upstream to downstream [32]. Excepting the regional frequency analysis of flooding, the regional frequency analysis of precipitation extremes using the L-moments approach was conducted in the Pearl River Basin by Yang et al., which is helpful for understanding the occurrence of floods and droughts across both space and time [29]. Similar studies have been reported in the Baisn and Guangdong Province [26,33]. Additionally, extreme precipitation events are the main causes for the flood hazards in the Hanjiang River Basin [5]. However, no systematic research on the regional frequency analysis of precipitation extremes using the L-moments approach, the pattern characteristics of rainfall extremes, seasonality of the precipitation extremes, and the potential link between heavy rain and floods has been conducted across the entire Hanjiang River Basin. Therefore, considering the significance of water security in the HJRB, efforts should be made for the regional frequency analysis of extreme precipitation in the basin. The present study aims to: (1) investigate and identify the hydrological homogeneous sub-regions for annual precipitation extremes in the Hanjiang River Basin; (2) hunt for the best probability distribution for precipitation extremes using the L-moments methods taking accuracy and uncertainty analysis into consideration; (3) analyze the characteristics of spatio-temporal patterns of extreme rainfall events in order to reveal the underlying impacts of climate variations dominated in the Hanjiang River Basin. Overall, this study is expected to benefit the understanding of the behaviors of precipitation and floods and the characteristics of extreme precipitation in the HJRB, which will be helpful for the policymaker to formulate reasonable flood control strategies in order to protect peoples’ lives and property safety, and to ensure the safe and reliable operation of the Middle Route Project of the South-to-North Water Diversion Project.

2. Study Area and Data The Hanjiang River Basin (HJRB) (106◦120–114◦140 E and 30◦080–34◦110 N, Figure1) is situated in the central part of China and is involved in the provinces of Shanxi, , Henan, Sichuan, Gansu, and [34,35]. The Hanjiang River (HJR) is the biggest tributary of the Yangtze River, covering a total drainage area of 159,000 km2 with a length of 1557 km [36,37]. The mainstream of the river originates from the southern slope of the Qinling Mountains and finally pours into the Yangtze River at Wuhan City. The average annual temperature of HJRB ranges from 15 ◦C to 17 ◦C[38]. The general climate in HJRB is mild, and it is characterized by a sub-tropical monsoon climate. The sub-tropical monsoon climate and varying topography result in a dramatic spatio-temporal diversity of water resource distribution. The average annual precipitation of HJRB ranges from 700 mm to 1800 mm [39]. There are big inter-annual variations and an uneven distribution of the precipitation in the HJRB, with 70%–80% of the annual total during May–October [38,39]. The runoff of HJR is closely related to rainfall and the runoff during May–October accounts for about 75% of the annual total. Flood and drought disasters take place frequently in this region. The Danjiangkou Reservoir (DJKR) located in the upper HJR, consisting of the Dan Reservoir (DR) and the Han Reservoir (HR), was constructed between 1958 and 2005. Designed as an important water source for the Middle Route Project of the South-to-North Water Diversion Project (SNWDP) [37], the HJRB is one of the important production bases of fresh water aquaculture in China, and is of crucial importance in both the economy and ecology of this region [35]. Atmosphere 2019, 10, 130 4 of 25 Atmosphere 2019, 10, x FOR PEER REVIEW 4 of 26

FigureFigure 1. The1. The Hanjiang Hanjiang RiverRiver Basin and and meteorological meteorological stations. stations.

DailyDaily precipitation precipitation observations observations forfor the the time period period 19 1951–201551–2015 were were provided provided by the by China the China MeteorologyMeteorology Administration Administration (CMA) (CMA) and and the the National Climate Climate Center, Center, which which is officially is officially in charge in charge of of monitoring,monitoring, collecting, collecting, compiling compiling and and releasing releasing high high-quality-quality hydrological hydrological data data in China. in China. Hence Hence the the qualityquality of data of data can can be guaranteedbe guaranteed in in this this study study [[29]29].. Note Note that that the the time time period period 1969 1969–2015–2015 was used was in used in this studythis study because because the length the length of continuous of continuous missing missing values values are moreare more than than one one year year before before 1969. 1969. Between Between 1969 and 2015, the continuous missing daily precipitation data (less than 0.01%) were filled 1969 and 2015, the continuous missing daily precipitation data (less than 0.01%) were filled by using the by using the average values of the same days [40–42]. A total of 25 stations in and around the HJRB averagewere values used, of 13 the of samewhich daysare within [40–42 the]. AHJRB total and of 25the stations rest are inoutside and around but close the to HJRBthe edges were of used, the 13 of whichbasin. are within The detailed the HJRB information and the is restshown are in outside Table 1. but Based close on tothe the daily edges precipitation of the basin. observations, The detailed informationfour indices is shown are derived in Table for analysis:1. Based (1) the on maximum the daily 1 precipitation-day precipitation observations, amount (RX1day); four indices(2) the are derivedmaximum for analysis: 5-day (1) precipitation the maximum amount 1-day (RX5day); precipitation (3) the amount maximum (RX1day); 7-day precipitation (2) the maximum amount 5-day precipitation(RX7day); amount and (4) (RX5day);the total amount (3) the of maximumprecipitation 7-day on those precipitation days that have amount precipitation (RX7day); above and the (4) the total amount95th percentile, of precipitation i.e., precipitation on those on very days wet that days have (R95P). precipitation Similar indices above have the also 95th been percentile, used in i.e., previous studies and are recommended by the World Meteorological Organization (WMO), the precipitation on very wet days (R95P). Similar indices have also been used in previous studies and are project on Climate Variability and Predictability (CLIVAR) and the Expert Team on Climate Change recommendedDetection, byMonitoring the World and Meteorological Indices (ETCCDMI) Organization [26,29,30,43] (WMO),. the project on Climate Variability and Predictability (CLIVAR) and the Expert Team on Climate Change Detection, Monitoring and Indices (ETCCDMI) [26,29,30,43].

Table 1. List of 25 stations and associated characteristics in the Hanjiang River Basin (HJRB).

Annual Station Station ID Abbreviation Latitude (N) Longitude (E) Altitude (m) Precipitation Name Total (mm) 57034 Wugong WG 34.25 108.22 447.8 581.29 57046 Huashan HS 34.48 110.08 2064.9 751.44 57067 Lushi LS 34.05 111.03 568.8 620.26 57077 Luanchuan LC 33.78 111.60 750.3 808.53 57106Atmosphere 2019 Lveyang, 10, x; doi: FOR PEER LY REVIEW 33.32 106.15www.mdpi.com/journal/ 794.2atmosphere 772.34 57127 Hanzhong HZ 33.07 107.03 509.5 849.14 57134 Foping FP 33.52 107.98 827.2 903.01 57143 Shangzhou SZ 33.87 109.97 742.2 674.58 57144 Zhen’an ZA 33.43 109.15 693.7 761.49 Atmosphere 2019, 10, 130 5 of 25

Table 1. Cont.

Annual Station Station ID Abbreviation Latitude (N) Longitude (E) Altitude (m) Precipitation Name Total (mm) 57178 Nanyang NY 33.03 112.58 129.2 766.35 57232 Shiquan SQ 33.05 108.27 484.9 876.98 57237 Wanyuan WY 32.07 108.03 674.0 1243.78 57245 Ankang AK 32.72 109.03 290.8 822.25 57251 Yunxi YX 33.00 110.42 249.1 767.23 57259 Fangxian FX 32.03 110.77 426.9 822.42 57265 LHK 32.38 111.67 90.0 807.80 57297 Xinyang XY 32.13 114.05 114.5 1076.68 57348 Fengjie FJ 31.02 109.53 299.8 1106.58 57355 Badong BD 31.03 110.37 334 1072.70 57378 Zhongxiang ZX 31.17 112.57 65.8 958.21 57461 YC 30.70 111.30 133.1 1132.25 57476 Jinzhou JZ 30.35 112.15 32.6 1068.80 57483 Tianmen TM 30.67 113.17 34.1 1103.62 57494 Wuhan WH 30.62 114.13 23.1 1265.20 57583 Jiayu JY 29.98 113.92 53.0 1410.85

3. Methodology

3.1. Stationarity Test and Serial Correlation Check The trend test is employed to examine the stationarity in hydrological series [29]. Trend identification is an important issue in hydrological time series analysis. It is the basis not only for understanding the long-term variations of hydrological processes, but also for revealing periodicities and other characteristics of hydrological processes. As a nonparametric test with the advantages of not requiring the data to conform to any particular distribution and its low sensitivity to outliers, the Mann-Kendall (M-K) method recommended by the WMO is applied in this study to assess the significance of monotonic trends in hydrological series [44–46]. To eliminate the effect of the serial correlation on the MK test, the trend free pre-whitening (TFPW) technique developed by Yue et al. was employed in this study [47,48]. The independence test was carried out for examining the autocorrelation coefficients of the time series. When the absolute values of the autocorrelation coefficients of different lag times calculated for √ a time series consisting of n observations are not larger than the typical critical value, i.e., 1.96/ n corresponding to the 5% significance level, the observations in the time series can be accepted as being independent from each other. According to the calculated autocorrelation coefficients of lag-1, lag-5 and lag-10 for each annual series, the observations in that series can be accepted as being independent at the 5% significance level [49,50].

3.2. L-moments Theory L-moments are statistical quantities that are derived from probability weighted moments (PWMs) and increase the accuracy and ease of use of PWM-based analysis. Compared to the convention moments, L-moments have the advantage of characterizing a wider range of distributions and are more robust towards outliers in datasets [51]. Further, L-moments enable more reliable inferences to be made from small samples about an underlying probability distribution [52]. Details about the L-moments approach and the advantages offered by L-moments over conventional moments in hypothesis testing, boundedness of the moment ratios and identification of distribution have been discussed by Hosking [23,25]. Basically, L-moments are linear functions of probability weighted moments (PWMs) and defined as follows [25]. Assuming F(x) is the distribution function of random variable X, X1:n ≤ ...... ≤ Xn:n are the order statistics of the samples. The L-moment of r is Atmosphere 2019, 10, 130 6 of 25

r−1 ! −1 k r − 1 λr = r ∑ (−1) E(Xr−k:r), r = 1, 2, . . . (1) k=0 k L-moment ratio is defined as

λ2 λr τ2 = and τr = r = 3, 4, . . . (2) λ1 λ1

Where τ2, τ3 and τ4 are L-variation (L-CV), L-skewness, and L-kurtosis coefficient, respectively. The sample L-moment ratios are defined as

t = l2/l1 and tr = lr/l2, r = 3, 4, . . . (3)

lr is the unbiased rth L-moments; t, t3 and t4 is the coefficient of variation (L-CV), L-skewness and L-kurtosis, respectively. The L-moment ratios will be used for homogeneity analysis in the regional frequency analysis.

3.3. Regional Frequency Analysis Based on L-moments Method

Suppose that there are N sites in the region with sample size n1, n2, ... nN, respectively. The sample i (i) (i) L-moment ratios (L-CV, L-Skewness and L-kurtosis) at-site i are denoted by t , t3 and t4 . The regional weighted average L-moment ratios are given by:

N N N N (i) (i) t = ∑ nit / ∑ ni and tr = ∑ nitr / ∑ ni r = 3, 4, . . . (4) i=1 i=1 i=1 i=1

Based on the L-moment method proposed by Hosking and Wallis, five steps of the regional frequency analysis method used in this study were summarized as follows: (1) identification of homogenous regions by cluster analysis; (2) screening the data using the discordancy measure; (3) homogeneity testing using the heterogeneity measure; (4) distribution selection using the goodness-of-fit measure; (5) regional extreme rainfall quantile estimations [24,25]. Therefore, these five steps were employed to conduct the regional frequency analysis for extreme precipitation in the Hanjiang River Basin.

3.3.1. Identification of Homogenous Regions by Cluster Analysis Cluster analysis (CA) is the task of grouping a set of objects in such a way that objects in the same group are more similar to each other than to those in other groups. CA is a common technique for statistical data analysis, used in hydrology to form regions for regional frequency analysis. A homogeneous region is defined as a group of stations the data of which can be described by the same probability distribution [25,53]. Recommended by Hosking and Wallis, Ward’s method is employed to form homogeneous sub-regions in this study [25]. Ward’s method is a criterion applied in hierarchical clustering analysis, which is based on minimizing the Euclidean distance in site characteristics space within each cluster. Four variables are selected to describe the precipitation climate, which are latitude, longitude, elevation and the mean annual precipitation. Considering that the observed scales of cluster analysis are very different and the methods are sensitive to such scale difference, the location and precipitation amount were rescaled to lie between 0 and 1 so that the ranges of these variables can be comparable.

3.3.2. Screening the Data using the Discordancy Measure Given a group of sites, the aim of the discordancy measure is to identify those sites that are grossly discordant with the group as a whole. Discordancy is measured in terms of the L-moments of the sites’ data. Atmosphere 2019, 10, 130 7 of 25

T h (i) (i) (i)i Let ui = t , t3 , t4 be the vector containing the t, t3 and t4 values for site i where the superscript T denotes the transposition of a vector or matrix. Let

N u = ∑ ui/N (5) i=1 be the (unweighted) regional average. Hosking and Wallis defined the discordancy measure Di as follows. 1 D = (u − u)T A−1(u − u) (6) i 3 i i N T where A = ∑ (ui − u)(ui − u) ; N is the number of stations. i=1 A large value of Di indicates that the site i is discordant with other sites in a sub-region. Hosking and Wallis found that the definition of “large” depends on the number of sites in the group and suggested that a site be regarded as discordant if its Di value exceeds the critical value [25].

3.3.3. Homogeneity Testing using the Heterogeneity Measure The aim of homogeneity testing is to estimate the degree of heterogeneity in a group of sites and to assess whether the sites might reasonably be treated as a homogenous region. The regional average R R R L-CV, L-skewness and L-kurtosis, denoted by t , t3 and t4 , respectively, are computed as [24,29,30]:

N N R (i) t = ∑ nit / ∑ ni (7) i=1 i=1

N N R (i) t3 = ∑ nit3 / ∑ ni (8) i=1 i=1 N N R = (i) t4 ∑ nit4 / ∑ ni (9) i=1 i=1 N where ni/ ∑i=1 ni denotes the weight applied to sample L-moment ratios at site i, which is proportional R to the recorded length of the site. The regional average mean l1 is set to be 1. Three heterogeneity measures H1, H2, and H3 are computed as:

V1 − µv H1 = (10) σv

V2 − µv2 H2 = (11) σv2

V3 − µv3 H3 = (12) σv3 where V1 denotes the weighted standard deviation of the at-site sample L-CVs and is computed as: 1  2  2 N h (i) Ri N V1 = ∑i=1 ni t − t / ∑i=1 ni ; V2 denotes the weighted average distance from the site to the group weighted mean in the two-dimensional space of L-CV and L-skewness and is calculated as: 1  2 2 2 N  (i) R  (i) R N V2 = ∑i=1 ni t2 − t2 + t3 − t3 / ∑i=1 ni; V3 denotes the weighted average distance from the site to the group weighted mean in the two-dimensional space of L-skewness and L-kurtosis and is 1  2  2 2 = N (i) − R + (i) − R N calculated as: V3 ∑i=1 ni t3 t3 t4 t4 / ∑i=1 ni. µv, µv2 and µv3 denote the mean and σv, σv2 and σv3 the standard deviation values of V1, V2 and V3, respectively, computed on the basis of a large number of simulated homogeneous regions. Atmosphere 2019, 10, 130 8 of 25

In order to obtain reliable values of µv and σv, the number of Nsim of Monte Carlo simulations need to be large and Nsim = 1000 was used in this study. Hosking and Wallis suggested that the region be regarded as “acceptably homogeneous” if H < 1, “possibly heterogeneous” if 1 ≤ H < 2, and “definitely heterogeneous” if H ≥ 2 [25]. In the above three measures, H1 is the standard deviation of the at-site L-CVs and a large value of H1 indicates that the observed L-moments are more dispersed than what is consistent with the hypothesis of homogeneity [24,27]. H2 indicates whether the at-site and regional estimates are close to each other and a large value of H2 indicates a large deviation between at-site and regional estimates. H3 measure indicates whether the at-site and the regional estimate will agree and a large value of H3 indicates a large deviation between at-site estimates and observed data. Hosking and Wallis found that H1 has a much better discriminatory power than H2 [25]. In this study, H1 and H2 were chosen to test the heterogeneity because the L-CV and L-skewness are required for fitting regional frequency curves with a GEV or GLO according to the method recommended by Norbiato et al. [27].

3.3.4. Distribution Selection using the Goodness-of-Fit Measure For each candidate distribution, the generalized extreme-value (GEV), generalized logistic (GLO), generalized normal (GNO), generalized Pareto (GPA), and Pearson type 3 (P III), the goodness-of-fit measure is computed as follows:

DIST  DIST  Z = τ4 − t4 + β4 /σ4 (13)

DIST where τ4 is the L-kurtosis of the fitted distribution to the data using the candidate distribution; 1      2  2 Nsim (m) −1 Nsim (m) 2 β4 = ∑m=1 t4 − t4 /Nsim and σ4 = (Nsim − 1) ∑m=1 t4 − t4 − Nsimβ4 are the bias (m) and standard deviation of the regional average L-kurosis t4 estimated using the Monte Carlo simulation samples by Kappa distribution.

If ZDIST is close to zero, the fit by the candidate distribution is considered to be adequate. If the criterion ZDIST ≤ 1.64, it indicates that the fit is acceptable at a confidence level of 90%. If more than one candidate distribution is acceptable, the one with the lowest ZDIST is regarded as the best-fit distribution. Besides, an L-moment ratio diagram is also used for selecting a probability distribution function by comparing its closeness to the L-skewness and L-kurtosis combination in the L-moment ratio diagram for regional frequency analysis. In this study, ZDIST measure and an L-moment ratio diagram were used to select a candidate distribution.

3.3.5. Regional Extreme Rainfall Quantile Estimations Index-flood procedures are a convenient way of pooling summary statistics from different data samples. Dalrymple applied the procedure to flood data in hydrology and then the term “index flood” arose [54]. The method is used to obtain extreme rainfall quantiles of the best-fit frequency distribution. The quantile estimates Qi(F) at site i is calculated by

Qi(F) = µiq(F) (14) where F is the non-exceedance probability; q(F) is the estimated regional growth curve, a dimensionless quantile function common to every site; µi is the index rainfall or flood value. In this study, the mean extreme precipitation is used as the index rainfall, which is the site-specific scale factor. In order to assess the results of regional frequency analysis, a large amount of the quantiles given by the best-fit distribution for each HOM region were compared with the observations having the same probabilities. The Gringorten formula is used to estimate the empirical frequency of an element in the series and is given by [55]: i − 0.44 P(i) = (15) n + 0.12 Atmosphere 2019, 10, 130 9 of 25 where i is the ith element in the series arranged in ascending order and n is the number of the elements in the series. And the mean absolute relative errors (MARE) is defined as [28]:

n 1 Piobserved − Pisimulated MARE = ∑ (16) n i=1 Piobserved where n is the number of elements in the series; Piobserved is the extreme precipitation observation values; Pisimulated is the extreme precipitation simulated values.

3.4. Accuracy Assessments and Uncertainty Analysis The Monte Carlo simulation method was employed to evaluate the accuracy and uncertainty of the estimated extreme precipitation quantiles. The simulated data was generated from the best-fit distribution with the same number of stations in the sub-region and the same record lengths in each station. In order to obtain the reliable simulated data, the number of the simulations need to be large and 1000 was used in this study. Due to the large numbers of simulations, the evaluation would not be affected by the outliers generated from the Monte Carlo simulations. The root mean square error (RMSE) of the estimated quantiles was employed to assess the accuracy of frequency analysis [26,27,56]. The relative RMSE given by Hosking and Wallis can be expressed as percentages of site-i quantile estimator [25]. M m 1/2 Qˆ (F) − Qi(F) R (F) = (M−1 i ) (17) i ∑ ( ) m=1 Qi F ˆ m where M is the number of simulations; Qi (F) is the site i quantile estimate for non-exceedance Qˆ m(F)−Q (F) probability F in the mth Monte Carlo simulation; i i represents the relative error of the quantile Qi(F) estimate for non-exceedance probability F. The regional average relative RMSE of the estimated quantiles is computed by

N R −1 R (F) = N ∑ Ri(F) (18) i=1

The corresponding 95% error bounds that are recommended by Hosking and Wallis were employed to assess the estimation uncertainty. And the smaller error bounds indicate the smaller estimation uncertainty [24,25].

4. Results

4.1. Stationarity Test and Serial Correlation Check In this study, the Mann-Kendall method is carried out for the trend test of precipitation extremes (RX1day, RX5day, RX7day, R95P) over the period between 1969 and 2015 in the HJRB. The results are tabulated in Table2, from which it can be seen that for precipitation extremes, SZ station shows an increasing trend for RX1day series with 5% confidence level, FJ station shows a decreasing trend for RX5day and RX7day series with 5% confidence level, WH station shows an increasing trend for RX5day and RX7day series with 5% confidence level, and the remaining 22 stations have no significant trends (at the 5% confidence level). Consequently, apart from SZ, FJ and WH station, the observations have no trends and can be treated as stationarity series on the basis of the results of Mann-Kendall test. Besides, it is beneficial to conduct the autocorrelation test for precipitation extremes before analysis. If the autocorrelation coefficients of lag-1, lag-5 and lag-10 for precipitation extremes are √ smaller than 1.96/ n, the stations are considered as independent. The results showed that all of the √ autocorrelation coefficients are smaller than 1.96/ n. Thus, the observations of the 22 stations with the exception of SZ, FJ and WH stations can be considered as independent series at the 5% confidence level and can be applied to precipitation frequency analysis. Atmosphere 2019, 10, 130 10 of 25

Table 2. Results of trend test for the precipitation extremes (RX1day, RX5day, RX7day and R95P) over the period (1969–2015) in the Hanjiang River Basin (HJRB) using MK test.

RX1day RX5day RX7day R95P Station Name Test Z Significance Test Z Significance Test Z Significance Test Z Significance WG 0.559 N+ 0.211 N+ 0.238 N+ 0.083 N+ HS −0.486 N− −1.11 N− −0.495 N− −0.33 N− LS 1.403 N+ 0.917 N+ 1.027 N+ 1.394 N+ LC 1.394 N+ 1.284 N+ 1.577 N+ 1.211 N+ LY −1.11 N− −1.211 N− −1.568 N− −0.752 N− HZ 0.559 N+ −0.238 N− −0.284 N− 0.844 N+ FP 1.073 N+ 1.348 N+ 1.192 N+ 1.366 N+ SZ 2.173 Y+ 0.734 N+ 0.825 N+ 1.394 N+ ZA 0.862 N+ 0.44 N+ 0.835 N+ 1.045 N+ NY 0.009 N+ −0.22 N− −0.083 N− 0.055 N+ SQ 0.101 N+ 1.449 N+ 1.752 N+ 0.679 N+ WY 0.724 N+ 1.706 N+ 1.779 N+ 1.513 N+ AK −0.807 N− −1.036 N− −0.963 N− −0.633 N− YX −0.605 N− −0.266 N− −0.449 N− 0.33 N+ FX −0.477 N− −1.357 N− −1.045 N− −0.532 N− LHK −1.513 N− −1.834 N− −1.632 N− −1.174 N− XY −0.009 N− −0.238 N− 0.147 N+ 0 N− FJ −1.045 N− −2.467 Y− −2.1 Y− −1.898 N− BD 0.22 N+ −0.688 N− −0.44 N− −0.275 N− ZX −0.981 N− −0.917 N− −1.1 N− −0.422 N− YC 0.147 N+ −0.688 N− −0.321 N− 0.954 N+ JZ −0.037 N− 0.624 N+ 0.156 N+ 0.532 N+ TM 0.761 N+ 0.147 N+ −0.083 N− 0.734 N+ WH 1.742 N+ 2.265 Y+ 2.128 Y+ 1.522 N+ JY −0.22 N− 0.138 N+ 0.055 N+ −0.238 N− Note: The absolute statistic of series is compared with the threshold of 1.96 with 5% significance level. If being bigger than 1.96, the trend is statistically significant (denoted as “Y”); if being smaller than 1.96, the trend is not statistically significant (denoted as “N”). The “(+)” sign means an upward trend, the”(−)” sign means a downward trend. The bold values denote 95% confidence level.

4.2. Regionalization of Precipitation Extremes Using L-Moment Technique Homogenous regions were initially formed by the clusters which were not the final results. The final results should be adjusted by taking into account the topography and physical reasons to form interpretable homogeneous regions. The discordancy test and heterogeneity measure were applied to examine whether the data of one site are discordant with the group in the sub-region and assess whether the sites might reasonably be treated as a homogenous region, respectively. Initially, 22 stations of the HJRB were divided into three clusters: Cluster I (Wugong, Lveyang, Hanzhong, Foping, Zhenan, Shiquan, Wanyuan, Ankang), Cluster II (Huashan, Lushi, Luanchuan, Nanyang, Yunxi, Fangxian, Laohekou), and Cluster III (Xinyang, Badong, Zhongxiang, Yichang, Jinzhou, Tianmen, Jiayu). Then, the sub-regions were refined manually. The Wugong station was regrouped into cluster II because the Di value of Wugong station was greater than the critical discordancy thresholds. Finally, the 22 stations in the HJRB can be divided into three regions: Region I (Lveyang, Hanzhong, Foping, Zhenan, Shiquan, Wanyuan, Ankang), Region II (Wugong, Huashan, Lushi, Luanchuan, Nanyang, Yunxi, Fangxian, Laohekou), and Region III (Xinyang, Badong, Zhongxiang, Yichang, Jinzhou, Tianmen, Jiayu). The results of discordancy measure and heterogeneity test for the 22 stations in HJRB are shown in Table3, which can be seen that all Di values are less than the critical discordancy thresholds. Consequently, all the 22 stations in the HJRB are regarded to pass the discordancy test and the whole heterogeneity measures are less than 1 (Table3). So the final set of regions is shown in Figure2, which indicates that the entire Hanjiang River Basin can be categorized into three homogeneous regions (named HOM) for each extreme daily precipitation index with heterogeneity measure H1,H2 < 1 according to the method recommended by Norbiato et al. [27]. The heterogeneity test results indicate that the three regions are reasonable to be considered homogeneous. Atmosphere 2019, 10, 130 11 of 25

Table 3. Results of discordance, heterogeneity, goodness-of-fit tests and MARE for 24 stations in the Hanjiang River Basin (HJRB).

Heterogeneity Item HOM Region Containing Sites (Di) Dcritical |Z| ≤ 1.64 Best Fit MARE(%) H1 H2 H3 LY(1.4), HZ(0.58), FP(0.42), ZA(1.78), SQ(1.41), I (7 sites) 1.917 0.64 −0.48 −0.13 0.04 GNO 4.05 WY(0.61), AK(0.79) RX1day WG(0.32), HS(1.19), LS(1.58), LC(0.42), NY(1.92), II (8 sites) 2.140 −0.28 −0.84 −1.11 −0.26 GLO 6.41 YX(2.26), FX(0.48), LHK(0.99) XY(1.31), BD(0.54), ZX(0.94), YC(0.36), JZ(0.66), III (7 sites) 1.917 −0.25 −0.99 −1.55 0.12 GEV 5.65 TM(1.59), JY(1.60) LY(1.74), HZ(1.49), FP(1.37), ZA(0.17), SQ(1.21), I (7 sites) 1.917 0.03 0.27 −0.28 0.41 PE3 4.27 WY(0.55), AK(0.48) RX5day WG(2.01), HS(0.49), LS(0.86), LC(0.05), NY(0.52), II (8 sites) 2.140 0.70 −0.82 −1.31 −0.11 GEV 4.04 YX(0.56), FX(0.58), LHK(2.47) XY(1.26), BD(0.61), ZX(1.60), YC(1.00), JZ(1.53), III (7 sites) 1.917 −0.57 0.10 0.64 −0.01 GEV 5.46 TM(0.25), JY(0.74) LY(1.89), HZ(0.32), FP(1.54), ZA(0.40), SQ(0.25), I (7 sites) 1.917 −0.58 −0.14 0.37 0.13 PE3 3.19 WY(1.34), AK(1.26) RX7day WG(0.44), HS(1.55), LS(0.68), LC(1.35), NY(0.38), II (8 sites) 2.140 −0.04 −0.95 −0.71 −0.57 GEV 5.18 YX(1.03), FX(0.72), LHK(2.04) XY(1.35), BD(0.97), ZX(1.46), YC(0.66), JZ(0.54), III (7 sites) 1.917 0.30 0.10 −0.38 0.37 GNO 5.66 TM(0.57), JY(1.46) LY(1.25), HZ(0.22), FP(0.46), ZA(1.89), SQ(1.66), I (7 sites) 1.917 −0.01 0.38 0.98 −0.06 PE3 3.72 WY(0.38), AK(1.14) R95P WG(1.56), HS(1.16), LS(0.53), LC(0.61), NY(0.46), II (8 sites) 2.140 0.63 0.81 0.61 −0.93 GNO 6.11 YX(1.84), FX(0.77), LHK(0.62) XY(1.39), BD(1.16), ZX(1.44), YC(0.33), JZ(1.19), III (7 sites) 1.917 0.72 −0.44 −1.13 −0.08 PE3 5.92 TM(0.57), JY(1.46) Atmosphere 2019, 10, x FOR PEER REVIEW Atmosphere 2019, 10, 130 12 of 25 13 of 26

FigureFigure 2. 2. IdentificationIdentification of of homogenous homogenous sub sub-regions-regions in in the the HJRB. HJRB. 4.3. Selection of Best-Fit Distribution 4.3. Selection of Best-Fit Distribution Five distributions including GEV, GLO, GNO, GPA, and P III are investigated in each of Five distributions including GEV, GLO, GNO, GPA, and P III are investigated in each of the the homogeneous regions for RX1day, RX5day, RX7day and R95P in the goodness-of-fit test [30]. homogeneous regions for RX1day, RX5day, RX7day and R95P in the goodness-of-fit test [30]. The The results, tabulated in Table3, indicate that they are satisfactory with |Z| ≤ 1.64, corresponding results, tabulated in Table 3, indicate that they are satisfactory with |Z| ≤ 1.64, corresponding to an to an acceptance of the hypothesized distribution at a confidence level of 90% [24,25]. For RX1day acceptance of the hypothesized distribution at a confidence level of 90% [24,25]. For RX1day series, series, GNO distribution is the optimal distribution for HOM region I, GLO distribution is the best-fit GNO distribution is the optimal distribution for HOM region I, GLO distribution is the best-fit distribution for HOM region II, and the GEV distribution performs well in fitting the precipitation distribution for HOM region II, and the GEV distribution performs well in fitting the precipitation extremes in HOM region III. For RX5day series, P III distribution is the optimal distribution for HOM extremes in HOM region III. For RX5day series, P III distribution is the optimal distribution for HOM region I, while GEV distribution is the best-fit distribution for HOM region II and III. For RX7day region I, while GEV distribution is the best-fit distribution for HOM region II and III. For RX7day series, P III distribution is the optimal distribution for HOM region I, GEV distribution is the best-fit series, P III distribution is the optimal distribution for HOM region I, GEV distribution is the best-fit distribution for HOM region II, and the GNO distribution performs well in fitting the precipitation distribution for HOM region II, and the GNO distribution performs well in fitting the precipitation extremes in HOM region III. For R95P series, P III distribution is the optimal distribution for HOM extremes in HOM region III. For R95P series, P III distribution is the optimal distribution for HOM region I and Region III, while the GNO distribution is the best-fit distribution for HOM region II. region I and Region III, while the GNO distribution is the best-fit distribution for HOM region II. In In conclusion, GNO, GEV, GLO and P III distributions perform well in fitting the precipitation extremes conclusion, GNO, GEV, GLO and P III distributions perform well in fitting the precipitation extremes in HJRB. in HJRB. In addition, an L-moment ratio plot is also used for selecting a probability distribution function In addition, an L-moment ratio plot is also used for selecting a probability distribution function by comparing its closeness to the L-skewness and L-kurtosis combination. The L-moment diagrams by comparing its closeness to the L-skewness and L-kurtosis combination. The L-moment diagrams for RX1day, RX5day, RX7day and R95P in three regions are illustrated in Figures3 and4, respectively. for RX1day, RX5day, RX7day and R95P in three regions are illustrated in Figure 3 and Figure 4, In terms of RX1day series as a paradigm, Figure3a–c show that the GNO distribution is closer to the respectively. In terms of RX1day series as a paradigm, Figure 3a–c show that the GNO distribution is corresponding regional average value in region I, the GLO distribution is closer to the corresponding closer to the corresponding regional average value in region I, the GLO distribution is closer to the regional average value in region II, and the GEV distribution is closer to the corresponding regional corresponding regional average value in region II, and the GEV distribution is closer to the average value in region III. Therefore, these figures demonstrate that the results of L-moment ratio corresponding regional average value in region III. Therefore, these figures demonstrate that the plots are consistent with the results of the goodness-of-fit measure. results of L-moment ratio plots are consistent with the results of the goodness-of-fit measure. Figure 5 and Figure 6 plot the observed and simulated values for each region of RX1day, RX5day, RX7day, R95P series, respectively. They show that the points fall on the line closely enough

Atmosphere 2019, 10, x; doi: FOR PEER REVIEW www.mdpi.com/journal/atmosphere Atmosphere 2019, 10, x FOR PEER REVIEW 14 of 26 for the optimal distributions for each HOM region. The MARE results for each HOM region of RX1day, RX5day, RX7day, R95P series summarized in the last column of Table 3 demonstrate that the MARE values range from 3.19% to 6.41% and the best-fit distribution for each HOM region can describe the precipitation extremes well. Hence, it is reasonable that the best-fit distributions for each Atmosphereof the2019 HOM, 10, 130 regions are adequate in predicting the quantile estimates according to the results13 of 25above.

Figure 3. L-moment ratio plot for RX1day (a,b,c) and RX5day (d,e,f) series at three HOM regions. Figure 3. L-moment ratio plot for RX1day (a,b,c) and RX5day (d,e,f) series at three HOM regions.

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Figure 4. L-moment ratio plot for RX7day (a,b,c) and R95P (d,e,f) series at three HOM regions. Figure 4. L-moment ratio plot for RX7day (a,b,c) and R95P (d,e,f) series at three HOM regions. Figures5 and6 plot the observed and simulated values for each region of RX1day, RX5day, RX7day, R95P series, respectively. They show that the points fall on the line closely enough for the optimal distributions for each HOM region. The MARE results for each HOM region of RX1day, RX5day, RX7day, R95P series summarized in the last column of Table3 demonstrate that the MARE values range from 3.19% to 6.41% and the best-fit distribution for each HOM region can describe the

Atmosphere 2019, 10, x; doi: FOR PEER REVIEW www.mdpi.com/journal/atmosphere Atmosphere 2019, 10, 130 15 of 25 precipitation extremes well. Hence, it is reasonable that the best-fit distributions for each of the HOM Atmosphere 2019, 10, x FOR PEER REVIEW regions are adequate in predicting the quantile estimates according to the results above. 16 of 26

Figure 5. Observation and simulation value of precipitation extremes in each region of RX1day (a,b,c) andFigure RX5day 5. Observation (d,e,f) series. and simulation value of precipitation extremes in each region of RX1day (a,b,c) and RX5day (d,e,f) series.

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FigureFigure 6. 6.Observation Observation and and simulation simulation value value of of precipitation precipitation extremes extremes in in each each region region of of RX7day RX7day ( a(a,b,b,c,c)) and R95P (d,e,f) series. and R95P (d,e,f) series.

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Table 4. Accuracy measures for estimated growth curve of the HJRB precipitation extreme.

RX1day RX5day RX7day R95P HOM Region F q(F) RMSE Bounds0.05 Bounds0.95 q(F) RMSE Bounds0.05 Bounds0.95 q(F) RMSE Bounds0.05 Bounds0.95 q(F) RMSE Bounds0.05 Bounds0.95 0.500 0.919 0.013 0.898 0.938 0.943 0.010 0.926 0.958 0.940 0.010 0.923 0.956 0.955 0.009 0.940 0.969 0.800 1.239 0.009 1.224 1.253 1.272 0.010 1.256 1.287 1.264 0.009 1.249 1.279 1.244 0.009 1.230 1.258 0.900 1.467 0.022 1.435 1.507 1.479 0.021 1.446 1.515 1.470 0.021 1.439 1.507 1.422 0.019 1.393 1.457 Region I 0.950 1.698 0.045 1.628 1.781 1.670 0.035 1.616 1.732 1.661 0.035 1.607 1.724 1.584 0.031 1.535 1.641 0.980 2.012 0.084 1.885 2.165 1.905 0.056 1.824 2.005 1.899 0.056 1.815 1.997 1.783 0.049 1.708 1.871 0.990 2.260 0.120 2.086 2.480 2.075 0.072 1.972 2.205 2.071 0.073 1.962 2.199 1.926 0.063 1.827 2.039 0.999 3.165 0.283 2.756 3.711 2.607 0.129 2.426 2.850 2.613 0.131 2.417 2.848 2.369 0.112 2.200 2.573 0.500 0.924 0.014 0.900 0.944 0.924 0.011 0.905 0.940 0.930 0.010 0.912 0.946 0.965 0.008 0.951 0.978 0.800 1.226 0.010 1.209 1.240 1.239 0.009 1.224 1.253 1.246 0.009 1.230 1.261 1.253 0.009 1.238 1.268 0.900 1.454 0.022 1.419 1.492 1.464 0.018 1.439 1.498 1.466 0.018 1.437 1.497 1.427 0.017 1.400 1.455 Region II 0.950 1.706 0.047 1.639 1.790 1.694 0.037 1.641 1.764 1.687 0.037 1.632 1.750 1.583 0.029 1.537 1.633 0.980 2.096 0.097 1.960 2.276 2.013 0.077 1.904 2.158 1.985 0.073 1.875 2.114 1.775 0.047 1.696 1.857 0.990 2.447 0.152 2.236 2.733 2.268 0.117 2.103 2.494 2.218 0.110 2.058 2.416 1.913 0.063 1.809 2.027 0.999 4.110 0.492 3.440 5.113 3.226 0.329 2.771 3.882 3.056 0.295 2.630 3.594 2.347 0.123 2.151 2.567 0.500 0.915 0.013 0.893 0.935 0.936 0.010 0.918 0.952 0.927 0.012 0.907 0.947 0.960 0.009 0.945 0.975 0.800 1.253 0.011 1.235 1.270 1.259 0.011 1.241 1.276 1.260 0.009 1.245 1.275 1.247 0.009 1.232 1.261 0.900 1.499 0.021 1.466 1.535 1.476 0.019 1.445 1.510 1.486 0.022 1.453 1.525 1.420 0.018 1.392 1.451 Region III 0.950 1.753 0.045 1.683 1.830 1.688 0.037 1.631 1.752 1.708 0.042 1.643 1.782 1.576 0.030 1.528 1.629 0.980 2.112 0.093 1.969 2.276 1.966 0.070 1.860 2.095 2.002 0.075 1.887 2.138 1.767 0.047 1.690 1.848 0.990 2.403 0.142 2.190 2.663 2.178 0.103 2.022 2.369 2.228 0.106 2.068 2.419 1.902 0.061 1.804 2.007 0.999 3.526 0.410 2.939 4.322 2.897 0.263 2.523 3.387 3.021 0.239 2.655 3.458 2.319 0.110 2.148 2.515 Note: Accuracy measures for the estimated growth curve are defined by Equations (17) and (18) but with Q_i (F) and Q ˆ_iˆm (F) replaced by q(F) and q ˆ_iˆm (F), respectively. Tabulated values are, for each nonexceedance probability F, the estimated regional quantiles, regional average relative RMSE of estimated growth curve and their 95% error bounds for the estimated growth curve. Atmosphere 2019, 10, 130 18 of 25 Atmosphere 2019, 10, x FOR PEER REVIEW 19 of 26 4.4.4.4. Accuracy Accuracy and and Uncertainty Uncertainty Analysis Analysis of Quantileof Quantile Estimations Estimations TheThe estimated estimated regional regional quantiles, quantiles, regional regional average average relative relative RMSE RMSE of of estimated estimated growth growth curve curve and and theirtheir 95% 95% error error bounds bounds for for the the estimated estimated growth growt curveh curve are are tabulated tabulated in in Table Table4. The4. The results results indicate indicate thatthat the the RMSE RMSE values values for for three three sub-regions sub-regions of of HJRB HJRB basically basically increase increase with with the the increase increase of of frequency frequency forfor all all series, series, and and RMSEs RMSEs range range from from 0.008 0.008 to to 0.152 0.15 when2 when return return periods periods are are less less than than 100 100 years; years; however,however, the the RMSE RMSE values values are are relatively relatively larger larger and and range range from from 0.110 0.110 to 0.492 to 0.4 when92 when the returnthe return period period is 1000is 1000 years, years, which which implies implies that thethat quantitle the quantitle estimates estimates are reliable are reliable enough enough when when return return periods period are lesss are thanless 100 than years, 100 and years, estimates and estimates of a higher of returna higher period return (e.g., period 1000 (e.g. years), 1000 become years) unreliable. become un In addition,reliable. In it canaddition be seen, it can from be Figure seen from7 that Figure the RMSEs 7 that of the R95P RMSEs series of areR95P about series 0.1 are and about the values 0.1 and of the the values three of regionsthe three are regions very close are when very close the return when periodthe return is equal period to is 1000 equal years. to 1000 If the years. historical If the recordshistorical are records not sufficientare not andsufficient the estimated and the quantilesestimated are quantiles needed are when needed the return when period the return is 1000 period years, is the1000 estimated years, the quantilesestimated of R95Pquantiles series of are R95P relatively series are reliable relatively in the reliable HJRB. in the HJRB.

0.5

0.4

0.3

RMSE 0.2

0.1

0 RX1day RX5day RX7day R95P Region I Region II Region III

Figure 7. The RMSE values of three HOM regions for RX1day, RX5day, RX7day and R95P when return periodFigure is 100 7. The years. RMSE values of three HOM regions for RX1day, RX5day, RX7day and R95P when return period is 100 years. 4.5. Spatial Characteristics of Annual Rainfall Extremes 4.5. Spatial Characteristics of Annual Rainfall Extremes The spatial associations of precipitation extremes between sites and the map of precipitation for HJRBThe are spatial quantified associations by kriging of precipitation interpolation. extrem Estimatedes between maps sites of annual and the precipitation map of precipitation extremes for inHJRB HJRB are for RX1day,quantified RX5day, by kriging RX7day interpolation. and R95P withEstimated the 100 map yearss of return annual periods precipitation are illustrated extremes in in FigureHJRB8. Itfor can RX1day, be observed RX5day, from RX7day Figure8 A–Dand R95P that precipitation with the 100 extremes years return in region periods I increase are illustrated gradually in fromFigure north 8. to It south, can be and observed plenty offrom precipitation Figures 8 observationsA–D that precipitation were made upstreamextremes in the region south I increase of the HJRBgradually next to from the Du north River, to south, South Riverand plenty and Daba of precipitation Mountain areas observation which ares were close made to the upstream Danjiangkou in the Reservoir.south of Thisthe HJRB provides next sufficientto the Du climateRiver, South conditions River (e.g.,and Daba humidity Mountain and precipitation) areas which are responsible close to the forDanjiangkou the occurring Reservoir. floods in This these provide regionss sufficient from the climate meteorological conditions point (e.g. of, humidity view. In regionand precipitation) II and III ofresponsible HJRB, it can for be the observed occurring that floods the precipitation in these regions extremes from gradually the meteorological increase from point the of northwestview. In region to theII southeast and III of and HJRB, the precipitationit can be observed extremes that are the mainly precipitation concentrated extremes in the gradually area of Tianmen, increase Wuhanfrom the andnorthwest Zhongxiang to the stations southeast which and are the located precipitation in Jianghan extremes Plain are in the mainly downstream concentrated part of in the the HJRB.area of TheTianmen, results of Wuhan seasonality and Zhongxiang of precipitation stations extremes which in 3are HOM located regions in Jianghan are illustrated Plain inin Figurethe downstream9. It can bepart observed of the that,HJRB. for The RX1day, results RX5dayof seasonality and RX7day of precipitation in the HJRB, extremes more in than 3 HOM 90% regions of the precipitation are illustrated extremein Figure events 9. It occur can be during observed the rainythat, seasonfor RX1day, from MayRX5day to October and RX7day and more in the than HJRB, 30% more of the than extreme 90% of eventsthe precipitation concentrate inextreme July. These events events occur willduri triggerng the floodsrainy season with different from May magnitudes, to October andand Julymore and than August30% of are the well extreme recognized events as the concentrate primary flood-season in July. These for such events regions. will trigger floods with different magnitudes, and July and August are well recognized as the primary flood-season for such regions.

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Figure 8. Spatial mapping of estimated annual precipitation extremes in HJRB when return periods areFigureFigure 100 8.8. years SpatialSpatial using mappingmapping L-moments of of estimated estimated based annual annual regional precipitation precipitation frequency extremes analysisextremes in approach, HJRBin HJRB when when (A return): return RX1day; periods periods (B are): RX5day;100are years 100 ( yearsC using): RX7day; using L-moments ( LD-moments): R95P. based basedregional regional frequency frequency analysis analysis approach, approach, (A): RX1day; (A): RX1day; (B): RX5day; (B): (RX5day;C): RX7day; (C): (RX7day;D): R95P. (D): R95P.

0.4 (A) Region I (B) Region II 0.4 0.35 (A) Region I (B) Region II 0.4 0.35 0.3 0.4 0.35 0.3 0.35 0.250.3 0.25 0.3 0.2 RX1day 0.2 0.25 0.25 RX1day 0.15 RX5day 0.15 Frequency 0.2 RX1day 0.2 RX5day 0.1 Frequency 0.1 RX1day 0.15 RX7dayRX5day 0.15 Frequency RX7dayRX5day Frequency 0.05 0.050.1 0.1 RX7day 0 0.050 0.05 RX7day 0 0

(C) Region III 0.4 0.35 (C) Region III 0.4 0.3 0.35 0.25 0.3 0.2 0.25 0.15 RX1day

Frequency 0.2 RX5day 0.1 RX1day 0.15 RX7day

Frequency 0.05 RX5day 0.1 0 RX7day 0.05 0

Figure 9. Seasonality of precipitation extremes in the three typical HOM regions. Figure 9. Seasonality of precipitation extremes in the three typical HOM regions. Figure 9. Seasonality of precipitation extremes in the three typical HOM regions.

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5. Discussion In the literature, a single index was often used in the analysis of extreme precipitation events [57,58]. However, the comprehensive characterization of extreme precipitation events should be described from multiple indicators, due to the limitations of a single index to capture the full picture of extreme precipitation events. In this study, four indices including RX1day, RX5day, RX7day and R95P are derived for analysis. These indices can be enough to capture the full picture of extreme precipitation events in the HJRB. L-moments based methods have been widely used in the regional frequency analysis [59,60]. In previous studies, limited attention was paid to testing stationarity and serial correlation to guarantee reliable estimates, which may lead to incorrect results and conclusions. In this study, the Mann-Kendall method and autocorrelation coefficients were employed to test the stationarity and independence of extreme precipitation, respectively. The stations (Shangzhou, Fengjie and Wuhan) showing significant trends were non-stationary and not included in the further analysis. The stations in Jianghan Plain have no significant trends except the Wuhan station which shows a significant increasing trend. As a megacity, Wuhan has a population of over 10 million. Many factors (e.g., global warming, land use change and urbanization) may lead to the upward trend for extreme precipitation in Wuhan. Urban environments are playing an increasingly important role in land-surface processes and climate change [61]. Urban areas modify boundary layer processes through the creation of “urban heat islands”. Early investigations noted evidence of warm seasonal rainfall increases of 9%–17% downwind of major cities [62,63]. Kishtawal et al. assessed the urbanization impacts on the heavy rainfall climatology during the Indian summer monsoon and concluded that the observed increasing trend in the frequency of heavy rainfall events over Indian monsoon regions is more likely to be over regions where the pace of urbanization is faster [61]. Analysis at a site-based scale is difficult in understanding the changing pattern and possible relations between external drivers, mainly due to the local scale variation (e.g., land use change and urbanization). Therefore, a regionalization by cluster analysis was employed to identify the homogeneous sub-regions and to study the spatio-temporal pattern characteristics of extreme precipitation in the HJRB. Hydrological regionalization is generally based on factors that affect the frequency distribution of precipitation. The stations that have the same or similar impact factors can be categorized into the same sub-region. There are many factors affecting precipitation, such as latitude, longitude, elevation, distance to water bodies, slope, etc., especially in mountainous areas. Geographic proximity is not the only criteria for hydrological regionalization and does not mean that the frequency distribution of the two sites is similar. The site characteristics used are judged to be of importance in defining a site’s precipitation climate, including indicators of precipitation amounts and the sites’ geographic location [29]. In this study, four variables are selected to describe the precipitation climate, which are latitude, longitude, elevation and the mean annual precipitation. Five distributions including GEV, GLO, GNO, GPA, and P III are investigated in each homogeneous region for RX1day, RX5day, RX7day and R95P in the goodness-of-fit test. MARE values range from 3.19% to 6.41% are calculated by using the best-fit distribution for each HOM region demonstrate that the best-fit distributions for each HOM regions are adequate in predicting the quantiles estimates. The RMSE values of the estimated quantiles for three HOM regions in the HJRB range from 0.008 to 0.152 when return periods are less than 100 years. However, the RMSE values are relatively large and range from 0.110 to 0.492 when the return period is 1000 years. These results indicate that quantile estimates are reliable enough when return periods are less than 100 years. Yang et al. utilized an index variable method and L-moments to analyze the extreme precipitation for the Pearl River Basin in China and pointed out that the quantile estimates from regional frequency analysis were reliable enough to support flood risk assessment and water resources management when return periods were less than 100 years [29]. Meanwhile, estimates for higher return periods were unreliable and required longer time series in order to enhance the reliability in the quantile estimation. Results also indicated Atmosphere 2019, 10, 130 21 of 25 that the estimated quantiles of R95P series are relatively reliable in the HJRB when return period is 1000 years, which is in line with the findings by Du et al. [29]. Floods occurred frequently in the HJRB and lead to considerable loss on economy and human life [10,13,14]. Actually, the floods are mainly caused by extreme precipitation events and an improved knowledge of extreme precipitation is required for better understanding the flood behavior and mitigating the hazard. The spatial patterns of annual rainfall extremes play an important role in integrated water resources management. Results indicated that excessive precipitation magnitude records are observed in the areas of Du River, South River and Daba Mountain and Jianghan plain, which provides sufficient climate conditions (e.g., humidity and precipitation) responsible for the occurring floods in these regions. In the HJRB, most of the precipitation extreme events (more than 90%) occur during rainy season from May to October and more than 30% of the extreme events concentrate in July, which is affected by the sub-tropical monsoon climate. In the upstream of HJRB, the prevailing southwest monsoon and the Qinling Mountains play an important role in forming the storm floods in July. Big floods occur in August because the southeast monsoon is very active. The precipitation characteristics for the HJRB are affected by the sub-tropical monsoon climate. It can also reveal the seasonal patterns of precipitation extremes for the three regions from Figure9A–C. The precipitation extremes events occurring in May and June increase from region I to region III and the opposite trend in September and October. This means that the precipitation extremes events mainly concentrated in autumn in region I and summer in region III, which is consistent with the previous researches on precipitation extremes in HJRB [64,65]. The trough between Baikal Lake and Balkhash Lake produced by the strong western Pacific subtropical high and Ural Mountain high pressure lead to the vapor transport from Bengal Bay to the upstream of HJRB. At the same time, the trough in Baikal Lake is gradually spilt leading the cold air south and making the warm and cold air converge, which exerts influences on the extreme precipitation events in the region I, especially in the area of Du River, South River and Daba Mountain which is the center of the precipitation events (Figure8)[ 64]. Yue analyzed the water vapor of the heavy rain in detail and found that the water vapor transport at 700 hPa had a great contribution to forming a rainstorm in the west of China in autumn [66]. He et al. analyzed the temporal and spatial characteristics of the circulation pattern at 500 hPa and vapor field at 700 hPa during the autumn waterlogging upstream of the with NECP data and found that the primary sources of vapor at 700 hPa came from the Bay of Bengal and the South China Sea, which provides the source of adequate water vapor for the precipitation events [64]. Additionally, the precipitation extremes concentrated in the Tianmen, Wuhan and Zhongxiang stations which are located in Jianghan Plain in the downstream of HJRB are climatically dominated by a strong convection in spring and summer and the precipitation pattern for this region is strongly affected by the East Asian monsoon system [67]. The flux of water vapor transport has an increasing trend from northwest to southeast and there is a good correlation between precipitation water and water vapor transport in the area of Tianmen, Wuhan and Zhongxiang stations. All these mentioned above affect the extreme precipitation events over this region in summer months [65]. Two areas of the HJRB, located in the upstream of Danjiangkou Reservoir and Jianghan Plain respectively, have the larger extreme precipitation records, which will increase the risk of natural hazards to these areas. The findings from this study are of great scientific and practical merit in the integrated basin-scale water resource and flood risk management.

6. Conclusions This study is motivated by the increasing frequency of extreme precipitation events and the growing impacts of the extreme precipitation events on human health and safety across the China and the world. In this paper, the L-moments methods were employed to conduct the regional frequency analysis of annual extreme precipitation records (1969–2015) at 25 stations in the HJRB, as well as the investigation of spatio-temporal pattern characteristics of extreme rainfall events in a regional scale after regionalization. Some conclusions summarized from this investigation are as follows: Atmosphere 2019, 10, 130 22 of 25

(1) The HanJiang River Basin can be categorized into three homogenous regions with the consideration of spatially continuous and physical reasons in the areas. The optimal distribution for each HOM region is adequate in predicting the quantile estimates. (2) The spatial patterns of the extreme precipitation with different return periods are similar. The extreme precipitation amount increases gradually from middle north to southwest and southeast in the HJRB. Excessive precipitation magnitude records are observed in the areas of Du River, South River and Daba Mountain and Jianghan plain, which provide sufficient climate conditions (e.g., humidity and precipitation) responsible for the occurring floods in these regions. (3) Most of the precipitation extreme events (more than 90%) occur during the rainy season from May to October and more than 30% of the extreme events concentrate in July.

Author Contributions: W.H. and Z.H. contributed to the conception of the study. W.H. and F.Y. contributed significantly to analysis and manuscript preparation. W.H. and Q.J. performed the data analyses and wrote the manuscript. W.H. and J.H. helped perform the analysis with constructive discussions. Funding: This research was funded by the National Key Research Projects of China (Grant Number 2018YFC1508001 and 2016YFC0402704) and China Scholarship Council (CSC). Acknowledgments: The daily precipitation observations in the Hanjiang River Basin used in this study were provided by China Meteorological Administration and the National Climate Center. They are highly appreciated. Comments and suggestions from an Associate Editor and two anonymous reviewers are gratefully acknowledged. Conflicts of Interest: The authors declare no conflict of interest.

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