Advances in Meteorology
Volume 2018 (2018), Article ID 5903451, 14 pages
https://doi.org/10.1155/2018/5903451

Research Article

The Spatiotemporal Variations of Runoff in the Yangtze River Basin under Climate Change

Ziwei Xiao,¹ Peng Shi,1,2 Peng Jiang,2,3 Jianwei Hu,⁴ Simin Qu,¹ Xingyu Chen,¹ Yingbing Chen,¹ Yunqiu Dai,¹ and Jianjin Wang¹

¹College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China
²State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
³Division of Hydrologic Sciences, Desert Research Institute, Las Vegas, NV 89119, USA
⁴Bureau of Hydrology, MWR, Beijing 100053, China

Correspondence should be addressed to Peng Jiang; peng.jiang@dri.edu

Received 3 October 2017; Accepted 5 February 2018; Published 11 March 2018

Academic Editor: Hisayuki Kubota

Copyright © 2018 Ziwei Xiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

A better understanding of the runoff variations contributes to a better utilization of water resources and water conservancy planning. In this paper, we analyzed the runoff changes in the Yangtze River Basin (YRB) including the spatiotemporal characteristics of intra-annual variation, the trend, the mutation point, and the period of annual runoff using various statistical methods. We also investigated how changes in the precipitation and temperature could impact on runoff. We found that the intra-annual runoff shows a decreasing trend from 1954 to 2008 and from upper stream to lower stream. On the annual runoff sequence, the upstream runoff has a high consistency and shows an increasing diversity from upper stream to lower stream. The mutation points of the annual runoff in the YRB are years 1961 and 2004. Annual runoff presents multitime scales for dry and abundance changes. Hurst values show that the runoffs at the main control stations all have Hurst phenomenon (the persistence of annual runoff). The sensitivity analyses of runoff variation to precipitation and temperature were also conducted. Our results show that the response of runoff to precipitation is more sensitive than that to temperature. The response of runoff to temperature is only one-third of the response to precipitation. A decrease in temperature may offset the impact of decreasing rainfall on runoff, while an increase in both rainfall and temperature leads to strongest runoff variations in the YRB.

1. Introduction

Climate change and human activities influence the global water cycle process [1]. Any change within the climate system and the impact of human activities at each link will be reflected in key elements of the hydrologic cycle [2–6]. Under the background of global warming and human disturbance, river runoff has changed significantly, which has aggravated the shortage of water resources and caused the deterioration of ecological environment [7]. Hence, understanding the changes of runoff in a watershed is critical to mitigate the water resources crisis, protect the ecological environment, and realize the sustainable development of society and economy [8–10].

The spatiotemporal variations of runoff have been extensively studied in Yangtze River Basin (YRB). Chen et al. analyzed annual mean runoff from Yichang, Wuhan, and Datong stations. They examined runoff variability of the YRB based on hydrological data from the three stations and found that the runoff in the middle and lower reaches tends to increase by about 50% over that in the upper reach above Yichang [11]. Zhang and Wen analyzed annual runoff of the upper YRB, showing that the annual runoff discharge in Jinsha recorded at Pingshan had normal variation during the past decades [12]. Xu et al. used the distributed hydrological model to analyze the spatial-temporal variation of runoff in the upper YRB; their results indicated that the annual river discharges at hydrological gauges on the mainstream show no significant trend [13]. Zhang and Wei analyzed the variation of runoff in the upper reaches of the YRB on the basis of monitoring data series from 1881 to 2006. They found that the average annual runoff after 1990 is obviously higher than that before 1990 [14]. Hong et al. calculated the streamflow drought index (SDI) series with 12-month time scale and assessed the hydrological drought of the upper YRB based on the daily streamflow data of the Yichang hydrological station from 1882 to 2009 [15]. However, to our knowledge, there have been relatively fewer studies that investigate the spatial differences of runoff changing trend in the whole basin and examine the multiscale temporal variability of runoff at different locations.

The changes of annual runoff in the YRB are affected by many factors, including meteorological factors such as precipitation, temperature, and the impact of human activities. In recent decades, with the rapid population growth, the YRB water resources development and utilization have been significantly improved. According to statistics, the YRB has built more than 46,000 dams and 7,000 culverts [16]. Lots of studies have been conducted describing a clear response to dam building in terms of sediment yield, runoff, and its impact on estuarine and coastal regions during this later period [17]. They found that human activities, especially large dam construction such as the Three Gorges Dam in the river basin, mainly effect the relocation of seasonal runoff and have little influence on the annual flow regime [18]. Zhang et al. indicated that human activities (deforestation, dam construction and operation, etc.) exert more influences on sediment loads than on annual runoff and indicated that the variation in the annual runoff is mainly controlled by climate fluctuation (i.e., precipitation variation) in the YRB [19]. Chen et al. adopted a multiple correlation analysis of discharge, precipitation, dam volume, population, and GDP in the YRB, showing that only precipitation is significantly correlated with discharge, explaining 80% of the variance [17]. The pattern of storage and release for the hydroelectric dams is that a part of the high flows towards the end of summer and into autumn are stored for later release through the turbines in the low flow period in late winter and spring [20]. This is revealed in changes to monthly flows but has little impact on total annual discharge. As a result, there has been increasing concern about climate change as a driver of annual runoff changes in the YRB [21–23].

Precipitation and temperature are the most critical climate factors, which control runoff variations [24, 25]. Studies have shown that, for every 10% increase in precipitation, river runoff will increase by 25% in Australia [26], 195% in the United States [27], and 27% in Huaihe River Basin, China [28]. At present, warming is the main feature of global climate change [29]. Studies have shown that climate warming will increase the water vapor content, accelerate the hydrological processes, and cause dry areas to be drier and humid areas to be more humid [30, 31]. However, warming strengthens the evapotranspiration, which results in less runoff [32–35]. Therefore, the runoff response analysis was mainly conducted in terms of precipitation and temperature.

Linear regression modeling approach is a common and simple method for runoff simulation in the YRB [36, 37]. However, the linear regression modeling tends to introduce more simulation error due to various nonlinear relationships in nature. In this study, a nonlinear regression model was used for runoff response analysis based on the research of the runoff changes in the YRB. Two control stations are selected in the upper, middle, and lower reaches of the YRB, respectively.

In this paper, we strive to offer a comprehensive analysis of the spatiotemporal variations of runoff in the YRB using various statistical methods. A number of hydrological stations in the upper, middle, and lower reaches are selected for the analysis. We seek here to investigate the spatial differences of the runoff changing trend in the YRB, present the multiscale temporal changes of runoff at different locations, and conduct a sensitivity analysis of runoff response to precipitation and temperature.

2. Study Area and Data

2.1. Study Area

The YRB (24° to 35°N, 90° to 122°E) covers 19 provinces, municipalities, and autonomous regions across the three major economic zones in eastern, central, and western China. It is the third largest basin in the world with a total catchment area of 1.8 million square kilometers, accounting for 18.8% of China’s land area. The basin has a wealth of natural resources. Yichang (YC) and Hukou (HK) stations are the demarcation points of the upper, middle, and lower reaches of the YRB. The average annual precipitation in the Yangtze River Basin is 1126.7 mm, which belongs to the area with abundant precipitation. The topography of the YRB is a multilevel stepped topography. The runoff flows through mountains, plateaus, basins (tributaries), hills, and plains. Due to the influence of local circulation and topography, the spatial distribution of annual precipitation is very uneven, decreasing from southeast to northwest [22]. The main land use/land cover in the YRB is forest, arable, and grassland, accounting for more than 90% of the total area of the basin. The proportions of water, urban and rural construction land, and other unused lands are relatively small [38].

2.2. Data Description

The average daily discharge data of two control stations in the upper, middle, and lower reaches of the Yangtze River Basin were chosen (Figure 1). All of these sites are located in the mainstream of the Yangtze River Basin. The data of these stations is not completely continuous; after removing the discontinuous data series, the measured data series of each site are shown in Table 1. The time series length is not consistent. As a result, we chose the average daily discharge data from 1954 to 2008 (55 years in total) for the analysis period.

Table 1: Data series of measured runoff in the Yangtze basin.

Yangtze River
Control station
Starting and ending year
Time series length (years)

Upper reach
Wanxian (WX)
1952–2008
57

Yichang (YC)
1945–2008
64

Middle reach
Luoshan (III) (LS)
1954–2008
55

Hankou (Wuhan Guan) (WHG)
1952–2008
57

Lower reach
Hukou (HK)
1950–2008
59

Datong (II) DT
1950–2008
59

Figure 1: Study area, Yangtze River Basin, and the locations of the selected discharge stations.

3. Methods

The distribution of runoff within a year is closely related to the source of river runoff and the natural geography of river basin. It is also one of the basic data needed by the national water sector and an important criterion for water resources assessment. Several typical indicators, such as the nonuniformity coefficient, are regarded to be better for denoting integral characteristics of intra-annual distribution of streamflow. They can serve for the decision of water resources management in the region with high social-economic development [39, 40]. The relative change amplitude index can further verify the nonuniformity of the annual distribution of runoff. Therefore, in this paper, the intra-annual distribution of runoff in the YRB was analyzed using the two indices: the coefficient of nonuniformity [41–43] and relative change amplitude.

In this study, cumulative anomaly curve method and linear propensity estimation method were used for trend analysis, wavelet analysis was used for cyclical characteristics analysis, method was used for runoff persistence analysis, and nonlinear regression model was used for runoff response analysis.

3.1. Cumulative Anomaly Curve Method

Cumulative anomaly is a commonly used method of judging the trend of change. We can visually determine the trend through the curve. When the cumulative anomaly curve is on the rise, it indicates the increase of anomaly, that is, the upward trend; otherwise it indicates the downward trend. For a hydrological sample sequence , the cumulative anomaly at a particular moment is expressed as

where is the cumulative anomaly from year 1 to year , is the hydrological sample value of year , and is the average value.

3.2. Linear Propensity Estimation Method

The sample series correspond to a value of at time , and a linear regression between and is established as follows:

where is the regression constant, is the regression coefficient, and and are estimated using the least squares method. The sign of the regression coefficient indicates the tendency of the scalar , the positive value indicates the increasing trend, and the negative value indicates the decreasing trend.

The correlation coefficient represents the degree of linearity of the linear correlation between and time . In order to judge whether the degree of change is significant, it is necessary to test the significance of . Determine the significance level α; if , it indicates that the trend of with time is significant; otherwise it shows that the trend is not obvious.

Due to the influence of hydrological cycles, natural conditions, and human activities, the hydrological regime tends to change in time or space, that is, obviously beyond the regularization of the system. For example, the statistical characteristics of the sequence (such as mean) in hydrological statistical significance have changed significantly, so that the hydrological sequence does not conform to the definition of “consistency” in a certain sense. However, in the calculation of hydrological frequency, the hydrological sequence must be consistent, and the nonconformity sequence should be processed. The key to the processing is to find the mutation point of the sequence. Therefore, in terms of hydrological modeling and forecasting, hydrological analysis, and so on, we need to understand and diagnose the mutation point of hydrological time series in any time so as to take the correct hydrological analysis and scheduling decisions. The statistical test method can be used to test the trend and jump components of the hydrological sequence.

Common mutant detection methods are low-pass filtering, sliding -test, Cramer method, and Mann-Kendall method. Different methods have different test sensitivity, so the results are slightly different [44]. For mutation analysis, Mann-Kendall nonparametric test method and -test were used in this study. Mann-Kendall nonparametric test was used to identify the mutation points first, and then the -test was used to further identify the abrupt points.

3.3. Mann-Kendall Nonparametric Test Method

The Mann-Kendall nonparametric test method (M-K method) has the advantage that the sample does not require a certain distribution of the sample and is not subject to a small number of anomalies, so the method is more suitable for type variables and sequential variables. Furthermore, its calculation is relatively simple. This method was originally used only to detect trends in the sequence. After continuous development, this method can be used to determine the starting position of various trends. Goossens and Berger applied this method to the reverse sequence for detecting the mutation point [45].

For a time series with sample sizes, construct a rank sequence:

where

The rank sequence is the cumulative number of which is larger than . Under the assumption that the time series are randomly independent, the order statistics are defined as

Here = 0; and are the mean and variance of , respectively. When are independent and have the same continuous distribution, let

Next we construct the inverse-order statistics. We repeat the above process by time reverse order . Let = (), and = 0.

If the and curves intersect and with the intersection between the critical lines, the time of the corresponding intersection is the beginning of the mutation.

3.4. -Test

If the mean difference between the two subsequences exceeds a certain significant level, the mean value is considered to be qualitative and the sequence has a mutation.

For a time series with sample sizes, a certain time is set as a reference point artificially. The sequence is divided into two subsequences, the number of samples is and , the average is and , and the variance is and . The statistic is defined as follows:

where

The statistic follows the distribution of degrees of freedom + − 2. Given a significant level of , if , it is considered a mutation.

3.5. Wavelet Analysis Method

Wavelet analysis is becoming a common tool for analyzing localized variations of power within a time series. By decomposing a time series into time-frequency space, one is able to determine both dominant modes of variability and how those modes vary in time [46]. The wavelet transform has been used for numerous studies in geophysics [47–49].

3.6. Method

analysis is a time series statistical method proposed by Hearst on the basis of a large number of empirical studies, which plays an important role in fractal theory. The Hearst exponent is closely related to the fractal dimension of the fractional Brownian motion, which indicates the persistence (or antipersistence) of the fractional Brownian motion [50]. The value of is in the range of (0, 1), corresponding to different value; its meaning is as follows: H (0, 0.5): that time series has antipersistence; that is, the general trend of future changes is contrary to the past. From an average point of view, the trend of the past diminishes the trend of increasing trends in the past, and the increase in the past suggests a tendency to decrease in the future. The smaller the value, the stronger the reverse resistance. H = 0.5: it means that the time series are independent of each other. That is, the value of any time has nothing to do with the past. H (0.5, 1): it indicates that the time series is persistent, which means that the changing trend in the future will be the same as the trend in the past. The smaller the value, the stronger the reverse resistance. The greater the value, the stronger the persistence. From the above analysis, we can see that the Hurst index can better reveal the trend components in the time series. is calculated from the following formula:

where is range, is standard deviation, is sample size, and is a constant.

3.7. Nonlinear Regression

The relationship between the dependent variable and the independent variable can be approximated by a linear equation. However, in nature, the nonlinear relationship exists in large numbers. The linear regression model requires that the variables must be linearly related. Curve estimation can only deal with nonlinear problems that can be linearly transformed by variable transformation, so these methods have some limitations. In contrast, nonlinear regression can be used to estimate the model between the variable and the independent variable, and the specific form of the estimation equation can be arbitrarily set according to the specific needs. The nonlinear regression process is a special nonlinear regression model fitting process, which uses iterative method to fit various complex curve models and extends the definition of residuals from the least squares method.

4. Results and Discussion

4.1. Runoff Characteristics and Trend Analysis

4.1.1. Intra-Annual Variation

Based on daily runoff data of 6 stations, the annual heterogeneity coefficient and relative change range of each site in different periods were calculated, which were divided by chronology and listed in Table 2.

Table 2: The nonuniform coefficient of annual runoff distribution () and relative variation range () in each station in the YRB.

Decade
WX
YC
LS
WHG
HK
DT

50
0.76
10.19
0.75
9.97
0.59
6.54
0.58
6.38
0.81
3.20
0.53
5.78

60
0.71
9.70
0.70
9.61
0.56
7.21
0.55
6.92
0.70
−7.45
0.50
6.07

70
0.68
8.80
0.68
8.91
0.57
6.84
0.55
6.08
0.68
9.33
0.51
5.57

80
0.73
9.40
0.72
9.54
0.56
6.96
0.55
6.29
0.58
10.30
0.46
5.21

90
0.72
9.44
0.72
9.91
0.59
7.13
0.57
6.54
0.62
8.19
0.52
5.86

The early 21st century
0.65
7.54
0.65
7.51
0.52
5.02
0.49
4.59
0.53
10.85
0.45
4.31

Mean
0.71
9.18
0.70
9.27
0.57
6.68
0.55
6.18
0.65
5.69
0.50
5.49

The high value indicated a high degree of nonuniformity as is the high value. Table 2 indicates that the distribution of annual runoff is not uniform, and the variation regularities of the value and value are similar. WX and YC control stations in the upper reaches of YRB had the lowest heterogeneity at the beginning of the 21st century and the highest inhomogeneity in 1950s. The inhomogeneities of the LS and WHG stations in the middle reaches of the YRB were similar in the 1950s and 1990s, and the inhomogeneity in the early 21st century was low. For the two downstream control stations, the inhomogeneity of the HK station varied greatly, with the highest in the 1950s and the lowest in the early 21st century and the negative change in the flow data due to the tidal effect, so the relative change in the 1960s amplitude is negative. On the whole, the heterogeneity of DT station is low, which is the lowest in the 21st century. As the tides have cyclical changes in the up and down tide replacement stage [51], the flow also will change in the opposite direction. HK station is located in the tidal reach, where runoff is affected by the tide, and the law of change is somewhat special. Thus, in general, the nonuniformity of the distribution of annual runoff presents temporal and spatial variation, which shows a downward trend from 1954 to 2008 and from upper stream to lower stream (HK station is an exception). This phenomenon may be related to the construction of more than 50,000 reservoirs in the YRB. The construction of the reservoirs changed the original regularity of natural runoff, which made the difference of runoff small. Meanwhile, the economy of the lower reaches of the YRB is more developed than that of the upper reaches, and the influence of human activities on runoff is large, so the heterogeneity of runoff is weakened.

4.1.2. Annual Runoff Characteristics

(1) Runoff Trend Diagnosis. The cumulative anomaly curves are divided into upper, middle, and lower reaches and are plotted in Figure 2.

Figure 2: The YRB’s upper, middle, and lower reaches’ cumulative anomaly graph.

From Figure 2, it can be seen that the cumulative anomaly curves of the two control stations in the upper reaches of the YRB are almost completely coincident with each other; the cumulative anomaly curves of the middle reaches are almost the same, but the runoff values are slightly different. The cumulative anomaly curve at downstream control stations is large, including data sizes and trend. In addition, 6 hydrological stations all show a clear upward trend at the end of the 20th century.

Linear propensity estimation method was used to estimate the trend of runoff, and the correlation coefficient was used to test the significance. The trend value , the correlation coefficient , and the significance of the annual runoff of the control station are shown in Table 3. The negative values indicate that runoffs at five stations all decrease with time, while runoff at HK station shows an increasing trend. This is consistent with the conclusion of Li et al.’s study about natural runoff from 1953 to 2011 in HK station in 2015 [52]. The significance test revealed that the runoff at YC station located in the upper reaches of the YRB displays a significant decreasing trend at the confidence level of 0.05. The results show that the annual runoff in the YRB is decreasing, and the annual runoff of the YC hydrological station in the upper reaches is obviously decreasing.

Table 3: The runoff linear propensity estimate table of the YRB.

Control station
b
r
Significance

WX
−20.985
−0.09648
No

YC
−22.106
−0.22921
Yes
The confidence level of 0.05

LS
−18.078
−0.12452
No

WHG
−10.887
−0.0639
No

HK
8.2035
0.098831
No

DT
−6.8429
−0.02711
No

(2) Runoff Mutation Test. The mutation points are identified by the M-K test. The UF and UB values were calculated according to the corresponding formulas, and the curves of UF and UB with time were plotted. Take the WX station as an example; the curves of the UF and UB changes with time were shown in Figure 3. Considering the influence of the data length, it can be seen that the UF and UB curves intersect in 1961 and 2004, and the intersection was within the critical line.

Figure 3: WX station’s runoff Mann-Kendall test.

The other stations curves of UF and UB with time were plotted in the same way, and then the variance points obtained by M-K test were summarized in Table 4. Then, the -test was performed on the variation points identified in Table 4, respectively, and the test results were shown in Table 5. If the absolute value of exceeds the critical value, it means that the significance test is passed.

Table 4: Preliminary study of aberrance point by M-K test.

Yangtze River
Control station
Variation point (preliminary)

Upper reach
WX
1961
2004

YC
1961
1972
2000

Middle reach
LS
1961
2004

WHG
1963
2004

Lower reach
HK
1988

DT
1968
1972
2004

Table 5: The runoff -test result table.

Control station
Variation point (preliminary)
( = 0.1)

Significance

WX
1961
= 12
1.782
−1.073
No

2004
= 8
1.86
1.6179
No

YC
1961
= 12
1.782
−1.8796
Yes

1972
= 18
1.734
1.2775
No

2000
= 16
1.746
0.7716
No

LS
1961
= 12
1.782
−0.3625
No

2004
= 8
1.86
2.317
Yes

WHG
1963
= 16
1.746
−0.2358
No

2004
= 8
1.86
1.982
Yes

HK
1988
= 18
1.734
−1.9719
Yes

DT
1968
= 18
1.734
−0.6975
No

1972
= 18
1.734
0.3123
No

2004
= 8
1.86
2.9108
Yes

The results show that the absolute value of annual runoff of YC station in 1961 is greater than the critical value of 0.1 significance level, which indicates that the mean mutation of YC station occurred in 1961. Similarly, the mean mutations of LS, WHG, HK, and DT stations occurred in 2004, 2004, 1998, and 2004, respectively.

(3) Runoff Cycle Analysis. Morlet wavelet was chosen for wavelet transform. The wavelet is a continuous plane wave modulated by a Gaussian function. The wavelet function is as follows:

where is the angular frequency, here taken to be 6 to satisfy the admissibility condition [53].

In Figure 4, “” represents a positive value center, indicating the runoff wet season, and “” represents a negative center, indicating the dry season of runoff. There are two obvious periods of change in annual runoff throughout the analysis period. During the period from 1975 to 1992, there was a periodical change of about 11 years; two centers were sandwiched by three positive centers runoff wet-dry oscillation. The periodical changes in the time scale around 18 years mainly existed from 1954 to 1973 and from 1993 to 2008; one center was sandwiched by two negative centers runoff dry-wet oscillation.

Figure 4: The contour of the real part of Morlet wavelet coefficients in YC station.

The modulus of Morlet wavelet coefficients reflects the distribution of energy density corresponding to the period of different time scales in the time domain. The larger the coefficient modulus, the stronger the periodicity of the corresponding period or scale. Figure 5 indicates that the 18-year scale has the largest modulus during runoff evolution, which means that the periodical variation of the 18 years is the most obvious. This periodicity became weaker from 1954 to 1973 and stronger from 1993 to 2008. The modulus at the time scale of about 11 years is relatively weaker, and the periodicity is constant in the period from 1975 to 1992.

Figure 5: The contour of module of Morlet wavelet transform coefficient in YC station.

The wavelet variance is obtained by integrating the square of the wavelet coefficients. And the contribution of wavelet energy is proportional to the modulus of wavelet coefficients. Therefore, the wavelet variance can be used to determine the relative intensity of different types of disturbance in the signal and the main time scale of existence, namely, the main period.

The annual runoff time series have the multiscale periodic characteristics. Some of the periodic changes in the time scale are obvious and some are not. The wavelet variance indicated that the first main cycle of the runoff period is 18 years; the second main cycle is 11 years. The results are shown in Table 6 for the wavelet analysis of the runoff of other stations.

Table 6: The streamflow wavelet analysis table.

Yangtze River
Control station
Period/a

Upper reach
WX
6
18

YC
6
11
18

Middle reach
LS
5
11
22

WHG
5
11
22

Lower reach
HK
6
11
15
22

DT
5
11
22

Previous studies suggested that solar activity may affect changes in the Earth’s climate, especially in the field of precipitation [54–57], thus affecting runoff. Wang et al. conducted a statistical analysis of the sunspot activity in the past 50 years, indicating that the solar activity has a quasi-11a period and a quasi-80a century cycle. In the declining period of solar activity 11a period, the YRB and its south of the region in the summer are prone to floods [58]. This also explains to some extent that 5 of the 6 hydrological stations in this paper have a quasi period of 11 years. On the other hand, the quasi-periodic variations in sea surface variables have shown growing promise for long-range precipitation variation. The 3–6-year periodical El Nino-Southern Oscillation (ENSO) is the best known oceanic-atmospheric index that can explain the variability of precipitation in YRB [59]. The other oceanic indices such as Pacific Decadal Oscillation and Atlantic Ocean Oscillation may have modulation effects on ENSO-precipitation relationship [56, 60, 61]. As a result, the runoff in YRB may present multiscale temporal variability (Table 6).

(4) Continuity Analysis of Runoff Variation. Figure 6 displays the Hurst values of WX, YC, LS, WHG, HK, and DT stations. Except for LS station, the annual runoff time series as a trajectory of the fractional Brownian movement shows persistence, which indicates that the annual runoff will exhibit the same trend as that in the past. The runoff sequence of the LS station is antipersistent. LS station is different from the other stations due to the following facts: LS station is located in the alluvial river, vulnerable to erosion and deposition changes. There are many tributaries along the river; the flood fluctuations of main stream and tributaries are not synchronized. It is located in the middle section; the runoff is affected not only by the upper stream flood fluctuations but also by the lower stream backwater.

Figure 6: Results of analysis.

4.2. Runoff Response Analysis

DT station was chosen for runoff response analysis. It is located in the lower reach of Yellow River, which controls a catchment area of about 1.7 million km². It covers about 94% of the total YRB. It is also an important station for water regime monitoring in the lower reaches of the YRB. Therefore, the runoff data of the DT station are usually used for analysis. The precipitation and temperature of the 120 meteorological stations in the watershed controlled by the DT Station were selected as the basic climatic factors. The precipitation and temperature are from the 1961–2008 data compiled by the National Meteorological Center. The temperature is the daily average, and the precipitation is the daily total value. The locations of the DT hydrological station and the corresponding weather stations are shown in Figure 7.

Figure 7: Study hydrological station, DT station, and its 122 weather stations.

4.2.1. Establishment of the Model

Considering the nonlinear relationship between water resources system and climate change and referring to Fu and Liu [62], the nonlinear regression model of , , and was established by mathematical method, where is the annual runoff depth of DT station; P is the regional average precipitation; is the regional average temperature. First we plotted the scatter matrix as shown in Figure 8.

Figure 8: Scatter matrix of , , and T.

According to the scatter matrix to determine the relationship between the three variables, as shown in Figure 8, the scatter matrix is divided into nine subgraphs, which describe the changes between the three variables. It can be seen that there is a significant linear relationship between and and , respectively. And by observing the scatter plot between and , there is a certain relationship between the two variables, which indicates that there may be a cross effect between the two dependent variables. Thus, the following nonlinear regression equation is established:

Table 7 shows the nonlinear regression model (see (11)). It can be seen that, after 13 iterations, the model reaches the convergence criterion and the optimal solution was found. Thus, the predictive regression model for , , and is as follows:

The -square of model was 0.828, indicating that the model in (12) on the DT annual runoff fitting effect is better.

Table 7: The iteration history recor.

Number of iteration
Residual square sum
Parameters

0.1
602098.061
1.000
1.000
1.000
1.000

1.1
1.755
.988
.918
.838
−.132

2.1
.160
.869
.703
−.370
.058

3.1
.141
.880
.799
−.404
.056

4.1
.140
3.691
.396
−.606
.085

5.1
.137
13.094
−.951
−1.280
.181

6.1
.134
38.175
−4.560
−3.105
.444

7.1
.133
43.424
−5.301
−3.463
.494

8.1
.133
38.177
−4.547
−3.081
.440

9.1
.133
38.172
−4.546
−3.081
.440

10.1
.133
38.177
−4.546
−3.081
.440

11.1
.133
38.177
−4.546
−3.081
.440

number of primary iterations is shown on the left side of the decimal, and the number of secondary iterations is shown on the right side of the decimal. model stops running after 13 iterations and the optimal solution has been found.

4.2.2. Response of Runoff to Climatic Factors

The optimal model was selected by nonlinear regression analysis to quantitatively assess the response of the runoff to the climatic factors. We constructed two types of climate factors change: each climate factor changes alone; multifactors change at the same time, that is, factors coupling changes.

Table 8 indicates that the difference between the factors of each element (including the extreme maximum and the extreme minimum) and the average are obvious, where the difference between and the average is about ±7% and the difference between and the average is about ±15%. Therefore, the average changes of regional factors are in the range of 7% to 15%. Based on the above analysis, the change amplitude in the design for the factors was in the middle of the actual data change. Tables 9 and 10, respectively, are the two types of changes and R response results, where has been converted into the relative rate of change.

Table 8: Regional feature characteristics statistics.

Climatic factors
Regional average
max
min

1072.7
175.9
−162.9

13.8
1.025
−0.651

Notes. represents the difference between the maximum and the average; represents the difference between the minimum and the average.

Table 9: Results of changes with the elements changes.

Degree of change
+5%
  −5%
+5%
  −5%

Change rate of (%)
2.00
−0.46
0.66
0.94

Change rate of (%)
13.43
−2.73
4.40
6.14

Table 10: Results of changes with the elements coupling changes.

Elements coupling
Change rate of (%)

+5%, +5%
14.21

+10%, +5%
24.43

+15%, +5%
35.06

  −5%, +5%
−4.99

  −10%, +5%
−13.98

  −15%, +5%
−22.54

+5%,   −5%
12.71

+10%,   −5%
19.37

+15%,   −5%
26.11

  −5%,   −5%
−0.36

  −10%,   −5%
−6.77

  −15%,   −5%
−13.09

Table 9 shows the relative change of at DT station caused by changes of a single climatic factor. The aim is to evaluate how the runoff could be impacted by the climatic factors with changes of the same level.

As can be seen from Table 9, when the degree of change of factors is the same, the response of is different. When the change of is +5%, the rate of change of is 13.43%. When is increased by 5%, the rate of change of is 4.4%, which is 1/3 of . Among the two factors, when the degree of change of factors is the same, has the most significant response to . When the climate factor is reduced, changes become more complex. When the change of is −5%, the rate of change of is −2.73%. When is decreased by 5%, the rate of change of is 6.14%. That is to say, when the temperature decreases, the runoff is increasing, and when precipitation decreases, the runoff is decreasing. This is because the temperature decreases lead to reducing the evaporation rate of water and then the amount of water used for evaporation loss is reduced, so the runoff increases. And precipitation is the most important source of runoff, so the reduction of precipitation will lead directly to the reduction of runoff.

Table 10 shows the relative changes in Chase-pass flow when multiclimatic factors change. In Table 3, we considered the conditions for the coupling variation of and T, and the symbols “+” and “−” denote increases and decreases, respectively.

It can be seen from Table 10 that, considering the and coupling changes, with and in the same direction or reverse changes, the impact of the is different. When increases with T, changes from +5% to +15%, and the increment can vary by about 20.85%. When decreases with T, changes from −5% to −15%, and the increment can vary by about −12.73%. When increases while decreases, changes from +5% to +15%, and the increment can vary by about 13.4%. When decreases while increases, changes from −5% to −15%, and the increment can vary by about −17.55%. This phenomenon shows that when rainfall and temperature are reduced at the same time, the impact on runoff is minimum; when the precipitation and temperature increase at the same time, the impact on runoff is maximum. And regardless of the increase or decrease in precipitation, the effect of temperature increase on runoff is greater than that of temperature reduction. This is because when the precipitation increases, the air vapor content is high, and the water holding capacity of air increases by about 7% per 1°C warming [30], which leads to increased water vapor in the atmosphere. In this situation, there is a tendency for more intense precipitation events which will further lead to additional runoff. When the precipitation decreases, increased heating leads to greater evaporation and thus surface drying, thereby increasing the intensity and duration of drought [30].

5. Conclusions

In this paper, different statistical methods were used to detect the trend, the mutation point, and multiscale variability: The intra-annual variation of runoff in the YRB was analyzed by using two indexes of nonuniformity coefficient and the relative change amplitude index. The annual variation of runoff was analyzed using cumulative anomaly curve method, linear propensity estimation method, Mann-Kendall nonparametric test method, -test, and Wavelet analysis method. The future trend was predicted using the Hurst index of runoff sequence, estimated by analysis. Furthermore, the runoff response analysis was conducted by quantitatively analyzing the response of runoff to the two most sensitive climatic factors (precipitation and temperature).

There is a significant change in spatiotemporal distribution of runoff in the YRB. The intra-annual runoff variation showed a decreasing nonuniformity from the 1950s to the beginning of the 21st century and from upper stream to lower stream, excluding the HK control station, of which the intra-annual runoff variation is impacted by the tidal effect. The historical changing trend of annual runoff is more consistent in the upper reaches than in the lower reaches of the YRB, which resulted from the impact of more human activities and more severe land use on runoff variation in the lower reaches [63, 64]. Annual runoff decreases with time in general and YC station showed a significant decreasing trend with a significance level of 0.05. The mutation point of the annual runoff sequence was mainly in 1961 and 2004, when the YRB experienced significant storm floods [65, 66], indicating that mutations in the annual runoff series may be caused by extreme precipitation events. In addition, the annual runoff has a multitime scale feature that is similar to that of solar activity [58]. The analysis of the annual runoff in the YRB shows that the values of the main control station annual runoff are not equal to 0.5; the Hurst phenomenon exists; that is, the runoff sequence of the LS station is antipersistent and the other runoff is persistent. And in the past 55 years, the values were different; the trend is not the same, so the future trend is also different. The historical runoff of WX, YC, LS, WHG, and DT stations decreased with time, and the historical trend of YC station was significantly reduced, while the historical runoff of HK station showed no significant upward trend. That is, WX, YC, WHG, and DT stations in the future may still be a reducing trend; HK station may still be an increasing trend in the future; the future trend of LS station is contrary to historical trends to be an increasing trend.

The runoff response analysis indicated that the effect of precipitation on runoff is three times that of the temperature at DT station. As a result, analysis on multiscale temporal variability of precipitation is important for investigating the runoff variations [67–69]. When the coupling sets of changes in climate factors are different, the influence degree of DT runoff is different. When the climate elements are coupled and increased in the same direction, the response of the runoff to any single climatic factor change is less than the response to the multielement coupling change; however, when the climate factor is coupled and the reverse changes when the precipitation is reduced, the runoff decreases, and if the temperature increases, the evaporation increases, which further leads the runoff to decrease; when the precipitation is increased, the runoff increases, and if the temperature decreases, the water vapor in the atmosphere decreases, which weakened the role of rainfall, thus inhibiting the increase in runoff.

Ethical Approval

The manuscript is prepared in accordance with the ethical standards of the responsible committee on human experimentation and with the latest version (2008) of Declaration of Helsinki of 1975.

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Authors’ Contributions

Peng Shi, Peng Jiang, Simin Qu, and Jianwei Hu conceived and designed the numerical simulation methods; Ziwei Xiao, Xingyu Chen, Yingbing Chen, and Yunqiu Dai implemented the methods; Ziwei Xiao and Jianjin Wang analyzed the data; Ziwei Xiao, Peng Shi, and Peng Jiang wrote the paper.

Acknowledgments

The first author acknowledges the following financial support: the National Key Technologies R&D Program of China (2017YFC0405601), the National Natural Science Foundation of China (no. 41730750/51479062/41371048), the Fundamental Research Funds for the Central Universities (2015B14314), and the UK-China Critical Zone Observatory (CZO) Program (41571130071). The corresponding author is supported by Open Research Fund Program of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (2015490611).

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