^{1}

^{1}

^{2}

^{2}

^{3}

^{4}

^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

^{2}

^{3}

^{4}

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.

Climate change and human activities influence the global water cycle process [

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 [

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 [

Precipitation and temperature are the most critical climate factors, which control runoff variations [

Linear regression modeling approach is a common and simple method for runoff simulation in the YRB [

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

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 [

The average daily discharge data of two control stations in the upper, middle, and lower reaches of the Yangtze River Basin were chosen (Figure

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 |

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

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 [

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,

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 sample series

The correlation coefficient

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

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 [

For a time series

The rank sequence

Here

Next we construct the inverse-order statistics. We repeat the above process by time reverse order

If the

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

The statistic

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 [

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.

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

The nonuniform coefficient of annual runoff distribution (

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

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

From Figure

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 runoff linear

Control station | | | 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 |

WX station’s runoff Mann-Kendall test.

The other stations curves of UF

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 |

The runoff

Control station | Variation point (preliminary) | | | Significance | |
---|---|---|---|---|---|

WX | 1961 | | 1.782 | −1.073 | No |

2004 | | 1.86 | 1.6179 | No | |

| |||||

YC | 1961 | | 1.782 | −1.8796 | Yes |

1972 | | 1.734 | 1.2775 | No | |

2000 | | 1.746 | 0.7716 | No | |

| |||||

LS | 1961 | | 1.782 | −0.3625 | No |

2004 | | 1.86 | 2.317 | Yes | |

| |||||

WHG | 1963 | | 1.746 | −0.2358 | No |

2004 | | 1.86 | 1.982 | Yes | |

| |||||

HK | 1988 | | 1.734 | −1.9719 | Yes |

| |||||

DT | 1968 | | 1.734 | −0.6975 | No |

1972 | | 1.734 | 0.3123 | No | |

2004 | | 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.

In Figure

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

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

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 [

Results of

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 km^{2}. 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

Study hydrological station, DT station, and its 122 weather stations.

Considering the nonlinear relationship between water resources system and climate change and referring to Fu and Liu [

Scatter matrix of

According to the scatter matrix to determine the relationship between the three variables, as shown in Figure

Table

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 |

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:

Table

Regional feature characteristics statistics.

Climatic factors | Regional average | | |
---|---|---|---|

| 1072.7 | 175.9 | −162.9 |

| 13.8 | 1.025 | −0.651 |

Results of

Degree of change | | | | |
---|---|---|---|---|

Change rate of | 2.00 | −0.46 | 0.66 | 0.94 |

Change rate of | 13.43 | −2.73 | 4.40 | 6.14 |

Results of

Elements coupling | Change rate of |
---|---|

| 14.21 |

| 24.43 |

| 35.06 |

| −4.99 |

| −13.98 |

| −22.54 |

| 12.71 |

| 19.37 |

| 26.11 |

| −0.36 |

| −6.77 |

| −13.09 |

Table

As can be seen from Table

Table

It can be seen from Table

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,

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 [

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 [

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.

The authors declare that there are no conflicts of interest.

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.

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).