Atmospheric methane (CH4) concentrations have been increasing since industrial times, surpassing 1900 ppb in 2021 (Lan et al., 2022) and contributing more than 20 % of total radiative forcing in the atmosphere (Etminan et al., 2016). Due to its relatively short atmospheric lifetime of ∼10 years (Canadell et al., 2021), reducing methane emissions to the atmosphere could play a key role in global warming mitigation strategies. However, the implementation of such strategies requires a thorough understanding of methane sources and sinks. Anthropogenic methane emissions (336–376 Tg yr-1) are rather well constrained and constitute ∼60 % of the total atmospheric budget (Saunois et al., 2020). Individual natural sources, on the other hand, are associated with comparably large uncertainties. This is particularly true for methane emissions originating from marine environments (5 to 28 Tg CH4 yr-1; Rosentreter et al., 2021).

The inner shelf (0–50 m water depth) only accounts for ∼3 % of the global ocean surface but is the main source of marine methane emissions to the atmosphere (Weber et al., 2019). In these shallow ecosystems, light availability as well as terrestrial inputs of nutrients support a high diversity of producers and consumers that generate huge quantities of organic matter (Philippart et al., 2009; Beck and Brumsack, 2012). Consequently, rates of organic-matter degradation, including methanogenesis in anoxic sediments are high, often leading to elevated levels of free and dissolved methane in sediments and porewaters (Bange et al., 1994; Røy et al., 2008; Wu et al., 2015). Transport of methane-rich porewaters and the ebullition of methane bubbles, in return, lead to elevated methane concentrations in the water column (Reeburgh, 2007; Grunwald et al., 2009; James et al., 2016). It is estimated that ∼5 % of shelf sea surface waters have methane concentrations above 100 nM (Weber et al., 2019). Nevertheless, a substantial amount of dissolved methane is oxidized by aerobic methanotrophic bacteria (MOB), which mediate the aerobic oxidation of methane (MOx) (Reeburgh, 2007): R1CH4+2O2→CO2+H2O. Similar to other metabolic processes involving small molecules, MOx discriminates against isotopically heavy methane (i.e. containing 13C and 2H (D) instead of 12C and 1H) so that the residual methane pool successively becomes 13C and D enriched as a result of ongoing MOx (Barker and Fritz, 1981; Whiticar, 1999).

MOB typically belong to the Gammaproteobacteria (type I and type X), Alphaproteobacteria (type II), Verrucomicrobia and members of candidate division NC10 (Hanson and Hanson, 1996; Knief, 2015). MOB build a microbial methane filter in the water column that functions as the ultimate sink for oceanic methane before reaching the atmosphere. Yet, little is known about the controls and capacity of this microbial filter in the inner-shelf ecosystems where the vertical distance between the sedimentary source and the atmosphere is short. Factors such as oxygen (Boetius and Wenzhöfer, 2013; Steinle et al., 2017) and methane availability (Mau et al., 2013; James et al., 2016) affect MOx, but increasing water temperatures also play a role by impacting metabolic rates of MOB (He et al., 2012). The capacity of the microbial methane filter in the water column is typically higher during extended periods of continuity, i.e. when the water column is more stagnant (Steinle et al., 2015; James et al., 2016). This increases the contact time of MOB with methane-rich waters so that the size of the MOB standing stock increases. However, water mass movement induced by destratification or seasonal winds leads to shifting mixing regimes that disrupt continuity on a seasonal scale (Gründger et al., 2021). On a daily scale, tides induce currents, which also disrupt continuity and hence can affect MOx, too (Steinle et al., 2015). This disruption of continuity is particularly strong in the extremely dynamic inner-shelf seas, where rapid changes in environmental conditions can lead to rapid changes in water column dynamics.

The Wadden Sea, a UNESCO heritage site that consists of the largest continuous tidal flat area worldwide (14 900 km2), is an extremely dynamic system, with major hydrological changes occurring at seasonal to diel timescales. The Wadden Sea stretches for about 500 km along the coast of the Netherlands, Germany and Denmark. Here, we investigated methane dynamics in the Dutch part of the Wadden Sea, which is separated from the North Sea by five barrier islands (Fig. 1). Our aim was to temporally resolve methane dynamics from an hourly to a seasonal scale to determine key controls on methane dynamics and to establish a methane budget for the Dutch Wadden Sea.

A chain of five barrier islands (located 5 to 30 km offshore) shelters the Dutch Wadden Sea from waves and strong westerly winds. Between these barrier islands and with the rhythm of the tides, large volumes of water are transported in and out of the Dutch Wadden Sea through deep tidal inlets, such as the Marsdiep (most western point of the Wadden Sea) and the Vlie inlet (Duran-Matute et al., 2014). Our fixed mooring station (53∘19.015 N, 5∘22.071 E) is in a branch of the Vlie inlet between the island of Terschelling and the mainland, roughly in the middle of the Dutch Wadden Sea (Fig. 1). This location was chosen as it remains submerged at low tide and lies in between the Wadden Sea's landward and offshore termination. The water flowing by this station thus equally integrates the tidal flat area, mostly during ebb tide, as well as the inflowing North Sea water during rising tide. Also, the station was relatively far away from the port of Harlingen (∼20 km) so that a potential influence of methane-rich port waters is minimized. The reference station was located 8 km north of the island Terschelling in the North Sea (53∘29.190 N, 5∘21.449 E).

Samples were recovered with the R/V Navicula during four sampling campaigns: winter (19–21 February 2019), spring (23–25 April 2019), summer (22–24 July 2019) and autumn (11–13 November 2019). During each campaign, we conducted hourly conductivity–temperature–depth (CTD) casts with discrete water sampling over a 2 d period. During CTD casts, water mass properties (temperature, salinity, depth) and oxygen concentrations were measured continuously using a Sea-Bird (SBE911) + CTD system. Discrete water samples were recovered with Niskin bottles from 1 and 3 m water depth and, upon recovery, immediately sampled for subsequent analyses of water column constituents (methane concentrations, methane isotopic composition and methane oxidation rates).

Sediment samples were retrieved using a box corer, and upon recovery, subsampled with small push cores (diameter 7 cm, ∼18 cm sediment recovery). Push cores were subsampled for methane concentrations by taking 5 mL of sediment every 2 cm that was quickly added to 60 mL glass bottles containing 30 mL of a saturated NaCl brine solution, and the bottles were immediately sealed with butyl rubber stoppers. Atmospheric flask samples (250 mL) were taken hourly at ∼10 m above the sea surface, in winter and spring. In summer and autumn, atmospheric methane concentrations were continuously measured using a cavity ring-down spectrometer (CRDS, Picarro model G2301).

Dissolved methane concentrations were determined using a headspace (HS) technique (Green, 2005). In brief, immediately upon CTD recovery, 260 mL glass serum bottles were filled HS-free, closed with black butyl rubber stoppers (Rubber B.V. the Netherlands) and crimp-top sealed. Next, we added a 5 mL N2 headspace and fixed the sample with 5 mL NaOH solution (25 % w/v). HS methane concentrations of sediments and dissolved methane were measured in our home laboratories with a gas chromatograph (GC; Thermo Scientific FOCUS GC equipped with a Restek stainless steel column HayeSep Q Packed GC Column, 80/100, General Configuration (length 2 m, 2 mm i.d., 1/8 in. o.d.). with flame ionization detection). The instrument was calibrated with a certified 100 ppm methane standard (Scott Specialty Gases Netherlands B.V.).

Similarly, seawater aliquots were taken for methane stable carbon and hydrogen isotope measurements, but these samples were fixed with 60 µL HgCl2 (2 mM). A continuous-flow isotope ratio mass spectrometry (CF-IRMS) system was used to quantify D-CH4 in the gas phase (Thermo Delta Plus XL, Thermo Fisher Scientific Inc., Germany) as described previously (Röckmann et al., 2016; Jacques et al., 2021). Isotopic values are represented in the delta notation against the Vienna Standard Mean Ocean Water (VSMOW) (δD). To monitor precision and accuracy, sample measurements were alternated with measurements of an in-house air standard (cross-calibrated against certified reference standards) containing 1975.5 ppb methane with a δD value of -90.81 ± 1.1 ‰. We constructed a two-endmember mixing model (Mariotti et al., 1981; Jacques et al., 2021) and a Rayleigh fractionation model. This was done to investigate whether enrichment of D in the residual methane was caused by MOx, which is known to discriminate against heavy isotopes (Barker and Fritz, 1981; Whiticar, 1999), or by mixing with comparably heavy atmospheric methane (see Supplement).

MOx was determined by ex situ incubations with trace amounts of 3H-labelled methane as described previously (Niemann et al., 2015). Briefly, aliquots from each Niskin bottle were filled HS-free in 20 mL glass vials in triplicate, sealed with grey bromobutyl stoppers known not to hamper methanotrophic activity and amended with 5 µL of 3H-CH4 in N2 (4.5 kBq, American Radiolabeled Chemicals, USA). The samples were incubated in a temperature-controlled incubator for 72 h in the dark, maintaining in situ temperature conditions. Activities of residual C3H4 and the MOx product 3H2O were measured by liquid scintillation counting.

The MOx first-order rate constant (k) was determined from the fractional tracer turnover (Reeburgh, 2007): 1k=3H2O3H2O+C3H4×1t, where t is incubation time in days. k was corrected for (negligible) tracer turnover in killed controls (KCs; fixed with 100 µL HgCl2 directly after sampling) and multiplied with dissolved methane concentrations [CH4], yielding MOx: 2MOx=k-kKC×CH4.

The diffusive sea–air methane flux was calculated based on a boundary layer model that considers the relation between wind, temperature and methane concentrations in the atmosphere and a well-mixed surface water layer (Wanninkhof, 2014): 3F=(pCH4w-pCH4a)K0kCH4. F denotes the diffusive methane flux. pCH4a and pCH4w (in atm) are the partial pressures of methane in the air and in the well-mixed surface water layer, respectively. pCH4a was measured with a Picarro G2301 gas concentration analyser on board. pCH4wwas determined from surface water methane concentrations (see above). K0 is the methane solubility in mol m-3 atm-1 (Wiesenberg and Guinasso, 1979) and was calculated from temperature and salinity obtained from corresponding CTD casts. kCH4 is the methane gas transfer velocity in metres per day, which was calculated using wind speed (U), the Schmidt number (ScCH4) and the normalized gas transfer velocity (k660) according to Wanninkhof (2014): 4kCH4=0.251U2(ScCH4660)-0.5.

Wind speed was measured on board at 10 m a.s.l. The Schmidt number describes the ratio between kinematic viscosity of water and the gas diffusion coefficient, which relates the different k values for different gases (Jähne et al., 1987; Wanninkhof, 2014).

A principal component analysis (PCA) was carried out to study the relationship between environmental variables and methanotrophic activity. The input variables for the PCA were temperature, salinity, density, k, MOx and dissolved methane concentrations. Prior to running the PCA, the variables were centred and scaled. the R software (R Core Team, 2022) with the package “FactoMineR” (Lê et al., 2008) for the PCAs.

Water column temperature varied between seasons and ranged from 6.3 to 24 ∘C (Fig. 2, Table 1). A clear distinction could be made between colder seasons (autumn and winter), in which temperature ranged from 6.3 to 9.1 ∘C, and warmer (spring and summer) seasons, when temperatures ranged from 14.2 to 24 ∘C. Water temperatures at the reference station were similar in winter (6.9 ∘C) but colder in spring (10.5 ∘C) and summer (20.3 ∘C) and warmer in autumn (11.8 ∘C) when compared to the Wadden Sea.

On a diel scale, variations in water temperature were related to the tidal phase. In winter, spring and summer, maximum water temperatures were observed around low tide (LT, here defined as the time when we encountered the lowest water depth during CTD casts, Fig. 2). This was 7.2 ∘C in winter, 17.3 ∘C in spring and 24.1 ∘C in summer. Minimum water temperatures were around high tide (HT, high tide, here defined as the time when we encountered maximum water depth during CTD casts, Fig. 2). This was 6.3 ∘C in winter, 14.2 ∘C in spring and 20.9 ∘C in summer. In autumn, this pattern was inverted with minimum water temperatures at LT (7.6 ∘C) and maximum ones at HT (9.1 ∘C).

Like temperature, salinity differed strongly between colder (18–27 psu) and warmer seasons (29–32 psu; Fig. 2, Table 1). Furthermore, salinity was higher during HT irrespective of season. Changes in density were caused by salinity rather than temperature during all four seasons, with one exception in spring: after 28 h of the time series, salinity remained stable, but water temperatures decreased, which lowered water density. Salinity levels at the reference station in the North Sea were stable (31.3–32.3 psu) without obvious seasonal fluctuations.

To study the relationship between environmental variables and methanotrophic activity, we conducted a principal component analysis (PCA). The outcome explained 92 % of the data variability in the first two components (Fig. 7, Table S2 in the Supplements). The main gradient (PC1: 69 %) showed a contrast between autumn and winter and summer and spring. Temperature, salinity, methane concentrations and MOx peaked in summer and spring, while lower values were measured in winter and autumn. The relatively small ellipse in spring indicates that samples show more similarity than in other seasons. The second gradient distinguished the spring samples from the summer samples, with higher k values observed in summer and greater density in spring (PC2: 23 %).

In general, we found a clear distinction between colder (autumn and winter) and warmer (spring and summer) seasons (Figs. 2, 7). North Sea waters with incoming tide flow through tidal inlets that in turn branch into successively smaller tidal creeks in which the water-flow direction alternates with the tidal phase. This then led to increasing water temperatures in autumn but decreasing water temperatures in winter. The high temperature of Wadden Sea waters during incoming tide in autumn can be explained by the fact that the shallow Wadden Sea cools rapidly once the summer is over, while the North Sea's large water volume takes longer to cool down.

Salinity levels were on average lower in colder seasons compared to warmer seasons, likely because land runoff and groundwater discharge are typically higher in autumn and winter because of the overall higher precipitation levels during the cold seasons (Van Aken, 2008). A higher level of freshwater inflow from land was also evident from the rapidly dropping salinity levels during falling and LT in autumn and winter (Fig. 2). This freshening effect is amplified at times when the Dutch Ministry of Infrastructure and Water management (Rijkswaterstaat) opens water gates to discharge excess water from Lake IJssel (Fig. 1), which occurs more often in colder seasons due to increased input of precipitation, groundwater discharge, and surface and riverine discharge to the lake. During the warmer and dryer seasons, water gates are mostly kept closed to ensure that the lake's water level stays high. However, freshwater inflow into the Wadden Sea was evident during all seasons because incoming North Sea water generally increased salinity levels at HT, independent of sampling time. The North Sea water mass entering the Wadden Sea during the incoming tide hence becomes overprinted in the Wadden Sea area as a result of mixing with waters from terrestrial sources.

Sediment and water column methane concentrations were highly elevated in summer (Figs. 3, S1 and Table 2). In fact, average sediment methane concentrations increased 17-fold in summer compared to spring 2 months earlier. This increase is probably related to the remineralization of the spring phytoplankton bloom that takes place in the months of April and May (Philippart et al., 2009) leading to elevated rates of methanogenesis in anaerobic sediments (Beck and Brumsack, 2012). A time lag of 1 to 2 months between the peak of the spring bloom and methane release from sediments was also observed in the Baltic Sea (Bange et al., 2010). In the Wadden Sea, where sediments are generally silty and organic-rich, it is likely that temperature plays a crucial role in controlling methanogenesis, in addition to the elevated inputs of organic matter. As water temperatures increase towards summer, microbial methanogenesis in the sediments is further enhanced (Yvon-Durocher et al., 2014; Borges et al., 2018). We indeed observed lower methane concentrations in autumn and winter compared to spring and summer, which is most likely related to both reduced organic-matter input and colder temperatures. It has to be noted that the sediment methane concentrations presented here are comparably low as sediment methane concentrations close to saturation levels were previously found at other locations in Wadden Sea sediments (Røy et al., 2008; Wu et al., 2015). We did not measure sulfate concentrations, but the methane profiles indicate that we only reached the upper part of the methane–sulfate transition zone below which methanogenesis proceeds. Also, sediment methane concentrations can be variable on spatial scales of metres. Depending on the hydrographic regime, the methane–sulfate transition zone can be metres below the tidal flat sediments (Wu et al., 2015), but pore water flow can also transport reduced compounds such as sulfide and methane to the sediment surface (Røy et al., 2008).

Methane release from sediments and the relatively low wind speed (and thus relatively low forcing to drive diffusive efflux) in summer led to charging of the water column with methane. MOx discriminates against isotopically heavy methane and thus causes an isotopic enrichment of residual methane. The isotopic discrimination effect manifests more pronouncedly at low methane concentrations. Indeed, we found more pronounced MOx-induced isotopic discrimination effects in autumn at low methane concentrations (<21 nM). At higher methane concentrations (>21 nM) values were more depleted and were comparable to summer δD-CH4 values. We relate the δD-CH4 values (∼-217 ‰ in autumn and ∼-244 ‰ in summer) at higher methane concentrations (>21 nM in autumn and >61 nM in summer) to the δD-CH4 source signal (Figs. 4a, 5). At these concentrations, the isotope effect imposed by MOx is masked by the high background methane and/or is overprinted by methane entering the water column from sediments.

The activity of MOB in the water column is determined by the availability of methane oxygen and nutrients and the size of the standing stock of the MOB community (Reeburgh, 2007; Crespo-Medina et al., 2014; Steinle et al., 2015). The Wadden Sea water column is a nutrient-rich and typically oxygenated environment; we hence argue that nutrient and O2 availability are not limiting factors for MOB activity. However, MOB in the Wadden Sea need to cope with high fluctuations in temperature, salinity and methane availability (see above).

We did not measure the size of the MOB community; nevertheless, it seems likely that the highly variable water column properties with admixture of different water masses and resuspension of particles affect the standing stock of the MOB community or its activity or a combination of both. Notably, North Sea waters with potentially low MOB standing stock (indicated by the low k value at the reference station) enter the Wadden Sea during incoming tides. As these waters traverse through the Wadden Sea, they acquire methane and likely carry microbes irrigated from sediments and/or originating from mixing with terrestrial waters; incoming North Sea waters hence undergo oceanographic (see above) and biogeochemical overprinting. On short timescales, microbes carried with the tidal current through the Wadden Sea will consequently be exposed to variable conditions regarding salinity and temperature levels and methane concentration.

Previous studies showed that elevated salinity often led to an immediate decrease in MOx in terrestrial/lacustrine systems (Ho et al., 2018; Zhang et al., 2023). Likewise, marine methanotrophs seem to function best at salinity levels of >20 psu (Osudar et al., 2017), while a sudden decrease in salinity can strongly inhibit MOx (Hirayama et al., 2013; Tavormina et al., 2015). This begs the question of whether waters with rapidly changing salinity levels such as the Wadden Sea are environments that are not especially conducive for MOx, in particular in colder months where salinity levels may drop to ∼20 psu because of elevated freshwater influx (see above). While MOx was indeed lower in autumn and winter, the relative decrease in MOx was moderate in comparison to the previous literature findings (Osudar et al., 2017; Zhang et al., 2023). Also, autumn and winter are colder and defined by lower methane levels, which reduces MOx further. Across seasons, the PCA (Fig. 7) and Pearson correlation coefficients of pairs of variables (Fig. S3) indicated that MOx (or k) and salinity (or density) are not or only weakly correlated. The Wadden Sea thus seems to host a euryhaline MOB community that contrast with MOB communities from terrestrial/lacustrine (Zhang et al., 2023) and oceanic origin (Osudar et al., 2015), which seem less able to cope with varying salinity levels.

Sediments and the water column in the Wadden Sea are increasingly fuelled by methane when ambient temperatures rise. The higher availability of methane could then enhance methanotrophic activity (Reeburgh, 2007). Indeed, we found a seasonal imprint with the highest MOx levels in summer that were 3-fold higher than those observed in spring, 9-fold higher than in autumn and 10-fold higher than in winter (Table 2). A correlation between methane, temperature and MOx was also apparent from the PCA (Figs. 7, S3). We note that not only MOx but also the first-order rate constant k was stimulated by higher methane concentrations (MOx is a function of k and [CH4]; see Eq. 3) and temperature. A positive effect of methane on MOx and k is often associated with changes in methane concentrations over several orders of magnitude (Crespo-Medina et al., 2014; James et al., 2016). Here we found that k doubled in summer compared to spring, while methane concentrations were only 30 nM higher, i.e. 1.7-fold. This suggests that a combination of methane availability and temperature determined k in our study; i.e. the MOB may have been stimulated on the enzymatic level. However, the fact that k remained stable in colder seasons with low water temperatures suggests that additional factors, likely MOB community size (Steinle et al., 2015), might play a more important role in maintaining k. For example, MOB from sediments can be resuspended into the water column due to tidal currents or transported from sediments to the water column with bubbles as has been found at other cold seeps (Steinle et al., 2016; Jordan et al., 2020; Jordan et al., 2021). Resuspension could thus be a key driver of the Wadden Sea water column MOB communities, with major consequences for maintaining a microbial filter under less favourable conditions.

Strong hydraulic dynamics are an important characteristic of the Dutch Wadden Sea, with tidal currents interchanging a large water volume with the North Sea twice per day (Gräwe et al., 2016). With the change in tidal phase, the hydrostatic pressure changes rapidly with water depth, which triggers porewater flow (tidal pumping; Røy et al., 2008; Santos et al., 2015)) but may also trigger the expansion and ebullition of gas bubbles (Schmale et al., 2015; Jordan et al., 2020). Similar effects are caused by tidal currents flowing over bathymetric features, which triggers porewater flow, too, and additionally resuspends sediments and MOB into the water column (Bussmann, 2005; Abril et al., 2007; Røy et al., 2008). On the other hand, incoming water from the open North Sea contains relatively low amounts of methane (<6 nM as measured at our reference station); hence, this will dilute the Dutch Wadden Sea's methane content, and outflowing water will export methane from the Dutch Wadden Sea main waterbody.

Temporal patterns of methane concentration and MOx did indeed correlate well with tidal oscillation (Figs. 3, S1, Table 2). Independent of the seasons, methane concentrations and MOx were elevated at LT. The tidal effect seemed most pronounced in spring, where at LT, methane concentrations (1.3-fold), k (2.5-fold) and MOx (4-fold) were higher than at HT, independent of depth. We found it surprising that, just like methane concentrations, k also was substantially higher during LT compared to HT independent of seasons and despite an overall lower salinity at low tide (Figs. 3, S1, Table 2). To the best of our knowledge, this has not been described before. It seems unlikely that the MOB community substantially grew or that the velocity of the MOB's metabolism increased/decreased in a time frame of a few hours. We argue instead that the observed oscillation is caused by a corresponding oscillation of shear force and hydrostatic pressure, leading to resuspension of MOB from sediments as well as elevated release of methane from the sea floor.

Grunwald et al. (2007, 2009) conducted time series measurements in the German sector of the Wadden Sea near the island of Spiekeroog. There, absolute methane concentrations were ∼3-fold higher in spring and summer and ∼15-fold higher in winter when compared to our study. This might be related to local factors, for example the vicinity of the estuaries of the rivers Ems and more importantly Weser close to Spiekeroog, which increase the background methane concentrations in this sector of the Wadden Sea. Like in our study, Grunwald et al. (2007, 2009) also reported a strong influence of tides, with the highest methane concentrations at low tide, probably related to tidal pumping, while inflowing waters showed concentrations typical for the open North Sea in the German Bight. The temporal aspects and processes determining methane dynamics discussed in our work are thus not a local feature but applicable to the entire Wadden Sea and likely to other mud flat areas influenced by tides, too.

Surface waters were supersaturated with methane with respect to the atmospheric equilibrium during all seasons; the Wadden Sea is consequently a constant source of methane to the atmosphere. Just as for dissolved methane concentrations and MOx, methane efflux to the atmosphere was higher during warmer seasons compared to colder seasons. This was primarily driven by methane concentrations rather than wind velocity: wind speeds were similar in autumn, winter and spring, but 2-fold higher methane concentrations in spring translate to a 4-fold higher sea–air flux when compared to autumn and winter. In summer, meteorological conditions were dominated by a heat wave with extremely low wind speeds. This resulted in a comparably low methane efflux to the atmosphere (though still higher than during the colder seasons) leading to an accumulation of methane in the water column. Previously described diffusive methane fluxes at coastal systems vary over several orders of magnitude and appear site specific. For instance, at the Baltic sea coast, fluxes of up to 15 µmol m-2 d-1 have been reported (Bange et al., 2010; Steinle et al., 2017), while in Arctic shelf seas, diffusive fluxes of up to 240 µmol m-2 d-1 were found (Thornton et al., 2016). In the Southern Bight of the North Sea, reported fluxes at the coast were up to 345 µmol m-2 d-1 (Borges et al., 2018). In comparison, estuarine research along the European Atlantic coast found a median flux of 130 µmol m-2 d-1 (Middelburg et al., 2002), which is similar to the fluxes that we found in the Dutch Wadden Sea (∼39 to 145 µmol m-2 d-1). Globally, tidal flats were estimated to emit CH4 at a median rate of ∼3.6 mg m-2 d-1 (226 µmol m-2 d-1; Rosentreter et al., 2021), which is similar (1.5 to 6-fold higher) than our flux estimates from the Wadden Sea.

Towards a roughly estimated methane budget for the Dutch Wadden Sea, we combined our diffusive flux, MOx and methane concentration data (Fig. 8) as well as estimates of the Wadden Sea water volume and tidal prism. Our flux estimates (Table 2) translate to an annual average sea-surface–atmosphere flux of 74 µmol m2 d-1. Extrapolating this to the area of the Dutch sector of the Wadden Sea (∼2200 km2; Materić et al., 2022) implies that 1.6×105 mol CH4 d-1 escapes from the Dutch Wadden Sea to the atmosphere (Table 2). The average water volume of the Dutch Wadden Sea is about 5.15 km3 (Materić et al., 2022); hence the annual average of 1.7 nM d-1 of MOx translates to 0.09×105 mol CH4 d-1 that is oxidized in the water column by MOB. In addition to atmospheric efflux and microbial consumption, methane-rich waters are also flushed into the North Sea. To estimate this, we simplified that the total tidal prism of 4.5 km3 (Gräwe et al., 2016) is an approximation of the net amount of water that leaves the Wadden Sea during LT. With respect to our measured mean methane concentration (36.8 nM), about 1.6×105 mol of methane is thus flushed towards the North Sea twice daily, i.e. 3.2×105 mol d-1. A large uncertainty in this calculation is caused by the delay of ∼3 h in tidal phases between the western and eastern part of the Dutch Wadden Sea. In other words, methane-rich waters flowing out of the tidal inlet in the west can be entrained in the current that starts flowing back into the Wadden Sea at eastern tidal inlets. Therefore, the net loss of methane to the Wadden Sea is probably lower than described above. Still, data from our reference station show only slightly oversaturated methane concentrations (<6 nM) suggesting that the amount of methane flowing back into the Wadden Sea is rather low. A similar observation was found during a tidal inlet study in the German Wadden Sea (Grunwald et al., 2009). Though overall methane concentrations were higher, methane concentrations in North Sea waters flowing into the Wadden Sea were 60 % lower compared to waters flowing out of the Wadden Sea at low tide. Excluding allochthonous methane sources (for example methane influx with freshwater from Lake IJssel), the Dutch Wadden Sea's methane budget must be supported by a total rate of methanogenesis that at least equals the sum of methane efflux to the atmosphere, water column methanotrophy and methane outflow to the North Sea; together these amount to 4.9×105 mol d-1. Per square metre, this is comparable to methanogenesis rates in the Eckernförde Bay in the Baltic Sea (Maltby et al., 2018). Note that this accounts for the amount of methane liberated from sediments, while it neglects methane oxidation in sediments (dominantly anaerobic oxidation of methane), which can retain a substantial fraction of methane in sediments (Reeburgh, 2007). Hence, the total rate of methanogenesis in the Wadden Sea is consequently much higher.

Taken all methane export terms and sinks considered together (MOx, efflux and tidal displacement amounting to 4.9×105 mol d-1), MOx reduces roughly 2 % of the Wadden Sea's methane budget, while about 1/3 of methane escapes to the atmosphere and the remaining ∼2/3 are flushed into the North Sea (where it may be further oxidized and released to the atmosphere). The effect of MOx on the Wadden Sea's methane budget is low when compared to the global ocean, where an estimated >90 % of water column methane is consumed by MOx (Reeburgh, 2007). As the Wadden Sea is very shallow, liberation of methane from sediments to the atmosphere is fast; in other words, MOB have a very limited time to consume methane released from the sediments before it is liberated to the atmosphere or flushed with tides to the North Sea. In a meta-study, Rosentreter et al. (2021) estimated a global median methane efflux from tidal flats (covering ∼128 000 km2 globally; Murray et al., 2019) to the atmosphere of 0.17 Tg yr-1. We found a total annual diffusive sea–air flux from the Dutch sector of the Wadden Sea (2200 km2) of ∼0.001 Tg yr-1, which alone already accounts for 0.6 % of the global methane emissions from tidal flats to the atmosphere.