Hydrodynamic Modeling of the St. Lawrence Fluvial Estuary. II: Reproduction of Spatial and Temporal Patterns

Detailed hydrodynamic data were collected in the SLFE during a field campaign conducted in the summer of 2009, as summarized in Part I. Data from an extended tide gauge network composed of 29 stations were obtained, along with water-level and velocity data simultaneously acquired along 13 transects [cf. Matte et al. (2017), Fig. 1], each repeatedly surveyed by boat during approximately one tidal cycle. At each measurement transect, the irregular mixed space–time data series were interpolated in space and in time, following a procedure developed by Matte et al. (2014b), to allow reconstruction of continuous and synoptic fields and facilitate comparison with model results. Details of the data processing and interpolation errors have been provided by Matte et al. (2014b, c).

In Part I, a replicative validation was performed, focusing on a comparison of observed and modeled water levels at the tide gauges and discharges at the transects. In this paper, a process-based validation is presented as a demonstration of the model’s capability to reproduce the real system dynamics. The same 15-day simulation periods starting on June 14, 2009, 00:00:00 EDT, and August 19, 2009, 00:00:00 EDT, where transect data were acquired were used for this purpose. Measured and simulated data were used for direct comparisons, whereas quantities representative of the tidal dynamics were extracted from the observed and modeled fields and compared both qualitatively and quantitatively. The validation process involved the following steps:

The model was validated by comparison with water-level and velocity measurements at the surveyed transects. Results are presented in Figs. 1–4 for a selected river cross section located at Grondines [river kilometer (rkm) 179.5].

Observed and modeled water levels are shown in Fig. 1. The agreement between the two was found to be good, both in terms of synchronicity of the signals and reproducibility of the lateral patterns. Of particular interest is the lateral gradient that formed during the falling tide between 1.0 and 1.7 km from the south shore, which is responsible for the emptying of the tidal flats into the channel. Variables extracted from the water-level fields are shown in Fig. 2, allowing a quantitative assessment of model performance at the transect. The timing and heights of HW and LW and tidal range are plotted as a function of cross-sectional distance. LW occurred slightly (∼1–5 min) earlier in the model data than in the observed data, with a later arrival and a higher level on the southern tidal flat (first kilometer). Modeled LW was also ∼10 cm higher than expected, but it exhibited lateral gradients similar to those in the observations. The timing of HW in the model was relatively similar to that in the observations but showed less lateral variability. The modeled heights of HW were also higher than the observed heights, with the differences being smaller than those for LW (<10 cm); they remained almost unchanged across the section. Overall, the LW is more sensitive than HW to lateral gradients in bathymetry. As a result, the tidal ranges were larger in the channel than on the shoal at Grondines. They were lower in the model compared with observations, but they followed a similar trend. Slightly decreasing friction near Grondines would potentially reduce the local predicted tidal heights and increase tidal range. However, the observed differences mostly remain within measurements errors (Matte et al. 2014b). They can also be partly explained by differences between the bathymetry measured along the section and that obtained from the Canadian Hydrographic Service (CHS) soundings; they are referred to as observed and modeled bathymetries in bottom panel of Fig. 2, the latter being the one actually incorporated in the NTM.

Depth-averaged u and v velocity components are shown in Fig. 3, corresponding to the along- and cross-channel velocities, respectively. Current reversals occurred only on the north shore during the surveyed period (identified as a white contour in Fig. 3). The highest u velocities were concentrated in the channel, whereas v velocities presented two distinct regions characterized by large positive values (oriented to the north). The southernmost region is the result of the tidal flats emptying into the channel, in concordance with the observed lateral gradients in water levels (cf. Fig. 1). The second region is in the channel and likely corresponds to the effects of local channel curvature on the velocity directions. These general flow features were adequately reproduced by the model, suggesting that the lateral variations in topography and friction were well captured. Variables extracted from the velocity fields are presented in Fig. 4. The modeled maximum u and v velocities were found to have patterns very similar to those of the observations, although they were slightly higher in the tidal flat, between 1.0 and 1.7 km. Part of these discrepancies may be explained by interpolation errors in the observed data, which amount to approximately 0.1 m/s at Grondines (Matte et al. 2014b). Conversely, the observed times of slack water in both the ebb-to-flood and flood-to-ebb transitions [i.e. the low-water slack (LWS) and high-water slack (HWS)] were found to be relatively well synchronized with the model. Current reversals, however, occurred within a shorter distance from the north shore in the model. Finally, the inclination of the tidal ellipse formed by the velocity vector over a tidal cycle (a measure of the relative strength of the lateral and longitudinal velocity components) presented generally small differences between the model and observations. The highest inclinations were found in the southern tidal flat, where lateral exchanges are maximal.

Although comparisons are herein limited to one cross section, detailed results for all surveyed transects have been given by Matte (2014, Appendix 3).

An appreciation of the longitudinal variations in tidal amplitude, signal distortion, and neap–spring variability in the system can be gained by comparing the observed and modeled water levels for the two simulation periods of June and August 2009 (Fig. 5). From downstream to upstream, the tidal wave is progressively damped and distorted, with significantly shorter rising than falling tides. Generally, the observed water levels were well reproduced by the model at the stations during both neap and spring tides. Fortnightly variations in MWL were also well captured at upstream stations [e.g., Trois-Rivières (rkm 231) and Bécancour (rkm 217)]. However, the differences between observed and modeled water levels at Bécancour were larger in August than June, with MWL being lower than expected in August (cf. Matte et al. 2017, Table 3). This points toward a gradual underestimation of friction in the Gentilly shoal, located 2 km downstream of Bécancour, following the growth of macrophytes during summer. The same friction field (cf. Matte et al. 2017, Fig. 3) was used during both simulation periods, but time-varying friction based on density and growth phase factors could be implemented to take this effect into account (Morin et al. 2000).

The observed and modeled signals at the stations were used to extract information on tidal range, HHW, MWL, and LLW. They are presented in Fig. 6 and compared with modeled longitudinal profiles aligned with the thalweg for the simulation of August 2009. Tidal ranges were significantly reduced landward, exceeding 6 m downstream during spring tides and almost vanishing upstream during neap tides. Most of the damping occurred between Portneuf (rkm 163.5) and Cap-à-la-Roche (rkm 186) as a result of the presence of rapids associated with a sharp increase of the bottom slope. Over the neap–spring cycle, modulations of the tidal ranges were significantly more pronounced at downstream stations, with differences in tidal range between spring and neap tides exceeding 3 m at Saint-Joseph-de-la-Rive (rkm 0). More specifically, during the analyzed period, observed tidal ranges were the largest in the St. Lawrence at Saint-Joseph-de-la-Rive (rkm 0) during spring tides, whereas during neap tides, they reached their maximum at Saint-François, about 66 rkm upstream. In other words, tidal amplification occurring in the estuary persists further landward during neap tides than spring tides. Overall, these features were well captured by the model, as shown by the proximity of the observed and modeled data (represented by circles and dots in Fig. 6, respectively). However, the model tended to push the amplitude maximum upstream toward Lauzon (rkm 100) during neap tides, possibly as a result of underestimated friction between the Orleans Island and the downstream boundary. Differences between the station data and the longitudinal profiles are an indication of the lateral variability in tidal ranges throughout the system. Smaller tidal ranges near the shore than in the channel were generally observed as the extent of tidal flats increased, for example, between Deschambault (rkm 168) and Cap-à-la-Roche (rkm 186), as also shown in Fig. 2. These smaller tidal ranges correlated with larger MWL on the shore.

Both HHW and MWL were systematically higher on spring tides than on neap or mean tides. Longitudinal variations of HHW were, however, smoother (almost linear landward of the Quebec Bridge; rkm 115) than MWL and LLW because they are less affected by longitudinal changes in bottom slope. In contrast, at the neap–spring scale, HHWs were quite variable throughout the system, with a range of variability decreasing landward. Downstream, differences in HHW between spring and neap tides were similar to those in LLW, as they mostly arise from the amplitude difference between M₂ and S₂. LLWs were higher on neap tides than on spring tides, but they presented almost identical heights over roughly 115 rkm during neap tides, from Saint-Joseph-de-la-Rive (rkm 0) to the Quebec Bridge (rkm 115). This follows the amplification of the tidal ranges only occurring between these stations during neap tides. The neap–spring modulations of MWL gradually increased from Saint-Joseph-de-la-Rive (rkm 0) landward, reaching a maximum between Portneuf (rkm 163.5) and Cap-à-la-Roche (rkm 186). Upstream, even though the tidal range became weak, the MWL still varied by more than 0.5 m over the neap–spring cycle as a result of the nonlinear growth of low-frequency compound tides (e.g., MSf), thus exceeding the semidiurnal tide in amplitude. As a result, both HHW and LLW presented larger variations than what tidal range alone could explain. Furthermore, because the MWL was much lower on neap tides, the LLW also occurs on neap tides at upstream locations. This shift in the relative levels of LLW between neap and spring tides typically occurs around Deschambault (rkm 168), where the amplitude of the fortnightly tidal component (MSf) is equal to that of S₂ (Hoitink and Jay 2016). However, it could appear sooner or later (in the rkm sense) depending on tidal and river flow conditions. In fact, in the present example, this transition seemed to occur earlier (around Neuville; rkm 138), although this may be a result of the rather short simulation period used to extract the tidal datum levels, comprising only one neap–spring cycle.

Lateral differences between the near-shore stations and the channel profiles were the most significant with HHW, especially during neap tides. Similarly, the discrepancies between observed and modeled HHW were the largest among all tidal datum levels. These differences could be attributable to lateral gradients in topography or friction, but further investigation is needed to identify the exact source of variability.

Tidal velocities were also characterized by strong longitudinal and neap–spring variability (Fig. 7). Maximum ebb velocities generally occur during the falling tide, slightly before low tide. They were the strongest around Íle aux Coudres (cf. Matte et al. 2017, Fig. 1) and under the Québec Bridge (rkm 115) and Richelieu rapids near Deschambault (rkm 168), where they exceeded 3 m/s under spring-tide conditions. Downstream, ebb velocities during spring tides were approximately twice as strong as during neap tides. This neap–spring variability was reduced moving upstream, up to Deschambault, landward of which the tidal range had practically no effect on peak ebb velocities, as they were mostly controlled by the river discharge. In contrast, peak flood velocities exhibited marked variations between neap- and spring-tide conditions throughout the system. They were the highest at the Québec Bridge constriction, the narrowest and deepest section of the St. Lawrence, but not so strong at Deschambault compared with its respective ebb velocities. This is attributable to the rapid widening of the Deschambault cross section on the rising tide, which is associated with large intertidal flats, proportionally reducing the flood velocities as they get flooded.

Another manifestation of the neap–spring variability appears in the location of the upstream limit of current reversal. This is illustrated in Fig. 7 by the flood velocities crossing zero (i.e., reaching slack current) before becoming positive. In the present case, the upstream limit of current reversals moved between rkm 154 (neap tide) and rkm 200 (spring tide), but it is expected to vary even further in each direction under more extreme conditions of tidal range and river flow. Upstream of this limit, the tidal current was decelerated during the rising tide and accelerated during the falling tide. Lateral patterns in flow reversal were also observed, as illustrated in Fig. 3 by the white contours identifying the slack waters. Overall, these lateral patterns were characterized by current reversals being lagged and occurring earlier near the shore than in the channel [see also Matte (2014), Appendix 3].

Fig. 8 provides a detailed picture of the longitudinal and temporal variability of water levels and velocities, separately for neap and spring tides, from which the longitudinal profiles of Figs. 6 and 7 were extracted. Although Fig. 8 summarizes some of the information noted previously, the following additional features are worthy of note:

Computed tidal discharges in the north and south arms of Orleans Island are presented in Fig. 9 to illustrate flow distribution around the island. Boat measurements in the two arms were taken 1 day apart from each other (Matte et al. 2014b) so that the river discharge conditions during each survey would be comparable. Similarly, the tidal range only slightly decreased between the 2 days (cf. Fig. 5). At both locations, observed and modeled discharges were found to compare very well over the tidal cycle, meaning that flow was well distributed between the channels. The average discharge at Québec was 11,600 m³/s during the measurement period, but the peak discharge exceeded 60,000 m³/s during ebb tide and reached almost the same (negative) value during flood tide in the south arm of Orleans Island. In the north arm, another 10,000 m³/s was discharged during ebb tide at its peak. These differences in discharge, measured during spring tide, follow the geometry of the channels, with the higher depths and wider sections being encountered in the south arm. However, to see how flow is partitioned in an average sense, the residual (tidally averaged) discharges should be computed at the two branches; such a comparison could not be performed here because of the length of the available discharge records, which did not exceed one tidal cycle.

Fig. 10 presents simulation results at the junction of Orleans Island at different stages of the tidal cycle. Results are presented for a spring tide, measured at Lauzon (rkm 100) on June 24, 2009, under approximately average discharge conditions (11,100 m³/s). Arrows indicate the mean direction of currents and recirculations. At high tide, currents were reversed in both arms of Orleans Island, with velocities reaching approximately 1.5 m/s in the deepest regions. One hour after HW, currents were weakened, and recirculation appeared in shallow regions where water was redirected downstream. Two hours after HW, currents were oriented downstream and increased in importance with the falling tide; tidal flats were also progressively dried. Currents were at their maximum approximately 1 hour before low tide, with velocities reaching 2.3 m/s. At low tide, currents started decreasing; they rapidly changed in the following hours as a result of the more abrupt rising tide. One hour after LW, slack water had reached Lauzon, but ebb currents were still strong in the north arm of Orleans Island. Two hours after LW, currents were completely reversed in the south arm; they were partly diverted into the north arm and partly directed upstream. Slack water finally arrived in the north arm 1 hour before the next HW, and currents were completely reversed thereafter for approximately the next 3 hours.

The flow patterns just described are in concordance with continuous water-level and velocity measurements taken at the junction of Orleans Island during the same tidal cycle as the one presented in Fig. 10 [cf. Matte (2014), Appendix 3].

Instantaneous momentum balances were computed for the spring tide of June 24, 2009, 08:00:00 EDT. Each term of the balance appears in the momentum conservation of the shallow-water equations given by Matte et al. [2017, Eq. (4)]. Their moduli are reported in Fig. 11, calculated from the x and y components of the balance. This snapshot encompasses the various features that can be observed during a tidal cycle (e.g., slack currents, peak ebb and flood currents), in contrast to tidally averaged momentum balances (not shown); the latter would be slightly less contrasted spatially but would highlight the regions where each term is the most influential in an average sense. The hydrodynamic conditions prevailing at the time of the snapshot are shown in Figs. 11(a and b). Upstream, the flow was unidirectional down to approximately Batiscan (rkm 199). A slack water before flood (or LWS) occurred at Deschambault (rkm 168), as shown by near-zero velocities and by a minimum in water levels close by [Figs. 11(a and b)]. This was then followed by a flood tide where currents were reversed and water-level gradients were positive (in the seaward direction). A slack before ebb (or HWS) was observed at the eastern end of Orleans Island, followed by increasing ebb currents in the seaward direction that were accompanied by a sharp decrease in water levels. Note that neither the LWS nor the HWS was exactly synchronized with the water-level extrema. They were both located downstream (or occurred later, in a time-reference frame) of the minimum and maximum in water levels, respectively.

Figs. 11(c–h) show the contribution of local acceleration $\left|\partial \left(H\mathbf{u}\right)/\partial t\right|$, advective acceleration $\left|\nabla ·\left(H\mathbf{u}\mathbf{u}\right)\right|$, pressure gradient $\left|gH\nabla h\right|$, bottom friction $\left|{\mathit{\tau }}^b/\rho \right|$, Coriolis acceleration $\left|f_{c}H\mathbf{u}\right|$, and turbulent viscosity $\left|\nabla ·\left({\nu }_{t}H\nabla \mathbf{u}\right)\right|$ to the momentum balance, respectively [cf. Matte et al. 2017, Eqs. (4a) and (4b)]. Clearly, the dynamic balance was dominated by the local acceleration and pressure gradients, which are the major driving force of the flow. At both full ebb and full flood, local and advective accelerations, bottom friction, and, to a lesser extent, Coriolis acceleration balanced the pressure gradient. In the two upstream regions of high velocities, the local and advective accelerations were comparable to the pressure gradient because of the relatively low-water-level slopes. In contrast, in the downstream ebb, the flow was primarily driven by gravity because of the much-steeper gradients of water levels. Ratios calculated between the terms (not presented) show that bottom friction dominated over the effects of pressure gradient almost exclusively in shallow areas (e.g., intertidal flats, shoals). The Coriolis acceleration, for its part, typically exceeded the advective acceleration in regions where velocities were lower than 1 m/s. As for turbulence, it was 1 order of magnitude smaller than the other terms. The highest values were located in the deepest portions of the river, in front of Québec and Íle aux Coudres, and around engineering structures and islands. Turbulence was also higher in the channel than in the intertidal regions. Near slack, only the pressure gradient remained significant, which was balanced by local acceleration.

Hench and Luettich (2003) analyzed the transient momentum balances at shallow barotropic tidal inlets and found that they oscillated between two dynamical states, depending on whether the phase of the tide was near maximum ebb or flood or near slack. Here, similar analyzes were carried out with complete coverage of the tidal cycle in space rather than in time. Similar conclusions can be drawn from the analyzed fields with respect to the differing dynamic states observed at high velocity versus near slack. Near maximum ebb or flood, the pressure gradients were balanced by the acceleration and bottom friction terms. As the dynamic state approached slack waters, the velocities were reduced, and the balance shifted between the pressure gradient and local acceleration only. Lateral variations in the respective contribution of each force could also be observed and are associated with cross-channel gradients in bathymetry and friction.

In the SLFE, large tidal ranges are responsible for rapid variations in flow conditions and in the wetted areas. At downstream locations, where tidal ranges exceed 6 m, increases in water levels of more than 1 m/h can be observed during the rising tide. These variations are the main driving force behind the flooding–drying processes, which play a key role not only in the transport of water over shallow areas but also in the strength of tidal currents in the main river channel. In fact, the convergence of lateral flow toward the channel tends to add mass and increase the magnitude of the along-estuary flow in the channel during ebb (Valle-Levinson et al. 2000). In contrast, the filling of intertidal flats during the rising tide reduces the flood velocities as part of the flow is redirected toward the shores. Ignoring these lateral exchanges could lead to significant under- and/or overestimation of the amplitude of tidal currents (Zheng et al. 2003).

Observations in the SLFE and other large tidal rivers [e.g., Jay et al. (2015)] have shown that LWs are higher on the tidal flats with respect to the channel (cf. Fig. 2) and may even be truncated when the floodplain is dried, depending on river flow and tidal conditions. Conversely, HWs remain relatively constant across the river section. As a result, tidal ranges are overall larger in the main channel than in the floodplain. Moreover, as observed by Valle-Levinson et al. (2000), lateral convergences are produced by phase lags of the tidal flow between the channel and the shoals, with magnitudes that are proportional to the along-estuary bathymetry gradients and to the tidal range. This is corroborated by results in the SLFE, where HW and LW timings were found to occur later over shallow topography than in the deeper channel, with the time lags of LWs being more significant than those of HWs (cf. Fig. 2). This yields a more pronounced tidal asymmetry in shallow areas. Laterally, these differences in amplitude and timing create gradients in velocity directing water toward the channel during ebb and toward the shores during flood.

Accurate representation of the floodplain topography, channel bathymetry, and bottom friction is therefore essential from a modeling perspective because they directly affect the magnitudes of these exchanges. In the SLFE, the availability of high-resolution LIDAR data and bathymetric soundings and detailed cross-sectional hydrodynamic data (i.e., simultaneous water levels and velocities) combined with a high-resolution finite-element mesh allowed for a precise description and validation of the flooding–drying processes occurring over shallow topography.

Factors influencing the strength of the tidal forcing over the tidal month include the neap–spring effect, the apogee–perigee effect, and the lunar declination, which is responsible for the diurnal inequality (Jay et al. 1990). Neap–spring variability in tidal systems is a well-known phenomenon that arises from the interaction of the dominant lunar and solar semidiurnal tides (M₂ and S₂, respectively), whereas apogee-perigee modulations and the diurnal inequality involve interactions between M₂ and N₂, and K₁ and O₁, respectively. In tidal rivers, the effects of these interactions are numerous, three of which are the longitudinal displacement of the tidal amplitude maximum [e.g., Jay et al. (1990)]; the fortnightly modulation of tidal ranges, HW, MWL, and LW [e.g., LeBlond (1979)]; and the longitudinal displacement of the upstream limit of current reversal [e.g., Jay (1984)].

As a result of topographic funneling effects, tides in the St. Lawrence are amplified as they enter the gulf and estuary. They reach their maximum amplitude between Íle aux Coudres and Orleans Island (Matte et al. 2017; Fig. 1), depending on the phase on the neap–spring tidal cycle and river discharge. The longitudinal position of the tidal amplitude maximum can be explained in terms of the tidal energy budget, where the tidal energy flux divergence is balanced against dissipation (Jay et al. 1990). Whereas the former is proportional to the square of the velocity, the latter is cubic in velocity, meaning that dissipation increases more than the incoming energy flux divergence as tidal range increases. This tends to damp the tide earlier and push any amplitude maximum seaward on spring tides. As a result, less energy is transmitted upriver, and the differences in tidal range between the neap and spring tides are smaller upstream than at the mouth (cf. Fig. 6).

In the SLFE, tides are increasingly distorted and damped as they propagate upriver as a result of nonlinear interactions of the incoming tide with river flow, friction, and topography. The respective contribution of these factors to the system’s internal variability is a function of both time and space, thus yielding distinct spatiotemporal patterns in water levels and velocities. Among these patterns are, for example, the flooding–drying processes occurring over shallow intertidal flats, marked changes in the tidal behavior associated with breaks in morphology [e.g., Matte et al. (2014a); Sassi et al. (2012)], and flow division at tidal junctions, for which topography and friction are known to be critical components (Buschman et al. 2010). In general, the timing of current reversals is strongly dependent on the geometry of the channel, and in the case of multiple channels (e.g., around the Orleans Island), their respective geometries will affect both tidal propagation and flow distribution. Cyclic exchanges occurring between the south and north arms of the Orleans Island are one example of the effects of asynchronous tidal propagation.

From downstream to upstream, tidal energy is progressively transferred from major astronomical constituents to overtides and subtidal frequencies. Overtides contribute to tidal asymmetry (i.e., wave steepening) by exerting an influence on the amplitude and timing of HW and LW. Low-frequency compound tides, for their part, contribute to the lowering of MWLs and LWs during neap tides with respect to spring tides (Aubrey and Speer 1985; Godin 1984, 1999; Jay et al. 2015; LeBlond 1978, 1979; Nidzieko 2010; Speer and Aubrey 1985). These effects are modulated by the river discharge, which adds to frictional damping and alters constituent amplitudes by stimulating energy transfers between frequency bands (Godin 1985, 1999; Jay and Flinchem 1997). In the St. Lawrence, the neap–spring reversal of MWLs begins seaward of the limit of salinity intrusion (which moves between Orleans Island and Íle aux Coudres), whereas the neap–spring reversal of LLWs more or less begins at Deschambault (rkm 168), that is, ∼100 rkm upstream of the salinity intrusion limit. Roughly, this corresponds to the point where the amplitude of MSf equals that of S₂ (Hoitink and Jay 2016). It also coincides with the location where the amplitude of MSf is maximal in the SLFE and where a change in tidal asymmetry occurs (Matte et al. 2014a). The amplitude of the fortnightly tide eventually exceeds that of the semidiurnal tide near Trois-Rivières (rkm 231), approximately 160 rkm beyond the salinity intrusion limit. In sum, the SLFE can be divided into four regions (Matte et al. 2014a): (1) a tide-dominated reach downstream of Portneuf (rkm 0–163.5); (2) a transitional reach between the tidal and tidal-fluvial regimes (rkm 163.5–186), characterized by a rapid increase in bottom slope at the Richelieu Rapid near Deschambault (rkm 168); (3) a tidal-fluvial reach from Cap-à-la-Roche to Laviolette Bridge near Trois-Rivières (rkm 186–235), acting as a major restriction to the flow; and (4) a river-dominated reach upstream (rkm 235–302), where most of the short-period tide gets extinguished but where long-period oscillations persist.

Downstream, where tidal flows are bidirectional, the tidal storage volume can be estimated from the volume differences between HWS and LWS (Zhang et al. 2015). The limit where currents cease to reverse (i.e., where the HWS and LWS coincide) moves between Regions (1) and (3) in the SLFE as a function of tidal range and river discharge. Although the tidal wave propagates beyond this limit, the water is no longer transported upstream by the tidal current during flood tide (cf. Fig. 7). Instead, the currents experience a tidal backwater effect, where they decelerate during the rising tide and accelerate during the falling tide as water is periodically stored and released. Similarly, at the neap–spring scale, water is temporarily stored in the system during spring tide and released as the neap tide approaches, with a direct consequence on flood currents but little effect on ebb currents in the tidal-fluvial reach (cf. Fig. 7). The main reason for this is that during spring tide, a higher surface-level gradient is needed to realize the same discharge than during neap tide (Hoitink and Jay 2016), causing a fortnightly oscillation in water levels and leaving the outgoing flow almost unaffected. On the long term, river–tide interaction creates an oscillatory gradient of the MWL and steepens the surface-level profile as a result of the enhanced subtidal friction, up to the point of tidal extinction or even beyond (Buschman et al. 2009, 2010; Sassi and Hoitink 2013).