Sediment Transport Capacity Under the River–Tide Interaction in the Changjiang Estuary

Sediment transport capacity is a fundamental parameter in sediment transport theory and its accurate calculation is important from both theoretical and engineering viewpoints. The capacity of sediment transport has been studied extensively by many researchers in the last decades. Nevertheless, the underlying mechanism behind sediment transport capacity in estuaries remains poorly understood. The current study aims to explore the impact of the river–tide interaction on sediment transport and establish a formula of sediment transport capacity under the river–tide interaction. The impact of the river–tide interaction on the hydrodynamics and sediment dynamics in the Changjiang Estuary was analyzed, a practical method for describing the variation in tide-runoff ratio was established, and a formula of sediment transport capacity considering the impact of river–tide interaction was proposed by introducing the tide-runoff ratio. The new method bridged the gap between two well-known sediment transport capacity methods by considering the variation in the index a for the gravitational term and overcomes the drawback of distinguishing flood/dry season or spring/ebb tide in the calculation of estuarine sediment transport. A large amount of flow and sediment data obtained from the Changjiang Estuary were collected to verify the proposed formula. The effect of salt-fresh water mixture and the morphological evolution on sediment transport capacity of the Changjiang Estuary were discussed.


Introduction
As the transition zone of fluvial to ocean, estuaries have been considered as one of the most attractive sites for human beings (Wolanski, 2007). Associated sediment transport processes in estuaries are complex because of the presence of various natural forces such as river runoff, tides, winds, and waves. Prediction of sediment transport in estuaries has been therefore receiving a large amount of attention due to its great theoretical and practical importance in estuarine morphology evolution, channel dredging and regulation, and benthic habitats (Grabowski et al., 2011). With intensified anthropogenic activities and remarkable changes in natural factors in the past decades, many estuaries around the world have experienced severe morphological changes (Yang et al., 2011;Anthony et al., 2015). Consequently, it is important to study the sediment transport in estuaries undergoing human intervention.
The sediment transport in estuaries is controlled by vari-ous natural forces, and it is difficult to quantitatively determine the effect of each force on sediment transport so far (Mayerle et al., 2015). Considerable efforts have been made to explore the most crucial factor influencing sediment transport (Sanford, 2008;Winterwerp et al., 2012). River-tide interaction, settling velocity and sediment transport capacity are generally considered as dominant factors controlling sediment transport in estuaries. River discharges carry a large amount of sediments into estuaries from upstream and alter the tidal propagation by reducing tidal amplitude. Tidal asymmetry is one of the controlling factors for residual sediment transport, and strong flood tidal currents can transport more sediment from seaward into tide-dominated estuaries. In addition, tide pumping is suggested as a major mechanism for the formation of estuarine turbidity maximum. Settling velocity determines directly the vertical distribution of suspended sediment concentration (SSC) and near-bed deposition flux.
Sediment transport capacity is another significant issue in sediment transport theory and practice. It is an important parameter that should be determined for accurate numerical simulations of sediment transport and riverbed deformation. Numerous studies have been conducted on sediment transport capacity, and a large number of empirical and semi-empirical methods have been proposed. Zhang and Xie (1993) proposed the sediment transport capacity formula based on a hypothesis that the turbulence attenuation by suspended sediment, many revisions and modifications of this formula have subsequently been made to adapt different problems (Wu and Li, 1992;Zhang and Zhang, 1992). Dou et al. (1995) assumed that sediment transport capacity for coastal regions is the direct sum of the sediment transport capacity of pure tidal current and pure wave. Cao et al. (2001) deduced the expression form for the bottom shear stress under the condition of wave-current interaction and subsequently obtained the sediment transport capacity formula for nearshore regions. Liu (2009) derived the sediment transport capacity formula by considering the main driving forces of nearshore regions which could be divided into three parts: wind-induced flow, tide, and wave. Based on the wave energy dissipation principle inside and outside the surf zone, Zhang et al. (2009) improved the sediment transport capacity formula proposed by Dou et al. (1995) for wave condition. Zheng et al. (2014) proposed the concept of ocean wave significant velocity, and derived a new formula of sediment transport capacity for nearshore waters. These previous studies enriched our knowledge of sediment transport capacity. However, little has been focused on the sediment transport capacity under the river-tide interaction, and the methods proposed under the undirectional flows or wave-current interaction were still applied to calculate the sediment transport capacity under the river-tide interaction. The lack of knowledge highlights the need to carry out a thorough study on the sediment transport capacity under river-tide interaction.
The Changjiang River is the longest river in Asia and the third longest river in the world. As the most important estuary in China, the hydrodynamic characteristics and morphological evolution patterns of the Changjiang Estuary have been the focus of scientific research Zhang et al., 2018). Since the closure of Three Gorges Dam (TGD), the hydrological processes and riverbed morphological characteristics along the Changjiang River downstream of the dam have been subjected to drastic changes. Sediment discharge at the hydrometric station of Yichang has decreased from 4.91×10 8 t/a in the pre-TGD period  to 0.48×10 8 t/a (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012) (Yang et al., 2014). The drastic decline in sediment discharge has contributed to noticeable morphological adjustments in downstream reaches, especially in a few hundred kilometers immediately downstream of the TGD. The river between Hankou and Datong changed from an equilibrium state in 1956-2002 to erosion at a rate of 0.16×10 8 t/a in 2003(Yang et al., 2014. Meanwhile, the Changjiang Estuary experienced sediment starvation that triggered dramatic erosion in the inner side of the mouth bar (Mei et al., 2018). The mean high tide level in the tidal river part of the Changjiang River increased because of an increased tidal range . Under the combined effects of river discharges and tidal currents, the Changjiang Estuary can be classified as a joint river-and tide-controlled estuary (Luan et al., 2016), except for the North Branch where is a tidedominated environment with negligible runoff impacts. The river-tide interaction, which has been investigated by many researchers, is a significant factor in controlling the sediment transport and associated morphological evolution of the Changjiang Estuary (Zhang et al., 2016). Accordingly, the Changjiang Estuary provides a suitable framework for exploring the sediment transport capacity under river-tide interaction.
The current study aims to elucidate the effect of the river-tide interaction on sediment transport and to propose a formula of sediment transport capacity for the Changjiang Estuary, where river and tide flows interact strongly. The structure of this paper is arranged as follows: (1) the spatial and temporal variations in hydrodynamics and sediment dynamics of the Changjiang Estuary are explored; (2) a practical method to calculate the tide-runoff ratio L, which is used to describe the relative strength between river flow and tidal currents, is established; and (3) a sediment transport capacity formula considering the river-tide interaction is proposed, and a great amount of flow and sediment data measured in the Changjiang Estuary are used to verify the proposed formula.

General characteristics of the Changjiang Estuary
In the past two millennia, the Changjiang Estuary has developed into a configuration of three-level bifurcation with four outlets because of the natural evolution and human intervention ( Fig. 1) (Chen et al., 1985). The first-level bifurcation consists of the North Branch and the South Branch, followed by the North Channel and South Channel as the second-level bifurcation; and finally the South Channel is divided into the North Passage and the South Passage by the Jiuduansha shoal, forming the third-level bifurcation (Zhu et al., 2016). Different bifurcations exhibit varying hydrological processes and morphological evolution patterns as a result of different water discharge diversion ratios and sediment loads entering the branches, riverbed topography, and human intervention. For example, due to the extensive land reclamation, water discharge entering the North Branch decreased drastically from 12% of the total river flow to the ocean in 1958 to 2% in 2012 (Huang et al., 2017). The mean water depth along the North Branch exhibited a gradually decreasing trend in recent decades (Dai et al., 2016). Because of the Deep Water Navigation Project, the North Passage has become an artificially controlled estuarine channel. The ebb flow has been strengthened because of dredging. The present average depth of the North Passage is 12.50 m, but severe deposition occurred in the peripheral groin fields along the shipping channel . By analyzing the bathymetric data between 1880 and 2013, Mei et al. (2018) found that the erosion/deposition pattern in the North Channel exhibited a distinct spatial difference, which is attributed to the change of upstream sediment supply and the variation in relative strength between river and tide flows subjected to the strong human intervention. The average annual water depth in the South Passage exhibited a decreasing trend between 1987 and 2012, with the volume capacity losing by approximately 13%, indicating that severe deposition occurred during this period (Dai et al., 2015).
The annual mean water discharge and sediment load entering the Changjiang Estuary from 1953 to 2016 were 892×10 9 m 3 and 3.64×10 8 t, respectively (Changjiang Water Resources Commission, 2016). The hydrology of the upstream river exhibits strong seasonal variations and the flood season from May to September accounts for 71% and 85% of the yearly water discharge and sediment load, re-spectively (Chen et al., 2007). The Changjiang Estuary is a partially mixed mesotidal estuary, and the astronomic tide around the Changjiang Estuary is semi-diurnal. Wind-induced waves in the Changjiang Estuary are weak under normal weather conditions. To distinguish the relative strength between river and tide flows, the Lower Changjiang River can be divided into three reaches: (1) the upper reach from Datong to Jiangyin with the flow conditions controlled mainly by the river discharges; (2) the inner reach from Jiangyin to Beicaozhong with river flow and tidal currents interacting strongly; and (3) the outer reach seaward from Beicaozhong with the flow conditions dominated by tidal currents (Yan, 1992, Fig. 1).

Data collection and process
The flow and sediment data measured hourly at 14 stations covering the neap-spring tidal cycle in 2010, 2011 and 2015 were collected for the current study. The sites of stations 1 to 10 distributed from different bifurcations of the inner reach where both river and tidal processes are important. Since the North Branch was mainly controlled by tide flows, it is therefore excluded in the current study with emphasis on other bifurcations characterized by strong river-tide interaction. Stations 11-14 were located in the outer reach where tide flows dominate. The specific locations and observation periods, as well as the measurement parameters are summarized in Table 1. The data of each vertical line were sampled at six layers in the water column with a relative depth of 0.05, 0.2, 0.4, 0.6, 0.8, and 0.95 from the bed. Flow velocity was measured by the rotor current meter. The SSC and salinity were measured from the water samples, and particle size distributions of the sediment samples were determined using a laser diffraction particle size analyzer. Unit tidal discharge during the flood was determined by the unit flood tide volume dividing the flood tide duration, whereas the unit tidal discharge during the ebb was determined by the unit ebb tidal volume divid-  FENG Zhi-yong et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 207-218 209 ing the ebb tide duration. In addition, the hourly river discharge at the Datong hydrometric station and the tidal level at the Beicaozhong gauging station in the same period were also collected in this study. The coefficient of flow dominance A, defined as unit tidal discharge during the ebb divided by the sum of unit tidal discharge during the ebb and flood periods, was calculated to represent the relative strength between the ebb tidal current and flood tidal current (Simmons, 1955). When the coefficient of flow dominance is over 50%, the flow is ebbdominated, and otherwise it is flood-dominated.

Phase lag effect
Given that SSC in the Changjiang Estuary is influenced significantly by tide flows, a phase lag exists between the instantaneous SSC and the flow velocity and water depth. To solve this problem, a common approach is to average SSC, water depth, and flow velocity over the period of flood, ebb, or semidiurnal tide (Zhou et al., 2013). In the current study, SSC, water depth, and flow velocity were averaged over the period of flood or ebb tide to eliminate the effect of phase lag.

Settling velocity
Settling velocity is an important parameter of sediment transport in estuaries that can be affected by numerous factors, including grain size, initial suspension concentration, the turbulent shear stress, and biological activities, which are often hard to describe at present (Wu and Wang, 2004). Therefore, the empirical settling velocity formula in Peng et al. (1987) calibrated by a series of flume experiments using the sediment taken from the Changjiang Estuary is used in the current study.
where ω 0 is the settling velocity of a single particles; ω f is the settling velocity of floc, and F is the flocculation parameter. When the salinity is below 0.5 PSU or if the median grain size is larger than 0.032 mm, F is set to 1; otherwise, F is calculated as mentioned above; S is the suspended sediment concentration; S a is the salinity; G is the turbulence intensity; d 50 is the median grain size; ; J is the energy gradient; and υ is the kinematic viscosity.

Performance scores
Three statistical parameters have been chosen to quantitatively indicate the goodness-of-fit between the measured data and computed results, with the definition of each parameter given as follows.
(1) The Pearson correlation coefficient where S com and S mea are the computed and measured sediment concentrations, respectively. The subscript i denotes the dataset number and the superscript "−" represents the averaging procedure over all datasets. For a perfect fit, R=1.
(2) The variation ratio for a perfect fit, F i =1.
(3) The root mean square error where N is the total number of datasets. For a perfect fit, RMSE=0.

Hydrodynamics and sediment dynamics under the rivertide interaction
The synchronous survey data measured from the inner reach to the outer reach in 2010 and 2011 were used to plot the spatial and temporal variations in flow dominance coefficient and SSC, with the aim of illustrating the impact of river-tide interaction on the hydrodynamics and sediment dynamics of the Changjiang Estuary.
The flow dominance coefficient varied significantly against space and time, nevertheless, it generally shows a decreasing trend from landward to seaward both in springneap tide and flood-dry season, with a more noticeable decline trend appearing in the flood season (Fig. 2a). Meanwhile, the flow dominance coefficients during the flood season were generally higher than the values during the dry season along the inner reach, whereas these results did not appear in the outer reach. Furthermore, the difference in the flow dominance coefficient of the inner reach between the spring tide and neap tide was more remarkable than that of the outer reach. The above results reflected that the variation in the flow dominance coefficient of the inner reach is controlled by the river-tide interaction. Specifically, flood tidal currents strength became pronounced from the inner reach to the outer reach, which contributes to the decline of flow dominance coefficient from upstream to downstream. Meanwhile, the river discharge is strong in the flood season and a strong river discharge attenuates tidal energy significantly in the inner reach, whereas in the outer reach, this phenomenon did not occur with the flow conditions of the outer reach dominated by tidal currents. Additionally, it should be noted that the spatial variation in flow dominance coefficient was not monotonous, indicating that the hydrodynam-ics were also affected by local topography, in addition to river discharge and tidal currents.
The obvious spatial and seasonal differences in SSC were detected from Fig. 2b. In the upper section of the inner reach (landward from 44 km in Fig. 2b), the SSC during the flood season is generally higher than that during the dry season no matter from spring tide or neap tide, indicating that the sediment transport at this section was mainly controlled by river discharges. However, in the lower section, the SSC during the spring tide in the dry season was overall higher than others, with the average value of 0.26 kg/m 3 , and the difference between the spring-neap tides was greater than the difference between the flood-dry seasons, indicating that the impact of tide flows on sediment transport at this section was pronounced. It is noteworthy that the SSC at the 14th station increased significantly during the spring tide, as compared with that during the neap tide. This phenomenon may be caused by the sediment resuspension under the strong tidal currents. The above results illustrate that the spatial and temporal variations in the SSC in the inner reach were influenced by the river-tide interaction and the variation in the SSC in the outer reach was dominated by tidal currents.
Based on the above analysis, pronounced spatial and temporal variations exist in the hydrodynamics and sediment dynamics of the inner reach and the river-tide interaction has been proved to be a significant factor controlling the hydrodynamics and sediment dynamics of the Changjiang Estuary where river flow and tidal current interact strongly.

Tide-runoff ratio
Since Simmons (1955) proposed flow dominance coefficient to represent the relative strength between the ebb tidal current and flood tidal current, much effort has been made to describe the variation in the relative strength between the river and tide flows. Yang et al. (2012) used the ratio of tidal range to river discharge describing the relative strength between river and tide flows: where L is the tide-runoff ratio; h (m) is the tidal range at the Jiangyin gauging station; and Q (m 3 /s) is the river discharge at the hydrometric station of Datong. It can be seen that L is not a dimensionless parameter in this definition which means that the parameter can only be used in the qualitative analysis. To overcome this drawback, Yang et al. (2013) considered the tide-runoff ratio as the ratio of flood tide discharge to the river discharge: where Q z (m 3 /s) is the flood tide discharge at Xuliujing and Q (m 3 /s) is the river discharge at the hydrometric station of Datong. However, because of neglecting the spatial variation in the flood tidal currents, Eq. (6) is not applicable to the inner reach where tidal dynamic exhibit significant spatial and temporal variations. In the Changjiang Estuary, the ratio of the flood discharge to the ebb discharge is generally used to determine the relative strength between river and tide flows.
where Q 1 (m 2 /s) is the unit tidal discharge during the flood and Q 2 (m 2 /s) is the unit tidal discharge during the ebb. However, the accurate determination of Q 1 and Q 2 is inconvenient and time-consuming, as it requires continuous observations of the water depth and flow velocity over the period of semidiurnal tide. Therefore, the need arises for a practical method to describe the variation in the relative strength between river and tide flows. Based on the above analysis, the spatial and temporal variations in the flow dominance coefficient in the inner reach were remarkably affected by river discharges and tide flows. Meanwhile, the spatial variation in this parameter was also affected by local topography. O'Brien (1969) proposed an empirical relationship between the cross-sectional area and the spring tidal prism based on the field measurements of 28 tidal entrances at the Florida's Atlantic Coast. The method can be expressed as: where A is the cross sectional area and P is the spring tidal prism. The coefficient a and the index m are calibrated by the measured data. As long as the cross-sectional area of tidal entrance can be computed by the spring tidal prism, a similar relationship must exist between the water depth and the corresponding unit tidal volume. Based on this theory, Guo et al. (2016) established an empirical method between the unit flood/ebb tide volume and water depth, which was successfully applied to Jiaojiang Estuary and Oujiang Estuary. Therefore, it is believed that the relative strength between river and tide flows of the inner reach is the function of river dynamic, tidal dynamic, and water depth. In the current study, the river discharge at Datong was chosen to represent the river dynamic and the tidal range at Beicaozhong was used to describe the tidal dynamic. Thus, the empirical method to describe the variation in the relative strength between river and tide flows in the inner reach can be expressed as follows: where h * is the normalized water depth; Q * is the normalized river discharge; and H * is the normalized tidal range. The values of a, m1, m2, and m3 depend on the sediment characteristics and channel pattern of the study area, and can be determined by the measured data. To keep the dimensional homogeneity, water depth, river discharge, and tidal range are all normalized by corresponding average value. Flow data from Station 1 to Station 10 in 2010, 2011 and 2015 and corresponding river discharge and tidal range data were used to test the applicability of Eq. (9). The annual average value of 28320 was used to normalize the river discharge and the water depth and tidal range were normalized by their measured average value, respectively. The tidal range and water depth were averaged over the period of semidiurnal tide in the verification procedure, which is reasonable for the case when the difference of tide range between flood and ebb tides is small. By taking the logarithm of both sides of Eq. (9), then performing multivariable linear regression with the measured data, the values of a, m1, m2, m3 can be determined. The water depth h, unit tidal discharge during the flood Q 1 and unit tidal discharge during the ebb Q 2 measured in the South Channel with corresponding river discharge Q and tidal range H are given in Table 2 as the example flow data used in the fitting procedure. Fig. 3 compares the measured and computed tide-runoff ratios in the inner reach of the Changjiang Estuary, indicating close agreement between the measured data and computed results in each bifurcation. About 79% and 95% of the computed results are within a factor of 1.5 and 2 of the measured data, respectively. In addition, the Pearson correlation coefficient R between the measured and computed tide-runoff ratios is 0.82, with the corresponding value of RMSE of 0.2. The gradually intensified tidal wave deformation from Beicaozhong to Xuliujing may be responsible for some deviations in the computed tide-runoff ratios of the South Branch because this process is solely reflected by the change of water depth in Eq. (9). The explicit expression obtained by a fitting procedure shows that the tide-runoff ratio L is inversely proportional to the river discharge and is proportional to the tidal range. This is because the increase in river discharge will attenuate the flood tidal currents, which results in a decrease in the tide-runoff ratio. However, an increase in the tidal range represents an increase in the tidal dynamic, thus causing an increase in the tide-runoff ratio. Overall, the proposed method can give reasonably good predictions of tide-runoff ratio.

Sediment transport capacity under the rivertide interaction
In the upper reach where the hydrodynamic conditions are controlled by river discharges, the sediment transport capacity formula suggested by Zhang and Xie (1993)  widely used because of its simple structure and clear physical mechanism, which can be written as:

has been
where S * is the sediment transport capacity in mass per unit volume; U is the depth-averaged velocity; h is the water depth; g is the gravity acceleration; ω is the settling velocity of sediment; and k, m are coefficients that need calibrating. A sediment transport capacity formula proposed by Deng (1989) based on the energy balance principle has been used by many researchers to calculate the sediment transport in the outer reach where the flow conditions are dominated by tide flows (Tang et al., 2008;Lei et al., 2013). It can be expressed as follows: To turn Eq. (11) into a dimensionless form, the gravity acceleration is introduced: The study of sediment transport capacity becomes more complicated in the inner reach where the relative strength between river and tide flows exhibits a remarkable variation. Currently, Eqs. (10) and (12) or the linear combination of these two formulae were still applied to calculate the sediment transport capacity in this area (Xie and Yan, 2011;Mo et al., 2012;Zhou et al., 2013), and distinguished the flood season from the dry season in the calculation to take account of the impact of river-tide interaction on sediment transport. However, this only considered the variation in river discharge between the dry season and the flood season, and the tidal wave deformation along the Changjiang Estuary was omitted. Therefore, the calculation accuracy of the existing sediment transport capacity methods was not im-proved significantly for the reach where river and tide flows interact strongly.
Since Eq. (10) can be used to compute the sediment transport capacity in the river-dominated reach, and the sediment transport capacity of the tide-dominated reach can be computed by Eq. (12), it can be inferred that the formula of sediment transport capacity under the river-tide interaction should be related to Eq. (10) and Eq. (12). A comparison between Eq. (10) and Eq. (12) shows that the difference between these two formulas lies in the gravitational term ω/U, and it changes from (ω/U) 1 in the upper reach to (ω/U) 0 in the outer reach. In order to incorporate the impact of river-tide interaction on sediment transport, the gravitational term in the inner reach can be treated as (ω/U) a , with the index a varying with the relative strength between river and tide flows. Thus, the sediment transport capacity of the inner reach can be written as follows: where a is related to the river-tide interaction. A larger a indicates a smaller gravitational term ω/U, which means that the flow conditions are mainly controlled by river discharges, whereas a smaller a means a greater gravitational term ω/U, indicating that the tidal dynamics cannot be neglected. The main mechanism behind this is that the impact of the flood tidal currents on the main dynamic factor of the sediment transport capacity gradually becomes significant with the intensified tidal strength, resulting in U 3 gradually decreased to U 2 from the upper reach to the outer reach. In addition, an increasing trend of salinity from landward to seaward makes it easy for suspended sediment to aggregate into large flocs to settle, thereby increasing the gravitational term. Overall, the effect of river-tide interaction on the sediment transport has been considered by variation in the index a of the gravitational term in Eq. (13). Since a practical method for calculating the tide-runoff ratio L has been established, the index a can be tentatively regarded as the inverse linear function of the tide-runoff ratio L. Thus, the formula of sediment transport capacity for the inner reach can be obtained: where L * is the normalized form of L, with the range of 0 to 1; and k, m are coefficients that need to be calibrated. When L * is equal to 0, Eq. (14) turns into Eq. (10), whereas in the case of L * equaling 1, Eq. (14) turns into Eq. (12), indicating that Eq. (14) has self-adaptability to suit the differ-

Verification of the proposed formula
Two groups of flow and sediment datasets were used in the verification procedure. The first group contains the measured data from different bifurcations of the inner reach, aiming to assess the applicability of Eq. (14) in each bifurcation separately. The measured flow velocities, water depths, and SSCs in the South Branch ranged from 0.03-1.09 m/s, 9-25.2 m, and 0.02-0.26 kg/m 3 , respectively. For the North Channel, the corresponding data ranged from 0.18-1.41 m/s, 11.73-22.06 m, and 0.03-0.46 kg/m 3 . The measured flow velocities, water depths, and SSCs in the South Channel ranged from 0.1-1.14 m/s, 11.39-17 m, and 0.047-0.54 kg/m 3 , with the corresponding value of the North Passage ranging from 0.13-1.71 m/s, 11.11-15.1 m, and 0.041-0.92 kg/m 3 . Table 3 gives the flow and sediment data measured in the South Channel with corresponding measured salinity and median grain size.
The second group covers the measured data from each bifurcation of the inner reach, with the aim of reflecting the overall performance of Eq. (14) in the inner reach of the Changjiang Estuary. Values of average water depth, average river discharge, and average tidal range used to normalize the fitting procedure of Eq. (9) are also used here to normalize the corresponding data. By taking logarithm of both sides of Eq. (14), and then performing linear regression with the measured data, the values of k, m can be determined. A comparison of the sediment concentration computed using Eq. (14) and the measured data is shown in Fig. 4 for the first group datasets and a comparison of the measured data and computed results of Eq. (14) is shown in Fig. 5 for the second group datasets, with the corresponding statistical parameters given in Table 4.
For the first group datasets, a good predictions for sediment concentrations were obtained by Eq. (14) for each bifurcation, indicating that it is reasonable to consider the impact of river-tide interaction on sediment transport capacity through the variation in the index a of the gravitational term. Specifically, Eq. (14) yields satisfactory results in the North Passage, the Pearson correlation coefficient R Table 3 Part of measured data used to verify Eq. (14). The SSC, water depth, and flow velocity data have been averaged over the period of flood or ebb tide  For the second group datasets, the calculated sediment concentrations by using Eq. (14) matched well the measured sediment concentrations. The value of R between them is 0.70 and the corresponding value of RMSE is 0.112 kg/m 3 . Additionally, the ratio of variation falling in the range of 0.67-1.5 and 0.5-2 are 58.9% and 80.7%, respectively. It can be found that Eq. (14) exhibits different adaptability in four bifurcations. The proposed formula possesses an acceptable accuracy for the North Channel and the South Channel, whereas for the South Branch and the North Passage, some discrepancies appear between the measured and computed sediment concentration. The calculation error in tide-runoff ratio of the South Branch may be responsible for the corresponding prediction deviations in the sediment transport capacity. Meanwhile, the turbidity maximum zone within the North Passage significantly alters the vertical   profile of SSC, resulting in a completely different sediment dynamics between the North Passage and other bifurcations.
With the numerous factors that influence the sediment transport of the Changjiang Estuary, we believe that the discrepancy between the measured and calculated sediment concentration by using Eq. (14) is acceptable. Overall, the applicability of Eq. (14) has been verified based on a great amount of flow and sediment data measured in the inner reach of the Changjiang Estuary and it is reasonable to use Eq. (14) to compute the sediment transport capacity in the inner reach of the Changjiang Estuary where river and tide flows interact strongly.

Discussion
5.1 Effect of salt-fresh water mixture on sediment transport capacity Salt-fresh water mixture has a significant effect on sediment transport in estuaries because it not only induces fine sediment flocculation but also causes a stratification effect on the flow patterns (Winterwerp, 2006). Moreover, the landward baroclinic pressure caused by different density currents will significantly alter the vertical distribution of SSC, and thus trigger the upstream net suspended sediment transport (Carlin et al., 2015). Salt-fresh water mixture can also affect the sediment transport capacity through the tiderunoff ratio. According to the above analysis, the index a of the gravitational term of Eq. (13) reflects the impact of river-tide interaction on the sediment transport. The gravitational circulation induced by the seaward barotropic pressure gradient and the landward baroclinic pressure gradient is also one of the most crucial factors that control the turbidity maximum magnitude and location (Song and Wang, 2013). With the presence of turbidity maximum, the vertical profile of SSC is significantly altered due to a high sediment concentration layer existing near the riverbed. This high sediment concentration layer will exert a great impact on the settling velocity, and thus affect the sediment transport. Overall, the mixture of salt-fresh water actions substantially influences the sediment transport capacity.

Changing sediment transport capacity in response to the morphological evolution and rivertide interaction
The relationship between the sediment transport capacity and the SSC determines whether erosion or deposition will occur in the riverbed. Riverbed deformation will in turn alter the sediment transport capacity. When aggregation occurs, the cross-section area will decrease, causing an increase in the flow velocity, followed by an increase in the sediment transport capacity. When degradation occurs, the opposite situation will happen. In the case of the inner reach of the Changjiang Estuary, the river-tide interaction also affects the sediment transport capacity. Table 5 shows the coefficient k and the index m of Eqs. (12) and (14) in different bifurcations and corresponding average unit tidal discharge, average water depth, and average normalized tiderunoff ratio, indicating a remarkable difference in the sediment transport capacity between different bifurcations of the Changjiang Estuary. Specifically, there is a negligible difference in the average unit tidal discharge between the South Branch and the North Passage. However, the average water depth of the North Passage has been reduced by 23%, as compared with that of the South Branch, therefore the sediment transport capacity of the North Channel increases as the flow velocity increases, which is consistent with the fitting results given in Table 5. Meanwhile, the comparison between the fitting results of Eqs. (12) and (14) in different bifurcations indicates that the coefficients k and m in Eq. (14) are quite different with those in Eq. (12) because of the impact of river-tide interaction on the sediment transport being incorporated in Eq. (14). In addition, it is worth noting that a positive correlation exists between the index m of Eq. (14) and the normalized tide-runoff ratio L * , which means that the river-tide interaction has a great impact on the sediment transport. Overall, the morphological evolution and river-tide interaction are considered to be the significant factors influencing the sediment transport capacity of the inner reach of the Changjiang Estuary where river and tide flows interact strongly.

Conclusions
A great number of flow and sediment data obtained from the Changjiang Estuary were collected for the current study to explore the impact of the river-tide interaction on sediment transport of the Changjiang Estuary and to derive a formula of sediment transport capacity under the river-tide interaction. The results and discussion lead to the following conclusions.
(1)Analyzing the spatial and temporal variations in the flow dominance coefficient and SSC of the Changjiang Estuary shows that the river-tide interaction has a great im- Table 5 Fitting results for different formulae of sediment transport capacity in each bifurcation of the Changjiang Estuary. Average unit tidal discharge Q, average water depth h, and average normalized tide-runoff ratio L * are also given pact on the hydrodynamics and sediment dynamics in the inner reach, and river discharge, tidal dynamic, and local topography have been proven to be the most important factors influencing the relative strength between river and tide flows in the inner reach.
(2)An empirical method to compute the tide-runoff ratio with clear physical mechanism has been established in the current study. The comparison between measured data and computed results verifies its applicability for the reach where river and tide flows interact strongly. (R=0.82).
(3)The impact of river-tide interaction on the sediment transport has been considered by the variation of index a of the gravitational term in the formula of sediment transport capacity. By normalizing the tide-runoff ratio to the range of 0 and 1 and assuming the inverse linear relationship existing between a and normalized tide-runoff ratio L * , a formula of sediment transport capacity considering the impact of river-tide interaction is thus proposed. The proposed formula bridges the gap between two well-used sediment transport formulae and overcomes the drawback of the existing methods which needs to distinguish flood season from dry season or spring tide from neap tide in calculating estuarine sediment transport. A comparison between the computed results using the proposed method and the measured data from two group datasets indicates that the proposed method gives good predictions of sediment concentration in the inner reach where river and tide flows interact strongly. Consequently, the proposed method considering the impact of river-tide interaction can be used to compute the sediment transport capacity in the Changjiang Estuary where river and tide flows interact strongly.