Two Teledyne RD Instruments Workhorse Monitor 1200 kHz ADCPs (http://www.teledynemarine.com/workhorse-monitor-adcp, last access: 8 December 2022) were mounted on the roll-on, roll-off ferry. One at each end of the ship, at 4.5 m below the sea surface. The ferry has identical bow and stern design and reverses sailing direction at each crossing (Fig. 1). In this configuration, one instrument is at the front of the ferry at any one time and undisturbed by the wake of the ship. Each instrument has four beams at angles of 20∘. Data were recorded in 50 bins of 0.5 m width. Further instrument settings are given in Table 2. In addition, both ends of the ferry were fitted with a differential GPS (JRC JLR-21/31), and a gyroscopic compass (Alphatron Alphaminicourse) to record position and orientation.

The ADCP, GPS and directional data were combined and stored by an on-board computer during the day and transmitted to a shore-based server when the ferry was in port at night. Recorded variables included navigational variables, water temperature, depth below the instrument for each beam, two orthogonal horizontal and one vertical velocity component for each bin, and signal attenuation along each beam for each bin. The horizontal velocities were converted to geo-referenced eastward and northward velocity components using the navigational data following the correction method for heading and tilt described by Joyce (1989); see also Buijsman and Ridderinkhof (2007). Water-depth and bin-depth measurements were automatically corrected by the instrument for variations in sound speed propagation using the instrument-mounted temperature sensor and a user-specified salinity of 28. Water depths were averaged over the four beams and corrected to depth below surface using the draught of the ship. The data also include the spike identification velocity (or “error velocity”) for each bin, which is a measure of the variation in the result when velocity is computed using different combinations of three of the four beams and is hence a measure for the reliability of the observations.

Typically, sailings started at 06:00, with an hourly outward-bound schedule from Texel and return journeys starting on the half hour from Den Helder (Fig. 1). Crossings typically took about 20 min. The last outward-bound sailing of the day started at 21:00, resulting in 32 single crossings per day. The sailing schedule was adjusted by the ferry operator in summer to account for daylight savings time. This schedule was maintained on most days of the year, with the exception of Christmas Day, New Year's Day, scheduled maintenance periods in January and November, and occasional unscheduled maintenance or extreme weather events (the latter typically occurs less than once a year). Occasionally, instrument failure also led to reduced data return. From March 2009 to July 2016 the ADCPs were mounted on the Dokter Wagemaker and from July 2016 to present on the Texelstroom. The setup on the Dokter Wagemaker was configured similarly to that described above but with a single GPS midships (Furuno SC110, https://www.furunousa.com/en/products/sc110, last access: 8 December 2022) and a single gyroscopic compass included in the GPS.

As an example of the QA procedure, eastward velocities measured on the transect sailed on 7 April 2021, 06:00 local time, are given (Fig. 2). The left two panels show the uncorrected eastward velocities for the front (a) and rear (c) ADCP, and the panels on the right (b, d) the corresponding quality-assured velocities. In Fig. 2c, the data affected by the ship's propulsion system are clearly visible and were effectively removed in Fig. 2d. The QA procedure also removed some data from the front ADCP (Fig. 2b). To further illustrate the procedure, the spike identification velocity for the second ADCP bin of both instruments was plotted along the transect, including the thresholds (Fig. 3).

An illustration of the latitudinal gridding of the quality-assured data of both ADCPs, combined for the same date and time shows a coherent profile without data gaps (Fig. 4a). Despite strong variation in the number of data points per grid cell (Fig. 4b) due to a combination of changes in vessel speed and gaps in the quality-assured data (Fig. 2), standard deviations showed no obvious pattern over the cross section (Fig. 4c) (except near the bottom as the two ADCPs, which are a ship's distance apart, may follow slightly different trajectories and encounter different seabed topography), suggesting uniform quality of the eastward current speeds constructed in this way for the cross section.

Time series of cross-sectionally averaged depth (Fig. 5a) showed an average of 18.4 m and a shoaling trend of 1.88 cm yr-1 with a standard error of 0.04 cm yr-1. Similarly, the cross-sectionally integrated volume flux (Fig. 5b) showed an average outflow that changed from around 1000 m3 s-1 in 2009 to around 0 in recent years, with a reducing trend of 98 m3 s-1 yr-1 and a standard error of 13 m3 s-1 yr-1, which continued compared with values reported for earlier years. Most notably, the volume flux has been transitioning to positive values (net inflow) in recent years. Finally, the amplitude of the O1 tidal constituent of the volume flux (Fig. 5c) more than doubled in the period considered, with a trend of 249 m3 s-1 yr-1 and a standard error of 68 m3 s-1 yr-1. This was the only tidal constituent in the ADCP data with a consistent trend exceeding 2 times the standard error.

Plotting the annual residual eastward volume fluxes as a function of the annual mean eastward wind-speed component did not suggest an evident correlation (not shown).

The annually averaged depths along the transect (Fig. 6) revealed the infilling of a substantial depression in the southern flank of the inlet around 52.975∘ N as well as an increase in the maximum depth along the transect between 52.990∘ N and 52.985∘ N but no major changes in the cross-sectional geometry. The apparent shift in the flank of the channel near Texel after 2017 coincides with the change-over of the instrumentation from the Dokter Wagemaker to the Texelstroom, and is likely an artefact, potentially related to a slight change in approach route related to differences in the handling of the ships, which differ considerably in size. Note that the profile of 2009 is less reliable than the others as only data from the later part of the year were available.

The 13-year residual eastward velocities showed outflow in the northern part of the inlet, with the highest values close to the coast of Texel in the upper part of the water column and inflow in the southern part of the inlet, with higher values in the lower part of the water column (Fig. 7a). Both inflow and outflow appear to consist of two kernels. The trends in the residual eastward velocity show a vertically banded structure of alternating increases and decreases, with the strongest band in the southern part of the inlet (Fig. 7c). A striking feature was a strongly negative trend near the bottom in the southern part of the inlet, likely related to the local shoaling (Fig. 6). Standard errors of the trend estimates were small, except near the surface and the bottom, where it increased to 0.002 m s-1yr-1 due to the fluctuating water levels and where local variations in depth associated with individual transects and morphodynamic changes affect the estimates. As a result, the near-surface and near-bottom trend estimates have a high level of uncertainty.

The northward velocities were positive near the surface in the southern part of the inlet and near the bottom in the northern part of the inlet (Fig. 7b). They were negative elsewhere, with the weakest negative values in the central part of the inlet. This pattern suggests a double gyre in the plane of the transect, but this could not be confirmed as the vertical velocities recorded by the ADCPs were affected by the flow induced by the forward motion of the ship. The trends in the northward velocity reflected the vertically banded structure of the trends in the eastward velocities but also indicated a weakening of both the positive and negative residual velocities, suggesting a weakening of the suspected double-gyre pattern (Fig. 7d). The standard errors of the trend estimates were similar to those of the eastward velocity.

Depth- and cross-section averages of the residual eastward velocities provide another way of presenting the main patterns and also allow for a depiction of the interannual variations. The depth averages of the 13-year residuals again showed the outflow in the northern part and the inflow in the southern part (Fig. 8a, thick black line). The individual years clustered relatively close to this line, with the largest variations near the maximum residual inflow in the southern part of the inlet. The cross-sectionally averaged values of the 13-year residual eastward velocity showed outflow in the top 10 m of the water column and inflow in the 15 m below that (Fig. 8b, thick black line), suggesting a component of estuarine circulation to the flow. Interannual variations were largest for the outflow velocities.

The overall cross-sectional pattern of inflow in the southern part of the inlet and outflow in the northern part of the inlet, with a weak estuarine circulation component in the vertical corresponds with the results of earlier investigations (Zimmerman, 1976a, b; Ridderinkhof, 1988; Buijsman and Ridderinkhof, 2007). Huijts et al. (2009) used a semi-analytical model of a schematised curved tidal channel to investigate the cross-sectional patterns of residual flows in the stream-wise and cross-channel directions caused by tidal rectification, along-channel density gradients, along-channel winds and river discharge. Their pattern for streamwise residual flow induced by tidal rectification corresponds well with the pattern of eastward residual flow in the Marsdiep, including the double inflow–outflow kernels, which only occur for the tidal rectification component. Their pattern for cross-channel residual flow by tidal rectification shows a double-gyre pattern like that of the northward residual currents in the Marsdiep but with reversed direction. The causes of this difference are not immediately clear, but the geometry of the Marsdiep (Fig. 1) is much more complex than the schematised curved channel in the model of Huijts et al. (2009): (i) the main channel is not aligned with the coasts and the angle is different at either side; (ii) just seaward of the transect, the main channel curves in the other direction, and on the basin side the main channel is more or less straight. Moreover, the ferry transect slants across the main channel at a fairly large angle, the exact value of which is difficult to estimate because of these changes in curvature. The direction of the gyre pattern corresponds with that observed by Nunes and Simpson (1985) during the flood phase of the tide in an estuary in Wales (UK) and explained by strong friction with the sides of the channel. Cui et al. (2018) also observed this pattern in an estuary in the Gulf of Mexico, where they also observed the reverse pattern during the ebb phase. So it is possible that, in a flood-dominant estuary like the Marsdiep, the flood-phase pattern is expressed in the long-term mean as we see in the observations presented here. As Huijts et al. (2009) used a purely sinusoidal tide superimposed on a river runoff, effectively creating ebb dominance in terms of residual flow and peak velocities in their model, this reasoning may explain the discrepancy if this effect dominates over the influence of geometric differences. Hence, the correspondence of the observed eastward residual flow pattern with the modelled streamwise residual flow pattern induced by tidal rectification is a strong indication that this mechanism is dominant in shaping the cross-sectional residual flow patterns in the Marsdiep.

The trends in the cross-sectional residual flow pattern suggest a slight intensification of both the outflow in the northern part of the inlet and of the inflow in the southern part of the inlet, in particular in later years, with the inflow increasing more than the outflow. There was also a weakening of the double-gyre pattern in the cross section. Moreover, there were slight latitudinal shifts in the double-kernel pattern, but these do not seem to have a systematic direction. There was also a local response to the infilling of a depression at 52.975∘ N. These trends suggest changes in the tidal rectification and frictional processes, possibly related to larger-scale morphodynamic changes such as the ongoing infilling, sea-level rise, and channel migration in the Wadden Sea and in the ebb-tidal delta (Wang et al., 2012; Elias et al., 2012). Slight changes in tides may also be involved, as is suggested by the observed trends in O1 currents and flows. These could be related to bathymetric changes (Benninghoff and Winter, 2019; Jacob and Stanev, 2021; Colina Alonso et al., 2021) and/or sea-level rise (Wachler et al, 2020) that may alter the resonance characteristics of the basin. Larger-scale changes in tides in the North Sea likely also play a role: these resulted in small increases in tidal range near the Marsdiep from 2010–2015 but also in differences in trends in tidal range between the Marsdiep and the Vlie inlets between 1958 and 2014 (Jänicke et al., 2021). Jänicke et al. (2021) identify two components driving the changes in tides in the North Sea: a large-scale barotropic component that involves the north Atlantic Ocean and a regional baroclinic component that relates to stronger stratification in the southern North Sea. It is not clear why the O1 component of the flow changes significantly, while the ADCP data could not detect significant changes in other constituents. Tide gauge data most likely offer a more accurate way to analyse trends in tides in the study area than the ADCP data analysed here as they are more accurate, have higher sampling frequency, measure continuously and cover a wider area. However, such a study is beyond the scope of this paper.

We found a significant trend in the cross-sectionally aggregated residual flow in the Marsdiep tidal inlet, suggesting an imminent reversal from net outflow to net inflow. Four processes can contribute to such changes: changes in wind climate, changes in freshwater input, morphodynamic changes and changes in tidal forcing.

We established that wind forcing, suggested in earlier studies to influence residual flows (Buijsman and Ridderinkhof, 2007; Duran-Matute et al., 2014), is not correlated to the trend observed in the ADCP data. Hence, even though wind and storms may affect the flow on timescales of days to weeks, we do not think that this process is primarily responsible for the observed reduction in residual flow on interannual timescales.

Discharge of fresh water into the western Wadden Sea was estimated to be 450 m3 s-1 on average (Ridderinkhof, 1990), much less than the historic residual outflow (Table 1). Also, freshwater discharge cannot reverse in direction. Thus, this process is not primarily responsible for the observed reduction in residual flow either.

Because the western Wadden Sea has reached near-equilibrium following the construction of the closure dam (Elias et al., 2012.), ongoing morphodynamic changes within the western Wadden Sea are likely dominated by relatively local, internal dynamics. Hence, it seems unlikely that the current morphodynamic processes are the main driver for the changes in residual flow. However, further work would be needed to confirm this.

Ridderinkhof (1988) showed that the outflow at that time was related to a residual circulation entering through the Vlie inlet and driven by differences in amplitudes and phases of the tides between the two inlets. Hence, we hypothesise that the main process driving the trend in residual flows is the baroclinically derived change in the difference in tides between the Marsdiep and Vlie inlets caused by climate change identified by Jänicke et al. (2021). As a result, with warming trends expected to continue, we expect a permanent reversal of the residual flow followed by a strengthening net inflow to occur in the next decade(s). Similar changes may happen in other multiple inlet systems bordering temperature-stratified seas elsewhere in the world.

The reversal of the residual flow in the Marsdiep will be linked with a reversal and potential changes in the residual flow patterns in the western Wadden Sea. This may influence physical factors such as temperature and salinity distributions and may also increase the import of fine suspended sediment through the Marsdiep inlet, while reducing that through the Vlie inlet. Moreover, it may change pathways of nutrient supply and transport of passive propagules (eggs and early stage larvae of marine organisms). Such changes may cascade up through the Wadden Sea ecosystem, that is already influenced by anthropogenic pressures and more direct effects of climate change. However, as the residual flows are much smaller than the tidal flows and even heterogeneous within the Marsdiep inlet itself, it is not possible to infer such effects from this study and further work is needed.

Further work is needed to fully understand the causes, significance and effects of the reversal of the residual flow in this multi-inlet tidal embayment. Next steps could include detailed analysis of the local tide gauge data to refine our understanding of the driving forces, model projections of climate-driven trends in North Sea tides, model studies detailing the processes driving the residual circulation in the Wadden Sea and projecting future changes as well as implications for the regional sediment budget, and model studies projecting changes in the ecosystem in response. Existing observations of ecosystem variables and components should be examined, and wider observational campaigns could be initiated to gain further understanding, underpin models and observe predicted effects.