Introduction

Affected by climatic factors (e.g., rainfall) and human activities (e.g., reservoir construction and soil and water conservation), the conditions of the sediment production and transport in the upper Yangtze River have undergone significant changes1,2,3,4,5,6,7. Without an obvious change in runoff, the sediment discharge has decreased significantly8. In particular, since the successive construction and operation of the cascade reservoirs (the Xiluodu and Xiangjiaba hydroelectric stations) in the middle and lower reaches of the Jinsha River in 2012, the largest cluster of reservoirs in the world has been formed in the upper Yangtze River. The completion and operation of this super cluster of reservoirs has not only changed the temporal–spatial conditions of the runoff in the basin, but it has also macroscopically changed the temporal–spatial distribution of the river sediment. Consequently, the characteristics of the water and sediment transported into the TGR has undergone new changes9,10.

For different areas of reservoir sedimentation research, domestic and foreign scholars also try to use different methods to do some research. Some scholars investigated debris flow deposition in the reservoir of the detention slit dams using a two-dimensional numerical model11; While others adopted multi-source data fusion to combine sonar sounding data, map data and manual measurement data to update and reconstruct the bottom topography of the reservoir, so as to calculate the reservoir sedimentation and its distribution12; Based on the artificial neural network (ANN) approach and the Modified Universal Soil Loss Equation model coupled with the multiple linear regression (MUSLE-MLR) model, Bilali et al.13 predicted yearly sedimentation in the Sidi Mohammed Ben Abdellah reservoir, located in a semi-arid region of Morocco. In addition, previous studies adopted non mechanism or mechanism model to study reservoir sediment transport and reservoir deposition14,15,16,17,18.

Since the 1990s, many studies have been carried out on the characteristics of water and sediment transport in the upper Yangtze River and the prediction of the volume of sediment transported into the TGR. These studies have yielded fruitful research results. Dai et al.19 used the statistical analysis method of the double cumulative curve of the measured annual runoff and the annual sediment discharge as well as the Spearman rank correlation test to analyze the decrease in the incoming water and sediment in the upper reaches of the TGR, and they observed correlation between the incoming water and sediment, which can be used to predict the recent annual volume of sediment transported into the TGR. Wang et al.20 applied the cumulative curve, the M–K sequence analysis method, and the cluster analysis method to explore the changes in the water and sediment characteristics of the trunk and tributaries in the upper Yangtze River from 1950 to 2014 and analyzed the influences of human activities. Chai et al.21 used the double cumulative curve to analyze the relationship between water and sediment at 7 hydrological stations in the Yangtze River Basin from 2000 to 2013. Their results show that the impoundment operation and continuous development of soil and water conservation in the TGR were the main reasons for significant decrease in the sediment discharge in the mainstream of the Yangtze River from 2000 to 2013, while the decrease in rainfall was one of the key factors leading to decline in runoff. According to the measured hydrological data after the impoundment operation of the TGR, Fu et al.22 revised the results of the sediment discharge ratio of the TGR reported by the Yangtze River Scientific Research Institute. Based on a series of water and sediment data from 1961 to 1970, the annual average volume of sediment transported into the TGR was predicted to decrease to 120 million t after the completion and operation of the Xiluodu, Xiangjiaba, and Jin’anqiao Reservoirs. By studying the influence of the sediment retaining effect of the reservoirs in the upper Yangtze River on the volume of sediment transported into the TGR, Li et al.23 concluded that on average, the sediment retaining effect of the reservoirs in the upper Yangtze River reduced the volume of sediment transported into the TGR by 110 million t/a from 1991 to 2005. Upon the operation of the proposed large reservoirs in the upper Yangtze River in the near future, the volume of sediment transported into the TGR will decrease to 90.3 million t/a, which is only 18.3% of the volume during 1956–1990. Duan et al.24 predicted that the volume of sediment transported into the TGR from 2015 to 2050 will decrease to about 60 million t/a, which is only about 15% of the average volume from 1991 to 2005, due to the outstanding sediment retaining effect of the reservoirs.

The above-mentioned studies provided insights into the changes in the water and sediment characteristics in the upper Yangtze River and how the sediment retaining effect of the reservoirs affects the water–sediment conditions of the TGR. Nonetheless, according to the measured data, the prediction is slightly conservative, and the sediment retaining effect of the reservoirs in the upper Yangtze River is significantly larger than expected. The volume of sediment transported into the TGR was only 34.4 million t in 2017, which indicates that the measured volume of the sediment transported into the reservoir is decreasing faster than expected. Thus, under the new water–sediment conditions, to ensure the long-term safe operation and optimized scheduling of the TGR, it is important to study the long-term scouring and silting changes and the sedimentation balance of the TGR.

In this study, based on the reservoir construction and the measured water and sediment data for the upper reaches of the Yangtze River from 1956 to 2018, the variation characteristics of the water and sediment transported into the TGR were analyzed, and the possible water–sediment combinations to the TGR in the future under new water–sediment conditions were predicted. Based on this, a one-dimensional unsteady water and sediment mathematical model of the trunk stream and tributaries of the TGR was established, and the main calculation parameters of the model were calibrated. In view of the different water–sediment combinations that may occur in the TGR under new water–sediment conditions, the model was used to study the long-term scouring and silting variations of the sediment and the sedimentation balance in the TGR area.

Analysis of the new water–sediment conditions

The data from the Cuntan and Wulong Stations were used in the demonstration stage of the Three Gorges Project, with the sum of the annual average runoff into the reservoir being 398.6 billion m3 and the sum of the sediment discharge being 494 million t. As for the mathematical model calculation and the physical model test, the annual water and sediment data from 1961 to 1970 served as the representative water–sediment conditions, in which the annual average runoff is 420.2 billion m3 and the annual average sediment discharge is 509 million t.

With an unclear variation trend in the runoff into the reservoir, the sediment discharge has decreased. The average volume of sediment transported into the TGR was 72.5 million t from 2013 to 2018, which is only 14.8% that from 1956 to 1990 and 35.8% that from 2003 to 2012 (Table 1).

Table 1 Statistical data for the water and sediment characteristics from 2003 to 2018.
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With the continuous construction of cascade reservoirs on the trunk streams and tributaries in the upper Yangtze River, the water and sediment system of the river basin has been increasingly prominently affected. The decreasing trend in the volume of sediment transported into the TGR will be faster than expected, and the rare phenomenon of a small amount of sand in a vast sea may even occur. The reduced volume of sediment transported into the reservoir will slow down the sedimentation rate of the sediment in the TGR and prolong the time required for the reservoir to reach a sedimentation balance25.

Establishing the water–sediment mathematical model

Basic equations of the model

Since there are many tributaries in the TGR area, both the water and sediment movement in the trunk stream and tributaries should be taken into consideration while establishing the one-dimensional unsteady water and sediment mathematical model of the TGR. The trunk stream and tributaries of the reservoir were regarded as single channels, and the confluence point of the rivers was defined as the branching point. The water and sediment mathematical model consists of 3 parts: the water–sediment movement equations of the single channels, the branching point connection equations, and the boundary conditions.

Basic equations for the water and sediment movements in a single river channel

The water flow continuity equation is26

$$\frac{{\partial A_{i} }}{\partial t} + \frac{{\partial Q_{i} }}{\partial x} = 0.$$
(1)

The water flow motion equation is

$$\frac{{\partial Q_{i} }}{\partial t} + \frac{\partial }{\partial x}\left( {\frac{{Q_{i}^{2} }}{{A_{i} }}} \right) + gA_{i} \left( {\frac{{\partial Z_{i} }}{\partial x} + \frac{{\left| {Q_{i} } \right|Q_{i} }}{{K_{i}^{2} }}} \right) = 0.$$
(2)

The sediment continuity equation is

$$\frac{{\partial Q_{i} S_{i} }}{\partial x} + \frac{{\partial A_{i} S_{i} }}{\partial t} + \alpha_{i} \omega_{i} B_{i} \left( {S_{i} - S_{*i} } \right) = 0.$$
(3)

The riverbed deformation equation is

$$\rho^{\prime } \frac{{\partial A_{d} }}{\partial t} = \alpha_{i} \omega_{i} B_{i} \left( {S_{i} - S_{*i} } \right).$$
(4)

here A is the discharge area, Q is the water discharge, t is the time, x refers to the coordinates along the flow path, i is the number of the section, Z is the water level, K is the modulus of the cross-sectional water discharge; S is the sediment concentration, ρ′ is the dry density of the sediment, d is the particle size, α is the recovery saturation coefficient, ω is the settling velocity of the sediment, B is the width of the cross-section, g is the gravitational acceleration, and Ad is the scouring and silting area of the riverbed.

Branching point connection equation

  1. (1)

    Discharge connection conditions

The water flowing in and out of each branching point must be balanced with the increase or decrease rate of the actual water within that branching point, that is,

$$\sum {Q_{i} } = \frac{\partial \Omega }{{\partial t}}$$
(5)

here \(\Omega\) is the amount of water stored at the branching point. If the point is generalized as a geometric point, then \(\Omega = 0\).

  1. (2)

    Dynamic connection conditions

If the branching point can be generalized as a geometric point, the water flowing in and out of each branching point is gentle, and there is no sudden change in water level. Thus, the water level at the cross-section of each branching point should be the same, that is,

$$Z_{i} = Z_{j} = \cdots = \overline{Z} .$$
(6)

Boundary conditions

In the calculation, instead of giving the boundary conditions separately for a single river, the boundary conditions were determined by regarding all of the trunk stream and tributaries included in the calculation as a whole. The water discharge and sediment concentration processes were provided at the inlet of each trunk stream and tributary. The water level process, water discharge process, and the relationship between the water level and water discharge were given at the outlet of the model.

Model solving

Solving the water flow equations

The third-order method was used to solve the water flow equations. First, Eqs. (1) and (2) were discretized using Pressman’s four-point implicit difference scheme, and the difference equation was obtained as follows:

$$B_{i1} Q_{i}^{n + 1} + B_{i2} Q_{i + 1}^{n + 1} + B_{i3} Z_{i}^{n + 1} + B_{i4} Z_{i + 1}^{n + 1} = B_{i5}$$
(7)
$$A_{i1} Q_{i}^{n + 1} + A_{i2} Q_{i + 1}^{n + 1} + A_{i3} Z_{i}^{n + 1} + A_{i4} Z_{i + 1}^{n + 1} = A_{i5}$$
(8)

where the coefficient was derived based on the practical conditions.

Assuming there were \(mL\) cross-sections in a specific reach, the micro-segment Eqs. (7) and (8) obtained from the difference in this reach were eliminated sequentially, and then, the unknown values were concentrated at the branching point using the recursive relationship to obtain the relationship between the water level and water discharge in the cross-sections at the head and tail of this reach:

$$Q_{1} = \alpha_{1} + \beta_{1} Z_{1} + \delta_{1} Z_{m}$$
(9)
$$Q_{{m{\text{L}}}} = \theta_{{m{\text{L}}}} + \eta_{{m{\text{L}}}} Z_{1} + \gamma_{{m{\text{L}}}} Z_{{m{\text{L}}}}$$
(10)

here the coefficients \(\alpha_{1}\), \(\beta_{1}\), \(\delta_{1}\), \(\theta_{mL}\), \(\eta_{mL}\), and \(\gamma_{mL}\) were solved using the recursive equation.

By substituting the boundary conditions and the relationship between the water level and water discharge at the cross-sections at the head and tail of each reach into the branching point connection equation, an algebraic equation set was established with the water level at each branching point of the trunk stream and tributaries in the TGR area being unknown. The water level at each branching point was obtained by solving this equation set. Through gradual back substitution, the water discharge at the end of the reach as well as the water level and water discharge inside each reach were obtained.

Solving the sediment equations

The sediment continuity Eq. (3) was discretized using the explicit scheme:

$$S_{i}^{j + 1} = \frac{{\Delta t\alpha_{i}^{j + 1} B_{i}^{j + 1} \omega_{i}^{j + 1} S_{ * i}^{j + 1} + A_{i}^{j} S_{i}^{j} + \frac{\Delta t}{{\Delta x_{i - 1} }}Q_{i - 1}^{j + 1} S_{i - 1}^{j + 1} }}{{A_{i}^{j + 1} + \Delta t\alpha_{i}^{j + 1} B_{i}^{j + 1} \omega_{i}^{j + 1} + \frac{\Delta t}{{\Delta x_{i - 1} }}Q_{i}^{j + 1} }}.$$
(11)

By substituting Eq. (3) into Eq. (4), the riverbed deformation Eq. (4) was discretized to obtain

$$\Delta A_{di} = \frac{{\Delta t(Q_{i - 1}^{j + 1} S_{i - 1}^{j + 1} - Q_{i}^{j + 1} S_{i}^{j + 1} )}}{{\Delta x\rho^{\prime } }} + \frac{{A_{i}^{j} S_{i}^{j} - A_{i}^{j + 1} S_{i}^{j + 1} }}{{\rho^{\prime } }}$$
(12)

here \(\Delta x\) is the spatial step; \(\Delta t\) is the time step; \(\Delta A_{di}\) is the deformation area of the riverbed with suspended sediment; and corner mark j is the time layer.

Once the water level and water discharge in all of the cross-sections of the trunk stream and tributaries were calculated, the sediment concentration of each cross-section was solved from top to bottom using Eq. (11). The sediment distribution ratio at the branching point was set as equal to the diversion ratio, and the riverbed deformation was calculated using Eq. (12).

Verification of the mathematical model

Verification of the computational conditions

Basic conditions

  1. (1)

    The sediment used in the calculation was non-uniform. The sediment was divided into 10 groups based on particle sizes, i.e., 0.002 mm, 0.002–0.004 mm, 0.004–0.008 mm, 0.008–0.016 mm, 0.016–0.031 mm, 0.031–0.062 mm, 0.062–0.125 mm, 0.125–0.250 mm, 0.250–0.50 mm, and 0.5–1 mm. The riverbed was divided into 3 layers: the surface layer, the middle layer, and the bottom layer. The surface layer is the sediment exchange layer, the middle layer is the transition layer, and the bottom layer is the limit layer of the sediment scouring.

  2. (2)

    The water–sediment conditions at the inlet and outlet were calculated. The average daily water discharge and sediment concentration at Zhutuo Station on the trunk stream, Beibei Station on the Jialing River, and Wulong Station on the Wujiang River from January 1, 2008, to December 31, 2017, were used to calculate the water–sediment conditions at the inlet, with the monthly average gradation being the granular composition of the suspended sediment.

  3. (3)

    The scope of the reach was calculated. Stretching from Zhutuo to Daba in the TGR area (Fig. 1), the calculated reach includes the trunk stream of the Yangtze River and some of the segments of the Jialing River and Wujiang River (tributaries of the Yangtze River). With a length of about 400 km, the trunk stream was divided into 400 calculated sections, with each section being an average of 1.9 km long. The 61.3 km long Jialing River flowing from Beibei to the estuary was divided into 26 sections, with each section being an average of 2.4 km long. The Wujiang River, which is 67.7 km long and flows from Wulong to the estuary, was divided into 36 sections, of which each is an average of 1.9 km long.

Figure 1
figure 1

Sketch map of the TGR area.

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Calibration of the roughness coefficient

The roughness coefficient was calibrated based on the relationship between the water level and the water discharge measured at each station before the impoundment and during the initial impoundment stage of the TGR. The entire reach of the trunk stream was divided into several segments. The roughness coefficients of the Jialing River and the Wujiang River were assigned based on experience, and the calibration results are shown in Table 2.

Table 2 Statistical table of the piecewise comprehensive roughness coefficients of the TGR.
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It is difficult to directly determine the roughness coefficient beyond the wet perimeter of the natural flood water level, and since the granular composition of bed sediments changes in the process of reservoir sedimentation, it is relatively difficult to determine the change in the roughness coefficient during the process of reservoir sedimentation. In this study, the proposed model suggests that the bed sand resistance and the sidewall resistance were assumed to determine the variation in the roughness coefficient during sedimentation.

Operation of the TGR during the verification

The verification stage in this study lasted from January 1, 2008, to December 31, 2017. The reservoir operated with the water level in front of the dam following the initial operation mode from January 2008 to September 2008; and from October 2008 to December 2017, and the reservoir operated with water levels in front of the dam of 175–145–155 m (Fig. 2).

Figure 2
figure 2

Water level process in front of the TGR from 2008.1.1 to 2017.12.31.

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Verification of the water level, water discharge, and sediment concentration processes

Based on currently available measured data, the calculated results were compared with the water level, water discharge, and sediment concentration process measured at the major hydrological stations along the route from January 1, 2008, to December 31, 2017. The results are shown in Fig. 3a–l. As shown in the figures, the variations in the water level, water discharge, and sediment concentration calculated by the model are consistent with that of the measured results, and the calculated results verified by the model are in good agreement with the measured values.

Figure 3
figure 3figure 3

a Verification results of water level at Cuntan from 2008.1.1 to 2017.12.31. b Verification results of discharge at Cuntan from 2008.1.1 to 2017.12.31. c Verification results of sediment concentration at Cuntan from 2008.1.1 to 2017.12.31. d Verification results of water level at Qingxichang from 2008.1.1 to 2017.12.31. e Verification results of discharge at Qingxichang from 2008.1.1 to 2017.12.31. f Verification results of sediment concentration at Qingxichang from 2008.1.1 to 2017.12.31. g Verification results of water level at Wanxian from 2008.1.1 to 2017.12.31. h Verification results of discharge at Wanxian from 2008.1.1 to 2017.12.31. i Verification results of sediment concentration at Wanxian from 2008.1.1 to 2017.12.31. j Verification results of water level at Miaohe from 2008.1.1 to 2017.12.31. k Verification results of discharge at Miaohe from 2008.1.1 to 2017.12.31. l Verification results of sediment concentration at Miaohe from 2008.1.1 to 2017.12.31.

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Based on the analysis of the error range of the daily flow process from January 1, 2008 to December 31, 2017, the water level error of each station within the ± 0.4 m interval has a confidence of about 80%, the water discharge error of each station within the ± 10% interval has a confidence coefficient of about 90%, and the sediment concentration error of each station within the ± 30% interval has a confidence of approximately 80% (Table 3).

Table 3 Analysis of the verification error range of the daily water flow process in the TGR from January 1, 2008, to December 31, 2017.
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Verification of the sediment discharge

Based on the verification results of the sediment concentration process of several major hydrological stations in the TGR area shown in Fig. 3 from January 1, 2008 to December 31, 2017, the calculated results of each station are basically consistent with the measured values, but the peak value of the calculated sediment concentration is smaller than the measured value. However, the calculated value is slightly larger for the medium and small water discharges. Since the calculated value is close to the measured value during most periods of time, the cumulative sediment discharge throughout the year is relatively close to the measured value (Table 4).

Table 4 Verification table of the sediment discharge at the main stations (unit: 100 million t).
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Comprehensive verification of the sedimentation volume

Sedimentation volume and its distribution (based on the cross-section)

According to the report27 issued by the Hydrology Bureau of the Changjiang Water Resources Commission in March 2018, from 2008 to 2017, the measured cumulative sedimentation volume in the trunk stream of the reservoir area was 850.8 million m3 (Table 5), of which the measured scoured quantity in the variable backwater area (Tongluoxia-Fuling) is 24.9 million m3, and the measured sedimentation volumes in the perennial backwater area (Miaohe-the dam site, Wushan-Miaohe, Fengjie-Wushan, Yunyang-Fengjie, Zhongxian-Yunyang, and Fuling-Zhongxian) are 65.9 million m3, 98.5 million m3, 26.4 million m3, 64.2 million m3, 412.3 million m3, and 206.3 million m3, respectively. According to the calculation results, the calculated value for the trunk stream of the reservoir area (Tongluoxia-the dam site) is 928.2 million m3, which is 79 million m3 larger than the measured value, with the relative error being 9.3%. The calculated value in the variable backwater area (Tongluoxia-Fuling) is − 26.4 million m3, with a relative error of 6.2%. Except for the relatively large error between the calculated and measured values in the river segment from Miaohe to the dam site, the relative error between the calculated and measured values of the other river segments in the perennial backwater area was less than 10%. According to the verification of the sedimentation volume of typical reaches of the trunk stream in the TGR area (Table 6), the measured sedimentation volumes of the Huanghuacheng segment, the Lanzhuba segment, the Fengweiba segment, the Tunaozi segment, the Qingyanzi segment, and the Luoqi segment were 60.548 million m3, 32.631 million m3, 20.089 million m3, 11.683 million m3, − 12.7055 million m3, and − 14.486 million m3, respectively. Compared to the measured results, except for the relatively large error of the sedimentation volume of the Qingyanzi segment, the relative errors between the calculated and measured values of the other typical river segments were all less than 5%. Thus, the calculated cumulative sedimentation volume and the sedimentation distribution are basically consistent to the measured values.

Table 5 Verification of the sedimentation volume and distribution in the trunk stream in the TGR area from 2008 to 2017 (based on the cross-section).
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Table 6 Verification of the sedimentation volume in typical reaches of the trunk stream in the TGR area from 2008 to 2017 (based on the cross-section).
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Sedimentation volume and its process (based on the sediment discharge)

From June 1, 2003, when the TGR began operating, to 2017, the reservoir was characterized by overall sedimentation. The river segment from Zhutuo to the dam site were selected as the river segment for sedimentation statistical analysis in this study. Based on the calculation performed using the sediment discharge method, the measured cumulative sedimentation volume in the reservoir area is 1.029 billion t (Table 7) and the calculated value is 1.065 billion t, which is 36 million t larger than the measured value, with a relative error of 3.5%. Judging from the sedimentation process, the error between the calculated and measured values is comparatively small, except for that in 2013. In addition, the absolute difference between the measured and calculated sedimentation volumes is less than 10 million t, with the relative error being less than 10.9%. Therefore, the cumulative sedimentation volume and process calculated using the model are in good agreement with the measured results.

Table 7 Verification of the annual sedimentation volume process after impoundment in the TGR (based on the water discharge).
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Application of the mathematical model

Setting of the computational schemes

Affected by climate change and human activities, especially the gradual construction of cascade power stations in the lower reaches of the Jinsha River, the impoundment and sediment retaining effect of the cascade reservoirs in the basin have begun to exert a new influence on the characteristics of the water and sediment transported into the TGR. According to the measured data, the sediment retaining effect of the reservoirs in the upper Yangtze River was stronger than expected. From 2013 to 2018, the annual average volume of sediment transported into the TGR is 72.5 million t, which is only 14.8% that from 1956 to 1990 and 35.8% that from 2003 to 2012. The volume of sediment transported into the reservoir in 2017 was only 34.4 million t, indicating that the measured volume of sediment transported into the reservoir is decreasing faster than expected. In view of the new water–sediment conditions, in this study, the sedimentation volume in the TGR was calculated over a long timespan, i.e., 600 years. Based on the measured annual runoff and sediment discharge from 2003 to 2018, the water–sediment combinations were determined as follows: the year with less water-more sediment (2003), the year with more water-more sediment (2005), the year with medium amount of water-more sediment (2007), the year with less water-medium amount of sediment (2011), the year with medium amount of water-medium amount of sediment (2013), the year with more water-less sediment (2014), the year with less water-less sediment (2015), the year with medium amount of water-less sediment (2017), and the year with more water-medium amount of sediment (2018). Moreover, the water–sediment combination during 1961–1970 and that during 1991–2000 were selected as the basic schemes for comparison.

The actual scheduling scheme of the TGR after impoundment served as the scheduling scheme in this study. After October 2008, the reservoir entered the experimental impoundment stage, with the follow-up scheduling schemes being consistent. In other words, the water level in front of the dam was set as 135–139 m from June 2003 to June 2006; the reservoir operated with the water level in front of the dam being 144–156 m from September 2006 to September 2008; and the water level in front of the dam was set as 175–145–155 m from October 2008 to June 2602 (Table 8).

Table 8 Computational conditions of the different schemes.
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Results and discussions

With the development of reservoir sedimentation, the reservoir finally entered a phase of sedimentation balance. According to the shape of the riverbed, the sedimentation balance can be divided into the longitudinal balance and the horizontal balance, and the sediment transport can be classified into the suspended sediment balance and the bed load balance28. Since this study focuses on the suspended sediment balance, when the sedimentation balance were along the longitudinal profile of the reservoir, it was considered that the reservoir sedimentation has basically reached a balanced state.

As shown in Fig. 4, 2 periods of time, i.e., 1961–1970 and 1991–2000, were involved in the calculation of the basic schemes. As for Scheme 1, under the water–sediment conditions in 1961–1970, after 100 years of operation, the cumulative sedimentation volume was 15.569 billion m3 in the reservoir. In Scheme 2, under the water–sediment conditions in 1991–2000, the cumulative sedimentation volume was 7.499 billion m3 after 100 years of operation, which was 8.07 billion m3 less than that of scheme 1.

Figure 4
figure 4

Accumulation process of the TGR under different calculation schemes.

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Under the water–sediment conditions of scheme 1, the cumulative sedimentation volumes were 15.569 billion m3, 22.96 billion m3, and 25.077 billion m3 after 100, 300, and 500 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation at this stage. From the perspective of the sedimentation rate, the sedimentation was rapid during the first 100 years, decreased from the 100 to the 210 years, and followed by an increasing trend. After 320 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The cumulative sedimentation volume was 23.288 billion m3 after 320 years of operation. Thus, the reservoir sedimentation is basically balanced.

Under the water–sediment conditions of scheme 2, the cumulative sedimentation volumes were 7.499 billion m3, 12.69 billion m3, and 18.5 billion m3 after 100, 300, and 500 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation at this stage. From the perspective of the sedimentation rate, the sedimentation was comparatively fast during the first 150 years, decreased from the 150 to the 240 years, and followed by an increasing trend. After 430 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The cumulative sedimentation volume was 17.43 billion m3 after 430 years of operation. Thus, the reservoir sedimentation is basically balanced.

Under the water–sediment conditions of scheme 3, the cumulative sedimentation volumes were 5.068 billion m3, 10.37 billion m3, 15.086 billion m3, and 15.763 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation at this stage. From the perspective of the sedimentation rate, the sedimentation was relatively fast during the first 140 years, decreased from the 140 to the 210 years, and followed by an increasing trend. After 480 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The reservoir sedimentation experiences a basic balance, and the cumulative sedimentation volume was 14.869 billion m3 after 480 years of operation.

Under the water–sediment conditions of scheme 4, the cumulative sedimentation volumes were 7.092 billion m3, 12.148 billion m3, 17.706 billion m3, and 18.567 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation at this stage. Regarding the sedimentation rate, the sedimentation was relatively fast during the first 160 years, followed by a declining trend from the 160 to the 240 years, and increased after 240 years. After 450 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The cumulative sedimentation volume was 16.87 billion m3 after 450 years of operation. Thus, the reservoir sedimentation is basically balanced.

Under the water–sediment conditions of scheme 5, the cumulative sedimentation volumes were 5.601 billion m3, 10.802 billion m3, 15.79 billion m3, and 16.526 billion m3 after 100, 300, 500, and 600 years of operation reservoir respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the sedimentation was relatively fast during the first 130 years, decreased from the 130 to the 240 years, and followed by an increasing trend. After 470 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The cumulative sedimentation volume was 15.428 billion m3 after 470 years of operation. Thus, the reservoir sedimentation is basically balanced.

Under the water–sediment conditions of scheme 6, the cumulative sedimentation volumes were 2.107 billion m3, 7.661 billion m3, 10.581 billion m3, and 11.059 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the sedimentation was comparatively fast during the first 80 years, decreased from the 80 to the 140 years, and followed by an increasing trend. After 520 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The reservoir sedimentation enters a basically balanced state, and the cumulative sedimentation volume was 10.684 billion m3 after 520 years of operation.

Under the water–sediment conditions of scheme 7, the cumulative sedimentation volumes were 2.971 billion m3, 8.888 billion m3, 12.561 billion m3, and 13.062 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the sedimentation was relatively fast during the first 110 years, decreased from the 110 to the 170 years, and followed by an increasing trend. After 510 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The cumulative sedimentation volume was 12.624 billion m3 after 510 years of operation. Thus, the reservoir sedimentation is basically balanced.

Under the water–sediment conditions of scheme 8, the cumulative sedimentation volumes were 1.847 billion m3, 7.179 billion m3, 9.877 billion m3, and 10.293 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the sedimentation was comparatively fast during the first 90 years, decreased from the 90 to the 140 years, and followed by an increasing trend. After 530 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The reservoir sedimentation enters a basically balanced state, and the cumulative sedimentation volume was 10.021 billion m3 after 530 years of operation.

Under the water–sediment conditions of scheme 9, the cumulative sedimentation volumes were 1.154 billion m3, 3.689 billion m3, 5.275 billion m3, and 5.806 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the cumulative sedimentation rate is relatively stable, exhibiting a slow and uniform sedimentation trend. After 560 years of operation, there was an inflection point on the cumulative sedimentation hydrograph. The cumulative sedimentation volume was 5.607 billion m3 after 560 years of operation. Thus, the reservoir sedimentation is basically balanced.

Under the water–sediment conditions of scheme 10, the cumulative sedimentation volumes in the reservoir area were 1.497 billion m3, 4.215 billion m3, 5.803 billion m3, and 6.328 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the cumulative sedimentation rate was relatively steady, exhibiting a slow and uniform sedimentation trend. After 540 years of operation, there was an inflection point on the cumulative sedimentation hydrograph. The reservoir sedimentation was a basically balanced state, and the cumulative sedimentation volume was 6.03 billion m3 after 540 years of operation.

Under the water–sediment conditions of scheme 11, the cumulative sedimentation volumes were 4.491 billion m3, 9.588 billion m3, 14.105 billion m3, and 14.748 billion m3 after 100, 300, 500, and 600 years of reservoir operation respectively, with the reservoir being in a state of cumulative sedimentation. From the perspective of the sedimentation rate, the sedimentation was comparatively fast during the first 130 years, decreased from the 130 to the 210 years, and followed by an increasing trend. After 500 years of operation, the sedimentation declined again, and there was an inflection point on the cumulative sedimentation hydrograph. The reservoir sedimentation enters a basically balanced state, and the cumulative sedimentation volume was 14.105 billion m3 after 500 years of operation.

In summary, under the water–sediment conditions during 1961–1970 and 1991–2000, it takes 320 years and 430 years, respectively, for the TGR to reach a sedimentation balance. Under the new water–sediment conditions, it takes 560 years at most and 450 years at least for the TGR to reach a sedimentation balance, with the corresponding water–sediment conditions being a typical year with less water-less sediment and a typical year with more water-more sediment, respectively.

As shown in Table 9, it takes 320 years and 430 years respectively for the TGR to reach the sediment balance under the water–sediment conditions during 1961–1970 and 1991–2000. Affected by climate change and human activities, especially the construction and operation of cascade hydropower stations on the Jinsha River in the upper Yangtze River, the conditions of the water and sediment transported into the TGR have experienced new changes. Under the new water–sediment conditions, it takes 560 years at most and 450 years at least for the TGR to reach a sedimentation balance, with the corresponding water–sediment conditions being a typical year with a small water flow and a small amount of sediment and a typical year with less water-less sediment and a typical year with more water-more sediment, respectively.

Table 9 Time required by the different computational schemes to achieve sedimentation balance.
Full size table

Many studies have been locally and globally conducted on reservoir sedimentation prediction. Maris et al.29 predicted the sedimentation area and the sediment deposition height in the Nipsa reservoir using a Geographical Information System (GIS) based TopRunDF model. As a result, the model predicted a significant future decrease in the reservoir stored water volume. However, the model can only predict the inflow runoff of the reservoir, not the sediment deposition of the reservoir. Using bathymetric survey, Ethiopian scholars30 studied the deposition of the abrajit reservoir in the North gojem sub basin of the Blue Nile River Basin, and estimated the water storage limit of the dam. However, this method only provides an estimate, and it is difficult to accurately estimate the limit of reservoir sedimentation balance. Abebe Tadesse et al.31 used the Soil and Water Assessment Tool(SWAT) model and Hydrologic Engineering Center-River Analysis System(HEC-RAS) model to estimate the sediment load reaching the Koka Dam Reservoir in Ethiopia. Although the model can predict the total amount of reservoir sedimentation, it does not explain how to reach the equilibrium of reservoir sedimentation under different water and sediment conditions. Taking into account the Longpan Cascade Hydropower Station, Huang32 reported that the reservoir reached a sedimentation balance after approximately 340 years of operation. Without considering the Longpan Cascade Hydropower Station, however, the model predicted an estimate of 370 years for the reservoir to reach a sedimentation balance based on the water–sediment conditions during 1991–2000. Because of the different initial conditions, boundary conditions, and scheduling modes, the calculation results are different under the two different water–sediment conditions. Nevertheless, the results of this study are in accordance with the measured results, which confirms the rationality and reliability of the findings of our study.

Conclusions

  1. (1)

    Under the new water–sediment conditions, the volume of sediment transported into the TGR accounted for only 14.8% and 35.8% of the amount of water and sediment transported into the reservoir during 1956–1990 and 2003–2012, respectively, with the measured volume of sediment transported into the reservoir decreasing faster than expected.

  2. (2)

    The variation in the water level, water discharge, and sediment concentration calculated using the model is consistent with that of the measured results, and the calculated cumulative sedimentation volume and sedimentation distribution are basically in line with the measured results, which suggests that the verification results of the model are characterized by good consistency and reliability.

  3. (3)

    Under the water–sediment conditions during 1961–1970 and 1991–2000, the model predicted the estimates of 320 and 430 years for the TGR to reach a sedimentation balance, respectively. Under the new water–sediment conditions, it takes 560 years at most and 450 years at least to reach the sedimentation balance for the TGR, and the corresponding condition is the typical year with less water-less sediment and more water-more sediment, respectively. The findings of this study could serve as a new reference for the long-term safe operation and optimized scheduling of the TGR.