The hydrodynamic datasets, used for calibration and validated with independent observations, are the same as those used in Muñoz-López et al. (2024), where a detailed description is provided. The observations used for validation include water-level records from nine tide gauges, which provide good coverage of the GE, velocity profiles collected at a single point located in the middle stretch of the estuary, and conductivity and water temperature from SAIH at Veta La Palma and Isla Mínima (see locations in Figure 1A ). SAIH observations from 2020 to the present are freely available in real-time. Salinity datasets are derived from conductivity and water temperature observations using the thermodynamic equation for seawater (https://www.teos-10.org/) and, in this case, the same datasets are used for both calibration and validation.

The hydrodynamic validation methodology follows that of Muñoz-López et al. (2024) and is briefly summarized here for completeness. Harmonic constants derived from water level observations were compared with those obtained from the model via harmonic analysis. The comparison shows that the amplitude differences for the principal M₂ constituent remain below 3 cm throughout the estuary, and phase differences do not exceed 10 minutes (see Figure 2 in Muñoz-López et al., 2024). Time series of observed and modeled water levels at two representative stations located in the lower and upper stretches of the GE (see Figure 1 , Muñoz-López et al., 2024) also show very good agreement, with Pearson correlation coefficients of 0.981 and 0.985, and a root mean square errors (RMSE) of 1.3 cm and 1.1 cm, respectively. Velocity profiles recorded in the middle stretch of the estuary and model outputs at the same location show similarly good agreement, with RMSE values below 5 cm/s (see Figure 3 in Muñoz-López et al., 2024). The reader is referred to this work for a more detailed assessment of model performance.

Using a 1D numerical model, Siles-Ajamil et al. (2019) suggested that tidal flats in the GE influence salinity distribution when they are coupled to the main channel through a relatively wide inlets (i.e., wider than ∼100 m). The topic is revisited here using the more sophisticated 3D model described above. The year 2021 was selected as a representative period for model validation and for evaluating the model’s ability to reproduce the observed salinity variability across the estuary, based on the availability of observational data.

The blue line in Figures 2B, C (which is hidden by the yellow line before May 2021) shows that the model slightly underestimates the observed salinity until May-June. This line represents the model’s output without manipulation of the freshwater inputs to the estuary, an aspect that needs to be revisited in the light the following observations: from May to September, observations show a steady increase in salinity that is not captured by the model, which fluctuates around a moderately constant value. From September onwards, the modeled salinity presents a clear increasing trend that is not reflected in the observations, which show a much weaker trend, if any. At the end of the year, a large freshwater discharge of about 200 m³/s brings the two salinity series ​​closer together, demonstrating the good response of the model to such events. At the tidal scale ( Figures 2D, E ) the model accurately reproduces the timing of the cycle, but neither the amplitude nor the “mean” value, which is lower, as explained above. A likely cause of the discrepancies between model and observations during the late spring to early autumn period, when the datasets diverge the most at both tidal and low-frequency (i.e., seasonal) scales, could be the use of freshwater for rice irrigation, which is not incorporated into the model.

Figure 5 illustrates the main features of the water exchange between the tidal flat and the estuary, which is driven by the water level difference between both systems. Around high water the flow across the inlet is zero as the water level in the tidal flat and the estuary are the same (see red arrows in Figure 5 ). When the falling tide starts, it does slightly earlier in the estuary and the tidal flat begins to empty (negative flow, green dashed line, in Figure 5 ). As the downstream flow in the estuary increases during ebb tide, the tidal flat empties faster and faster until it reaches a maximum negative flow across the inlet. As the water level in the tidal flat drops and the thickness of the water sheet decreases, friction becomes more important and controls the flow towards the estuary, which declines progressively. Before the water level in the tidal flat reaches the bottom (i.e., before it dries completely), the next rising tide arrives at the tidal flat entrance, marking the beginning of the positive flow (red dot in Figure 5 ), and the tidal flat starts to refill. This flow increases rapidly due to a faster rise of the tide in the estuary than in the tidal flat, causing a water level gradient towards the latter. The solid and dashed blue lines in Figure 5 illustrate this situation. As the high-water approaches, both blue lines come closer together, and the gradient —and, consequently, the positive flow— progressively decreases after reaching a peak. Refilling continues at a slower rate until high water, at which point the flow stops and a new cycle begins.

Solid and dashed black lines in Figure 6A show the time evolution of the surface salinity at a point in the estuary, just in front of TF2 (white dot in Figure 1B or black dots in Figures 6B–G ), in the cases with and without the tidal flat, respectively. Six moments of special interest (vertical lines B to G), are highlighted in the series. The time-averaged salinity is clearly larger in presence of the tidal flat and its range of fluctuation is clearly smaller. The solid pink line represents the salinity at the center of the tidal flat, which is always lower than at the estuary, except for a brief period around low tide (time C in Figure 6A ). Its range of variation is also smaller than in the estuary and remains fairly constant most of the time. The point of interest here is the distorted profile of salinity in the estuary observed around high tide (solid line around time E in Figure 6A ), which attains a minimum shortly after high water (see inset in Figure 6E ). This contrasts with the maximum found in the absence of tidal flat (dashed black line), which is the expected result, since salinity must increase as long as the flood continues.

In order to explain this pattern, snapshots of the velocity and surface salinity fields at the six selected moments of the tidal cycle are represented in Figures 6B–G . Around low tide, the water in the tidal flat is saltier than that of the estuary ( Figure 6B ; time B in Figure 6A ). This is the only moment when this occurs. When the flood tide begins, the tidal flat fills with water that is less saline than the water inside ( Figure 6C ; time C in Figure 6A ). Shortly after, the water coming from the ocean begins to flood the tidal flat that is already saltier ( Figure 6D ; time D in Figure 6A ), and the salinity of the tidal flat increases until it reaches a rather constant value. It continues increasing in the estuary until the salinity curve shifts from rising to falling. The reason is the flow through the inlet of the tidal flat, which has reversed near the high tide, as explained above, and now moves toward the estuary, carrying fresher water ( Figure 6E ; time E in Figure 6A ). At this moment, the water upstream of the tidal flat is saltier than the water exiting the tidal flat but still moves landward. When the tidal flow upstream reverses, this saltier water flows in front of the tidal flat again ( Figure 6F ; time F in Figure 6A ), increasing the salinity, which attains the second maximum shown in Figure 6A . Afterward, the salinity in the estuary gradually decreases, completing the cycle. The salinity in the tidal flat remains fairly constant until the new cycle brings in fresher water ( Figure 6B ). In some sense, the tidal flat acts as a salinity reservoir, storing waters that are, on average, saltier than those found in the estuary without the tidal flat, and whose exchange with the estuary creates the region of tidal flat influence defined earlier.

The resulting two-maximum pattern is responsible for the notable reduction of the horizontal salinity gradient in Figure 4C around and downstream of the tidal flat compared to the reference situation. As we approach the upstream limit of the region of tidal flat influence ( Figure 4B ), the horizontal salinity gradient exceeds that of the reference situation ( Figure 4C ), since salinity decreases more rapidly because of the intrusion of fresher riverine water entering after the previous low tide ( Figure 4A ). Since local salinity changes are driven by tidal advection, this pattern reduces salinity fluctuations downstream of the tidal flat and increases them upstream ( Figure 4D ). It is as though the presence of the tidal flat homogenizes the estuary’s salinity field in its vicinity, causing tidal salinity fluctuations to be largely reduced there.

The mean water level decreases systematically around the tidal flat, following a pattern similar to the one displayed in Figure 3A . The reduction is greater for deeper tidal flats. Shorter inlets result in smaller modifications in the mean water level compared to longer inlets, while the area of the tidal flat is the least influential parameter. In any case, changes in the mean water level are less than 1.5 cm and therefore negligible (results not shown).

Figure 7 shows the harmonic constants of the water level for the M₂ constituent. For all configurations, tidal amplitude decreases, and the phase increases in the vicinity of the tidal flat location, with changes gradually fading out away from its location. These changes follow the pattern discussed in the previous section. Tidal amplitudes and phases are clearly sensitive to the size of the tidal flat (compare Figures 7A–D , with Figures 7E–H ). For a given area and inlet size, deeper bathymetries cause greater differences, while the size of the inlet has a relatively minor effect. Overall, the impact of the modeled tidal flats on the GE water level, compared to the reference situation, is always less than 10%, a value that is only reached under the most extreme configurations (large area, inlet, and depth). Considering all configurations, the average departure from the case without a tidal flat is around 5%.

Table 2 presents the M₂ harmonic constants of volume transport across the mouth section (SM, Figure 1B ) for twelve of the sixteen configurations implemented in TF2 (the +0.5 m bathymetry causes negligible variations and is not included). The amplitude always increases compared to the reference situation, ranging from 9.4% for the most extreme case (largest area, largest inlet, and deepest bathymetry, as discussed in Section 4.1) to 2.4% in the least extreme one (smallest area, smallest inlet, and shallowest bathymetry). For a given tidal flat extension and inlet configuration (shaded blocks, also identified by the letter code in the second column of Table 2 ), volume transport is relatively sensitive to bathymetry, with an increase approximately twice as large for the -1 m bathymetry compared to the 0 m bathymetry (see Table 2 , last column). The phase always increases, but by less than 2° (within the confidence interval) in all cases, and by less than 1° in most of them. These phase changes are so small that they can be neglected and are not analyzed here. From a hydrodynamic perspective, however, this phase increase, even if small, corroborates that tidal flats produce the same effect as an increase in friction within the estuary, as discussed in Section 4.1.

Regarding the other parameters, the inlet size has a greater influence than the tidal flat area, as evidenced by comparing blocks LL (gray shade) and LS (yellow) in Table 2 . For a given area, the volume transport through section SM is between ∼2% and ∼4% higher when the tidal flat’s inlet is large rather than small (compare the gray and yellow blocks for the large area and green and red for the small one). When comparing blocks with the same inlet size but different areas (gray and green blocks on one hand, yellow and red on the other), the variations remain below 0.7% for all bathymetries.

Figure 8 illustrates the water exchange between the estuary and the tidal flat with the largest area and inlet for the four bathymetries considered (+0.5 m included). The general behavior follows the description already provided in Section 4.2.1, where the tidal flat fills and drains in response to the tidal cycle, influenced by friction and water level gradients. The same mechanisms driving the inflow and outflow of the tidal flat apply. However, the inclusion of shallower bathymetries introduces additional nuances, which are discussed next.

The relevant difference arises from the fact that the water level in the estuary eventually falls below the bottom of the tidal flat for all bathymetries except -1 m (vertical lines in Figure 8A ). In such cases, friction increasingly controls the drainage of the tidal flat as the water table thins, to the point of preventing complete drying. This is illustrated in Figure 8B , which shows that during periods when the tidal flat is expected to be dry (i.e., during the interval between the color-coded vertical lines in Figure 8 , when the water level in the estuary is below the tidal flat bottom), it remains partially flooded. Instead of fully drying, it exhibits an asymptotic decrease in water level ( Figure 8B ), a pattern also reflected in the flow through the inlet ( Figure 8A ). For the deeper bathymetry (-1 m), where the water level in the estuary stays above the tidal flat bottom (no vertical blue lines in Figure 8 ), the asymptotic drainage patterns are less prominent, but still detectable, particularly in the inlet flow (blue line, Figure 8A ). Friction delays the tidal flat’s low tide, which lags the low-water tide in the estuary: the shallower the bathymetry, the greater the delay and the flatter the asymptotic tail of the water level curve ( Figure 8B ). A similar pattern applies to the flow through the inlet in Figure 8A .

Additionally, Figure 8 shows that the refilling process depends on bathymetry. It begins when the water level in the estuary rises above the tidal flat bottom (colored dots in Figure 8A ), whereas the onset of drainage (negative flow) is identical in all cases (see red arrows), as it only depends on the high tide in the estuary.

The core of this analysis applies to other configurations with different extension and inlet sizes, where the results obtained show only small and irrelevant changes compared to those explained above.

The mean water level ( Figure 10A ) decreases to a minimum a short distance downstream of the tidal flat inlet. The closer the tidal flat is to the estuary mouth, the more marked the minimum becomes. Farther downstream, the mean level recovers to the value of the reference situation, whereas upstream, all configurations display a very slight increase compared to this situation. Changes hardly reach 1.5 cm for TF1 (the most downstream location) and can be neglected.

Tidal flats always reduce the amplitude of the tide (exemplified by the M₂ constituent), regardless of their location ( Figure 10B ). The reduction mainly occurs downstream of the tidal flat, and the farther upstream the tidal flat is, the greater the changes, which can reach almost 10 cm in the case of TF4. In all cases, upstream the tidal flat inlets, the amplitude maintains the same difference relative to the reference case that was already reached near the tidal flat location. In other words, no additional changes occur upstream of the inlet; only those that have already taken place are maintained. Phases show a monotonic, slight phase increase between the mouth of the estuary and the tidal flat, peaking around the location of the latter ( Figure 10C ), which in turn implies a slightly longer transit time between the two sites. The farther upstream the tidal flat is, the greater the delay, which can reach ∼18 min (8°) in the case of TF4. Upstream of the tidal flat, no further delay accumulates. On the contrary, it is reduced slightly (negative slope in the curves of Figure 10C ), but not enough to compensate for the increase experienced downstream of the tidal flat. The result is longer transit times from the mouth to the head of the estuary. The further upstream the tidal flat is, the longer this time.

Overall, the tidal flats modify the wave progression by reducing the amplitude and increasing the transit time. Both effects occur mainly between the mouth of the estuary and the location of the flat, and they become more notable the farther upstream the tidal flat is located. In all cases, the resulting changes reach a maximum of approximately 10% and, therefore, are of limited relevance.

Table 3 shows the harmonic constants of volume transport at the SM section ( Figure 1B ) for the harmonic constants of the M₂ constituent. As mentioned in Section 4, the presence of tidal flats always increases the volume transport through SM: the closer the tidal flat is to SM, the greater the increase (column SM (diff), Table 3 ). For instance, the amplitude of the M₂ constituent increases by 9.5% in the TF1 case compared to the reference situation, but only by 1.8% in the TF4 case. Similar trends are observed for the remaining constituents ( Supplementary Table S1 ). In contrast, the phase generally increases with the distance from SM, except for the semidiurnal constituents in the TF1 case, which show minimal changes.

Regarding the volume transport at the downstream and upstream sections of each tidal flat (see Figure 1B ), the amplitude is always greater downstream (compare columns DS and US, Table 3 ), which is explained by the different tidal range in both sections when no tidal flat is present, and by the different tidal range plus—primarily—the flow through the tidal flat inlet (column TFI) when it is present. The phase difference between the DS and US sections reflects the time needed for the tidal wave to move from one section to the other. A tidal flat between the two increases the phase difference, meaning the wave takes longer to propagate. As mentioned earlier, the tidal flat can be considered a source of increased friction in the estuary, leading to a reduction in wave amplitude ( Figure 10B ) and an increase in phase ( Figure 10C ).

One might hypothesize that the reduction in the increment of water transport through section SM as the tidal flat is located farther from the mouth (column SM (diff), Table 3 ) could be due to a decrease in water uptake by the tidal flat itself. In fact, column TFIn in Table 3 , which shows the M₂ amplitude of water transport across the flat inlets normalized by the tidal flat areas, follows the same pattern as column SM (diff). However, the normalized amplitude (column TFIn, Table 3 ) does not decrease as significantly as the water transport across section SM (SM (diff)), which refutes the hypothesis. Instead, the explanation lies in the V-shape of the tidal amplitude in the estuary ( Figure 10B ; see also Muñoz-López et al (2024) for a comprehensive explanation of the origin of this V-shape). The four tidal flats analyzed are spatially arranged in the direction of decreasing tidal amplitude ( Figure 10B ). The smaller the tidal amplitude at the tidal flat, the smaller the amount of water exchanged with the estuary in each tidal cycle and, consequently, the smaller the required increase in water transport through the SM section.