Keywords

1 Introduction

The Yangtze River is the third largest river in the world and the largest river in China. From the source of the Yangtze River to Yichang, Hubei Province, the Yangtze River is about 4500 km long, with a total catchment area of about 1 million km2 (Wang et al. 2020; Liu et al. 2019; Tan et al. 2019). The runoff in the upper Yangtze River mainly comes from Jinsha River, Minjiang River, Tuojiang River, Jialing River and Wujiang River, and the sediment mainly comes from Jinsha River and Jialing River. The change of water and sediment conditions in the upper Yangtze River has a great impact on the sediment deposition and regulation in The TGR area, as well as the flood control and ecological environment in the middle and lower Yangtze River. Since the 1990s, with the construction of a large number of reservoirs, the largest reservoir group has been built in the upper Yangtze River in the world. The operation and joint operation of the reservoir group in the upper Yangtze River with The TGR as the core has changed the temporal and spatial distribution of sediment macroscopically (Liu et al. 2020; Tan et al. 2019).

Since 1950s, many experts and scholars have studied the characteristics of runoff and sediment in the upper reaches of the Yangtze River. Based on the analysis of the changes of runoff and sediment transport at Yichang station, Pingshan station and Beibei station of Jialing River in the upper Yangtze River since the 1950s, it is considered that the obvious differences in the way and degree of human activities, vegetation destruction and restoration, soil and water loss control, sediment retention by water conservancy projects and sediment increase by engineering construction are the main reasons for the different changes of runoff and sediment in Jialing River and Jinsha River since the 1980s reason (Zhang 1999; Zhang and Wen 2002). Based on the measured data from 1954 to 1992, Spearman rank correlation test, Kendell rank correlation test and linear regression test are used to analyze the discharge and sediment discharge of Pingshan station on Jinshajiang River, and the variation trend of water and sediment is analyzed and tested. It is concluded that there is no obvious trend of water and sediment variation (Huang et al. 2002). Based on the measured data of runoff and sediment in the Yangtze River Basin in recent 50 years, the variation trend of runoff and sediment in the main stations of the main stream and tributaries is analyzed macroscopically. It is found that the average annual sediment discharge of Hankou station, Datong station and Yichang station of the main stream has a significant decreasing trend (Renshou et al. 2003). The variation of runoff and sediment in the upper reaches of the Yangtze River in recent decades is analyzed by using the statistical analysis method of double cumulative curve of measured annual runoff and annual sediment discharge and Spearman rank correlation test (Dai et al. 2007). Based on the analysis of recent runoff and sediment conditions and their changing trend in the upper reaches of the Yangtze River, it is found that there is no obvious change in the composition of runoff and sediment in the upper reaches of the Yangtze River, but the composition of sediment has changed greatly (Quanxi et al. 2004; Xu et al. 2005, Xu et al. 2009). Based on the measured runoff and sediment data of Pingshan, Cuntan, Yichang and other control stations in the main stream of the Yangtze River from 1950 to 2005, the temporal, spatial and correlation variation characteristics and trends of runoff and sediment in the main stream of the Yangtze River are studied by using the methods of time interval analysis, regression analysis, correlation analysis, moving average, frequency analysis, modulus coefficient comparison and cumulative curve(Dong et al. 2008). By means of wavelet analysis, Mann Kendall test, runoff concentration degree and concentration period, the interannual and interannual variations of runoff in Yichang station in recent decades are studied. The results show that the operation of The TGR aggravates the trend of runoff decrease in flood season and increase in dry season in the upper reaches of the Yangtze River, and reduces the difference of annual distribution (Zhao et al. 2012). Based on the 60 year series of runoff and sediment data from the main stream of the upper reaches of the Yangtze River and its main tributaries, Minjiang River and Jialing River Control hydrological stations, and based on the M-K test method and R/S analysis method, the variation characteristics and development trend of runoff sediment transport time series are preliminarily analyzed by calculating the characteristic curve (Xiao et al. 2017). In addition, Zhu (2000) discussed the changes of sediment transport and concentration in the upper Yangtze River and the ways of sediment reduction, and Xiang (1993) studied the source, transport and sedimentary characteristics of sediment in the Yangtze River, Li (2001) studied the temporal and spatial distribution characteristics of water and sediment transport in the Yangtze River, Chen (2001) and Chen (2001) studied the variation characteristics of water and sediment transport in the Yangtze River, and analyzed the variation of water flow into the sea in the dry season, Lu (2003) also analyzed the variation characteristics of sediment transport in the upper Yangtze River, Su (2005) preliminarily predicted the variation trend of water and sediment in the Yangtze River Basin, and Yang (1993) respectively predicted the Yangtze River movement under the influence of human activities In addition, Hu (1993) also made a preliminary study on the water and sediment variation of Jialing River.

At present, in view of the research on the variation characteristics of water and sediment in the upper Yangtze River, the relevant scholars only recognize the “new water and sediment conditions” from the time level (time point, mutation, periodicity, etc.), and ignore the analysis and discussion from the spatial level to a certain extent. However, the movement of water and sediment not only changes with the passage of time, but also changes in different spatial categories. As an objective natural phenomenon, the movement of water and sediment can be explored more comprehensively only by fully covering its spatial and temporal characteristics. Therefore, based on the hydrological and sediment observation data of the upper Yangtze River and the main stream from 1956 to 2018, this paper analyzes the spatiotemporal evolution characteristics of water and sediment in Sanxin reservoir from four aspects of mutation, periodicity, complexity and chaos, and defines the “new water and sediment conditions” of the TGR. The main factors affecting the temporal and spatial variation of water and sediment in the TGR are discussed.

2 Data and Methods

2.1 Data

Taking Zhutuo and Cuntan in the main stream of upper Yangtze River, Beibei in the Jialing River and Wulong in the Wujiang River as representative stations, the data of Cuntan + Wulong (1956–2002) and Zhutuo + Beibei + Wulong (2003–2018) are used for The TGR. The runoff and sediment data of the upper Yangtze River from 1956 to 2018 provided by the Bureau of hydrology of the Yangtze River Water Resources Commission and the Yangtze River Sediment bulletin are used as the basic data for the study. The river system boundary and hydrological stations in the upper Yangtze River are shown in Fig. 1.

Fig. 1.
figure 1

Drainage boundary and hydrological control stations in the upper Yangtze River

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2.2 Methods

  1. (1)

    M-K test method: It is very effective for the change test of change elements from a relatively stable state to another state. M-K test method is widely recognized by hydrologists because it does not require the original data to obey a specific probability distribution and only satisfies the random independence of time series (Chai et al. 2017).

  2. (2)

    Wavelet analysis method: The basic idea is to use a cluster of wavelet function system to represent or approximate a signal or function (Wu et al. 2016). Water and sediment time series are non-stationary signals and have multi time scale characteristics. Wavelet analysis has multi-resolution function, which is suitable for analyzing water and sediment time series, realizing the localization of time-frequency domain and revealing the variation characteristics of water and sediment time series.

  3. (3)

    Approximate entropy (ApEn) method: ApEn is a method to quantify the complexity of time series based on edge probability distribution statistics. The calculation process is simple, and the requirements for the length of time series and other conditions are relatively low, so it has high practical value (Chen et al. 2019; Yang et al. 1997). It is a new way to understand the dynamic characteristics of runoff and sediment transport from the perspective of approximate entropy.

  4. (4)

    Lyapunov exponent method: Lyapunov exponent can quantitatively describe the separation or contraction direction of trajectories between two adjacent points at exponential rate. In chaos identification, only the maximum Lyapunov exponent \({\uplambda }_{max}\) is usually calculated. As long as \({\uplambda }_{max}\) > 0, chaos exists. The larger the value is, the stronger the chaotic characteristics of the system are; the smaller the value is, the weaker the chaotic characteristics of the system are (Xu et al. 2017).

3 Results

3.1 Mutation

From 1956 to 2018, the results of M-K test of runoff and sediment discharge in the upper Yangtze River and the TGR (Fig. 2) show that: (1) There is no significant change in the annual runoff of the TGR control station, but the annual runoff of the TGR mutated in 2003. (2) The annual sediment discharge of the upper Yangtze River and the TGR has obvious abrupt change. The annual sediment discharge of Zhutuo station changed abruptly in 2008; Cuntan station changed abruptly in 2001; Beibei station changed abruptly in 1989; Wulong station changed abruptly in 2002; The TGR changed abruptly in 2003. (3) The M-K test of abrupt change significance of runoff and sediment discharge in the upper Yangtze River and the TGR has been passed (Table 1).

Fig. 2.
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M-K test results of annual runoff and sediment series in the upper Yangtze River and the TGR

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Table 1. Significance test of M-K mutation of water and sediment in Upper Yangtze River and TGR in recent 60 years
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3.2 Periodicity

Morlet wavelet is used as the base wavelet to transform the annual runoff and sediment of Zhutuo, Beibei, Wulong and The TGR respectively, and the wavelet transform coefficients Wf(a,b) are obtained. Then, the time-frequency distribution of Wf(a,b) wavelet coefficients is drawn with b as abscissa and a as ordinate. Finally, the wavelet variance is obtained from the wavelet transform coefficients, and the wavelet variance diagram is drawn according to the variation of wavelet variance with a. According to the time-frequency distribution of wavelet coefficients, the characteristics of hydrological time series can be analyzed. The wavelet coefficients under different time scales can reflect the variation characteristics of water and sediment in corresponding time scales, that is, if the wavelet coefficient is positive, it indicates that the period is wet (or sandy), if the wavelet coefficient is not negative, it indicates that the period is dry (or sandy), if the wavelet coefficient is zero, it corresponds to the mutation point. The larger the absolute value of the wavelet coefficient is, the more significant the time scale change is. According to the wavelet variance diagram, the main period of each sequence can be found out. The larger the wavelet variance is, the stronger the time scale oscillation is and the more significant the period is. Figure 3 and Fig. 4 show the time-frequency distribution of wavelet coefficients of annual runoff and annual sediment of each station respectively. The solid line indicates that the wavelet coefficients are positive, and the dotted line indicates that the wavelet coefficients are negative.

It can be seen that the structure of runoff variation at Zhutuo station is different at different time scales, and more complex small-scale oscillations are nested in large-scale oscillations. In the larger scale of 8–9 years, the periodic oscillation of annual runoff is very obvious, there are six alternations of wet and dry. Before 1960, 1967–1976, 1987–1995 and 2003–2011, the wavelet coefficients were positive, indicating the wet season, while the other years were the dry season. In the scale of 4–6 years, there are 12 alternations of wet and dry in the past 60 years, and the location and distribution of mutation points are relatively clear. There are many abrupt changes in the 2–3 year scale(Fig. 3). There are four peaks in wavelet variance, which indicates that the first, second, third and fourth main periods of annual runoff change at Zhutuo station are 16 years, 12 years, 9 years and 4 years respectively. The wavelet characteristics of annual sediment discharge at Zhutuo station are similar to and different from those of annual runoff. On the scale of 6–8 years, the sediment discharge presents a cycle of “more-less”, with abrupt changes in 1965, 1976, 1982, 1990 and 2004. The smaller the scale, the more complex the phase change and the more mutation points. The main periods of annual sediment discharge at Zhutuo station are 12 years and 4 years, which corresponding to the result of real frequency distribution (Fig. 4).

It can be seen that the scales of annual runoff change at Beibei station are mainly 10–12 years, 5–6 years and 2–3 years. On the scale of 10–12 years, the mutation point is clear, and there are six alternations of wet and dry. The mutation points of wet and dry are 1976, 1985, 1996 and 2006. On the scale of 5–6 years, there are 11 alternations of wet and dry in the past 60 years. On the scale of 2–3 years, there are many abrupt changes and frequent phase transformation (Fig. 3). The main periods of annual runoff change of Beibei station are 10 years, 8 years and 2 years. On the scale of 9–11 years, the annual sediment discharge of Beibei station also presents a cycle of “more-less”, with abrupt changes in 1976, 1990 and 2006. With the decrease of time scale, the mutation points increase. The main periods of annual sediment discharge at Beibei station are 14 years, 8 years and 4 years, which corresponding to the result of real frequency distribution (Fig. 4).

It can be seen that the scales of annual runoff change at Wulong station are mainly 8–10 years and 3–4 years. On the scale of 8–10 years, the mutation points were clear, and there were 7 alternations of wet and dry seasons. The mutation points of wet and dry seasons were 1965, 1973, 1982, 1990, 1998 and 2006. On the scale of 3–4 years, there are many abrupt changes and frequent phase transformation (Fig. 3). The main periods of annual runoff change at Wulong station are 18 years, 10 years and 4 years. It can be seen that the annual sediment discharge of Wulong station also presents a cycle of “more-less” on the scale of 7–9 years, with abrupt changes in 1978, 1984 and 2002. With the decrease of time scale, the mutation points increase. The main periods of annual sediment discharge at Wulong station are 7 years and 4 years, which corresponding to the result of real frequency distribution (Fig. 4).

It can be seen that the scale of annual runoff variation of the TGR is mainly 15–17 years, 8–9 years and 4–5 years. On the scale of 15–17 years, the mutation points were clear, and there were 8 alternations of wet and dry seasons. The mutation points were 1961, 1970, 1979, 1988, 1998, 2003 and 2010. On the scale of 4–5 years, there are many abrupt changes and frequent phase transformation(Fig. 3). The main periods of annual runoff variation of the TGR are 17 years, 9 years and 3 years. On the scale of 7–9 years, the annual sediment discharge of the TGR also presents a cycle of “more-less”, with abrupt changes in 1964, 1971, 1979, 1987, 1995, 2003 and 2008. With the decrease of time scale, the mutation points increase. The main periods of annual sediment discharge are 17 years, 9 years and 2 years, which corresponding to the result of real frequency distribution(Fig. 4).

Fig. 3.
figure 3

Real frequency distribution of annual runoff and sediment of Zhutuo, Beibei, Wulong and TGR

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Fig. 4.
figure 4

Wavelet variogram of annual runoff and sediment of Zhutuo, Beibei, Wulong and TGR

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3.3 Complexity

The complexity of runoff and sediment transport time series in the upper Yangtze River and the TGR is studied based on ApEn. Firstly, the approximate entropy values of the original runoff and sediment transport time series of each hydrological station are calculated; secondly, the approximate entropy values of the runoff and sediment transport time series of each hydrological station are compared, and the temporal and spatial variation laws of the annual runoff and sediment transport complexity of each hydrological station are analyzed qualitatively and quantitatively. Based on the runoff and sediment transport data of Zhutuo, Beibei, Wulong and the TGR from 1956 to 2018, this paper uses ApEn method to calculate the approximate entropy of each station, and uses the approximate entropy to express the complexity of annual runoff and sediment transport. It can be seen that both runoff and sediment transport in the upper Yangtze River and the TGR are complicated. The complexity of water and sediment transport in Zhutuo station of the main stream is greater than that in Beibei station and Wulong station, and the complexity of sediment transport in each station is greater than that of runoff, which indicates that the variation of sediment transport in the upper Yangtze River and the TGR is more obvious (Table 2).

Table 2. ApEn values of runoff and sediment in the upper Yangtze River and the TGR
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3.4 Chaos

Based on the chaos theory, the chaotic characteristics of runoff and sediment transport time series in the upper reaches of the Yangtze River and the TGR are quantitatively analyzed by calculating the saturation correlation dimension, and the chaotic characteristics are further verified by using the maximum Lyapunov exponent method.

3.4.1 Delay Time

The variation of autocorrelation function with delay time of annual average runoff time series of TGR is shown in Fig. 5. According to the numerical test results, the time corresponding to the first zero crossing of the correlation function curve is taken as the best delay time. The best delay time of reconstructing the phase space of the TGR annual average runoff time series is T = 3.

Fig. 5.
figure 5

Autocorrelation function of annual runoff in the TGR

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3.4.2 Embedding Dimension

Fig. 6.
figure 6

Embedding dimension of annual runoff in the TGR

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According to the delay time τ of the annual average runoff time series of The TGR, the Cao method is used to calculate the embedding dimension m, and the relationship curves between E1(m) and E2(m) and the embedding dimension m are obtained (Fig. 6). When m = 7, E1(m) changes little. At this time, M = 8 is the embedding dimension of the phase space reconstruction of The TGR annual average runoff time series. At the same time, the simulation results show that E2(m) fluctuates up and down at 1, so it can be determined that the average annual runoff time series of The TGR is chaotic time series.

3.4.3 Saturation Correlation Dimension

According to the delay time of the TGR annual average runoff time series T = 3, the G-P algorithm is used to obtain the lnC(r)-lnr curves under different embedding dimensions m (Fig. 7) and the relationship between correlation dimension D and different embedding dimensions m (Fig. 8).

Fig. 7.
figure 7

LnC(r)-Lnr relationship of annual runoff in the TGR

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Fig. 8.
figure 8

D(m)-m relationship of annual runoff in the TGR

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Under different embedding dimensions m, each curve in lnC(r)-lnr graph has a straight line segment, and the slope of this segment is the correlation dimension d corresponding to each embedding dimension M (Fig. 7). This process is illustrated in Fig. 10 to obtain the relationship between the embedding dimension m and the correlation dimension D. It can be seen that the correlation dimension reaches a saturation value of D2 = 4.135 when the embedding dimension M = 8. This means that when the embedded phase space of the annual mean runoff time series reaches dimension 8, the system will have a stable attractor dimension. Therefore, the annual average runoff series of The TGR has chaotic characteristics.

3.4.4 Largest Lyapunov Exponents

The existence of saturation correlation dimension indicates that the system has a singular attractor, that is, the average annual runoff series of the TGR has chaotic characteristics. In order to further verify its chaotic characteristics, the maximum Lyapunov exponent method is used to identify the chaotic characteristics of the TGR annual average runoff series when the delay time is determined to be 3. The maximum Lyapunov exponent under different embedding dimensions is obtained as shown in the table below (Table 3).

Table 3. Comparison of embedding dimension and maximum Lyapunov exponent of annual runoff in the TGR
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It can be seen that when the embedding dimension increases to 8, the maximum Lyapunov exponent no longer changes greatly with the increase of m value, with \({\mathrm{L}}_{\mathrm{E}} \) = 0.1747. The maximum predictable scale is 5.72 according to \(\mathrm{t}0\approx \frac{1}{{\mathrm{L}}_{\mathrm{E}}}\). The actual physical meaning is that when using the actual data of the average annual runoff of the TGR to predict, the maximum prediction time is at most six years under the condition of less serious loss of accuracy. In addition, \({\mathrm{L}}_{\mathrm{E}}\) > 0 indicates that the annual mean runoff of Yichang station is chaotic. Combined with the results of Cao method and saturation correlation dimension, it can be confirmed that the average annual runoff of the TGR has chaotic property.

Table 4. Chaos analysis results of annual runoff and sediment in the TGR
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It can be seen that both the annual average runoff and sediment of the TGR have saturation correlation dimension, and the maximum Lyapunov exponent is greater than 0. Therefore, it can be confirmed that the annual average runoff and sediment of the TGR have chaotic characteristics. In addition, the state space dimension of runoff and sediment of representative stations in the upper Yangtze River gradually increases from upstream to downstream, and the corresponding saturation correlation dimension also increases from upstream to downstream (Table 4). This shows that the characteristics of runoff and sediment in the upper Yangtze River are more and more complex, and the complexity of runoff and sediment sequence increases from upstream to downstream, which is consistent with the results of the previous complexity analysis.

3.5 Connotation of “New Water and Sediment Conditions”

This paper analyzes the temporal and spatial evolution characteristics of water and sediment in the TGR from four aspects of mutation, periodicity, complexity and chaos. The connotation of “new water and sediment conditions” is as follows: After the impoundment of the TGR, the runoff does not change much and the sediment discharge decreases sharply; from the perspective of time scale, there is no obvious mutation in runoff and sediment discharge, and the main cycle of water and sediment change is basically the same; from the perspective of space scale The results show that the complexity and chaos of sediment transport are significantly greater than that of runoff, and the change degree of sediment transport is more significant than that of runoff.

4 Influencing Factors of “New Water and Sediment Conditions”

The main factors affecting the change of water and sediment in the TGR can be divided into two aspects: natural and man-made. Natural factors mainly refer to climate (rainfall), soil and vegetation conditions, geology and geomorphology, while human factors mainly include soil and water conservation, water conservancy project sand blocking, river sand mining, etc. (Ding et al. 2008). The results show that: (1) Climate change is mainly composed of precipitation, regional distribution of rainfall and rainfall intensity, which has a great impact on sediment yield and transportation in the basin, and its randomness is strong, and generally has a certain periodicity; (2) The sediment reduction caused by the reservoir intercepting sediment also has a certain long-term effect. The initial sediment retention benefit is very significant, but when the reservoir sedimentation is balanced, it will no longer have the sediment retention benefit, and the upstream sediment inflow will return to the natural state. The main reason is that when there is no obvious change in the amount of erosion in the basin, the sediment transport ratio will be greatly reduced in a certain period of time due to the blocking effect of the reservoir, but when the upstream reservoir is full, the sediment transport ratio will return to the previous situation or greater, and the sediment entering the TGR will increase; (3) The sediment reduction caused by soil erosion control has a certain long-term nature, but it will reach the limit value of relative equilibrium in a certain period of time; (4) The impacts of other human activities, such as increasing or reducing sediment in engineering construction, sand mining in river channel, water use in industry and agriculture, will change with the development of social economy, and also affect the change of water and sediment in river basin.

The relationship between precipitation and sediment discharge and the relationship between runoff and sediment discharge are power functions: \({W}_{s}=a\times {P}^{b}\) and \({W}_{s}=a\times {R}^{b}\). Where, \({W}_{s}\) is annual sediment discharge,\(P\) is annual rainfall and \(R\) is annual runoff, a and b are fitting coefficients and indexes respectively. Generally, the relationship can be used to roughly estimate the effect of precipitation/runoff on sediment transport. The relationship between runoff and sediment discharge in the upper Yangtze River is complex, and the correlation varies greatly in different periods. Based on the results of M-K mutation test, the contribution of climate change and human activities to sediment transport in the upper Yangtze River was further separated and quantified.

According to the preliminary estimation of the relationship between runoff and sediment discharge, the actual sediment reduction in the upper Yangtze River from 1991 to 2002 is 0.108 billion t/a, and the runoff is 7 billion m3/a less than that before 1990. Among them, the sediment reduction caused by the change of precipitation/runoff (under the underlying surface conditions before 1990, the same below) is 0.067 billion t/a, and the sediment change caused by rainfall accounts for 79.8%. From 2003 to 2018, the actual sediment reduction was 0.206 billion t/a and the runoff decreased by 19.5 billion m3/a compared with that before 1990. Among them, the sediment reduction caused by precipitation/runoff (under the underlying surface conditions before 1990, the same below) was 0.043 billion t/a, and the sediment change caused by rainfall accounted for 20.9% (Fig. 9).

To sum up, climate change (rainfall) was an important factor affecting the sediment discharge in the upper Yangtze River from 1991 to 2002. From 2003 to 2018, the impact of climate change on the sediment discharge in the upper Yangtze River was relatively insignificant, and human activities became the most important factor (Table 5).

Table 5. Statistics of rainfall (mm), runoff (billion m3) and sediment (billion t) in the upper Yangtze river
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Fig. 9.
figure 9

Annual runoff-sediment and rainfall- sediment at different periods in the upper Yangtze River

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5 Conclusion

Based on the hydrological and sediment observation data of the upper Yangtze River and the main stream from 1956 to 2018, this paper analyzes the spatiotemporal evolution characteristics of the incoming water and sediment of the TGR from four aspects of mutation, periodicity, complexity and chaos based on the M-K test method, wavelet analysis method, ApEn method and Lyapunov exponent method, and defines the connotation of “new water and sediment conditions” of the TGR, The main factors affecting the temporal and spatial variation of water and sediment in theTGR are discussed. The main conclusions are as follows:

  1. (1)

    Except Pingshan station of Jinsha River, Fushun station of Tuojiang River and Wulong station of Wujiang River, the runoff of other main and tributaries and The TGR in the upper Yangtze River has no significant change, but the sediment discharge has obvious mutation, and the runoff and sediment have periodic changes in different degrees;

  2. (2)

    The complexity of annual runoff and sediment transport in the upper Yangtze River increases gradually, and the complexity of sediment transport is greater than that of runoff. Both annual runoff and sediment transport are chaotic, and the complexity of runoff and sediment transport sequence increases gradually from the upper reaches to the lower reaches;

  3. (3)

    The connotation of “new water and sediment condition” shows that there is no obvious mutation in runoff and sediment transport in time scale, the main cycle of water and sediment change is basically the same, and the complexity and chaos of sediment transport in space scale are significantly greater than runoff, and the change degree of sediment transport is more significant than runoff;

  4. (4)

    From 1991 to 2002, climate change (rainfall) was an important factor affecting the sediment discharge in the upper Yangtze River. From 2003 to 2018, the impact of climate change was relatively insignificant, and human activities became the most important factor.