A numerical model was implemented using the Telemac-3D finite element open-source model , following the configurations of . The model uses Prandtl's mixing length model with Munk Anderson damping function for the vertical turbulence closure and constant values for horizontal turbulence . Wetting and drying options were activated to account for the tidal flats in the estuary (Fig. ). The model consists of nine terrain-following vertical layers that expand and contract following the tides. The number of layers was set to nine because of computational constraints. However, to increase the resolution of larger gradients near the bed, we use a mesh transformation that allows a refinement near the bottom. The model time-step was 30 s and snapshots of the model were saved every 20 min for 10 months of 2018 (February–November). Two upstream freshwater boundaries were defined and forced with realistic river discharge data available every 12 h which was collected by French government agencies (data available at https://data.ofb.fr/, last access:January 2024). The salinity at the offshore boundary was set to 35 gkg-1 based on previous work on the region . The tidal forcing was extracted from the North East Atlantic tidal model including 46 tidal constituents and storm surges at the open offshore boundary. To study sediment dynamics, Telemac-3D was coupled with GAIA, a module of Telemac that simulates sediment transport for multiple sediment classes, bed evolution processes and that includes fine and cohesive suspended sediments that are actively incorporated into hydrodynamic calculations . In the present study, however, only one class of fine sediment is considered, and bed evolution is supposed to be negligible at the simulated time-scales.

In the configuration analyzed by , several settling-velocity parameterizations were tested in the Gironde estuary, each with advantages and limitations for reproducing SSC observations and ETM dynamics. For the present study, we adopt the van Leussen parameterization, which provided the best validation of SSC maxima. The present model only considers a single cohesive sediment class (diameter of 0.00006 m), with a settling velocity computed dynamically through the van Leussen flocculation parameterization . While this formulation has clear advantages for reproducing the upstream migration of the ETM and capturing high SSC levels , it also tends to underestimate SSC near the bottom during neap tides. Nevertheless, the focus of this work is to study whether SSC could impact the exchange flow and because the original configuration was already validated, we consider the model suitable to study the impact of suspended sediments on the exchange flow.

Several studies have shown that suspended sediments have an impact on hydrodynamics , tidal amplification , velocity shear , stratification or lateral circulation . Therefore, to isolate sediment-induced effects on the exchange flow we ran two models: one where water density is quantified using both SSC and salinity, what we refer to as the “active model” (ρall), and another where water density is quantified using only salinity, referred to as the “passive model ” (ρSal). Both models used the same GAIA configuration to model sediment transport.

To differentiate the effects of salinity and SSC on water density, we assume that the total density (ρall) can be decomposed considering the contribution by salinity (ρSal) and suspended sediments (ρSSC) independently following previous works . Therefore, the water density can be decomposed as: 1ρall=ρSal+ρSSC.

In Telemac-3D, the variation of density due to salinity is calculated as: 2ρSal=ρref+0.75S, where, ρref = 999.972 kgm-3 is the reference density at 4 °C when the salinity S is zero. The variation of density considering the sediment concentration is: 3ρSSC=SSC×ρs-ρrefρs=0.62SSC, where ρs is the specific density for primary particles of cohesive sediment and SSC is the suspended sediment concentration. We used ρs = 2650 kgm-3 following the value used in . Both models include suspended sediments but only in the active model they are considered into water density calculations. The active model corresponds to the RY3 configuration model by . In the passive model, since ρSSC is not considered, ρall should be of similar magnitude than ρSal. An analysis of the passive model showed that the density of the model ρall and the density due to salinity alone ρSal have differences of the order of 1 × 10⁻⁷ kgm-3, which are likely due to numerical errors. Temperature effects were neglected into density calculations in both models, which is typical in estuarine studies.

The influence of suspended sediment on stratification was analyzed considering the gradient Richardson number Ri=N2/S2, a dimensionless ratio between buoyancy and velocity shear. The buoyancy frequency, N2, was calculated as 4N2=-gρ0∂ρ∂z, where g is acceleration due to gravity and ρ0 is the mean density. The squared vertical shear S2 was calculated as 5S2=∂u∂z2+∂v∂z2, where u and v are the longitudinal and horizontal velocities, respectively. We will denote the buoyancy frequency and the gradient Richardson number as Nall2 and Riall, respectively, to indicate the use of ρall which includes both SSC and salinity. Similarly, we will denote as NSal and RiSal to indicate the use of ρSal in the passive model. The value of Ri > 0.25 is usually considered indicative of total suppression of shear-driving mixing due to density changes . To differentiate the effects of salinity and suspended sediments on the vertical density gradient, and based on the principle of linearity in differentiation from Eq. (), a linear decomposition was calculated as: 6∂ρall∂z=∂ρSal∂z+∂ρSSC∂z.

To determine the dominant periods of variability of the vertical density gradients presented above, and to establish links between stratification induced by salinity and SSC on the exchange flow, we applied a wavelet analysis to the time series of each density gradient component. This includes the total density gradient (∂ρall/∂z), the salinity-induced density gradient (∂ρSal/∂z), and the sediment component (∂ρSSC/∂z) according to () . Because the wavelet formulation developed by has a bias in the spectral estimate favoring large-scale features, we applied the wavelet rectification algorithm of allowing the comparison of the spectral peaks across scales.

The total exchange flow (TEF) analysis is a consistent framework to calculate water and salt fluxes in estuarine systems using salinity coordinates according to the Knudsen relations . In this study we follow the dividing salinity methodology where the TEF analysis framework was generalized to scenarios where the salinity ranges through a cross-section can be small , as can be the case in the Gironde Estuary. The time-averaged volume transport (Qc) of a tracer c, through a cross-sectional area A, is defined as: 7Qc(S)=∫A(S)cudA, where u is the velocity component normal to the cross-section and 〈〉 represents a temporal average. The integration in Eq. () is carried out in the area with salinity greater than S. The convention is that a positive along-channel velocity, u, is directed in-estuary. The volume flux of the tracer c per salinity class is obtained by differentiating Qc(S) with respect to S: 8qc(S)=-∂Qc(S)∂S.

The inflow and outflow components of the volume transport, or bulk values, can be obtained using no tracer, (c=1), as: 9Qin=∫SdivSmax⁡qdS,   Qout=∫Smin⁡SdivqdS, where the integrals are carried out using the extrema of Q(S) to define the salinity class Sdiv that separate inflows and outflows. The parameters Smin⁡ and Smax⁡ represent the minimum and maximum salinity that occurs in the section, respectively. The minimum and maximum salinity values, as well as the dividing salinity classes, were calculated following the algorithm developed by .

The TEF volume transports were computed using both the active (QinActive and QoutActive) and the passive (QinPassive and QoutPassive) models. Calculations of Qin+Qout were carried out in both models to check that mass was always conserved . All time-series of TEF, SSCs, gradient Richardson number, and vertical density gradients were filtered using a 25 h Godin filter to remove tidal variability . To analyze the differences between TEF volume inflows quantified on the active and passive models we applied a subtraction as, 10QinPassive-Active=QinPassive-QinActive.

To assess the longitudinal variability of QinPassive versus QinActive, three along-channel sections were considered in this study according to their location relative to the ETM (red lines, Fig. ). The middle location was chosen to be the location where the ETM is developed during the wet period while the other two were downstream and upstream of the ETM. We also computed the bulk-values of the volume transports for spring and neap tides and also over a 5 month period (February–June).

Since Telemac-3D uses an unstructured grid, pre-processing was necessary before any analysis. An interpolation of current velocities, water levels, salinity, and sediment onto a uniform grid was required before TEF quantification. The interpolation was carried out such that the grid resolution was close to the minimum distance between adjacent points of the numerical grid. The velocities were rotated to a normal axis with respect to the channel orientation using a principal-axis analysis resulting in cross-sectionally and tidally averaged secondary flows of zero, ensuring mass conservation .

Finally, we also calculated the along-channel density gradient, ∂ρ/∂x, to quantify the change in the baroclinic forcing due to sediments. For this, we considered the cross-sectional average density at the mouth and the head of the estuary. We then applied a 25 h Godin filter to remove tidal variability .

To study the importance of the SSC over density calculations, the following sections are focused on the wet-season period (February–June). During this period, the ETM is located in the downstream region of the estuary and it was well reproduced by the model (Fig. c). It spans ∼ 70 km with maximum depth-averaged concentrations close to 3 gL-1. Particularly, enhanced SSC exceeding depth averages of 4 gL-1 occurred after events of increased river discharge (exceeding 1500 m3s-1) in February, April, or June but only during spring tides.

The depth-averaged SSC shows a fortnightly cycle with enhanced concentrations during spring tides, reaching up to 3 gL-1, and decreased values during neap tides, with concentrations less than 0.2 gL-1. The concentration levels during spring tides are in agreement with those found in the Gironde indicating that the model is adequately reproducing the ETM. Lower depth-averaged SSC during neap tides are also expected as during these periods, less energetic currents allow the settlement of suspended sediments. However, our model indicates unrealistic low values near the bottom (< 0.5 gL-1) compared to previously reported concentrations . Since the focus of this work is not on SSC dynamics, we consider the results sufficiently reasonable to study the effects of SSC on water density calculations. Further, the selected settling velocity approach maintains the location of the ETM (Fig. c) which also allow us to study the effect of SSC on monthly time-scales.

To examine where SSC have a large impact over density calculations, we calculate the depth-average of the difference between the active model (ρall) and the passive model (ρSal, Fig. d). On intratidal time-scales, as SSC are transported upstream during flood and downstream during ebb, the differences span a large region covering ∼ 50 km during flooding and ∼ 40 km during ebbing. The differences increase with the tidal range, exceeding 2 gL-1 when the tidal range is maximum (> 4 m). During these periods, the differences between ρall and ρSal are maximum near the 2 gkg-1 isohaline (Fig. d). Based on the location of this maximum difference, we define three estuarine cross-sections: downstream (6.5 km from the mouth), ETM (19.6 km), and upstream (33 km), represented by vertical dashed-red lines in Fig. d. In the following section, we calculate TEF quantities focusing on these three cross-sections.

To study the effects of SSC on exchange flow, time-series of TEF volume transport (Eq. ) were calculated for both the active and passive models at three cross-channel locations (red lines in Fig. ). For simplicity, we focus only on the TEF inflow Qin for the presentation of the results (Fig. ). We also calculated the longitudinal density gradient as the density difference between the mouth and the head of the estuary over the corresponding distance.

The longitudinal density gradient appears qualitatively to be influenced by the river discharge regime. As the river discharge decreases, the longitudinal density gradient from both the active and passive models is enhanced. The combined river regime during February varied between 1500 to 2000 m3s-1 and the longitudinal density gradient varied between 0.18 to 0.25 kgm-3km-1. Towards the end of June, when the combined river discharge was below 1000 m3s-1, the longitudinal density gradient was > 0.3 kgm-3km-1.

In general, the TEF volume inflow Qin was larger at the mouth of the estuary (downstream location) and decreased towards the head (ETM and upstream locations, Fig. ). The volume inflow Qin at the downstream and the ETM sections exhibit fortnightly variability with large values during spring tides, which is enhanced at the downstream location. At this location, the inflow from both the active and passive models peaks at approximately 5000 m3s-1 during spring tides and dips below 2000 m3s-1 during neap tides (Fig. b). Similar variability occurred at the ETM location in both the active and passive models, but with lower magnitude and with other higher frequency variability (around 7 d) also detectable (Fig. c). In the case of the upstream section, there were instances during neap tides (i.e., 11 February and 25 February) that the volume Qin decreases to values near zero, likely due to the lack of salinity at those times due to increased river discharge (Fig. a and d).

The differences between the TEF volume inflow for the active (QinActive) and passive (QinPassive) models were largest during spring tides when SSCs reached their highest values. During spring tides, the longitudinal density gradient decreased in the active model compared to the passive model, although only slightly. During these periods, peak differences up to ∼ 1000 m3s-1 occurred downstream, ∼ 2000 m3s-1 at the ETM and ∼ 1000 m3s-1 upstream (Fig. b–d). The differences between models were smaller when SSCs decrease during neap tides due to large settlement of sediments. During periods of low SSC (neap tides), the TEF volume inflow QinActive and QinPassive have negligible differences of the order of O (10⁻⁷) m3s-1 in all 3 sections (Fig. b–d). Similarly, the longitudinal density gradient difference between models was < 10⁻⁴ kgm-3km-1 during neap tides.

In the downstream section during spring tides, QinActive was at times smaller and at other times larger than QinPassive, indicating that including SSC in density can either decrease or increase the TEF volume inflow (Fig. ). However, in each case, the differences were not as pronounced as those at the stations further upstream. At the ETM and upstream section, the overall effect of SSC led to a decrease in the TEF volume inflow (QinActive<QinPassive), showing that TEF volume inflows can be reduced by a factor of 2 when sediments are considered in density calculations. When considering the entire period shown in Fig.  (5 months), the bulk-value of the TEF volume inflow did not change greatly between the active and passive models (see Table ). The percentage difference was less than 4 % downstream, 1.35 % at the ETM and 2.1 % in the upstream section. However, the difference between the TEF volume inflow Qin along the estuary when considering neap and spring tides increased landward suggesting a more important role of SSCs upstream. Noticeably, the mean percentage difference of the volume inflow was more than ∼ 22 % at the ETM location and more than ∼ 70 % at the upstream section, suggesting that SSCs exert a larger influence on exchange flows at the ETM and upstream.

To further investigate the cause of the variability in the TEF volume inflow between the active and passive models, we compared the longitudinal density gradient with the difference in TEF inflows from each model (QinPassive-Active) at each along-channel location considered. We also quantified the cross-sectionally averaged vertical density gradient including salinity and SSCs (-∂ρall/∂z), only including salinity (-∂ρSal/∂z), and only including SSC (-∂ρssc/∂z) (Fig. ).

The longitudinal density gradient between the models showed large (> 0.01 kgm-3km-1) differences only during spring tides. The consistent positive difference of ∂ρ/∂xPassive-Active indicates that the longitudinal density gradient decreases in the active model or when SSC are included in water density calculations. Downstream the vertical density gradient is dominated by salinity and only during spring tides SSCs increases amplifying -∂ρssc/∂z (Fig. b). The situation is similar in the most upstream section, but the roles of salinity and SSCs are reversed due to the lack of salinity in the water column in this section. In fact, the vertical salinity gradient is less than 0.05 gkg-1m-1 throughout the study period and the vertical density gradient -∂ρall/∂z is clearly dominated by -∂ρssc/∂z (Fig. d).

While the changes in TEF volume inflow are not significant on the downstream region (Fig. b), the overall change landward was a decrease in the TEF volume inflow when the longitudinal density gradient decreased during spring tides (Fig. a). During spring tides, the vertical density gradient due to sediments (∂ρssc/∂z) was not zero at the ETM and upstream. During neap tides at the ETM, the vertical density gradient was enhanced due to salinity effects when SSCs were low. The interplay between salinity and SSCs produced a shorter variability over the vertical density gradient not observed in the other locations. A wavelet analysis was performed over 5 months of the vertical density gradient and its components at the ETM to determine the dominant frequencies of variability (Fig. ). In all three gradients, the dominant significant frequency bands were between 7–30 d. The highest energy band was at 28–32 d in the vertical density gradient (∂ρall/∂z) while the salinity and SSC components have a maximum at 14–16 d. Since the impact of suspended sediments was larger at the ETM, where the salinity and SSC components of the vertical density gradient showed a fortnightly variability, in the discussion we explore why these frequencies appear.

To understand the changes observed on TEF, here we examine the along-channel variability of the cross-sectionally averaged SSC, density, and Richardson number (and its components), averaged over 5 months (February–June) for both the active and passive models (Fig. ).

While the location of the ETM does not change considerably between the models (Fig. a and f), larger SSC occurred in the case of the passive model near the surface similar to the findings of . The locations of the isopycnals and the isohalines are similar in the downstream region of the estuary in both models (Fig. a, b, f, and g). In the upper-reaches of the estuary, the isopycnals show enhanced stratification in the active model compared to the passive model (upstream of ∼ 30 km, Fig. a and f). The most pronounced difference between the two models is the enhanced buoyancy frequency in the upper-reaches of the estuary, between ∼ 30 and ∼ 62 km, in the active model (Fig. c and h).

The squared vertical shear S2 is larger throughout the estuary, albeit slightly, in the active model, indicating that the sediments enhanced vertical shear of horizontal velocity. Despite the minimal difference in S2 between the models, the change in stratification quantified through Nall2 is large enough to shift the region where Riall > 0.25, or where mixing is expected to be suppressed by buoyancy. In the case of the passive model, the contour line of RiSal = 0.25 reached the surface at ∼ 30 km from the mouth. In the case of the active model, this region extends landward an additional 30 km, suggesting that buoyancy driven by sediment-induced stratification is strong enough to inhibit near-surface mixing upstream of the salinity intrusion limit (Fig. c, e, h, and j).

This study confirms previous studies showing that SSCs induce effects over density and stratification (Fig. ). The buoyancy frequency and gradient Richardson number aided in answering the first research question of this study: where is density impacted by SSC? The upstream stretch shows the largest differences between the active and passive models, with a stronger density gradient in the active model that increases both buoyancy frequency and gradient Richardson number. This indicates that buoyancy dominates over shear production in this upstream stretch when sediments are considered in the quantification of water density.

Using an one-dimensional vertical (1DV) numerical model, argued that the main contribution of large SSCs to estuary hydrodynamics was to modify the velocity shear, which in turn changes stratification. However, while we found that the incorporation of SSCs in water density affects the velocity shear (Fig. d and i), these changes were small: the differences were of the order of O (1 × 10⁻⁴ s-2) between the models. We find that the primary effect of SSCs was to enhance stratification causing changes of the order of O (1 × 10⁻³ s-2) (Fig. c, h and e, j). The elevated stratification caused by SSCs in the active model inhibits the vertical flux of SSC, allowing a larger accumulation of sediments near the bed (Fig. a). This explains the strengthening of the vertical gradient of SSCs near the ETM in the active model (compare Fig. a and f). These results are in agreement with who also found that the vertical sediment flux decreased due the sediment-induced density gradient. Further, the sediment-induced stratification alters settling velocities which play a major role in the maintenance of the ETM . These effects are expected to increase near the ETM due to the proximity of the salinity intrusion limit and large SSCs as well as flocculation or hindered settling . In addition, sediment-induced stratification can alter the shape of the ETM with a larger extension upstream compared to downstream as was found in our model (Fig. a compared to f). Because the extension of the ETM is larger when sediments are included in water density, the region where SSCs dampen shear-induced mixing is also extended upstream, explaining the larger region where the Ri > 0.25 (Fig. e and j).

found that sediment-induced density gradients are pronounced only when salinity stratification is also present. In our case, the effects of stratification caused by SSCs were more relevant in regions where they correspond to a large fraction of the total stratification, but did not completely dominate, suggesting that the salinity stratification is also important. At the downstream location, the vertical density gradient (∂ρall/∂z) is largely dominated by salinity (∂ρSal/∂z) as the vertical density gradient with sediments (∂ρssc/∂z) is negligible except for small increases during spring tides (Fig. b). The upstream location is close to the salinity intrusion limit (Fig. c and d). Because of this, the vertical density gradient computed only with salt (∂ρSal/∂z) is small in this section (Fig. d) allowing the SSCs to play a larger role in suppressing mixing (Fig. ).

At the ETM we found that salinity and SSCs enhanced the total vertical density gradient (∂ρall/∂z) at different phases of the spring-neap cycle. The magnitudes of ∂ρSal/∂z and ∂ρssc/∂z were of similar order, except for three neap tides when ∂ρSal/∂z exceeded ∂ρssc/∂z (11 March, 12 April, 9 May; Fig. b), but featured different fortnightly variability. The weaker currents during neap tides affected density in two ways: (1) they allow the settlement of suspended sediments decreasing the vertical SSC gradient and (2) the vertical salinity gradient increases due to less intense mixing. These two effects cause the salinity to dominate the ∂ρall/∂z at the ETM during neap tides. Similarly, there are two effects on density during spring tides: (1) the resuspension of sediments intensify the vertical SSC gradient and (2) salinity-induced stratification decreases because of enhanced turbulent mixing. This enhances ∂ρssc/∂z and decreases ∂ρSal/∂z during spring tides, and both are modulated on the fortnightly cycle, but on opposite phases (Fig. c). It has to be noted that the model did not reproduce benthic fluid mud layers, where SSC can reach 100 gL-1 over 1 m thick. These layers form typically in neap tides, and can significantly affect near-bed turbulence due to high local density stratification and increased water viscosity .

To extract the dominant periods of variability, we applied the wavelet analysis to each of the three vertical density gradients (Fig. ). The vertical density gradient with only salinity (∂ρSal/∂z) shows a dominant fortnightly periodicity with a lesser lunar monthly (28–32 d) periodicity. The vertical density gradient with only SSCs (∂ρssc/∂z) also shows a dominant fortnightly periodicity, with very little energy at other periodicities. However, the total vertical density gradient (∂ρall/∂z) shows several additional dominant periods. The modulation of the fortnightly cycle of the ∂ρSal/∂z and ∂ρssc/∂z interacts to produce a dominant variability of 7.35 d in ∂ρall/∂z. The fortnightly variability of the vertical SSC gradient (14.7 d) and the monthly lunar variability of the salinity (27.55 d) also interact to create a distortion (subtraction) of 9.51 d and a modulation (sum) of 31.84 d on ∂ρall/∂z (Fig. e), just like compound tides . Because of these interactions the band of 28–32 d is the most energetic band for the total vertical density gradient (∂ρall/∂z). An analysis on the passive model revealed that this frequency band is not present when SSCs are not considered in water density calculations (not shown). These results highlight that neglecting SSCs in the quantification of water density will exclude potentially influential dynamics affecting stratification in estuaries, in particular close to the ETM.

We have found that the omission of suspended sediments in the calculation of water density leads to differences in TEF values (Fig.  and Table ). The percent difference of the bulk-values from the active to passive model when quantified over the entire study period (5 months) were found to be relatively small (less than 4 %), likely because of the enhancement of SSCs during only the spring tides, allowing for their contribution to be diminished when averaged over long time-periods. This was reinforced by the quantification of TEF bulk values during neap and spring tides separately, which have percent differences between the active and passive models that were considerably larger, specifically at the upstream location (up to 70 %).

Using an analytical model, showed that the sediment-induced density gradient enhances the salinity-driven estuarine circulation upstream of the ETM whereas it causes a decrease downstream of the ETM. Similar results were later confirmed by a 3D modeling study in the Yangtze estuary . Since we are not considering estuarine circulation but rather calculations of the inflow volume transport using salinity coordinates (TEF), we cannot directly compare results with those of , but some linkages can be made. Our results show that the most significant impact of SSCs on the TEF volume inflow was observed at the ETM and at the upstream location. Although slightly, the bulk-values over the entire period agree with both papers as the TEF volume inflow decreases at the downstream and the ETM locations whereas it increases at the upstream location (Table ). However, SSC-induced effects were not in agreement with either of the above mentioned studies when considering tidal bulk-values for neap and spring. Both of these show a decrease in the active model indicating that the SSCs induced effect was to decrease the TEF volume inflows on tidal scales. In particular, at the ETM and the most landward location, the SSCs tended to decrease the TEF inflow (QinPassive-Active>0) rather than increase it (Fig. b and c). The most pronounced changes in QinPassive-Active occurred during spring tides at the ETM and upstream when SSCs reached concentrations of ∼ 6 and ∼ 4 gL-1, respectively. At the downstream location QinPassive-Active was overall smaller than at the ETM and upstream locations, even during spring tides, likely due to the location being far enough from the ETM that ∂ρssc/∂z was negligible. The changes in the longitudinal density gradient are likely the cause of the temporal modulation of QinPassive-Active.

Figure  schematizes the changes due to SSC. The incorporation of SSC in water density calculations increases the stratification in the upper-reaches of the estuary. Despite these changes not being large, they decrease the depth-averaged longitudinal density gradient, which in turn allows for less intense exchange flows than when sediments are not included in density calculations (Fig. ). The changes in the fortnightly variability of ∂ρssc/∂z and ∂ρSal/∂z at the ETM produces a near weekly modulation of the vertical density gradient (Fig. ). Both the vertical and horizontal dynamics will ultimately be neglected when SSCs are not incorporated into water density calculations, causing overestimates of the exchange inflow Qin leading to incorrect assumptions about systems.

This study was designed to analyze the contribution of SSCs to water density and the TEF in a macrotidal and turbid estuary. To accomplish this goal several assumptions and simplifications were made. It is important to note that sediment dynamics are very sensitive to the parametrization of settling velocity. Van Leussen flocculation formulation has proven effective in reproducing the position of the ETM, with fairly realistic SSC on spring tides but with too low values during neaps tides. Vertical gradients of sediments and the effect of near-bed SSC on stratification were thus underestimated during neaps.

More research is needed to determine the extent of the present results with consideration of different particle sizes, settling velocities, and sediment concentrations. As every parameterization, the van Leussen parameterization used in this study has advantages and limitations for reproducing SSC observations and ETM dynamics . While this formulation has clear advantages for reproducing the upstream migration of the ETM and capturing high SSC levels , it also tends to underestimate SSC near the bottom during neap tides which could likely affect vertical fluxes. The extension of our results to other systems required that the model is able to reproduce to right orders of magnitude of SSC in each system, and thus more careful calibration of settling velocity is recommended. Further, we only consider nine layers in this model due to computational constraints. Although we use a mesh transformation that increases the resolution near the bed, future studies should use a larger number of layers if possible to correctly resolve larger gradients near the bed.

Also relevant in this study is the consideration of non-linear effects between salinity and SSCs when calculating water density. We followed the previously employed assumption that salinity and suspended sediments can be added linearly to the water density calculations used by several authors i.e.,. In the study by , for example, the authors include non-linear effects between salinity and SSC (their Eq. 7), but they implicitly work on a linear relationship ignoring the non-linear effects of salinity and SSCs. This was likely because the contribution of the non-linear effects was regarded as small relative to the linear contributions. More recently, estimated the non-linear interactions between salinity and SSC using numerical simulations. Among their findings, the authors found that the total stratification resulting from salinity and SSC was significantly different than the sum of the individual effects. Further, they also identify that the non-linear interaction between the salinity-induced stratification and the sediment-induced stratification vary from stabilizing to destabilizing depending on the tidal phase. Despite the limitations of the study as a one-dimensional numerical model, the findings by reveal that the consideration of non-linear effects between salinity and SSC can be important in the study of suspended sediments and thus in estuarine exchange flow studies as flood-ebb asymmetries could also cause exchange flows similarly to the strain-induced periodic stratification, SIPS . A comparison between the water density calculated following Eqs. ()–(), and the formulation of , showed maximum differences of 0.3836 kgm-3 (not shown). These differences were maximum near the ETM during spring tide with larger differences near the bottom than near the surface. The small magnitude of the non-linear effects, less than 1 % in our case, justifies the use of the simplification where both sediments and salinity effects can be added linearly. Nevertheless, although the magnitude of the non-linear effects is small, the importance of this variability and the magnitude of the effects caused by it require further research and were not explored in this study.

Finally, the use of TEF in hyperturbid systems must be interpreted carefully. Because of the use of salinity coordinates, the spatial variability of the volume transports (the TEF inflow and outflow) can only be assumed in relation to where one would expect salinity classes to be (i.e., where water is brackish versus the upstream riverine section that may still be tidal). However, hyperturbid systems could present stratification where there is no salinity. Further, a consequence of the sediment-induced stratification is the existence of inverted salinity profiles. These have been reported in systems with large SSCs such as the Gironde Estuary , the Ems estuary , the Ouse estuary or the Huanghe . The existence of these inverse salinity profiles challenges the assumption that higher salinity values must be closer to the bottom advising caution on how to interpret TEF profiles in hyperturbid systems. As a final remark, it is important to highlight that this study was focused on high-river regime conditions. The conditions that exist during low river regime will likely modify the dynamics along the estuary and therefore warrants further investigation.