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Reservoir construction alters the hydrodynamic characteristics of the flow and sediment regimes, resulting in the enhancement of the hysteresis effect between the flood and sediment peaks. In this study, a 3D numerical model was adopted to investigate the propagation characteristics of sediment peak and the management method of reservoir sediment release. The results indicate that the incoming flow rate and the storage water level have a great influence on the propagation time of the sediment peak, and the incoming flow rate has a large influence on the attenuation rate of the sediment peak while the storage water level and the incoming suspended sediment concentration have a small effect on the attenuation rate of the sediment peak. An empirical formula based on inflow rate, water level elevation, water depth and length and storage capacity of reservoirs was established to predict the lag time between the flood and sediment peaks. The asynchronous movement between the incoming flood and sediment peaks has a clear influence on the propagation characteristics of the sediment peak. The hysteresis effect of the flood and sediment peaks can be fully utilized by reservoir managers to reduce reservoir sedimentation and improve sedimentation distribution.

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  • The effect of the hysteresis effect of flood and sediment peaks affects the propagation characteristics of the sediment peak.

  • The lag time of flood and sediment peaks can be predicted based on inflow rate, water depth and length and storage capacity of reservoirs.

  • The hysteresis effect of the flood and sediment peaks provides an effective way to improve reservoir sedimentation.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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flood peak, hysteresis effect, reservoir sedimentation, sediment peak, Xiluodu Reservoir
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Global river systems have been increasingly altered by dam construction, and after reservoir impoundment, the increase of water depth leads to the change of the hydrodynamic characteristics of the flow and sediment regimes (Huang et al. 2019b). The decrease of flow velocity leads to the decrease of sediment carrying capacity, and the sediment is gradually deposited in the reservoir, which affects the overall efficiency of the reservoir for flood control, power generation, navigation, water supply, irrigation, and recreation. In natural rivers and reservoirs, the flood peak (the peak in flow rate) and the sediment peak (the peak in suspended sediment concentration) are not always in phase, and the sediment peak may precede, coincide with, or follow the flood peak during a flood event (Heidel 1956; Bull 1997; Baca 2008). Inconsistency in the phase between flood peaks and sediment peaks in the process of flood propagation and sediment transport is the so-called hysteresis effect (Williams 1989).

Depending on the variation in discharge and sediment concentration versus time, different hysteretic concentration-discharge curves can be generated, including clockwise, anticlockwise, and figure eight (Williams 1989; Marouf & Remini 2011; Megnounif et al. 2013; Aich et al. 2014; Pietroń et al. 2015; Cheraghi et al. 2016; Lv et al. 2020; Ren et al. 2020). The hysteresis effect of the flow rate and sediment concentration is a complex multifactor-driven process (Vercruysse et al. 2017; Huang et al. 2019a). The factors include the uneven distribution in time and space of rainfall, different mechanisms of runoff and sediment yield, the runoff inflow of tributaries, attenuation of the sediment concentration, vegetation, and human activities (Fang et al. 2011; Zhang et al. 2021b). Hysteresis effects are also observed in soil erosion (Cheraghi et al. 2016) and water quality analysis (Lloyd et al. 2016). The hysteresis effect of flood and sediment peaks mainly contributes to the sources of water and sediment, hydrodynamic and sediment characteristics.

According to Saint-Venant equations, the type of flood wave will change from kinematic wave to dynamic wave with an increase in water depth, and the propagation velocity of flood wave increases gradually (Miller 1984; Singh & Li 1993). However, the transport velocity of suspended sediment is basically equal to the average flow velocity and decreases as the water depth increases. This hydrodynamic physical mechanism explains the hysteresis effect between flood and sediment peaks in the progress of flood wave propagation and sediment transport in deeper rivers or reservoirs. Based on this hysteresis effect between flood and sediment peaks, the management strategy of sediment peak is proposed under the operational strategy of ‘storing clear water and releasing muddy water’. The sediment peak regulation process in reservoirs is as follows: based on the lag time between flood and sediment peaks, the reservoir will store the water when the flood peak reaches the dam and then release the water when the sediment peak reaches the dam during flood events (Zhang et al. 2021a). To reduce reservoir sedimentation, the Three Gorges Reservoir preliminarily carried out this operational strategy of sediment peak regulation during the flood seasons of 2012, 2013 and 2018 and improved the efficiency of sediment release (Dong et al. 2014a, 2014b; Chen et al. 2018). At present, sediment peak operation is seldom carried out due to restrictions on the accurate and real-time prediction of the time and magnitude of flood and sediment peaks reaching a dam. The amount of sediment released from a reservoir depends on the magnitude of the discharge flow and suspended sediment concentration, therefore, the propagation characteristics of sediment peak and a reliable and accurate empirical formula to predict the lag time between the flood and sediment peaks are extremely important for sediment peak operation strategies. At the same time, the effect of the hysteresis between the incoming flood and sediment peaks on the sediment peak propagation is also worth studying.

For decades, the hydraulic model has been an effective tool to predict flood propagation and the corresponding sediment transport, erosion, and deposition in hydraulic engineering. The one-dimensional (1D) or two-dimensional (2D) hydrodynamic models, with small computing resources, have been widely applied to simulate flood wave propagation in reservoir sedimentation and flushing (Ahn et al. 2013; Wang et al. 2016). However, the interactions among flow, sediment transport, and geomorphic evolution in the field-scale river, especially with floodplains, high bend channels, large bedforms, and submerged islands, are a very complicated hydrodynamic phenomenon. Under such circumstances, 3D hydrodynamic effects, such as strong secondary flow, curvature effect, and flow separation, are significant in sediment transport, erosion and deposition (Khosronejad et al. 2016; Munoz & Constantinescu 2018).

In this study, the processes of flood propagation and sediment transport in July 2018 in an almost 190 km reach upstream of the Xiluodu (XLD) Reservoir are simulated using the 3D numerical model. The purposes of this paper are to investigate (1) the sensitivity analysis of the influencing factors of sediment peak propagation characteristics and to establish an empirical formula to predict the lag time between flood and sediment peaks; (2) the effect of the hysteresis on the sediment peak propagation; and (3) the application of the hysteresis effect between flood and sediment peaks in the sediment release of the XLD Reservoir. The paper is organized as follows: Section 2 presents the methodology, including the governing equations of hydrodynamics, sediment transport and bed morphodynamic models. Section 3 presents the site and data sources of the study area and the setup and validation of the numerical model. Section 4 investigates the sensitivity analysis of the sediment peak propagation characteristics, the empirical formula to predict the lag time between flood and sediment peaks and the effect of the hysteresis on sediment peak propagation. An analysis of sediment release in the XLD Reservoir is presented in Section 5. Finally, the main conclusions in the present study are summarized.

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A SCHISM 3D numerical model based on an unstructured-grid model (Zhang & Baptista 2008; Zhang et al. 2016) is adopted in this study. SCHISM is an open-source community supported modeling system (http://ccrm.vims.edu/schismweb/) based on mixed triangular-quadrangular unstructured grids in the horizontal direction and a very flexible coordinate system in the vertical direction (Zhang et al. 2015). The model is evaluated with finite-element and finite-volume techniques. Semi-implicit schemes are applied to solve the Navier–Stokes equations to improve stability and maximize efficiency. To treat the advection terms in the momentum equation, the model uses a higher-order Eulerian–Lagrangian method, allowing the use of large time steps without compromising the model precision and stability. The wetting and drying boundary algorithm in the model is suitable for flood propagation and inundation studies.

Flow governing equations

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In a Cartesian coordinate system, the governing equations for hydrostatic and Boussinesq approximations based on the Reynolds-averaged Navier–Stokes equations are as follows.

The continuity equation is:
(1)
The momentum equations are:
(2)
(3)
where x and y are the horizontal coordinates; z and zb are the vertical coordinates and vertical bed coordinates with positive upward directions, respectively; u, v and w are the velocities in the x, y and z directions, respectively; t is time; f is the Coriolis factor; is the free-surface elevation; ρ0 is the reference water density; ρ is the water density considering salinity and temperature; pA is the atmospheric pressure at the free surface; g is the acceleration of gravity; Kmh is the horizontal eddy viscosity coefficient, which is a model-specific constant; and Kmv is the vertical eddy viscosity coefficient, which is closed with the turbulence closure.
The Generic Length Scale (GLS) turbulence closure proposed by Umlauf & Burchard (2003) is used in the numerical model, which has the advantage of encompassing most of the 2.5-equation closure models (κ − ε (Rodi 1984); κ − ω (Wilcox 1998)). The two standard equations of the turbulent kinetic energy (κ) and a generic length-scale variable (ψ) are expressed by:
(4)
(5)
where σκ and σψ are the Schmidt numbers for κ and ψ; c1, c2, c3 are model-specific constants (Umlauf & Burchard 2003), Fω is a wall proximity function, M and N are the shear and buoyancy frequencies, respectively, is a dissipation rate, and ω is ε /βκ , where β = 0.09 is a model constant.
The generic length-scale, the dissipation rate and the frequency of the turbulence decay process is defined as:
(6)
(7)
(8)
where and l is the turbulence mixing length. The specific choices of the constants p, m and n depend on the different closure models (Galperin et al. 1988; Kantha & Clayson 1994; Canuto et al. 2001). In this study, a k – ε model is adopted as the turbulence closure model, and the related parameters in the model are listed in Table 1.
Table 1

Parameters for turbulence modes in the k-ε model

mnpσκσψc1c2c3
3 1.5 −1 1 1.3 1.44 1.92 1 
mnpσκσψc1c2c3
3 1.5 −1 1 1.3 1.44 1.92 1 
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A classic logarithmic distribution of the vertical velocity in the interior boundary layer is defined by the shear velocity and bottom roughness length:
(9)
(10)
(11)
where κ0 = 0.4, the von Kármán constant, z0 is the bottom roughness length and δb is the bottom computational layer thickness.

Sediment transport module

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The suspended sediment transport for noncohesive sediment in SCHISM is derived from the coupling of the transport formulation and the ROMS sediment transport formulation (Warner et al. 2008). The model has the advantage of being able to calculate an unlimited number of noncohesive sediment size classes. For each sediment class, the model solves the horizontal and vertical advection, vertical diffusion, vertical settling velocity and bottom sediment deposition or erosion.

The suspended sediment transport for each sediment class is calculated by solving the advection-diffusion equation as follows:
(12)
where Cqi and ωqi are the sediment concentration and sediment settling velocity for class i. Fn is the net erosion and deposition flux.
The sediment settling velocity proposed by Soulsby (1997) for sediment class i is calculated by:
(13)
where υ is the kinematic viscosity of water, D*,qi is a dimensionless sediment diameter for class i, and the expression is given by:
(14)
where si = ρi /ρ0 is the sediment specific density and ρi is the sediment density for class i. The sediment exchange between the bed and the flow is calculated based on the erosion flux (Eq) and deposition flux (Dq) acting on the bottom computational cell. Thus, the net suspended sediment flux is given by Dq- Eq. The deposition flux is defined by:
(15)
where cd1 is the sediment concentration computed at the bottom computational cell.
The erosion flux proposed by Ariathurai & Arulanandan (1978) is written as:
(16)
(17)
where E0,qi is a bed erodibility constant and is determined based on local bed sediment conditions with values ranging from 10−4 to 10−2 kgm−2s−1 (Xu et al. 2002; Blaas et al. 2007). q is the porosity of the bed sediment layer, is the volumetric fraction of each sediment class i, τcr,i is the critical shear stress for class i, and is the bed shear stress.
The bed shear stress is very important for sediment entrainment and affects the sediment transport rate. The dimensional critical shear stress is derived from the critical Shields parameter, and its value is determined following Soulsby & Whitehouse (1997):
(18)
In the present study, the density field is determined from an equation of state that accounts for suspended sediment concentrations. The water density is calculated as follows:
(19)
where ρ is the fluid local density (including the salinity, temperature and sediment effects), ρf is the water density (including salinity and temperature effects), n is the total number of sediment classes. The effect of salinity and temperature on the density field is neglected in the present study.

Bed evolution module

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A sediment bed changes due to local erosion and deposition under bed shear stress. The total depth variation is calculated in the prism center and is given by the sum of the depth variations of each sediment class due to suspended sediment transport.

The net sediment bed change due to suspended sediment transport is calculated for each sediment class i as:
(20)
The change from the prism centers to the nodes is calculated as follows:
(21)
where Δhsn is the element depth variation due to the suspended transport and is the number of elements that contain node n. Ae is the element area. The sediment bed is assumed to be a user-specified constant number of sediment layers and total sediment thickness beneath a water column. Each layer in the sediment bed is initialized with a given thickness, sediment class distribution, and porosity. The bed layers are modified at each time step to account for erosion, deposition and track stratigraphy. More details can be found in the paper of Warner et al. (2008).
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Site and data sources of the study area

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The Jinsha River basin, covering an area of 4.7 × 105 km2, is located in the upper reach of the Yangtze River basin and is approximately 26% of the Yangtze River basin (Figure 1(a)). The Jinsha River is in the upper reaches of the Yangtze River, and it is 3364 km long, accounting for 55% of the total length of the main stream of the Yangtze River. In the flood season, the Jinsha River basin is influenced by the maritime southwest monsoon and southeast monsoon, which bring abundant precipitation. Rainfall and runoff are mainly concentrated in the flood season from June to October, and the annual average precipitation is approximately 710 mm (Zhang et al. 2021c). The runoff of the main stream of the Jinsha River and its tributary, the Yalong River, during the flood season accounts for approximately 75% of the total annual runoff. The Jinsha River has a steep slope and a large drop, so it is rich in hydropower resources, especially in the lower reaches of the Jinsha River, due to the inflow of the Yalong River tributary. Up to 112.4 million kW, which accounts for approximately 16.7% of China's total hydropower resources, are generated along the Jinsha River. Cascade reservoirs, including the (WDD) Wudongde, (BHT) Baihetan, (XLD) Xiluodu and (XJB) Xiangjiaba hydropower stations, have been built in the lower reaches of the Jinsha River (Figure 1(a)). The flood in the Jinsha River basin mainly occurs over 7 ∼ 9 months. As the riverbed is steep, the water is highly erosive. The sediment transport of the Jinsha River during the flood season accounts for approximately 80% of the annual sediment transport. The annual average sediment transport is 2.55 × 107 t, approximately 48% of the annual average sediment transport at the Yichang station. The Jinsha River is one of the main sources of sediment at the Yichang station along the main stream of the Yangtze River (Du et al. 2013).
Figure 1
Site of the study area. (a) Jinsha River basin and cascade reservoirs, (b) Gauging stations and tributary into the XLD reservoir.
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Site of the study area. (a) Jinsha River basin and cascade reservoirs, (b) Gauging stations and tributary into the XLD reservoir.

Figure 1
Site of the study area. (a) Jinsha River basin and cascade reservoirs, (b) Gauging stations and tributary into the XLD reservoir.
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Site of the study area. (a) Jinsha River basin and cascade reservoirs, (b) Gauging stations and tributary into the XLD reservoir.

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The XLD hydropower station is a power generating project with huge comprehensive benefits, such as flood control, sediment control and navigation improvement downstream. The XLD Reservoir has the characteristics of a typical river channel and is approximately 200 km long. The normal water level elevation of the XLD reservoir is 600 m, and the water depth is 260 m. The total storage capacity of the reservoir at the normal water level elevation is 1.27 × 1010 m3, and the flood control reservoir capacity is 4.65 × 109 m3. The dead water level elevation is 540 m, and the flood control level elevation in the flood season is 560 m. Reasonable operation of the XLD reservoir can reduce the sediment concentration of the Three Gorges Reservoir area by more than 34% compared with the natural state. This paper mainly studies the hysteresis effect of water and sediment in the XLD reservoir and the corresponding measures to reduce reservoir sedimentation.

Hydrological data, including the flow rate, sediment concentration and sediment gradation and topographic scatter data in the study zone, are mainly from the Three Gorges Reservoir Management and Operation Center. The BHT hydrological station is the main stream control station, which is located approximately 4.5 km downstream of the BHT hydropower station. The water level elevation in front of the dam is measured by the Huangjiaobao (HJB) station, 3.2 km away from the dam, and the XLD hydrological station is located 8 km downstream of the dam. The main tributaries in the study area include the Meigu River and the Niulan River (Figure 1(b)). According to the analysis of the flow rate of the tributaries, the total flow rate of the tributaries contributes little to the flow rate of the main stream, so the tributaries are not considered in this study.

The main hydrological data in the study region were obtained from the 2018 hydrological report of China. In this study, the flow rate and suspended sediment concentration are obtained for the BHT hydrologic station, which are used for the inlet boundary condition in the model; the elevation of the water level is obtained from the HJB hydrologic station, which is used for the outlet boundary condition in the model. It is noted that the the flow rate, suspended sediment concentration and water level are the daily-averaged values. The temporal variation in the inflow rate and suspended sediment concentration recorded during a flood event at the BHT station is shown in Figure 2(a), which indicates that the flood and sediment peaks propagate synchronously; the temporal variation in the water level elevation recorded during the same flood event at the HJB station is shown in Figure 2(b). The time interval from July 1 to August 6 covers the entire process of flood propagation and sediment transport during the flood event.
Figure 2
Boundary conditions of the numerical model. (a) Flow rate and suspended sediment concentration at the BHT hydrologic station. (b) Water level elevation at the HJB hydrologic station.
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Boundary conditions of the numerical model. (a) Flow rate and suspended sediment concentration at the BHT hydrologic station. (b) Water level elevation at the HJB hydrologic station.

Figure 2
Boundary conditions of the numerical model. (a) Flow rate and suspended sediment concentration at the BHT hydrologic station. (b) Water level elevation at the HJB hydrologic station.
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Boundary conditions of the numerical model. (a) Flow rate and suspended sediment concentration at the BHT hydrologic station. (b) Water level elevation at the HJB hydrologic station.

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The sediment in the XLD Reservoir mainly comes from the discharge flow of the BHT hydropower station and is mainly suspended sediment. During the flood period in July 2018, the grain size of sediment measured at the BHT hydrological station was 0.002–0.125 mm. Considering that the sizes of sediment diameters of 0.002 and 0.004 mm are small, the two classes of sediment are regarded as 0.003 mm in the model. Five classes of sediment size are selected for the simulation, as shown in Table 2.

Table 2
Diameter (mm) 0.003 0.008 0.016 0.031 0.062 0.125 
(%) 15.7 13.4 15.8 15.2 16 23.9 
Diameter (mm) 0.003 0.008 0.016 0.031 0.062 0.125 
(%) 15.7 13.4 15.8 15.2 16 23.9 
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Setup and parameter sensitivity analysis of the numerical model

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For such a large-scale numerical simulation, setup of the numerical model is not only very important to the accuracy of the results, but also can save some computational resources. In this study, a sensitivity analysis was conducted to evaluate the effect of parameter setting of the numerical model on the accuracy of the results and calculation efficiency. Comparisons between the measured and modelled water level at the BHT hydrological station and suspended sediment concentration at the XLD station reflect the parameter sensitivity analysis. All sensitivity analysis cases were simulated using 192 cores on a parallel high-performance computing cluster.

The mesh size of a numerical model is very important to the accuracy and computational resources of the numerical simulation. Ehab et al. (2012) conducted numerical modeling of hydrodynamics and sediment transport in the lower Mississippi River, and a grid sensitivity analysis indicated that the solution had good stability at grid sizes of 20 m or smaller. Zhang et al. (2021a) studied flood propagation and sediment transport in the Three Gorges Reservoir, with a horizontal grid size of 23–24 m and a vertical grid size of 5 m. In this study, the effects of horizontal and vertical grid size on the accuracy of the results and computational resources were evaluated by some cases.

The horizontal grid of the model was set as triangular mesh, and the detailed parameters are shown in Table 3. Figure 3 presents the effect of the setup size of the horizontal grid on the water level and suspended sediment concentration. It indicates that the modeled water level and suspended sediment concentration gradually decrease as the horizontal grid size decreases. It is noted that the average daily sediment concentration is based on the interpolation of the instantaneous measured values using a sediment concentration regression model. Furthermore, the simulation time increases as the horizontal grid decreases. When the mesh size was set to 16–20 m, the modelled results were in good agreement with the measured results.
Table 3

Setup of model parameters and computation time

ParametersGrid size (m)Node countElement countMean vertical grid countSimulation time (h)
Case1 24 533,685 278,516 5.5 27 
Case2 20 765,776 396,967 5.5 34 
Case3 16 1,192,843 614,083 5.5 47 
ParametersGrid size (m)Node countElement countMean vertical grid countSimulation time (h)
Case1 24 533,685 278,516 5.5 27 
Case2 20 765,776 396,967 5.5 34 
Case3 16 1,192,843 614,083 5.5 47 
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Figure 3
Effect of the setup size of the horizontal grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.
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Effect of the setup size of the horizontal grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.

Figure 3
Effect of the setup size of the horizontal grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.
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Effect of the setup size of the horizontal grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.

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Based on the simulated Case 2, the different vertical grids were set to 25, 20 and 15 m in the model, respectively. Figure 4 presents the effect of the setup size of the vertical grid on the water level and suspended sediment concentration. This indicates that the modeled water level and suspended sediment concentration gradually decrease as the vertical grid size decreases. The computation time increases as the vertical grid decreases, and is 32, 34 and 42 h, respectively. When the vertical mesh size was set to 15–20 m, the modelled results were in good agreement with the measured results. The simulation of model time with the different vertical and horizontal grids, using very fine meshes, is not a better option over a large computational domain, and huge computational costs are required to simulate flood propagation and sediment transport in a 3D numerical model (Munoz & Constantinescu 2018).
Figure 4
Effect of the setup size of the vertical grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.
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Effect of the setup size of the vertical grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.

Figure 4
Effect of the setup size of the vertical grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.
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Effect of the setup size of the vertical grid on the water level and suspended sediment concentration. (a) Water level. (b) Suspended sediment concentration.

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For the natural river, water level is generally used as the boundary condition of downstream in numerical simulation. For reservoirs with large water depths, the dam alters the natural characteristics of water flow and sediment transport. Therefore, the effects of the boundary condition at the dam location on the modeled results were investigated in this study. Setups of boundary condition at the dam location in the numerical model are shown in Figure 5. Figure 6 presents the effect of setup of boundary condition at the dam location on the modelled suspended sediment concentration at XLD station. It is indicated that the setup of boundary condition at the dam location had an insignificant influence on the propagation time and size of the sediment peak. This is due to the small flow velocity in front of the dam, which is basically less than 0.2 m/s in this study.
Figure 5
Setup of boundary condition of the dam location in the numerical model. (a) Water level boundary condition without dam. (b) Water level boundary condition with dam.
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Setup of boundary condition of the dam location in the numerical model. (a) Water level boundary condition without dam. (b) Water level boundary condition with dam.

Figure 5
Setup of boundary condition of the dam location in the numerical model. (a) Water level boundary condition without dam. (b) Water level boundary condition with dam.
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Setup of boundary condition of the dam location in the numerical model. (a) Water level boundary condition without dam. (b) Water level boundary condition with dam.

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Figure 6
Effect of setup of boundary condition at the dam location on the modelled suspended sediment concentration at XLD station.
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Effect of setup of boundary condition at the dam location on the modelled suspended sediment concentration at XLD station.

Figure 6
Effect of setup of boundary condition at the dam location on the modelled suspended sediment concentration at XLD station.
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Effect of setup of boundary condition at the dam location on the modelled suspended sediment concentration at XLD station.

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The Manning roughness coefficient is also very important for the accuracy of a numerical simulation. Castillo et al. (2015) indicated that the Manning roughness coefficients for the floodplain and main channel were different, and the coefficient value decreased as the flow rate increased. In our previous study, it indicates that the effect of the Manning roughness coefficient on the discharge and sediment concentration was small under the condition of large discharge in the numerical modeling of flood propagation and sediment transport in the Three Gorges Reservoir (Zhang et al. 2021a). Therefore, the Manning roughness coefficient for the main channel is set at 0.015 under a water level elevation of 540 m, and for the floodplain, the Manning roughness coefficient is set at 0.02 in this study.

Validation of the numerical model

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Numerical models have been applied in open channels to investigate sediment concentration profiles and morphologic evolution (Pinto et al. 2012), flood propagation and sediment transport (Ye et al. 2020; Zhang et al. 2021b). In the following section, the numerical model is validated by comparing it with the measured data in the XLD Reservoir during the flood period in 2018.

In this study, the numerical model is set up as a mixed triangular-quadrangular horizontal grid to reduce computational resources. To adapt to complex terrain, a quadrangular grid is used in the wide main channel, and an irregular triangular grid is used in the floodplain and tributary at 20–24 m. The total numbers of nodes and elements in the calculation zone are 385,552 and 239,168, respectively, in the horizontal dimension. The elevation of each node is interpolated using the measured scatter topography from 2016, and the elevation and grid setup of the whole calculation zone are shown in Figure 7(a) and 7(b). To adapt to the sharp slope, a new vertical coordinate system dubbed LSC2 (Localized Sigma Coordinates with Shaved Cell), proposed by Zhang et al. (2015), is adopted in this study. The space of the vertical grid is set to 7 m, and the vertical grid of the local cross-section is shown in Figure 7(c). To accommodate the size of these grids, the time step in this simulation is set to 30 s.
Figure 7
Configuration of the horizontal and vertical grids. (a) Grid of the wide reach. (b) Grid of the narrow reach. (c) Grid of the vertical cross section.
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Configuration of the horizontal and vertical grids. (a) Grid of the wide reach. (b) Grid of the narrow reach. (c) Grid of the vertical cross section.

Figure 7
Configuration of the horizontal and vertical grids. (a) Grid of the wide reach. (b) Grid of the narrow reach. (c) Grid of the vertical cross section.
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Configuration of the horizontal and vertical grids. (a) Grid of the wide reach. (b) Grid of the narrow reach. (c) Grid of the vertical cross section.

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The instantaneous modeled results of the entire three-dimensional flow velocity field and local three-dimensional flow velocity field in the XLD Reservoir are indicated in Figure 8. The instantaneous velocity and suspended sediment concentration distribution of the longitudinal section of the XLD reservoir are shown in Figures 9 and 10. The results indicate that the flow velocity at the upstream of the XLD Reservoir is larger, and approximately 1–4 m/s, while the flow velocity near the XLD dam is smaller, and is basically less than 0.2 m/s. The suspended sediment is deposited gradually as the flood propagates downstream.
Figure 8
Instantaneous three-dimensional flow velocity field of the XLD reservoir.
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Instantaneous three-dimensional flow velocity field of the XLD reservoir.

Figure 8
Instantaneous three-dimensional flow velocity field of the XLD reservoir.
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Instantaneous three-dimensional flow velocity field of the XLD reservoir.

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Figure 9
Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 19 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.
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Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 19 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.

Figure 9
Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 19 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.
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Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 19 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.

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Figure 10
Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 25 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.
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Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 25 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.

Figure 10
Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 25 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.
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Instantaneous velocity and suspended sediment concentration distribution of the longitudinal section on 25 July, 2018. (a) instantaneous velocity distribution. (b) instantaneous suspended sediment concentration.

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Figure 11 presents the comparison of the water level elevation between the modeled results and measured results at the BHT hydrologic station. The modeled water level elevation is basically consistent with the measured results, and the local difference may be caused by the grid size and the local Manning roughness coefficient.
Figure 11
Comparison of the water level elevation between the numerical model and the BHT hydrological station.
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Comparison of the water level elevation between the numerical model and the BHT hydrological station.

Figure 11
Comparison of the water level elevation between the numerical model and the BHT hydrological station.
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Comparison of the water level elevation between the numerical model and the BHT hydrological station.

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Figure 12 presents the comparison of the flow rate between the modeled results and measured results at the XLD hydrologic station. The modeled results are basically in good agreement with the measured results. The local difference may result from the small inflow of tributaries. In the present study, the inflow of tributaries is not considered in the model.
Figure 12
Comparison of the flow rate between the numerical model and the XLD hydrological station.
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Comparison of the flow rate between the numerical model and the XLD hydrological station.

Figure 12
Comparison of the flow rate between the numerical model and the XLD hydrological station.
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Comparison of the flow rate between the numerical model and the XLD hydrological station.

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Figure 13 presents the comparison of the suspended sediment concentration between the modeled results and measured results at the XLD hydrologic station. The modeled results are basically consistent with the average daily sediment concentration. The minor difference between the modeled results and average daily sediment concentration may result from local erosion and deposition in such complicated terrain. However, compared with the measured data, there are some errors due to measurement errors in bad weather during the flood season.
Figure 13
Comparison of the suspended sediment concentration between the numerical model and the XLD hydrologic station.
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Comparison of the suspended sediment concentration between the numerical model and the XLD hydrologic station.

Figure 13
Comparison of the suspended sediment concentration between the numerical model and the XLD hydrologic station.
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Comparison of the suspended sediment concentration between the numerical model and the XLD hydrologic station.

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Characteristics of the flood wave and sediment peak propagation

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There are various flood wave types based on the different forms of Saint-Venant equations of continuity and momentum, including kinematic, diffusion, gravity, and dynamic waves. The kinematic wave neglects both the inertia term and the pressure-gradient term caused by varying flow depths over distance. Diffusion wave neglects the inertia term. Gravity wave neglects the effects of bed slope and viscous energy losses. Dynamic waves are described by retaining all terms of the momentum equation. Hence, these wave models have different celerities (Miller 1984; Singh & Li 1993). A flood wave propagation diagram of the XLD Reservoir is shown in Figure 14. A flood wave has the characteristics of both kinematic and dynamic waves. Referring to Figure 14, is the water depth; and are the wave height at a certain section and the maximum height, respectively; is the half wavelength; and i is the bed slope. When ≫ ⁠, the kinematic wave is dominant, and thus, the flood wave is a kinematic wave. A kinematic wave is transported at a celerity:
(22)
where k is coefficient. When ≪ ⁠, the dynamic wave is dominant, and thus, the flood wave is a dynamic wave. The celerity of a dynamic wave is:
(23)
where U is the average flow velocity. During the propagation of flood waves, based on the relative heights of the wave amplitude and water depth, when the flood wave propagates in a river-course reservoir, it gradually changes from a kinematic wave to a dynamic wave (Figure 14).
Figure 14
A flood wave propagation diagram of the XLD Reservoir.
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A flood wave propagation diagram of the XLD Reservoir.

Figure 14
A flood wave propagation diagram of the XLD Reservoir.
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A flood wave propagation diagram of the XLD Reservoir.

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When a flood wave propagates downstream in deep reservoirs, the water depth is much greater than the flood wave amplitude, and the flood wave propagates as a dynamic wave. The propagation time during a flood peak is:
(24)
where L is the length of backwater zone in the reservoir. Generally, sediment is transported along with the water flow. The velocity of sediment transport is basically equal to the average flow velocity. Then, the propagation time of the sediment peak is:
(25)
where Q is the flow rate; A is the area of the channel section; and V is the flow volume in the channel (Huang et al. 2019a; Zhang et al. 2021a). For a deep reservoir, the water depth is much larger and the average flow velocity is very small; thus, the propagation time of a flood peak is approximately equal to and is mainly determined by the water depth and length of the backwater zone. The propagation time of the sediment peak is mainly determined by the flow rate and reservoir storage.
Figure 15 presents the relationship between the water level elevation and reservoir storage in the XLD Reservoir.
Figure 15
Relationship between the water level elevation and reservoir storage in the XLD Reservoir.
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Relationship between the water level elevation and reservoir storage in the XLD Reservoir.

Figure 15
Relationship between the water level elevation and reservoir storage in the XLD Reservoir.
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Relationship between the water level elevation and reservoir storage in the XLD Reservoir.

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The empirical relationship between the reservoir storage and water level elevation obtained through curve fitting is as follows:
(26)
where is the water level elevation in front of the dam.
Combined with Equations (24)–(26), the empirical formula for the lag time between the sediment peak behind a flood peak is:
(27)

Therefore, the lag time between the sediment peak and the flood peak mainly depends on the inflow rate, water level elevation, water depth and length of the backwater zone. The formula for flood wave velocity is applied to shallow water wave motion, so the empirical formula is used to predict to the lag time between the sediment peak and the flood peak in shallow water motion.

Another characteristic of sediment peak propagation is the attenuation rate, which is expressed as:
(28)
where and are the maximum sediment concentrations upstream and downstream of the reach, respectively. If > 0, the sediment concentration gradually decreases as the sediment peak propagates. If < 0, the sediment concentration gradually increases as the sediment peak propagates.

The normal water level elevation of the XLD Reservoir is 600 m, and it is approximately 190 km long; the water depth is 260 m. The flood control level elevation in the flood season is 560 m, and the water depth is 190 m. In this deep reservoir, the natural flow regimes of floods and sediment are greatly changed, and the hysteresis effect of flood peaks and sediment peaks is enhanced. To further analyze the hysteresis effect of flood and sediment peaks in the upstream reaches of the XLD Reservoir during the flood season, in this study, some numerical cases are conducted for a sensitivity analysis of the influencing factors of the flood and sediment peak propagation characteristics.

Effect of the incoming flow rate on the propagation characteristics of the sediment peak

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The measured maximum incoming flow rate is 29,000 m3/s. The historical maximum incoming flow rate is 36,900 m3/s. The maximum discharge flow of the spillway tunnel and power generation is 24,440 m3/s. To investigate the effect of the incoming flow rate on the propagation characteristics of the sediment peak, cases under different incoming flow rates are simulated. It is worth noting that all parameters of water and sediment were kept unchanged, and only the incoming discharge flow was different for each case, as shown in Table 4.

Table 4

Calculation configuration for different incoming flow rates

CaseFlow rate (m3/s)Peak value of the suspended sediment concentration (kg/m3)Water level elevation (m)
C1 8000 2.3 560 
C2 12,000 2.3 560 
C3 16,000 2.3 560 
C4 20,000 2.3 560 
C5 24,000 2.3 560 
C6 28,000 2.3 560 
CaseFlow rate (m3/s)Peak value of the suspended sediment concentration (kg/m3)Water level elevation (m)
C1 8000 2.3 560 
C2 12,000 2.3 560 
C3 16,000 2.3 560 
C4 20,000 2.3 560 
C5 24,000 2.3 560 
C6 28,000 2.3 560 
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The simulated results of the influence of the average inflow flow on the propagation characteristics of the sediment peak are shown in Table 5. This indicates that with the increase in the average incoming flow rate, the propagation time of the sediment peak decreases gradually, and the attenuation rate of the sediment peak in the propagation process also decreases gradually. When the average incoming flow rate increases from 8000 to 28,000 m3/s, the propagation time of the sediment peak decreases by 68%, and the attenuation rate of the sediment peak decreases by 21%. That is, the incoming flow rate has a great influence on the propagation time and attenuation of the sediment peak.

Table 5

Propagation characteristics of the sediment peak under different incoming flow rates

CasesC1C2C3C4C5C6
Propagation time (d) 8.7 5.9 4.8 3.8 3.3 2.8 
Attenuation rate of the sediment peak (%) 99 95 89 85 80 78 
CasesC1C2C3C4C5C6
Propagation time (d) 8.7 5.9 4.8 3.8 3.3 2.8 
Attenuation rate of the sediment peak (%) 99 95 89 85 80 78 
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The comparison of the lag time of the sediment peak following the flood peak between the model results and empirical formula under the different flow rates are presented in Figure 16. The numerical simulation results are in good agreement with the empirical formulas except in the case of a small flow rate. It is also indicated that the empirical formula can predict the lag time of the sediment peak following the flood peak.
Figure 16
Comparison of the lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different flow rates.
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Comparison of the lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different flow rates.

Figure 16
Comparison of the lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different flow rates.
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Comparison of the lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different flow rates.

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Effect of the water level elevation on the propagation characteristics of the sediment peak

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The normal storage level elevation of the XLD reservoir is 600 m, the flood control level elevation is 560 m, and the dead water level elevation is 540 m. During the flood season, the storage water level elevation in front of the dam varies from 550 to 580 m. To investigate the effect of the storage water level elevation on the propagation characteristics of the sediment peak, cases under different storage water level elevations are simulated. It is worth noting that all parameters of water and sediment were kept unchanged, and only the storage water level elevation was different for each case, as shown in Table 6.

Table 6

Calculation configuration for different incoming flow rates

CaseFlow rate (m3/s)Suspended sediment concentration of the sediment peak (kg/m3)Storage water level elevation (m)
L1 12,000 2.3 550 
L2 12,000 2.3 560 
L3 12,000 2.3 570 
L4 12,000 2.3 580 
CaseFlow rate (m3/s)Suspended sediment concentration of the sediment peak (kg/m3)Storage water level elevation (m)
L1 12,000 2.3 550 
L2 12,000 2.3 560 
L3 12,000 2.3 570 
L4 12,000 2.3 580 
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The simulated results of the influence of the storage water level elevation on the propagation characteristics of the sediment peak are shown in Table 7. This indicates that with an increase in the storage water level elevation in front of the dam, the propagation time of the sediment peak gradually increases, and the attenuation rate of the sediment peak also gradually increases. When the storage water level elevation in front of the dam increases from 550 to 580 m, the propagation time of the sediment peak increases by 39%, and the attenuation rate of the sediment peak increases by 2%. In other words, an increase in the storage water level elevation in front of the dam has a great influence on the propagation time of the sediment peak but a small influence on the attenuation rate of the sediment peak.

Table 7

Modeled results of the propagation characteristics of the sediment peak under different storage water level elevations

CasesL1L2L3L4
Propagation time (d) 5.4 5.9 6.7 7.5 
Attenuation rate of the sediment peak (%) 94 95 96 96 
CasesL1L2L3L4
Propagation time (d) 5.4 5.9 6.7 7.5 
Attenuation rate of the sediment peak (%) 94 95 96 96 
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The comparisons of the lag time of the sediment peak following the flood peak between the model results and empirical formula under the different water level elevations are presented in Figure 17. The numerical simulation results are in good agreement with the empirical formulas. It is also indicated that the empirical formula can well predict the lag time of the sediment peak following the flood peak.
Figure 17
Comparison of lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different water level elevations.
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Comparison of lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different water level elevations.

Figure 17
Comparison of lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different water level elevations.
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Comparison of lag time of the sediment peak following the flood peak between the model results and the empirical formula under the different water level elevations.

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Effect of the incoming suspended sediment concentration on the propagation characteristics of the sediment peak

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Based on the measured data of the suspended sediment concentration of the sediment peak at the BHT hydrological station during the flood seasons of 2014–2019, the suspended sediment concentration of the sediment peak basically ranges from 3 to 8 kg/m3. To investigate the effect of the incoming suspended sediment concentration on the propagation characteristics of the sediment peak, cases under different incoming suspended sediment concentrations are simulated, as shown in Table 8.

Table 8

Calculation configuration for different incoming suspended sediment concentrations

CaseFlow rate (m3/s)Suspended sediment concentration of the sediment peak (kg/m3)Storage water level elevation (m)
L1 12,000 2 560 
L2 12,000 4 560 
L3 12,000 6 560 
L4 12,000 8 560 
CaseFlow rate (m3/s)Suspended sediment concentration of the sediment peak (kg/m3)Storage water level elevation (m)
L1 12,000 2 560 
L2 12,000 4 560 
L3 12,000 6 560 
L4 12,000 8 560 
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The modeled results of the influence of the incoming suspended sediment concentration on the propagation characteristics of the sediment peak are shown in Table 9. This indicates that with an increase in the incoming suspended sediment concentration, the attenuation rate of the sediment peak gradually increases. When the incoming suspended sediment concentration increases from 2 to 8 kg/m3, the attenuation rate of the sediment peak increases by 2%; that is, an increase in the incoming suspended sediment concentration has no clear effect on the attenuation rate of the sediment peak.

Table 9

Modeled results of the propagation characteristics of the sediment peak under different incoming suspended sediment concentrations

CaseL1L2L3L4
Attenuation rate of the sediment peak (%) 94.9 95.9 96.4 96.7 
CaseL1L2L3L4
Attenuation rate of the sediment peak (%) 94.9 95.9 96.4 96.7 
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Effect of the hysteresis time between the flood peak and sediment peak on the propagation characteristics of the sediment peak

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Flow and sediment sources come from different areas in the upper stream of the Jinsha River, and the construction of cascade reservoirs in the lower stream of the Jinsha River contributes to the asynchronous movement phenomenon of the flood and sediment peaks. Figure 18 presents a schematic diagram of the asynchronous propagation of the flood waves and sediment waves. To study the influence of the lag time between the incoming flood and sediment peaks on the propagation characteristics of the sediment peak, some cases under different time lags of the sediment peak preceding, coinciding with and following the flood peak are simulated, as shown in Table 10. The period of the flood and sediment peaks is 12 days, and the base flow and peak value of flood wave and sediment wave are 6000 and 14,000 m3/s, and 0.04 and 5 kg/m3, respectively.
Table 10

Different time lags between the flood and sediment peaks in the cases

CaseFS-4FS-3FS-2FS-1FS-0FS-1FS-2FS-3FS-4
Time lag (d) − 4 − 3 − 2 − 1 0 1 2 3 4 
CaseFS-4FS-3FS-2FS-1FS-0FS-1FS-2FS-3FS-4
Time lag (d) − 4 − 3 − 2 − 1 0 1 2 3 4 

Note: A negative sign before a time lag indicates that the flood peak follows the sediment peak; 0 indicates that the flood peak coincides with the sediment peak; a positive sign indicates that the flood peak precedes the sediment peak.

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Figure 18
Schematic diagram of the flood wave and sediment wave.
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Schematic diagram of the flood wave and sediment wave.

Figure 18
Schematic diagram of the flood wave and sediment wave.
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Schematic diagram of the flood wave and sediment wave.

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To analyze the influence of the hysteresis effect between the flood and sediment peaks on the characteristics of the sediment peak propagation, the maximum sediment concentration at different locations was extracted based on the numerical results. Under various calculation conditions, the variation in the sediment peak attenuation rate at different locations along the XLD Reservoir is shown in Figure 19, and the statistical results of the sediment peak attenuation rate are shown in Table 11. The asynchronous movement between the flood peak and sediment peak has a clear influence on the sediment peak propagation in the deep reservoir. When the flood peak and sediment peak are synchronized, the attenuation rate of the sediment peak is small (FS0 case), which is conducive to suspended sediment transportation to the dam. However, the different propagation mechanisms between the flood and sediment peaks result in the difference of propagation velocity between the flood and sediment peaks, so the asynchronous movement relationships of the incoming flood and sediment peaks cause the following transitions: (1) The synchronous movement between the flood and sediment peaks into the reservoir gradually changes to the sediment peak lagging behind the flood peak during the propagation process; the farther downstream the hysteresis effect becomes stronger, the more unfavorable it is to suspended sediment transport. (2) The sediment peak lags behind the flood peak when entering the reservoir, and the hysteresis effect is further aggravated during the propagation process, which is not conducive to suspended sediment transport, as is seen in the FS1, FS2, FS3 and FS4 cases. (3) The sediment peak precedes the flood peak when entering the reservoir, and the flood peak will catch up with the sediment peak during the propagation process. In this case, according to the different times of the sediment peak preceding the flood peak when entering the reservoir, the effect of the hysteresis between the flood and sediment peak on the propagation characteristics of the sediment peak is different; accordingly, the sedimentation position of the reservoir is different. If the time of the sediment peak preceding the flood peak is small, the sediment peak attenuation rate is large upstream of the XLD Reservoir, while the sediment peak attenuation rate is small downstream of the XLD Reservoir; in this case, it is conducive to sediment transport at the tail of the reservoir and is detrimental to the sediment discharge of the reservoir, as seen in the FS2 case. However, if the time of the sediment peak preceding the flood peak is large, the sediment peak attenuation rate is smaller upstream of the XLD Reservoir and is conducive to suspended sediment transport in the reservoir; in this case, it is beneficial to the sediment discharge of the reservoir, as seen in the FS-4 case.
Table 11

Attenuation rate (%) of the sediment peak at different locations under different cases

Location (km)30507090110130150170190
FS-4 29.10 41.71 54.38 67.35 76.89 85.76 90.47 94.04 96.69 
FS-3 32.26 46.83 58.60 70.56 79.06 86.97 91.05 94.11 96.48 
FS-2 39.17 50.50 61.64 73.39 81.56 88.59 92.03 94.56 96.64 
FS-1 41.84 54.51 64.96 75.86 83.42 89.81 92.93 95.14 96.93 
FS0 27.36 39.15 52.38 65.84 76.28 85.76 90.68 94.41 97.10 
FS1 25.79 37.74 51.28 65.45 76.28 85.97 91.51 95.18 97.60 
FS2 27.99 43.15 55.47 68.60 78.65 87.54 92.73 96.11 98.17 
FS3 29.89 45.02 58.51 72.23 82.28 89.77 94.21 97.04 98.64 
FS4 36.30 50.06 62.25 74.95 85.40 92.08 95.61 97.78 98.94 
Location (km)30507090110130150170190
FS-4 29.10 41.71 54.38 67.35 76.89 85.76 90.47 94.04 96.69 
FS-3 32.26 46.83 58.60 70.56 79.06 86.97 91.05 94.11 96.48 
FS-2 39.17 50.50 61.64 73.39 81.56 88.59 92.03 94.56 96.64 
FS-1 41.84 54.51 64.96 75.86 83.42 89.81 92.93 95.14 96.93 
FS0 27.36 39.15 52.38 65.84 76.28 85.76 90.68 94.41 97.10 
FS1 25.79 37.74 51.28 65.45 76.28 85.97 91.51 95.18 97.60 
FS2 27.99 43.15 55.47 68.60 78.65 87.54 92.73 96.11 98.17 
FS3 29.89 45.02 58.51 72.23 82.28 89.77 94.21 97.04 98.64 
FS4 36.30 50.06 62.25 74.95 85.40 92.08 95.61 97.78 98.94 
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Figure 19
Variation in the sediment peak attenuation rate at different locations under various conditions.
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Variation in the sediment peak attenuation rate at different locations under various conditions.

Figure 19
Variation in the sediment peak attenuation rate at different locations under various conditions.
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Variation in the sediment peak attenuation rate at different locations under various conditions.

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Therefore, the different hysteresis effects between the flood and sediment peaks lead to different propagation characteristics of the sediment peak. As cascade reservoirs are built in the lower reaches of the Jinsha River, artificial flood waves can be created by suddenly increasing the amount of water discharged from the dam to intervene in the propagation of the sediment peak, reduce sedimentation and optimize the sedimentation distribution in the reservoir.

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Basic principle of the sediment peak discharge operation

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In a deep reservoir, the hysteresis effect of the flood and sediment peaks is derived from different propagation mechanisms. The asynchronous propagation characteristics of flood and sediment peaks are enhanced as a flood wave propagates downstream, which provides favorable conditions for the operational strategy of sediment peak regulation. A schematic diagram of sediment peak regulation is proposed by Zhang et al. (2021b). The process of sediment peak operation can be divided into three phases: (I) Flood peak blocking and retaining. (II) Sediment peak propagation. (III) Sediment peak release. For details of sediment peak operation refer to Zhang et al. (2021b). In the following study, the efficiency of sediment flushing using different operation strategies and the corresponding sedimentation distribution in the XLD Reservoir are evaluated.

Analysis of sediment release in the Xiluodu Reservoir

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The annual average runoff of the Jinsha River is 4570 m3/s, the maximum measured runoff is 29,000 m3/s, and the historical maximum runoff is 36,900 m3/s. The XLD hydropower station is located in the lower reaches of the Jinsha River. The XLD Reservoir is a typical river-channel reservoir and is approximately 200 km long at the normal water level elevation (600 m); the water depth is 260 m, and the flood control level elevation in the flood season is 560 m (Figure 14). The maximum discharge capacity of a single spillway of the XLD hydropower station is more than 4000 m3/s, and the maximum discharge capacity of the four spillways is 16,700 m3/s, accounting for 33% of the total discharge capacity.

In the XLD Reservoir with such deep water depth and long distance, the flood and sediment peaks have clear hysteresis effects in the process of flood propagation downstream. Therefore, the clear hysteresis effect between the flood and sediment peaks provides a favorable opportunity for sediment peak discharge operation. The effectiveness of the sediment peak discharge operation at the XLD Reservoir is discussed.

To meet flood control, power generation and navigation requirements, the elevation of storage water level in front of the dam for the sediment peak discharge scheme is derived based on the storage capacity, inflow discharge and actual operating water level elevation. The comparisons of the discharged flow and the elevation of the storage water level in front of the dam during actual operation and sediment peak discharge are shown in Figure 20.
Figure 20
Discharged flow and corresponding storage water level elevation during different operation strategies.
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Discharged flow and corresponding storage water level elevation during different operation strategies.

Figure 20
Discharged flow and corresponding storage water level elevation during different operation strategies.
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Discharged flow and corresponding storage water level elevation during different operation strategies.

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The comparison of the discharge flow and suspended sediment concentration near the dam are shown in Figure 21. This indicates that during actual operation, the maximum discharge flow and the maximum suspended sediment concentration are not in the same time interval, while during sediment peak operation, the maximum discharge flow and the maximum suspended sediment concentration are in the same time interval. The sediment release from the reservoir depends on the magnitude of the discharge flow and suspended sediment concentration. The amount of sediment released from July 14 to August 25 during actual operation and sediment peak operation was 3.66 × 105 and 3.86 × 105 t, respectively, and the efficiency of sediment release increased by 6.6%. Therefore, the sediment peak operation strategy based on the hysteresis effect of the flood and sediment peaks can clearly improve the amount of sediment released from a reservoir and reduce reservoir sedimentation.
Figure 21
Comparison of the flow rate and sediment concentration at different hydrological stations for different operation strategies.
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Comparison of the flow rate and sediment concentration at different hydrological stations for different operation strategies.

Figure 21
Comparison of the flow rate and sediment concentration at different hydrological stations for different operation strategies.
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Comparison of the flow rate and sediment concentration at different hydrological stations for different operation strategies.

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In this paper, a SCHISM 3D numerical model is adopted to simulate the processes of flood propagation and sediment transport in July 2018 in an almost 190 km reach upstream of the XLD Reservoir. It investigates the hysteresis effect between the flood and sediment peaks, the sensitivity analysis of the influencing factors of the sediment peak propagation characteristics and the application of the hysteresis effect in the sediment release of the XLD Reservoir. The main conclusions are summarized as follows:

Dam construction alters the hydrodynamic characteristics of the flow and sediment regimes in a river, resulting in the enhancement of the hysteresis effect between the flood and sediment peaks. The incoming flow rate has a great influence on the propagation time and attenuation of the sediment peak. The storage water level in a reservoir has a great influence on the propagation time of the sediment peak but a small influence on the attenuation rate of the sediment peak. The incoming suspended sediment concentration has no clear effect on the attenuation rate of the sediment peak. The empirical formula established based on inflow rate, water level elevation, water depth and length and storage capacity of reservoirs can predict the lag time between the flood peak and sediment peak in shallow water motion, which is extremely important for a sediment peak operation strategy.

The asynchronous movement between the incoming flood and sediment peaks has a clear influence on the sediment peak propagation in a deep reservoir. When the flood peak and sediment peak are synchronized, the attenuation rate of the sediment peak is smaller. When the sediment peak lags behind the flood peak when entering the reservoir, the attenuation rate of the sediment peak is larger. When the sediment peak precedes the flood peak when entering the reservoir, if the time of the sediment peak preceding the flood peak is small, the sediment peak attenuation rate is smaller, while if the time of the sediment peak preceding the flood peak is large, the sediment peak attenuation rate is larger. Therefore, an artificial flood wave in the cascade reservoir can be created by suddenly increasing the amount of water discharged from the dam to intervene in the propagation of the sediment peak, reducing the sedimentation and optimizing the sedimentation distribution in a reservoir. The research results can provide the scientific references for further optimizing the operation mode of water and sediment in reservoir.

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This work was financed by the National Natural Science Foundation of China (Grant No. U2040217), the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (Grant No. SKL2020ZY08; SKL2022ZY04).

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All relevant data are included in the paper.

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The authors declare that we have no competing interests.

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

Ahn
J.
,
Yang
C. T.
,
Boyd
P. M.
,
Pridal
D. B.
 &
Remus
J. I.
2013
Numerical modeling of sediment flushing from lewis and clark lake
.
International Journal of Sediment Research
28
(
2
),
182
–
193
.
Google Scholar
Crossref
Search ADS
 
Ariathurai
R.
 &
Arulanandan
K.
1978
Erosion rates of cohesive soils
.
Journal of Hydraulic Division
104
(
2
),
279
–
283
.
Google Scholar
Crossref
Search ADS
 
Blaas
M.
,
Dong
C.
,
Marchesiello
P.
,
McWilliams
J. C.
 &
Stolzenbach
K. D.
2007
Sediment-transport modeling on Southern Californian shelves: a ROMS study
.
Continental Shelf Research
27
,
832
–
853
.
Google Scholar
Crossref
Search ADS
 
Canuto
V. M.
,
Howard
A.
,
Cheng
Y.
 &
Dubovikov
M. S.
2001
Ocean turbulence. Part I: one-point closure model-momentum and heat vertical diffusivities
.
Journal of Physical Oceanography
31
(
6
),
1413
–
1426
.
Google Scholar
Crossref
Search ADS
 
Castillo
L. G.
,
Carrillo
J. M.
 &
Álvarez
M. A.
2015
Complementary methods for determining the sedimentation and flushing in a reservoir
.
Journal of Hydraulic Engineering
141
(
11
),
05015004
.
Google Scholar
Crossref
Search ADS
 
Chen
G. Y.
,
Dong
B. J.
,
Jiang
L. L.
,
Li
Y.
 &
Xu
Q. X.
2018
Analysis of sediment peak scheduling of Three Gorges Reservoir in No. 2 flood of Changjiang River in 2018
.
Yangtze River
49
(
19
),
6
–
10
.
(In Chinese)
.
Google Scholar
 
Cheraghi
M.
,
Jomaa
S.
,
Sander
G. C.
 &
Barry
D. A.
2016
Hysteretic sediment fluxes in rainfall-driven soil erosion: particle size effects
.
Water Resources Research
52
(
11
),
8613
–
8629
.
Google Scholar
Crossref
Search ADS
 
Dong
B. J.
,
Chen
X. W.
 &
Xu
Q. X.
2014a
Investigations and considerations on peak sediment regulation of Three Georges Reservoir
.
Yangtze River
45
(
19
),
1
–
5
.
(In Chinese)
.
Google Scholar
 
Dong
B. J.
,
Qiao
W.
 &
Xu
Q. X.
2014b
Study on sediment peak regulation of Three Gorges Reservoir in flood season and preliminary practice
.
Yangtze River
45
(
3
),
7
–
11
.
(In Chinese)
.
Google Scholar
 
Du
J.
,
Shi
C.
 &
Zhang
C.
2013
Modeling and analysis of effects of precipitation and vegetation coverage on runoff and sediment yield in Jinsha River Basin
.
Water Science and Engineering
6
(
1
),
44
–
58
.
Google Scholar
 
Ehab
A. M.
,
Ioannis
G.
,
Mead
A. A.
 &
John
A. M.
2012
Numerical modeling of hydrodynamics and sediment transport in lower Mississippi at a proposed delta building diversion
.
Journal of Hydrology
472
,
340
–
354
.
Google Scholar
 
Galperin
B.
,
Kantha
L. H.
,
Hassid
S.
 &
Rosati
A.
1988
A quasi-equilibrium turbulent energy model for geophysical flows
.
Journal of the Atmospheric Sciences
45
(
1
),
55
–
62
.
Google Scholar
Crossref
Search ADS
 
Heidel
S. G.
1956
The progressive lag of sediment concentration with flood waves
.
Journal of the Japanese Forestry Society
38
(
1
),
56
–
66
.
Google Scholar
 
Huang
R. Y.
,
Shu
C. W.
 &
Tan
G. M.
2019a
Preliminary study on transportation characteristics of sediment concentration peak of the Three Gorges Reservoir in flood season
.
Journal of Basic Science and Engineering
27
(
6
),
1202
–
1210
.
(In Chinese)
.
Google Scholar
 
Huang
L.
,
Li
X.
,
Fang
H. W.
,
Yin
D. Q.
,
Si
Y.
,
Wei
J. H.
,
Liu
J. H.
,
Hu
X. Y.
 &
Zhang
L.
2019b
Balancing social, economic and ecological benefits of reservoir operation during the flood season: a case study of the Three Gorges Project, China
.
Journal of Hydrology
572
,
422
–
434
.
Google Scholar
Crossref
Search ADS
 
Kantha
L. H.
 &
Clayson
C. A.
1994
An improved mixed layer model for geophysical applications
.
Journal of Geophysical Research
99
(
25
),
235
–
266
.
Google Scholar
 
Khosronejad
A.
,
Le
T.
,
Dewall
P.
,
Bartelt
N.
,
Woldeamlak
S.
,
Yang
X.
 &
Sotiropoulos
F.
2016
High-fidelity numerical modeling of the upper Mississippi River under extreme flood condition
.
Advances in Water Resources
98
,
97
–
113
.
Google Scholar
Crossref
Search ADS
 
Lv
Y.
,
Fagherazzi
S.
,
Zheng
S.
,
Tan
G.
 &
Shu
C.
2020
Enhanced hysteresis of suspended sediment transport in response to upstream damming: an example of the middle Yangtze River downstream of the Three Gorges Dam
.
Earth Surface Processes and Landforms
45
(
8
),
1846
–
1859
.
Google Scholar
 
Miller
J. E.
1984
Basic concepts of kinematic- wave models. Geological Survey Professional Paper, 1302
.
Munoz
D. H.
 &
Constantinescu
G.
2018
A fully 3-D numerical model to predict flood wave propagation and assess efficiency of flood protection measures
.
Advances in Water Resources
122
(
DEC
),
148
–
165
.
Google Scholar
 
Pietroń
J.
,
Jarsjö
J.
,
Romanchenko
A. O.
 &
Chalov
S. R.
2015
Model analyses of the contribution of in-channel processes to sediment concentration hysteresis loops
.
Journal of Hydrology
527
,
576
–
589
.
Google Scholar
Crossref
Search ADS
 
Pinto
L.
,
Fortunato
A. B.
,
Zhang
Y.
,
Oliveira
A.
 &
Sancho
F. E. P.
2012
Development and validation of a three-dimensional morphodynamic modelling system for non-cohesive sediments
.
Ocean Modelling
57–58
,
1
–
14
.
Google Scholar
 
Rodi
W.
1984
Turbulence Models and Their Applications in Hydraulics: A State of the art Review
.
International Association for Hydraulics Research
,
Delft
,
The Netherlands
.
Google Scholar
 
Singh
V. P.
 &
Li
J.
1993
Identification of reservoir flood-wave models
.
Journal of Hydraulic Research
31
(
6
),
811
–
824
.
Google Scholar
Crossref
Search ADS
 
Soulsby
R. L.
1997
Dynamics of Marine Sands, A Manual for Practical Applications
.
H.R. Wallingford
,
Thomas Telford
,
England
.
Google Scholar
 
Soulsby
R. L.
 &
Whitehouse
R. J. S
.
1997
Threshold of sediment motion in coastal environments
. In:
Proceedings of the Pacific Coasts and Ports'97 Conference
(
Stive
M. J. F.
, ed.).
University of Canterbury
,
Christchurch
,
New Zealand
, pp.
149
–
154
.
Google Scholar
 
Umlauf
L.
 &
Burchard
H.
2003
A generic length-scale equation for geophysical turbulence models
.
Journal of Marine Research
61
(
2
),
235
–
265
.
Google Scholar
Crossref
Search ADS
 
Vercruysse
K.
,
Grabowski
R. C.
 &
Rickson
R. J.
2017
Suspended sediment transport dynamics in rivers: multi-scale drivers of temporal variation
.
Earth-Science Reviews
166
,
38
–
52
.
Google Scholar
Crossref
Search ADS
 
Warner
J. C.
,
Sherwood
C. R.
,
Signell
R. P.
,
Harris
C. K.
 &
Arango
H. G.
2008
Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model
.
Computers and Geosciences
34
(
10
),
1284
–
1306
.
Google Scholar
Crossref
Search ADS
 
Xu
J. P.
,
Noble
M.
 &
Eittreim
S. L.
2002
Suspended sediment transport on the continental shelf near Davemport, California
.
Marine Geology
181
,
171
–
193
.
Google Scholar
Crossref
Search ADS
 
Ye, F., Zhang, Y., Yu, H., Sun,W., Moghimi, S., Myers, E., Nunez, K., Zhang, R. Y., Wang, H. V., Roland, A., Martins, K., Bertin, X., Du, J. B. & Liu, Z.
2020
Simulating storm surge and compound flooding events with a creek-to-ocean model: importance of baroclinic effects
.
Ocean Modelling
145
,
101526
.
Crossref
Search ADS
 
Zhang
Y. J.
,
Ateljevich
E.
,
Yu
H. C.
,
Wu
C. H.
 &
Yu
J. C. S.
2015
A new vertical coordinate system for a 3D unstructured-grid model
.
Ocean Model
85
,
16
–
31
.
Google Scholar
Crossref
Search ADS
 
Zhang
Y. J.
,
Ye
F.
,
Stanev
E. V.
 &
Grashorn
S.
2016
Seamless cross-scale modelling with SCHISM
.
Ocean Model
102
,
64
–
81
.
Google Scholar
Crossref
Search ADS
 
Zhang
B. W.
,
Wu
B. S.
,
Ren
S.
,
Zhang
R. Y.
,
Zhang
W.
,
Ren
J. Q.
 &
Chen
Y.
2021a
Large-scale 3D numerical modelling of flood propagation and sediment transport and operational strategy in the Three Gorges Reservoir, China
.
Journal of Hydro-Environment Research
36
,
33
–
49
.
Google Scholar
Crossref
Search ADS
 
Zhang
B. W.
,
Wu
B. S.
,
Zhang
R. Y.
,
Ren
S.
 &
Li
M. H.
2021b
3D numerical modelling of asynchronous propagation characteristics of flood and sediment peaks in Three Gorges Reservoir
.
Journal of Hydrology
593
(
2
),
125896
.
Google Scholar
 
Zhang
D.
,
Wang
W. S.
,
Yu
S. Y.
,
Liang
S. H.
 &
Hu
Q. F.
2021c
Assessment of the contributions of climate change and human activities to runoff variation: case study in four subregions of the Jinsha River Basin, China
.
Journal of Hydraulic Engineering
26
(
9
),
05021024
.
Google Scholar
 
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