# Changing Properties of Daily Precipitation Concentration in the Hai River Basin, China

Authors: Ren Zheng; Zhao Yong; Chen Ling; Gong Jiaguo; Wang Li
Journal: Scientific Programming
 (2023)

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## Abstract

Understanding the spatiotemporal pattern of precipitation concentration is important for the assessment of flood and drought risk and utilization of water resources. In this study, the daily precipitation concentration index in the Hai River basin in China was calculated based on the Gini coefficient obtained from the observed data of 51 meteorological stations from 1951 to 2018 and spatiotemporal pattern variations were investigated. The trends and abrupt changes of DPCI were tested by the Mann–Kendall and the Pettitt methods, respectively. The relationships among DPCI, percentage of precipitation contributed by the rainiest days, and disaster losses were discussed by the linear correlation analysis. The results showed that the DPCI value ranges between 0.6471 and 0.7938, decreases westward and northward, which is negatively related to latitude and elevation, and is positively related to longitude. Negative trends of the DPCI were found at most stations, and the PCI trends of more than 80% stations were statistically significant. Abrupt changes of the DPCI have a postponement trend from west to east with time. Daily heterogeneity of the rainfall in a year is highly correlated with the heavy rainfall amount of the 25% rainiest days. For a year, higher DPCI coupled with more precipitation is easy to cause a flood disaster; conversely, higher DPCI along with less precipitation is easy to cause a drought disaster. In the future, the risk of flood disasters would be reduced, but the drought disasters would be increased in the Hai River basin.


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## Body

## 1. Introduction

The study regarding climatic variables has received considerable attention from researchers throughout the world. In general, there are two main climatic variables, which are temperature with cold and warm changes and precipitation with dry and wet changes [1–3]. Precipitation, as an important factor in the water cycle, determines the availability of water resources, the type and extent of agriculture, and natural physical phenomena [4]. With climate warming, precipitation intensity, amounts, and patterns are expected to change, and natural disasters are likely to occur more frequently [5–7]. Precipitation extremes, such as heavy precipitation events occurring over very few days that account for high percentages of the annual total, are directly responsible for flood occurrences and will bring more frequent disasters for human society [8]. One typical example of the daily precipitation concentration degree involved in the precipitation in Henan province of China on 20 July, 2021, when the equivalent fell of what exceeds 40% of the annual total precipitation. The flood involved 14.786 million people of 150 regions in Henan province, and the direct economic loss reached 120.06 billion yuan. Thus, the analysis of daily precipitation concentration is an important issue in climate research and can be useful to evaluate risks linked to extreme precipitation events [9].The daily precipitation concentration index (DPCI) is an index for describing the varying involvement of daily precipitation, considering the contribution of days with the greatest amount of precipitation to the total amount of precipitation [10]. Higher values of precipitation concentration in a certain region mean that precipitation amount would mostly concentrate within a shorter period of time. Since the DPCI has been developed by Cortesi et al., it has been widely used in the analysis of precipitation concentration in Europe [11], Peninsular Malaysia [12], Iran [8, 13], Southern Russia [14], Central-Southern Chile [4], Puerto Rico [15], and Central Asia [16]. In China, spatial and temporal variabilities of DPCI have been investigated in different regions. However, systematic differences exist. On the basis of 40 sites in the Pearl River basin measured during 1960–2005, Zhang et al. identified lower and decreasing DPCI in the southwest and northeast parts, but higher and increasing DPCI in the northwest and south parts [17]. The study by Li et al. showed that higher DPCIs were mainly observed in Southern Xinjiang, whereas lower DPCIs were mostly detected in Northern Xinjiang. The most parts of Xinjiang are characterized by no significant trends of DPCI at the 0.05 significance level [18]. Shi et al. found that the lowest DPCIs occurred mainly in the upper reaches of the Lancang River basin, where a significant and negative trend in DPCI that exceeding the 95th percentile was also detected [10]. However, positive trends in the DPCI were found at most stations in the upper reaches of the Huai River basin, although none of the DPCI trends were statistically significant [19]. Yuan et al. also discussed the trends of DPCI in Shanxi province and showed that there were negative trends of DPCI with larger trends in the plain area than in the alpine area [20]. Wang et al. discovered spatiotemporal changes of the DPCI in Northeast China, where the DPCIs decreased slightly in most areas and the regions of the highest value were in Liaoning province [21]. More recently, Mei et al. examined changes to the distribution of the DPCI from 36 meteorological stations in the Yangtze River Delta from 1960 to 2017, and they found that DPCIs of 22 stations (accounting for 61%) showed increasing trends, while three stations increased significantly at the 95% significant level [22].The Hai River basin (HRB) is of particular interest because it is an important water source for Beijing, the capital of China, and Xiong’an New Area, a national new area. Understanding the effects of spatial-temporal variations in the precipitation concentration index in the HRB is a key to urban water resources management, especially in the context of climate change and human activities. A few studies have addressed these changes in precipitation within the HRB. These studies identified precipitation trends during the annual and seasonal spells [23], as well as extreme precipitation events [24, 25]. However, few studies have analyzed the contribution of daily rainstorm to total precipitation amount of a certain spells. Investigating the DPCI in the HRB could provide a solid basis for analyzing the relationship between water resources and climate change within the basin. At the same time, this investigation would provide support for making decisions about water resource allocation in the middle route of the South-to-North Water Transfer project and for urban construction to reduce risks of urban flood-induced impacts. The main purpose of this paper is to explore (i) the spatial pattern variations of daily precipitation concentration; (ii) temporal trends and abrupt changes of daily precipitation concentration; and (iii) the relationship between daily precipitation distribution in a year and percentage of precipitation contributed by the rainiest days. This paper is organized as follows. Section 2 describes the study area and data employed in this study. Section 3 introduces the DPCI and other methods involved in this paper. The results and discussion are presented in Sections 4 and 5, respectively. Finally, conclusions are drawn in Section 6.


## 2. Study Area and Data

### 2.1. Study Area

The HRB (Figure1), the most important grain-production regions in northern China, lies between approximately 112° E and 120° E and 35° N and 43° N [26]. The basin includes most or part of eight provincial administrative regions (Beijing, Tianjin, Hebei, Shanxi, Henan, Shandong, Inner Mongolia, and Liaoning) and has an area of about 318,000 km2, which accounts for 3.3% of the entire land area of China [27]. The basin has been the political, economic, and cultural center of China since ancient times and has a current population of 154 million, accounting for 11% of China’s total population. There are eight main tributaries (Luan River, Jiyun River, Chaobai River, Yongding River, Daqing River, Ziya River, Nanyun River, and Majia River) that flow eastward to the Sea of Bohai with elevations ranging from 0 to 3024 m above the mean sea level based on a digital elevation model (30 m × 30 m grids) of the basin.Figure 1
Location of meteorological stations in the Hai River basin.The climate of the HRB, determined by the monsoon, is typically semi-humid and semiarid [26]. In the wet season (May–October), the influence of southwest monsoon from the Bay of Bengal and southeast monsoon from the West Pacific favors large amounts of precipitation. In contrast, the dry season (November–April) is prone to serious drought. Therefore, there is an uneven distribution of precipitation throughout the year. The average annual precipitation in the basin is about 548 mm, which is mainly concentrated in the wet season. Moreover, about 80% of the annual precipitation occurs in the flood season from June to September [27].


### 2.2. Data

The daily precipitation data for the HRB and its surroundings are provided by the National Climatic Center (NCC) of the China Meteorological Administration (CMA) and can be downloaded fromhttps://data.cma.cn/data/cdcindex/cid/6d1b5efbdcbf9a58.html. Within the HRB, daily precipitation data at 51 meteorological stations, the locations of which are shown in Figure 1, are used to analyze the temporal and spatial variability of daily precipitation concentration (Table 1). The longest time series of daily precipitation data among 51 meteorological stations are 68 years from 1951 to 2018. In contrast, the shortest time series are 46 years from 1973 to 2018. To ensure data continuity and integrity, the daily precipitation data gaps at a specific station were interpolated by an inverse distance weighting (IDW) [28] based on data from adjacent meteorological stations and thus daily precipitation data of 51 stations were all extended to the period of 1951–2018.Table 1
Description of 51 meteorological stations of the Hai River basin.
Station names (Abbr.)Station numbersLatitude (°N)Longitude (°E)Elevation (m)Data seriesZhangbei (ZB)5339941.15114.701393.31956–2018Youyu (YY)5347840.00112.451345.81957–2018Datong (DT)5348740.08113.421052.61955–2018Tianzhen (TZ)5349040.43114.051014.71957–2018Shuozhou (SZ)5357839.37112.431114.81957–2018Daixian (DX)5357939.02112.90859.71957–2018Wutaishan (WTS)5358838.95113.522209.31956–2018Yuxian (YX)5359339.83114.57910.51954–2018Lingqiu (LQ)5359439.45114.18938.71971–2018Yuanping (YP)5367338.73112.72828.21954–2018Pingding (PD)5368737.78113.63753.01972–2018Shijiazhuang (SJZ)5369838.07114.35103.61955–2018Taigu (TG)5377537.42112.60786.71959–2018Yushe (YS)5378737.07112.981042.31957–2018Xingtai (XT)5379837.07114.5078.51954–2018Anze (AZ)5387736.17112.25861.01957–2018Changzhi (CZ)5388236.07113.031046.91973–2018Xiangyuan (XY)5388436.52113.03877.91957–2018Anyang (AY)5389836.05114.13194.81951–2018Xinxiang (XX)5398635.32113.8873.21951–2018Linxi xian (LXX)5411543.63118.03825.01952–2018Duolunxian (DLX)5420842.18116.471245.41952–2018Fengning (FN)5430841.20116.63736.31956–2018Weichang (WC)5431141.97117.77893.81951–2018Zhangjiakou (ZJK)5440140.77114.92772.81956–2018Huailai (HL)5440540.42115.50570.91954–2018Yanqing (YQ)5440640.45115.97487.91959–2018Miyun (MY)5441640.38116.8771.81957–2018Chengde (CD)5442340.97117.92422.31951–2018Zunhua (ZH)5442940.20117.9554.91956–2018Qinglong (QL)5443640.42118.95255.41957–2018Qinhuangdao (QHD)5444939.85119.522.41954–2018Jianchang (JC)5445240.80119.82365.51959–2018Beijing (BJ)5451139.80116.4731.31951–2018Bazhou (BZ)5451839.17116.408.91957–2018Baodi (BD)5452539.73117.285.11959–2018Tianjin (TJ)5452739.08117.053.51951–2018Tangshan (TS)5453439.65118.1023.21957–2018Caofeidian (CFD)5453539.28118.473.21956–2018Laoting (LT)5453939.43118.888.51957–2018Baoding (BDG)5460238.73115.4816.81955–2018Raoyang (RY)5460638.23115.7319.01957–2018Botou (BT)5461838.08116.5513.21957–2018Tanggu (TGG)5462339.05117.724.81951–2018Huanghua (HH)5462438.40117.324.51956–2018Nangong (NG)5470537.37115.3828.61958–2018Lingxian (LX)5471537.32116.5718.61962–2018Huimin (HM)5472537.50117.5311.71951–2018Kenli (KL)5474437.58118.558.51967–2018Shenxian (SX)5480836.23115.6339.11957–2018Jinan (JN)5482336.60117.00171.21951–2018The loss data of flood and drought disasters in the HRB comes from the “flood and drought disasters in the Haihe River Basin” composed by the Haihe River Water Conservancy Commission, Ministry of Water Resources of the People’s Republic of China (MWR) [29].


## 2.1. Study Area

The HRB (Figure1), the most important grain-production regions in northern China, lies between approximately 112° E and 120° E and 35° N and 43° N [26]. The basin includes most or part of eight provincial administrative regions (Beijing, Tianjin, Hebei, Shanxi, Henan, Shandong, Inner Mongolia, and Liaoning) and has an area of about 318,000 km2, which accounts for 3.3% of the entire land area of China [27]. The basin has been the political, economic, and cultural center of China since ancient times and has a current population of 154 million, accounting for 11% of China’s total population. There are eight main tributaries (Luan River, Jiyun River, Chaobai River, Yongding River, Daqing River, Ziya River, Nanyun River, and Majia River) that flow eastward to the Sea of Bohai with elevations ranging from 0 to 3024 m above the mean sea level based on a digital elevation model (30 m × 30 m grids) of the basin.Figure 1
Location of meteorological stations in the Hai River basin.The climate of the HRB, determined by the monsoon, is typically semi-humid and semiarid [26]. In the wet season (May–October), the influence of southwest monsoon from the Bay of Bengal and southeast monsoon from the West Pacific favors large amounts of precipitation. In contrast, the dry season (November–April) is prone to serious drought. Therefore, there is an uneven distribution of precipitation throughout the year. The average annual precipitation in the basin is about 548 mm, which is mainly concentrated in the wet season. Moreover, about 80% of the annual precipitation occurs in the flood season from June to September [27].


## 2.2. Data

The daily precipitation data for the HRB and its surroundings are provided by the National Climatic Center (NCC) of the China Meteorological Administration (CMA) and can be downloaded fromhttps://data.cma.cn/data/cdcindex/cid/6d1b5efbdcbf9a58.html. Within the HRB, daily precipitation data at 51 meteorological stations, the locations of which are shown in Figure 1, are used to analyze the temporal and spatial variability of daily precipitation concentration (Table 1). The longest time series of daily precipitation data among 51 meteorological stations are 68 years from 1951 to 2018. In contrast, the shortest time series are 46 years from 1973 to 2018. To ensure data continuity and integrity, the daily precipitation data gaps at a specific station were interpolated by an inverse distance weighting (IDW) [28] based on data from adjacent meteorological stations and thus daily precipitation data of 51 stations were all extended to the period of 1951–2018.Table 1
Description of 51 meteorological stations of the Hai River basin.
Station names (Abbr.)Station numbersLatitude (°N)Longitude (°E)Elevation (m)Data seriesZhangbei (ZB)5339941.15114.701393.31956–2018Youyu (YY)5347840.00112.451345.81957–2018Datong (DT)5348740.08113.421052.61955–2018Tianzhen (TZ)5349040.43114.051014.71957–2018Shuozhou (SZ)5357839.37112.431114.81957–2018Daixian (DX)5357939.02112.90859.71957–2018Wutaishan (WTS)5358838.95113.522209.31956–2018Yuxian (YX)5359339.83114.57910.51954–2018Lingqiu (LQ)5359439.45114.18938.71971–2018Yuanping (YP)5367338.73112.72828.21954–2018Pingding (PD)5368737.78113.63753.01972–2018Shijiazhuang (SJZ)5369838.07114.35103.61955–2018Taigu (TG)5377537.42112.60786.71959–2018Yushe (YS)5378737.07112.981042.31957–2018Xingtai (XT)5379837.07114.5078.51954–2018Anze (AZ)5387736.17112.25861.01957–2018Changzhi (CZ)5388236.07113.031046.91973–2018Xiangyuan (XY)5388436.52113.03877.91957–2018Anyang (AY)5389836.05114.13194.81951–2018Xinxiang (XX)5398635.32113.8873.21951–2018Linxi xian (LXX)5411543.63118.03825.01952–2018Duolunxian (DLX)5420842.18116.471245.41952–2018Fengning (FN)5430841.20116.63736.31956–2018Weichang (WC)5431141.97117.77893.81951–2018Zhangjiakou (ZJK)5440140.77114.92772.81956–2018Huailai (HL)5440540.42115.50570.91954–2018Yanqing (YQ)5440640.45115.97487.91959–2018Miyun (MY)5441640.38116.8771.81957–2018Chengde (CD)5442340.97117.92422.31951–2018Zunhua (ZH)5442940.20117.9554.91956–2018Qinglong (QL)5443640.42118.95255.41957–2018Qinhuangdao (QHD)5444939.85119.522.41954–2018Jianchang (JC)5445240.80119.82365.51959–2018Beijing (BJ)5451139.80116.4731.31951–2018Bazhou (BZ)5451839.17116.408.91957–2018Baodi (BD)5452539.73117.285.11959–2018Tianjin (TJ)5452739.08117.053.51951–2018Tangshan (TS)5453439.65118.1023.21957–2018Caofeidian (CFD)5453539.28118.473.21956–2018Laoting (LT)5453939.43118.888.51957–2018Baoding (BDG)5460238.73115.4816.81955–2018Raoyang (RY)5460638.23115.7319.01957–2018Botou (BT)5461838.08116.5513.21957–2018Tanggu (TGG)5462339.05117.724.81951–2018Huanghua (HH)5462438.40117.324.51956–2018Nangong (NG)5470537.37115.3828.61958–2018Lingxian (LX)5471537.32116.5718.61962–2018Huimin (HM)5472537.50117.5311.71951–2018Kenli (KL)5474437.58118.558.51967–2018Shenxian (SX)5480836.23115.6339.11957–2018Jinan (JN)5482336.60117.00171.21951–2018The loss data of flood and drought disasters in the HRB comes from the “flood and drought disasters in the Haihe River Basin” composed by the Haihe River Water Conservancy Commission, Ministry of Water Resources of the People’s Republic of China (MWR) [29].


## 3. Methodology

### 3.1. DPCI Calculation

The DPCI is an important indicator that is used to evaluate the relative importance of the daily precipitation classes, especially the contribution of the largest daily event to the total amount and the cumulative percentage of precipitation contributed by the cumulative percentage of days when precipitation occurred [4]. Among many daily precipitation concentration indices, the Gini coefficient (GC) was recommended to characterize daily precipitation concentration [30]. Generally, the GC with a range from 0 to 1 is a common indicator used to measure the income/wealth gap of residents in a country or region [31]. The greater GC means the greater national income gap. In this paper, the GC was used to measure daily precipitation concentration, and the DPCI can be calculated as follows [16, 32, 33]:(1)DPCI=1nn+1−2∑i=1nn+1−iyi∑i=1nyi,where n is the number of rainy days in a year, yi is precipitation in ith rainy day (mm), and yi ≤ yi+1. The day with precipitation over 0.1 mm defined as a rainy day in meteorology was used to separate rainy and rainless days [34].


### 3.2. Trend Test

The Mann–Kendall (MK) test is a nonparametric test method proposed by Mann and Kendall [35], which widely was used to evaluate statistically significant trends in hydro-meteorological time series. For a time series X=x1,x2,…,xi,…,xm (m > 10), the MK test statistic Z is calculated as follows [36]:(2)Z=S−1VarS,S>0,0,S=0,S+1VarS,S<0.In which,(3)S=∑i=2m∑j=1i−1Sgnxi−xj,where Sgnθ is equal to 1, 0, or −1 when θ is greater than, equal to, or less than 0, respectively; VarS is variance of S and can be calculated by the following formula:(4)VarS=mm−12m+518.For the MK test, the positive value ofZ represents an upward trend and the negative value represents a downward trend. If Z is greater than 1.64, 1.96, and 2.57, the trends of X have significance levels of 10%, 5%, and 1%, respectively. More detailed procedures of the MK test can be found in the study by Shi et al. [10].


### 3.3. Abrupt Change Analysis

The Pettitt (P) test developed by Pettitt (1979) was used to determine the occurrence of a change point in this paper. For a time seriesX=x1,x2,…,xi,…,xm, the P test statistic U is calculated as follows [16, 37, 38]:(5)Ut=Ut−1+∑i=1mSgmxt−xi,where Sgmϕ is equal to 1, 0, or −1 when ϕ is greater than, equal to, or less than 0, respectively; t=2,3,…,m. Its statistic Zt and the associated probabilities used in the significance testing are calculated by the following equation as follows:(6)Zt=max1≤t≤mUt,P=2exp−6Zt2m2+m3.IfP is less than 0.05, a significant change point exists [37].


## 3.1. DPCI Calculation

The DPCI is an important indicator that is used to evaluate the relative importance of the daily precipitation classes, especially the contribution of the largest daily event to the total amount and the cumulative percentage of precipitation contributed by the cumulative percentage of days when precipitation occurred [4]. Among many daily precipitation concentration indices, the Gini coefficient (GC) was recommended to characterize daily precipitation concentration [30]. Generally, the GC with a range from 0 to 1 is a common indicator used to measure the income/wealth gap of residents in a country or region [31]. The greater GC means the greater national income gap. In this paper, the GC was used to measure daily precipitation concentration, and the DPCI can be calculated as follows [16, 32, 33]:(1)DPCI=1nn+1−2∑i=1nn+1−iyi∑i=1nyi,where n is the number of rainy days in a year, yi is precipitation in ith rainy day (mm), and yi ≤ yi+1. The day with precipitation over 0.1 mm defined as a rainy day in meteorology was used to separate rainy and rainless days [34].


## 3.2. Trend Test

The Mann–Kendall (MK) test is a nonparametric test method proposed by Mann and Kendall [35], which widely was used to evaluate statistically significant trends in hydro-meteorological time series. For a time series X=x1,x2,…,xi,…,xm (m > 10), the MK test statistic Z is calculated as follows [36]:(2)Z=S−1VarS,S>0,0,S=0,S+1VarS,S<0.In which,(3)S=∑i=2m∑j=1i−1Sgnxi−xj,where Sgnθ is equal to 1, 0, or −1 when θ is greater than, equal to, or less than 0, respectively; VarS is variance of S and can be calculated by the following formula:(4)VarS=mm−12m+518.For the MK test, the positive value ofZ represents an upward trend and the negative value represents a downward trend. If Z is greater than 1.64, 1.96, and 2.57, the trends of X have significance levels of 10%, 5%, and 1%, respectively. More detailed procedures of the MK test can be found in the study by Shi et al. [10].


## 3.3. Abrupt Change Analysis

The Pettitt (P) test developed by Pettitt (1979) was used to determine the occurrence of a change point in this paper. For a time seriesX=x1,x2,…,xi,…,xm, the P test statistic U is calculated as follows [16, 37, 38]:(5)Ut=Ut−1+∑i=1mSgmxt−xi,where Sgmϕ is equal to 1, 0, or −1 when ϕ is greater than, equal to, or less than 0, respectively; t=2,3,…,m. Its statistic Zt and the associated probabilities used in the significance testing are calculated by the following equation as follows:(6)Zt=max1≤t≤mUt,P=2exp−6Zt2m2+m3.IfP is less than 0.05, a significant change point exists [37].


## 4. Results

### 4.1. Spatial Distribution of Average DPCI Values

The annual DPCI values were calculated for 51 meteorological stations in the HRB for the period from 1951 to 2018. The average PDCI across almost every decade years and all the years, for each of 51 stations separately, is listed in Table2. The average PDCI for 51 stations during 1951–2018 ranges between 0.6471 and 0.7938. The highest value of the DPCI is recorded at Beijing (BJ) station, which suffered the heaviest rainstorm of recent 61 years in July, 2012. On the contrary, the lowest value of the DPCI occurs at Datong (DT) station in the northwest of the basin. Through the analysis of the DPCI value in different periods, the following were found: (1) the average DPCI value of Beijing (BJ) station is at a higher value, and the lowest value in different periods is greater than 0.768, but that of Datong (DT) station is at a low value, and the highest value is less than 0.671; (2) the average DPCI value of Beijing (BJ) station as the highest value appeared in the 1950s, 1960s, and 2010s, and that of Datong (DT) station as the lowest value appeared in the 1950s, 1990s, 2000s, and 2010s; and (3) the highest average DPCI value (0.8242) appeared in Beijing (BJ) station in 1960s, but the lowest one (0.6156) appeared in Datong (DT) station in 2010s.Table 2
Values for the average DPCI for almost every decade years and whole period during 1951–2018 at 51 stations of HRB.
Names1950s1960s1970s1980s1990s2000s2010s1951–2018ZB0.68330.69310.69940.66970.67250.67040.64790.6769YY0.68650.67470.66850.64990.66390.66050.64020.6635DT0.67010.65520.66710.64640.63540.63940.61560.6471TZ0.67470.66660.66140.64620.65220.64620.62460.6532SZ0.69170.67750.67480.66260.65280.67190.65730.6697DX0.71090.67850.68210.67060.67440.66960.65970.6778WTS0.70390.67990.68900.67010.66750.67230.67690.6796YX0.67690.67300.66880.66170.64830.64400.62950.6576LQ0.67690.65810.67340.64590.64770.65490.64190.6569YP0.69120.68270.70080.68240.67310.68520.68480.6857PD0.71150.70220.68820.70310.68960.68570.66830.6927SJZ0.68520.69020.67910.69200.68260.67800.65900.6811TG0.70490.69210.68500.70410.66790.67750.66430.6851YS0.71580.65070.66360.67720.65820.68440.65160.6713XT0.71150.69850.68410.68780.68210.67820.66450.6866AZ0.71130.66860.68570.67840.66320.67050.64130.6741CZ0.71920.67590.67510.68230.67650.68360.65670.6811XY0.70760.66570.66660.68300.64980.65750.64450.6676AY0.80960.80820.79590.79800.79250.77590.74820.7901XX0.79250.79560.79200.80620.79890.77770.74280.7871LXX0.76520.78750.78430.78480.77400.77190.73560.7725DLX0.67770.67340.67000.66140.66500.64040.66480.6645FN0.68920.70200.69200.68010.67910.66540.67900.6838WC0.77310.77760.77490.76080.76150.70740.71800.7536ZJK0.68590.67210.67600.65780.64840.64530.63750.6604HL0.70790.71750.69250.67420.68030.67490.66540.6876YQ0.70470.69830.70060.66860.66670.64910.63650.6751MY0.71930.70400.71350.69210.68410.66230.68620.6943CD0.78090.76440.76960.76970.74800.74140.72080.7565ZH0.70150.69890.69990.69390.68560.67800.70090.6939QL0.71110.71840.71240.68920.70000.68220.70530.7025QHD0.69100.70460.71130.70250.70560.68150.69770.6993JC0.70700.70730.71540.70060.71200.69650.71290.7073BJ0.81940.82420.81140.78710.77740.76830.76890.7938BZ0.71270.72680.72540.70480.68080.69580.68730.7049BD0.70640.73380.71660.70400.67600.68460.68780.7014TJ0.79280.81230.80890.79210.75920.78040.73910.7841TS0.70790.71690.71870.70010.69080.67830.68850.7002CFD0.71430.73180.73130.72430.70750.68610.69190.7127LT0.71770.73300.74580.72420.71590.70360.69940.7203BDG0.71270.73140.72130.74610.69530.67590.66660.7075RY0.70980.71560.69680.71610.67980.67340.66970.6946BT0.70610.71710.70390.72160.67200.66660.67440.6946TGG0.77400.81170.81290.80390.78920.77150.75600.7891HH0.70540.71860.72780.72430.68300.70140.68880.7073NG0.70100.70070.69200.71010.67970.67570.66770.6897LX0.69360.68680.69060.71550.69170.67780.67920.6909HM0.78500.80910.80080.79110.78280.75540.72820.7795KL0.71320.71430.71460.71860.70560.68460.68530.7053SX0.68730.69690.68340.69670.68470.68250.65390.6840JN0.76050.78520.77680.78430.78250.76390.71340.7675The DPCI values during 1951–2018 for each grid cell (30 m × 30 m) over HBR were spatially interpolated by the IDW method from 51 stations (Figure 2(h)). For the most part, high DPCI values, with averages of 0.70 in different periods, are found in eastern regions where high precipitation levels are recorded [23]. The spatial distribution characteristic of average DPCI is consistent in different periods. The DPCI values in the central and southern parts over the HRB exceed 0.675, which is consistent with the result of the study by Tong et al. [39]. There are four discrete high-value regions of DPCI, which are controlled by the Beijing (BJ) and Tianjin (TJ) stations in the Bohai Bay, Weichang (WC), and Chengde (CD) station in the northeast, Huimin (HM) station in the south, and Xinxiang (XX) and Anyang (AY) stations in the southwest. The spatial values of DPCI showed a decreasing trend in different period (Figures 2(a)–2(g)). Before 1990, the downward trend of the DPCI was relatively small, but after that, the downward trend increased significantly.Figure 2
Spatial distributions of the mean DPCI in different periods.Figure3 shows the relationship between the geographical factors (latitude, longitude, and elevation) and multiyear DPCI at 51 stations over the HRB. The DPCI changes tend to be negatively related to the altitude with R2 of 0.0065 (Figure 3(a)) and the elevation with R2 of 0.2312(Figure 3(c)) but tend to be positively related to the longitude with R2 of 0.1985 (Figure 3(b)) during 1951–2018. The lower the linear coefficients of determination (R2) indicate the existence of a nonsignificant correlation between DPCI and altitude, longitude, and elevation. In general, the average DPCI values in different periods (Figure 2) decrease northward to high altitude (Figure 3(a)), decrease westward to low longitude (Figure 3(b)), which is consistent with the results in Central-Southern Chile [4], and decrease westward and northward to high elevation (Figure 3(c)), which is consistent with the results in the Yangtze River Delta, China [22].Figure 3
The multiyear average PDCI versus latitude (a), longitude (b), and elevation (c) at 51 stations over the HRB.
(a)(b)(c)


### 4.2. Spatial Characteristics of Annual DPCI Trend

The annual DPCI values exhibit a varying temporal trend, which can be characterized as spatially heterogeneous among stations (Figure4(a)). Exception without trend in Jianchang (JC) station, other stations show negative annual DPCI trends, of which 5 stations have the trend greater than 0.001/a, 15 stations have the trend between 0.0007/a and 0.00099/a, 25 stations have the trend between 0.0004/a and 0.00069/a, and the trends of the remaining stations are less than 0.00039/a. Based on the MK test, the annual DPCI trends are also tested, and the results are shown in Figure 4(b). For the annual DPCI trend, more than 80% of the stations show significant changes at a 0.1 significance level. Among them, 37 out of 41 stations exhibit significant trends at a 0.05 significance level (|Z| > 1.96), and 29 out of 41 stations are dominated by a significant trend at a 0.01 significance level (|Z| > 2.57). The analysis results are consistent with those of Tong et al. that the daily precipitation concentrations at most stations in North China show a significant downward trend from 1960 to 2011 [39].Figure 4
Spatial trend variations of annual DPCI (a) and MK test (b) at 51 stations.
(a)(b)


### 4.3. Spatial Characteristics of Abrupt Change of Annual DPCI

Figure5 shows the possible abrupt change of annual DPCI based on the Pettitt test from 1951 to 2018. In all records, there are 22 out of 51 stations with statistically significant change points at the significant level of 5%. Meanwhile, abrupt changes are more likely to occur during the 1980s, accounting for 47.06% of all stations, followed by those occurring during the 1970s (17.65%).Figure 5
Spatial abrupt years (a) and statistical results (b) of annual DPCI at 51 stations.
(a)(b)There is a postponement trend, in which abrupt changes move from west to east with time. Before 1970, there were only three stations with a change point, namely, Changzhi (CZ) Station at 1958, Yushe (YS) Station at 1959, and Xingtai (XT) Station at 1964, which were located in the southwest of the HRB and fail to pass the significant level of 5%. After 1990, there are 15 stations with a change point, which are mostly distributed at the southern and eastern edges of the HRB.


## 4.1. Spatial Distribution of Average DPCI Values

The annual DPCI values were calculated for 51 meteorological stations in the HRB for the period from 1951 to 2018. The average PDCI across almost every decade years and all the years, for each of 51 stations separately, is listed in Table2. The average PDCI for 51 stations during 1951–2018 ranges between 0.6471 and 0.7938. The highest value of the DPCI is recorded at Beijing (BJ) station, which suffered the heaviest rainstorm of recent 61 years in July, 2012. On the contrary, the lowest value of the DPCI occurs at Datong (DT) station in the northwest of the basin. Through the analysis of the DPCI value in different periods, the following were found: (1) the average DPCI value of Beijing (BJ) station is at a higher value, and the lowest value in different periods is greater than 0.768, but that of Datong (DT) station is at a low value, and the highest value is less than 0.671; (2) the average DPCI value of Beijing (BJ) station as the highest value appeared in the 1950s, 1960s, and 2010s, and that of Datong (DT) station as the lowest value appeared in the 1950s, 1990s, 2000s, and 2010s; and (3) the highest average DPCI value (0.8242) appeared in Beijing (BJ) station in 1960s, but the lowest one (0.6156) appeared in Datong (DT) station in 2010s.Table 2
Values for the average DPCI for almost every decade years and whole period during 1951–2018 at 51 stations of HRB.
Names1950s1960s1970s1980s1990s2000s2010s1951–2018ZB0.68330.69310.69940.66970.67250.67040.64790.6769YY0.68650.67470.66850.64990.66390.66050.64020.6635DT0.67010.65520.66710.64640.63540.63940.61560.6471TZ0.67470.66660.66140.64620.65220.64620.62460.6532SZ0.69170.67750.67480.66260.65280.67190.65730.6697DX0.71090.67850.68210.67060.67440.66960.65970.6778WTS0.70390.67990.68900.67010.66750.67230.67690.6796YX0.67690.67300.66880.66170.64830.64400.62950.6576LQ0.67690.65810.67340.64590.64770.65490.64190.6569YP0.69120.68270.70080.68240.67310.68520.68480.6857PD0.71150.70220.68820.70310.68960.68570.66830.6927SJZ0.68520.69020.67910.69200.68260.67800.65900.6811TG0.70490.69210.68500.70410.66790.67750.66430.6851YS0.71580.65070.66360.67720.65820.68440.65160.6713XT0.71150.69850.68410.68780.68210.67820.66450.6866AZ0.71130.66860.68570.67840.66320.67050.64130.6741CZ0.71920.67590.67510.68230.67650.68360.65670.6811XY0.70760.66570.66660.68300.64980.65750.64450.6676AY0.80960.80820.79590.79800.79250.77590.74820.7901XX0.79250.79560.79200.80620.79890.77770.74280.7871LXX0.76520.78750.78430.78480.77400.77190.73560.7725DLX0.67770.67340.67000.66140.66500.64040.66480.6645FN0.68920.70200.69200.68010.67910.66540.67900.6838WC0.77310.77760.77490.76080.76150.70740.71800.7536ZJK0.68590.67210.67600.65780.64840.64530.63750.6604HL0.70790.71750.69250.67420.68030.67490.66540.6876YQ0.70470.69830.70060.66860.66670.64910.63650.6751MY0.71930.70400.71350.69210.68410.66230.68620.6943CD0.78090.76440.76960.76970.74800.74140.72080.7565ZH0.70150.69890.69990.69390.68560.67800.70090.6939QL0.71110.71840.71240.68920.70000.68220.70530.7025QHD0.69100.70460.71130.70250.70560.68150.69770.6993JC0.70700.70730.71540.70060.71200.69650.71290.7073BJ0.81940.82420.81140.78710.77740.76830.76890.7938BZ0.71270.72680.72540.70480.68080.69580.68730.7049BD0.70640.73380.71660.70400.67600.68460.68780.7014TJ0.79280.81230.80890.79210.75920.78040.73910.7841TS0.70790.71690.71870.70010.69080.67830.68850.7002CFD0.71430.73180.73130.72430.70750.68610.69190.7127LT0.71770.73300.74580.72420.71590.70360.69940.7203BDG0.71270.73140.72130.74610.69530.67590.66660.7075RY0.70980.71560.69680.71610.67980.67340.66970.6946BT0.70610.71710.70390.72160.67200.66660.67440.6946TGG0.77400.81170.81290.80390.78920.77150.75600.7891HH0.70540.71860.72780.72430.68300.70140.68880.7073NG0.70100.70070.69200.71010.67970.67570.66770.6897LX0.69360.68680.69060.71550.69170.67780.67920.6909HM0.78500.80910.80080.79110.78280.75540.72820.7795KL0.71320.71430.71460.71860.70560.68460.68530.7053SX0.68730.69690.68340.69670.68470.68250.65390.6840JN0.76050.78520.77680.78430.78250.76390.71340.7675The DPCI values during 1951–2018 for each grid cell (30 m × 30 m) over HBR were spatially interpolated by the IDW method from 51 stations (Figure 2(h)). For the most part, high DPCI values, with averages of 0.70 in different periods, are found in eastern regions where high precipitation levels are recorded [23]. The spatial distribution characteristic of average DPCI is consistent in different periods. The DPCI values in the central and southern parts over the HRB exceed 0.675, which is consistent with the result of the study by Tong et al. [39]. There are four discrete high-value regions of DPCI, which are controlled by the Beijing (BJ) and Tianjin (TJ) stations in the Bohai Bay, Weichang (WC), and Chengde (CD) station in the northeast, Huimin (HM) station in the south, and Xinxiang (XX) and Anyang (AY) stations in the southwest. The spatial values of DPCI showed a decreasing trend in different period (Figures 2(a)–2(g)). Before 1990, the downward trend of the DPCI was relatively small, but after that, the downward trend increased significantly.Figure 2
Spatial distributions of the mean DPCI in different periods.Figure3 shows the relationship between the geographical factors (latitude, longitude, and elevation) and multiyear DPCI at 51 stations over the HRB. The DPCI changes tend to be negatively related to the altitude with R2 of 0.0065 (Figure 3(a)) and the elevation with R2 of 0.2312(Figure 3(c)) but tend to be positively related to the longitude with R2 of 0.1985 (Figure 3(b)) during 1951–2018. The lower the linear coefficients of determination (R2) indicate the existence of a nonsignificant correlation between DPCI and altitude, longitude, and elevation. In general, the average DPCI values in different periods (Figure 2) decrease northward to high altitude (Figure 3(a)), decrease westward to low longitude (Figure 3(b)), which is consistent with the results in Central-Southern Chile [4], and decrease westward and northward to high elevation (Figure 3(c)), which is consistent with the results in the Yangtze River Delta, China [22].Figure 3
The multiyear average PDCI versus latitude (a), longitude (b), and elevation (c) at 51 stations over the HRB.
(a)(b)(c)


## 4.2. Spatial Characteristics of Annual DPCI Trend

The annual DPCI values exhibit a varying temporal trend, which can be characterized as spatially heterogeneous among stations (Figure4(a)). Exception without trend in Jianchang (JC) station, other stations show negative annual DPCI trends, of which 5 stations have the trend greater than 0.001/a, 15 stations have the trend between 0.0007/a and 0.00099/a, 25 stations have the trend between 0.0004/a and 0.00069/a, and the trends of the remaining stations are less than 0.00039/a. Based on the MK test, the annual DPCI trends are also tested, and the results are shown in Figure 4(b). For the annual DPCI trend, more than 80% of the stations show significant changes at a 0.1 significance level. Among them, 37 out of 41 stations exhibit significant trends at a 0.05 significance level (|Z| > 1.96), and 29 out of 41 stations are dominated by a significant trend at a 0.01 significance level (|Z| > 2.57). The analysis results are consistent with those of Tong et al. that the daily precipitation concentrations at most stations in North China show a significant downward trend from 1960 to 2011 [39].Figure 4
Spatial trend variations of annual DPCI (a) and MK test (b) at 51 stations.
(a)(b)


## 4.3. Spatial Characteristics of Abrupt Change of Annual DPCI

Figure5 shows the possible abrupt change of annual DPCI based on the Pettitt test from 1951 to 2018. In all records, there are 22 out of 51 stations with statistically significant change points at the significant level of 5%. Meanwhile, abrupt changes are more likely to occur during the 1980s, accounting for 47.06% of all stations, followed by those occurring during the 1970s (17.65%).Figure 5
Spatial abrupt years (a) and statistical results (b) of annual DPCI at 51 stations.
(a)(b)There is a postponement trend, in which abrupt changes move from west to east with time. Before 1970, there were only three stations with a change point, namely, Changzhi (CZ) Station at 1958, Yushe (YS) Station at 1959, and Xingtai (XT) Station at 1964, which were located in the southwest of the HRB and fail to pass the significant level of 5%. After 1990, there are 15 stations with a change point, which are mostly distributed at the southern and eastern edges of the HRB.


## 5. Discussion

### 5.1. Comparison between the Results in the HRB and Other Areas of China

To understand the characteristic of the DPCI in the HBR, we collected published study results from other regions of China (Table3). The DPCI of the HRB range from 0.64 to 0.79 is relatively close to the Huai River basin (0.64–0.72) but greatly lower than the Pearl River basin (0.74–0.80). Table 3 indicates that DPCIs of the Lancang River basin, Xinjiang and Shanxi provinces are 0.57–0.73, 0.58–0.70, and 0.59–0.64, respectively, which are lower than those of northeast China (0.64–0.70), The Huai River basin (0.64–0.72) and the Hai River basin (0.64–0.79). However, the DPCI of the Pearl River basin with range between 0.74 and 0.80 is largest in Table 3. These findings confirm the characteristic that the eastern DPCIs are higher than the eastern DPCIs in China and the DPCIs in south China and north China are relatively large.Table 3
Comparison of DPCI between different regions in China.
SourcesStudy regionsNumber of stationsPeriodsRange of DPCIZhang et al. [17]Pearl River basin421960–20050.74–0.80Li et al. [18]Xinjiang province501961–20080.58–0.70Shi et al. [10]Lancang River basin311960–20100.57–0.73Shi et al. [19]Huai River basin381951–20100.64–0.72Yuan et al. [20]Shanxi province141957–20140.59–0.64Wang et al. [21]Northeast China711961–20160.64–0.70This studyHai River basin511951–20180.64–0.79


### 5.2. The Influence of Data Length on the Characteristics of DPCI

It can be seen from the abovementioned that the temporal and spatial distribution characteristics of DPCI in the HRB are based on the daily precipitation data of 51 stations from 1951 to 2018. However, how do the characteristics of the DPCI depend on the length of the time series? To describe the impact of the data length on the characteristics of the DPCI, the following two indicators are defined.(7)MaxEPn=max1≤m≤MMean_DPCIm,n−Mean_DPCIm,n−1,MaxETn=max1≤m≤MTrend_DPCIm,n−Trend_DPCIm,n−1,where MaxEPn is the maximum change value of the annual average DPCI from n − 1 to n years for all stations in the HRB; MaxETn is the maximum change value of the DPCI trend from n − 1 to n years for all stations in the HRB; Mean_DPCIm,n is the average DPCI of mth station from 1 to nth year; M is the number of station in the HRB and is equal to 58 in the paper; Trend_DPCIm,n is the DPCI trend of mth station from 1 to nth year. The serial number of year 1, 2, …, 68 is corresponding to 1951, 1952, …, 2018, respectively.Figure6 shows that the MaxEP and MaxET decrease with the increase of the data length and converge to a smaller interval. After 2000, the range of MaxEP is from 0.00086 to 0.00265 with the mean value of 0.0016, which accounts for 0.23% of multiyear average PDCI (0.7032) from 1951 to 2018 in the HRB. Similarly, the range of MaxEP is from 0.00086 to 0.00265 with the mean value of 0.00015, which accounts for 2.34% of average Trend (−0.00641) from 1951 to 2018 in the HRB. That is to say, the spatial and temporal variability of the DPCI based on the time series over 50 years can represent the distribution characteristics of the DPCI in the HRB. However, compared with the spatial distribution (corresponding to the multiyear average DPCI), the temporal distribution (corresponding to the trend of DPCI) more greatly depends on the length of the time series.Figure 6
The MaxEP and MaxET change with year.


### 5.3. Relationship between Short and Long Term Precipitation Patterns

Figure7 shows that the higher that the DPCI will be, the higher proportion of the annual total precipitation (PTP) that falls on the rainiest days at a station. 5% of the rainiest days accounts for 30.26–45.79% of the total rainfall, 10% for 46.54–65.24%, 15% for 58.47–76.70%, 20% for 67.35–84.04%, 25% for 74.17–89.23%, and 30% for 79.70–92.76%. The linear coefficients of determination (R2) between the DPCIs and the PTPs for 5%, 10%, 15%, 20%, 25%, and 30% were 0.9747, 0.9906, 0.9963, 0.9988, 0.9989, and 0.9980, respectively. The daily precipitation heterogeneity over a year is dominated by percentages of precipitation amount provided by the highest quartile of rainy days or large daily amount of precipitation [19]. Due to 25% of the rainiest days with the highest R2 of 0.9989, the daily heterogeneity of the rainfall within a year can be best accounted by the PTP contributed by 25% of the rainiest days in the HRB.Figure 7
The multiyear average PDCI versus the PTP contributed by 5–30% of the rainiest days for 51 stations over the HRB.Figure8 shows that the DPCI changes tend to be positively related to annual precipitation amount with R2 of 0.1612 but negatively relate to the annual precipitation day with R2 of 0.0146 during 1951–2018. In other words, more annual precipitation amount means higher daily heterogeneity, and less annual precipitation day means higher daily heterogeneity. Thus, a few very rainy days can change a year’s rainfall total and dry or wet situation. The lower precipitation levels based on higher daily heterogeneity indicate a higher risk of drought in I region, and the higher precipitation levels coupled with relatively higher PDCIs would increase the risk of flood in II region [21]. For example, at Weichang (WC) station with the higher daily rainfall heterogeneity (multiyear DPCI of 0.7536) and the lower annual precipitation amount (455.28 mm) in I region, precipitation amount within 25% of the rainiest days (about 32 days) is 388.63 mm; then, the precipitation amount in the remaining 333 days of the year is only 66.65 mm, which is bound to cause a higher drought risk. However, at Beijing (BJ) station with the highest daily rainfall heterogeneity (multiyear DPCI of 0.7938) and the higher annual precipitation amount (591.12 mm) in II region, precipitation amount within 5% of the rainiest days (about 5 days) is 269.79 mm, and the daily precipitation amount reaches 53.99 mm, which can easily lead to flood disaster. As a whole, a high value of the DPCI mainly indicates that drought and flood disasters are more frequent in I region and II region, respectively.Figure 8
The multiyear average PDCI versus annual total precipitation (a) and annual total precipitation day (b) at 51 stations over the HRB.
(a)(b)


### 5.4. Relationship between Disaster Losses and DPCI

To further explore the possible natural disasters associated with high DPCI value, the relationships between flood and drought losses and annual DPCI are analyzed based on the linear correlation analysis. The higher DPCI values lead to greater flood losses with theR2 of 0.3883 (Figure 9(a)) and more drought losses with the R2 of 0.1358 (Figure 9(b)). The DPCI value in flood years is much greater than that in drought years, and the loss of flood disasters is also much greater than that of drought disasters. Flood or drought disasters with higher DPCI value are closely related to the annual precipitation. Generally speaking, in a dry year, when the precipitation anomaly is negative, it is easy to cause drought losses, while in wet years, when the precipitation anomaly is positive, it tends to cause flood losses (Figure 9(c)). For flood losses, although the annual precipitation was only 588.32 mm in 1963, the highest DPCI value led to the greatest flood loss. However, the annual precipitation reached 812.97 mm in 1964, which was the highest annual precipitation during 1951–2018, while the relatively lower DPCI value led to the smaller flood loss. For drought losses, the higher DPCI value coupled with the lower annual precipitation (442.78 mm) led to the greatest drought loss in 1981. Then, the lower DPCI value coupled with the lowest annual precipitation (350.29 mm) during 1951–2018 led to the greater drought loss in 1965. There are similar DPCI values in 1965 (0.6984) and in 1987 (0.7013), and the annual precipitation (561.49 mm) in 1987 is much higher than that (350.29 mm) in 1965. Then, the drought loss (22.92 billion yuan) in 1987 was greater than that (13.36 billion yuan) in 1965. The possible reason is that there were several consecutive wet years in the early 1965, resulting in higher soil moisture content. In addition, the regulation and storage of water conservancy projects reduced the drought losses.Figure 9
The PDCI versus flood (a) and drought (b) losses before 1990 and corresponding annual precipitation anomaly (c) over the HRB.
(a)(b)(c)


### 5.5. Trend Analysis of Flood and Drought Disasters

To understand the risk of flood and drought in the HRB in the future, the relationships between the average annual DPCI and annual DPCI trend (Figure10(a)) and between the average annual precipitation and annual precipitation trend (Figure 10(b)) are analyzed based on 51 stations over the HRB. We would analyze the risk of flood and drought disasters of the HRB from two perspectives. First, the stations show the negative trends of annual DPCI except for Jianchang (JC) station during 1951–2018, and a greater downward trend is accompanied by the higher average annual DPCI values with the R2 of 0.0763 (Figure 9(a)). The annual DPCI value of each station would decrease, and the differences of annual DPCI among different stations may become smaller and smaller. The risk of local flood disasters would be gradually reduced in the future [24]. Second, the stations show the negative trends of annual precipitation except for Jinan (JN) and Weichang (WC) stations during 1951–2018. The higher change rate appears in stations where the average annual precipitation amounts are between 500 mm and 600 mm. Especially in Beijing station, the inter-annual variation rate of precipitation, reaching −3.16 mm/a, is the largest and passes the 0.1 significance level based on the MK method. The risk of regional drought disasters would become more serious [40, 41]. In the future, the risk of flood disasters would be reduced, but the drought disasters would be increased in the HRB. Especially in the mega cities, with the social and economic development, the demand for water resources will increase, which will further exacerbate the contradiction between supply and demand of water resources.Figure 10
The average PDCI versus DPCI trend (a) and the average precipitation versus precipitation trend (b) at 51 stations over the HRB.
(a)(b)


## 5.1. Comparison between the Results in the HRB and Other Areas of China

To understand the characteristic of the DPCI in the HBR, we collected published study results from other regions of China (Table3). The DPCI of the HRB range from 0.64 to 0.79 is relatively close to the Huai River basin (0.64–0.72) but greatly lower than the Pearl River basin (0.74–0.80). Table 3 indicates that DPCIs of the Lancang River basin, Xinjiang and Shanxi provinces are 0.57–0.73, 0.58–0.70, and 0.59–0.64, respectively, which are lower than those of northeast China (0.64–0.70), The Huai River basin (0.64–0.72) and the Hai River basin (0.64–0.79). However, the DPCI of the Pearl River basin with range between 0.74 and 0.80 is largest in Table 3. These findings confirm the characteristic that the eastern DPCIs are higher than the eastern DPCIs in China and the DPCIs in south China and north China are relatively large.Table 3
Comparison of DPCI between different regions in China.
SourcesStudy regionsNumber of stationsPeriodsRange of DPCIZhang et al. [17]Pearl River basin421960–20050.74–0.80Li et al. [18]Xinjiang province501961–20080.58–0.70Shi et al. [10]Lancang River basin311960–20100.57–0.73Shi et al. [19]Huai River basin381951–20100.64–0.72Yuan et al. [20]Shanxi province141957–20140.59–0.64Wang et al. [21]Northeast China711961–20160.64–0.70This studyHai River basin511951–20180.64–0.79


## 5.2. The Influence of Data Length on the Characteristics of DPCI

It can be seen from the abovementioned that the temporal and spatial distribution characteristics of DPCI in the HRB are based on the daily precipitation data of 51 stations from 1951 to 2018. However, how do the characteristics of the DPCI depend on the length of the time series? To describe the impact of the data length on the characteristics of the DPCI, the following two indicators are defined.(7)MaxEPn=max1≤m≤MMean_DPCIm,n−Mean_DPCIm,n−1,MaxETn=max1≤m≤MTrend_DPCIm,n−Trend_DPCIm,n−1,where MaxEPn is the maximum change value of the annual average DPCI from n − 1 to n years for all stations in the HRB; MaxETn is the maximum change value of the DPCI trend from n − 1 to n years for all stations in the HRB; Mean_DPCIm,n is the average DPCI of mth station from 1 to nth year; M is the number of station in the HRB and is equal to 58 in the paper; Trend_DPCIm,n is the DPCI trend of mth station from 1 to nth year. The serial number of year 1, 2, …, 68 is corresponding to 1951, 1952, …, 2018, respectively.Figure6 shows that the MaxEP and MaxET decrease with the increase of the data length and converge to a smaller interval. After 2000, the range of MaxEP is from 0.00086 to 0.00265 with the mean value of 0.0016, which accounts for 0.23% of multiyear average PDCI (0.7032) from 1951 to 2018 in the HRB. Similarly, the range of MaxEP is from 0.00086 to 0.00265 with the mean value of 0.00015, which accounts for 2.34% of average Trend (−0.00641) from 1951 to 2018 in the HRB. That is to say, the spatial and temporal variability of the DPCI based on the time series over 50 years can represent the distribution characteristics of the DPCI in the HRB. However, compared with the spatial distribution (corresponding to the multiyear average DPCI), the temporal distribution (corresponding to the trend of DPCI) more greatly depends on the length of the time series.Figure 6
The MaxEP and MaxET change with year.


## 5.3. Relationship between Short and Long Term Precipitation Patterns

Figure7 shows that the higher that the DPCI will be, the higher proportion of the annual total precipitation (PTP) that falls on the rainiest days at a station. 5% of the rainiest days accounts for 30.26–45.79% of the total rainfall, 10% for 46.54–65.24%, 15% for 58.47–76.70%, 20% for 67.35–84.04%, 25% for 74.17–89.23%, and 30% for 79.70–92.76%. The linear coefficients of determination (R2) between the DPCIs and the PTPs for 5%, 10%, 15%, 20%, 25%, and 30% were 0.9747, 0.9906, 0.9963, 0.9988, 0.9989, and 0.9980, respectively. The daily precipitation heterogeneity over a year is dominated by percentages of precipitation amount provided by the highest quartile of rainy days or large daily amount of precipitation [19]. Due to 25% of the rainiest days with the highest R2 of 0.9989, the daily heterogeneity of the rainfall within a year can be best accounted by the PTP contributed by 25% of the rainiest days in the HRB.Figure 7
The multiyear average PDCI versus the PTP contributed by 5–30% of the rainiest days for 51 stations over the HRB.Figure8 shows that the DPCI changes tend to be positively related to annual precipitation amount with R2 of 0.1612 but negatively relate to the annual precipitation day with R2 of 0.0146 during 1951–2018. In other words, more annual precipitation amount means higher daily heterogeneity, and less annual precipitation day means higher daily heterogeneity. Thus, a few very rainy days can change a year’s rainfall total and dry or wet situation. The lower precipitation levels based on higher daily heterogeneity indicate a higher risk of drought in I region, and the higher precipitation levels coupled with relatively higher PDCIs would increase the risk of flood in II region [21]. For example, at Weichang (WC) station with the higher daily rainfall heterogeneity (multiyear DPCI of 0.7536) and the lower annual precipitation amount (455.28 mm) in I region, precipitation amount within 25% of the rainiest days (about 32 days) is 388.63 mm; then, the precipitation amount in the remaining 333 days of the year is only 66.65 mm, which is bound to cause a higher drought risk. However, at Beijing (BJ) station with the highest daily rainfall heterogeneity (multiyear DPCI of 0.7938) and the higher annual precipitation amount (591.12 mm) in II region, precipitation amount within 5% of the rainiest days (about 5 days) is 269.79 mm, and the daily precipitation amount reaches 53.99 mm, which can easily lead to flood disaster. As a whole, a high value of the DPCI mainly indicates that drought and flood disasters are more frequent in I region and II region, respectively.Figure 8
The multiyear average PDCI versus annual total precipitation (a) and annual total precipitation day (b) at 51 stations over the HRB.
(a)(b)


## 5.4. Relationship between Disaster Losses and DPCI

To further explore the possible natural disasters associated with high DPCI value, the relationships between flood and drought losses and annual DPCI are analyzed based on the linear correlation analysis. The higher DPCI values lead to greater flood losses with theR2 of 0.3883 (Figure 9(a)) and more drought losses with the R2 of 0.1358 (Figure 9(b)). The DPCI value in flood years is much greater than that in drought years, and the loss of flood disasters is also much greater than that of drought disasters. Flood or drought disasters with higher DPCI value are closely related to the annual precipitation. Generally speaking, in a dry year, when the precipitation anomaly is negative, it is easy to cause drought losses, while in wet years, when the precipitation anomaly is positive, it tends to cause flood losses (Figure 9(c)). For flood losses, although the annual precipitation was only 588.32 mm in 1963, the highest DPCI value led to the greatest flood loss. However, the annual precipitation reached 812.97 mm in 1964, which was the highest annual precipitation during 1951–2018, while the relatively lower DPCI value led to the smaller flood loss. For drought losses, the higher DPCI value coupled with the lower annual precipitation (442.78 mm) led to the greatest drought loss in 1981. Then, the lower DPCI value coupled with the lowest annual precipitation (350.29 mm) during 1951–2018 led to the greater drought loss in 1965. There are similar DPCI values in 1965 (0.6984) and in 1987 (0.7013), and the annual precipitation (561.49 mm) in 1987 is much higher than that (350.29 mm) in 1965. Then, the drought loss (22.92 billion yuan) in 1987 was greater than that (13.36 billion yuan) in 1965. The possible reason is that there were several consecutive wet years in the early 1965, resulting in higher soil moisture content. In addition, the regulation and storage of water conservancy projects reduced the drought losses.Figure 9
The PDCI versus flood (a) and drought (b) losses before 1990 and corresponding annual precipitation anomaly (c) over the HRB.
(a)(b)(c)


## 5.5. Trend Analysis of Flood and Drought Disasters

To understand the risk of flood and drought in the HRB in the future, the relationships between the average annual DPCI and annual DPCI trend (Figure10(a)) and between the average annual precipitation and annual precipitation trend (Figure 10(b)) are analyzed based on 51 stations over the HRB. We would analyze the risk of flood and drought disasters of the HRB from two perspectives. First, the stations show the negative trends of annual DPCI except for Jianchang (JC) station during 1951–2018, and a greater downward trend is accompanied by the higher average annual DPCI values with the R2 of 0.0763 (Figure 9(a)). The annual DPCI value of each station would decrease, and the differences of annual DPCI among different stations may become smaller and smaller. The risk of local flood disasters would be gradually reduced in the future [24]. Second, the stations show the negative trends of annual precipitation except for Jinan (JN) and Weichang (WC) stations during 1951–2018. The higher change rate appears in stations where the average annual precipitation amounts are between 500 mm and 600 mm. Especially in Beijing station, the inter-annual variation rate of precipitation, reaching −3.16 mm/a, is the largest and passes the 0.1 significance level based on the MK method. The risk of regional drought disasters would become more serious [40, 41]. In the future, the risk of flood disasters would be reduced, but the drought disasters would be increased in the HRB. Especially in the mega cities, with the social and economic development, the demand for water resources will increase, which will further exacerbate the contradiction between supply and demand of water resources.Figure 10
The average PDCI versus DPCI trend (a) and the average precipitation versus precipitation trend (b) at 51 stations over the HRB.
(a)(b)


## 6. Conclusion

In this study, we set up the DPCI based on the Gini coefficient and analyzed spatial and temporal variability of the DPCI based on the Mann–Kendall and Pettitt tests in the HRB. The results of the time series of the DPCI from 1951 to 2018 show that the high values of the multiyear average DPCI are mainly situated in the southern and eastern parts, that the stations show DPCI trends except for Jianchang (JC) station, and that the abrupt changes are concentrated in 1980s accounting for 47.06% for 51 stations.The higher DPCI is greatly correlated with the higher PTP that falls on the rainiest days at a station, and the higher DPCI values lead to greater flood or drought losses. The higher DPCI coupled with more precipitation is easy to cause flood disaster; conversely, the higher DPCI along with less precipitation is easy to cause drought disaster. In the future, the risk of flood disasters would be reduced, but the drought disasters would be increased in the HRB.However, the correlation between the DPCI and disaster loss is still slight, which indicates that disaster loss may relate to soil moisture content, changes of underlying surface and disaster resilience, and so on. Understanding the relationships among them requires a more scientific knowledge of the geomorphological, hydrological, socioeconomic changes as a concrete basis for assessment of flood and drought risk and utilization of water resources.



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*Source: 1149108-2023-02-06.xml*