The pH sensor recorded continuous voltage measurement (electromotive force EMF) in mV throughout the deployment. At discrete times, water samples were collected and their pH was measured in the laboratory using spectrophotometry, providing reference pH values for calibration. The EMF data were converted into pH using the Nernst equation (Eq. 1), which relates pH to temperature and voltage. For each discrete pH measurement, the reference potential voltage (EMF⁰) was calculated using the Nernst equation and the corresponding sensor EMF values. Afterwards, a piecewise cubic Hermite interpolating polynomial (PCHIP) was applied to obtain continuous EMF⁰ values across the entire dataset. Using the interpolated values, along with the sensor's EMF values and the temperature data, the EMF values were then converted into pH using the conversion function in Calkulate v23.5 (Humphreys and Matthews, 2023). This calibration process ensured accurate calibration of the sensor's values with the pH measurement obtained through spectrophotometry throughout the deployment (Fig. 2). 1EMF=EMF0+(RT/F)⋅ln⁡([H+]) where R is the ideal gas constant (8.3145 J K⁻¹ mol⁻¹), T is temperature (in K), and F is the Faraday constant (96.485 kC mol⁻¹).

Following the calibration process described above, we estimated the uncertainty measurement of the corrected pH time-series. Uncertainty in the pH time-series measurements was estimated by adapting principles from the kriging method, a geostatistical method generally used for spatial interpolations. In the kriging method, the spatial correlation between points is analysed to predict values at unmeasured locations based on observed data at nearby locations. The spatial relationship between the observations is calculated using a semivariogram that describes how the variance between data points changes as a function of distance. By modelling these relationships, kriging can interpolate the unknown values and estimate their associated uncertainty. Here, we adapt the kriging concept to a temporal context in order to quantify the uncertainty related to the pH measurements by examining the temporal differences between all possible pairs of measurements. This method provides a robust way for assessing uncertainty in the time-series that accounts for the time since or until the nearest calibration point, helping to understand how measurement uncertainty evolves over time. This uncertainty quantification does not apply any additional corrections to the pH values, it only estimates the uncertainty of each measurement.

This choice of interpolation and the modified approach we employed is particularly well-suited for this study due to the challenges presented by the pH electrode sensor used to collect pH data, which is prone to drift. Furthermore, the discrete calibration samples were unevenly distributed in time. The semivariogram approach to estimating uncertainty incorporates the effects of both of these factors.

First, the offsets between the uncalibrated continuous pH sensor data and the discrete calibration pH data were calculated. Then, the absolute difference between each possible pair of offsets was computed, along with their corresponding difference in time (Figs. 3 and S1). Next, these temporal differences were binned into specific time intervals. The bin width varied over time, starting with narrow intervals (containing between 120 to 40 values per bin) at the beginning and expanding over time where there were fewer pairs of observations (bin containing less than 40 to 1 value per bin). Within each bin, the mean of the offset values was calculated. The absolute values of the mean offsets were used to determine the standard deviations within each bin and represent how quickly the pH offset changed through time.

To model the relationship between time and uncertainty, we used a curve fitting approach (Eq. 2) to capture the non-linear variation in uncertainty over time (Fig. 4d): 2σpH=a⋅Δt+b+c⋅Δt where σ(pH) is the uncertainty as a function of time difference (Δt), a, b, and c are least-squares fitted parameters.

Equation (2) was then used to calculate the uncertainty at each sensor measurement point while accounting, for the time between the current measurement and the previous calibration point (t0) and the time remaining until the next one (t1). The uncertainties calculated for those intervals are expressed as σ0 and σ1 respectively. By weighting these uncertainties (σ0 and σ1) and their corresponding time factors (t0 and t1), the uncertainty at each measurement point is expressed using the following equation: 3uncertainty=t0σ02+t1σ12 The uncertainty is the result of the combined uncertainties σ0 and σ1 through a weighted sum in which the weights represent t0 and t1.

The MLR performance was assessed using three statistical methods: the coefficient of determination R2, the RMSD and the Nash-Sutcliff model efficiency (NSE, Nash and Sutcliffe, 1970), as similarly applied by Nondal et al. (2009), which assess how well model predictions match the observed data. The NSE values close to 1 indicate perfect model performance, values near 0 suggest the model performs similarly to using mean of observations and negative values to indicate that the model performs worse than the mean.

The comparison between TA_pred and measured TA showed that the MLR (Eq. 4) successfully captured the main observed pattern and variability (Fig. 4c). The RMSD between the measured TA and TA_pred was 17.5 µmol kg⁻¹ with an R² of 0.82. This RMSD is considerably smaller than both the observed seasonal TA range (231.7 ± 12.7 µmol kg⁻¹) and the average daily range (46.4 ± 13.1 µmol kg⁻¹), representing 7.6 ± 0.7 % of the seasonal variation and 37.7 ± 11.0 % of the daily variation.

The time series (Fig. 4c) and the high-resolution data (Fig. 5a) confirm that the model successfully tracked the seasonal and daily TA cycles, reproducing the magnitude and timing of variations accurately enough for our purposes. Across the 59 TA observations the model showed a strong linear relationship, however, tended to underestimate TA in the lower and higher ranges (< 2375, > 2450 µmol kg⁻¹) and overestimated it in the mid-range (∼2375–2450 µmol kg⁻¹) (Fig. S2a in the Supplement). Additionally, the MLR predictions showed some oscillation patterns that are not present in the discrete TA observations, which could be attributed to the annual harmonic terms that capture the seasonal variation across the study period. Nevertheless, the model demonstrates strong performance for seasonal scale predictions and reasonable ability to capture daily fluctuations.

To further validate the TA prediction model, we evaluated its performance on a shorter time scale where high-resolution sampling was conducted from 29 March to 1 April, during which 12 samples of TA, DIC and pH were collected (Fig. 5). These samples were not used to develop nor train the MLR, ensuring unbiased validation. Despite the reduced temporal scale, the RMSD remained smaller, representing 26.6 ± 3.7 % of the daily ranges (65.8 ± 3.2 µmol kg⁻¹), confirming the model's performance on both short and long-term scales.

Correlation analysis between the MLR components and TA revealed varying relationships (Table 1). Seasonal variability (sine component) exhibited the strongest correlation with TA, followed by temporal trends and salinity. Water level difference showed no direct significant correlation with TA. However, including it in the MLR significantly improved the MLR performance with R2 increasing from 0.76 to 0.82, RMSD decreasing from 20.3 to 17.5 µmol kg⁻¹ and the NSE increasing from 0.76±0.008 to 0.82 ± 0.006. Model performance increased by 8.2±1.35 % and a reduced uncertainty of 2.8 ± 2.5 µmol kg⁻¹. While this improvement suggests that water level captured a real tidal influence on TA, its inclusion in the MLR may also create TA-tidal pattern similarities.

The MLR model was also assessed for potential biases. Results showed no significant correlations between MLR components and alkalinity residuals (TA_res) (Table 2), which confirms that the model accurately captures the main alkalinity variation without systematic bias. The TA_res times series (Fig. S2b) confirms no temporal bias, with residual variability reflecting the irregular sampling frequency.

The monthly model performance revealed varying RMSD closely linked to sampling frequency (Fig. S2c). During high sampling periods (March–July, n= 7–13), RMSD estimates remained relatively consistent, ranging between 15.3 and 21.3 µmol kg⁻¹. In contrast, months with limited sampling (n= 1–2), showed unreliable RMSD estimates. With fewer samples, the model is less well-constrained, limiting the ability to evaluate model performance in these months. Results from well-sampled periods (March–July) suggests that the MLR approach is reliable, and performance in under-sampled months would likely improve with increased sampling frequency.

The overall RMSD estimates (17.5 µmol kg⁻¹) are consistent with those of other coastal MLR studies. While global ocean TA prediction typically achieves uncertainties lower than 10 µmol kg⁻¹ (Carter et al., 2016; Lee et al., 2006; McNeil et al., 2007), MLR performances vary considerably with system complexity and heterogeneity. Regional-scale coastal studies achieve lower uncertainties, where for instance Gemayel et al. (2015) reported an uncertainty of 10.6 µmol kg⁻¹ across the Mediterranean Sea, while Alin et al. (2012) reported an uncertainty of 6.4 µmol kg⁻¹ along the South Californian coast. Complex coastal systems exhibit substantially higher uncertainties, as indicated by Rheuban et al. (2021) with uncertainties ranging from 48 to 121.1 µmol kg⁻¹ across various estuarine systems along the northeast US coast. Similarly, Fassbender et al. (2017) achieved identical performances as in this study with an uncertainty of 17 µmol kg⁻¹ in Washington state nearshore and estuarine environments. Comparing the high RMSD observed in this study with the RMSD estimated for open ocean or regional coastal system reflects the biogeochemical complexity of the Wadden Sea. TA in these systems is primarily controlled by conservative mixing processes and presents a strong correlation with salinity. However, in the Wadden Sea various biogeochemical processes, such as denitrification and sulfate reduction in anoxic sediments contribute to TA generation (Thomas et al., 2009). Moreover, organic compounds in seawater can also contribute to TA (Goldman and Brewer, 1980), and this is known as organic alkalinity (OrgAlk). In order to assess the contribution of OrgAlk to the MLR prediction errors, OrgAlk was estimated from subtracting calculated TA (TA_calc) from measured TA, with TA_calc calculated from DIC and pH using PyCO2SYS v1.8.2 (Humphreys et al., 2023). OrgAlk showed weak correlation with salinity and TA_res (Fig. S3; R2= 0.292 and R2= 0.061, respectively), indicating that OrgAlk does not explain the MLR prediction errors. Therefore, likely other processes, such as denitrification and sulfate reduction in the Wadden Sea, are affecting TA variability, which are not (fully) captured by the MLR model.

Overall, based on the conducted statistical tests and the degree of complexity of the MLR, which included tidal and temporal influences, the overall MLR is adequate for the application in this study for seasonal and daily TA variability.

DIC was calculated from TA_pred and the calibrated pH sensor data. The calculated DIC, DIC_calc, closely aligns with measured DIC through the year, effectively capturing the patterns observed in the measured DIC (Fig. 4e). Because measured DIC was obtained through discrete laboratory analysis, independent from the TA_pred model and continuous pH measurements used for DIC_calc, the strong agreement between DIC_calc and measured DIC provides confidence in both the TA_pred predictions and pH sensor calibration.

The RMSD between the measured DIC and DIC_calc was 19.8 µmol kg⁻¹, with an R2 of 0.87. Considering the observed seasonal variation in DIC of 419.3 ± 4.9 µmol kg⁻¹, the model uncertainty accounted for only 4.7 ± 0.5 % of the seasonal range and 27.1 ± 11.0 % of the average daily variation (73.1 ± 28.8 µmol kg⁻¹).

The high-resolution validation period, as described above, was also used to assess the DIC_calc (Fig. 5b). During this period, the RMSD remained small compared to the observed daily ranges (75.1 ± 1.3 µmol kg⁻¹), with model uncertainty representing 26.4 ± 4.0 % of the daily variation, confirming the model's performance on predicting TA_pred and its reliability in using the predicted values to calculate DIC_calc. However, the DIC_calc overestimated the measured values by up to 25 µmol kg⁻¹, especially during the first day of this high-resolution sampling period, possibly due to an underestimation of the hydrodynamic effects in TA_pred.

Additionally, to assess the sensitivity of DIC_calc to pH calibration, the pH sensor data was recalibrated by progressively omitting measured pH values, reducing the number of measured pH values used during calibration from 12 calibration samples up to scenarios where only one pH calibration sample remained. Those changes were applied only during the high-resolution sampling period. For each scenario, the recalibrated pH, combined with TA_pred, was then used to recalculate DIC_calc, and then compared to those calculated from the fully calibrated pH sensor data. The results showed that even in the most extreme scenario (with only one single pH calibration sample used), the difference in DIC_calc remained small, ranging between -5.23 to 14.46 µmol kg⁻¹. As expected, the pH values changed when using fewer calibration samples compared to the full calibration dataset (Fig. S4b). Statistical analysis revealed no significant differences between the DIC_calc with fully pH calibrated data and DIC_calc under different calibration scenarios (p-value > 0.05). This suggests that variation in TA had a greater influence on DIC than changes in pH.

The water temperature varied from a minimum of around 4 ± 0.2 °C in December to 23 ± 0.2 °C in August (Fig. 4a). Salinity followed a typical pattern (Ridderinkhof et al., 2002) with a less clear cycle, being lower and more variable in the winter and higher and more consistent in the summer (Fig. 4b). Salinity is generally lower in winter because precipitation, especially over the land, is higher, which increases the freshwater flow from the IJsselmeer, other rivers flowing directly into the Wadden Sea, and the Rhine plume entering through the Marsdiep tidal inlet. The higher variability in salinity arises because the greater precipitation is strongly linked to ephemeral stormy weather (Van Aken, 2008b). However, increased salinities during summer periods, especially during the recent years with increased extreme droughts, are likely due to reduced or completely stopped discharge of freshwater from the IJsselmeer into the Wadden Sea. This water management approach is implemented in order to preserve freshwater for agricultural use and consumption (Philippart et al., 2024).

TA presented to first order an opposite pattern to salinity, with higher values in the winter/spring (∼2500 ± 17.5 µmol kg⁻¹) and lower in the summer/autumn (∼2350 ± 17.5 µmol kg⁻¹), but its variability was more consistent throughout the year (Fig. 4c). The opposite patterns of TA and salinity arose because the low-salinity endmember water type generally had higher TA than the high-salinity endmember (Fig. 6). However, this TA-salinity relationship varied seasonally. From the regressions between TA and salinity for different months, both TA and salinity at the low-salinity waters displayed large range of variation (163.6 ± 65.2 µmol kg⁻¹ and 5.1 ± 2.1 respectively), while the high-salinity waters exhibited more variable TA but relatively stable salinities (115.0 ± 43.6 µmol kg⁻¹ and 3.0 ± 1.0 respectively). This suggests that the three water types (Wadden Sea, IJsselmeer, and North Sea) become more or less dominant at different times, resulting in the seasonal variability observed in both TA and salinity (Hoppema, 1990, 1993).

The lack of freshwater end-member data prevents us here from establishing a reliable relationship between TA, DIC and salinity. As observed in Fig. 6, different TA values were recorded for the same salinity values, indicating the influence of mixing between multiple endmembers. This variability is the result of the dominance or lack of dominance of different water types in the Wadden Sea depending on the hydrodynamic conditions. The western Wadden Sea in particular exhibits a strong gradient and highly variable hydrographic characteristics, both on tidal and longer time scales. This variability is due to multiple factors including, tidal exchange, variable freshwater discharges and changing Dutch North Sea coastal waters properties (Postma, 1954). Therefore, understanding the TA-S relationship is essential for estimating the characteristics of the different water types which interact based on hydrographic conditions (the Wadden Sea endmember, the IJsselmeer endmember and the North Sea endmember) and calculating the influence of biogeochemical processes on the carbonate system. Without direct measurement of the freshwater endmember, the TA and DIC seasonal variations can only provide indirect insights into potential sources and sinks of TA, independently of DIC fluctuations. Consequently, understanding the interplay between tidal cycles, freshwater discharges and biogeochemical processes is essential, yet challenging, to fully characterise and understand the carbonate system in the Wadden Sea. Further research incorporating freshwater end members, along other measurements, will be essential in order to refine our understanding of these interactions.

pH exhibited strong seasonal variations, with a maximum of 8.35 ± 0.04 during spring and a minimum of 7.75 ± 0.02 during summer (Fig. 4d). The high pH observed in spring was likely due to a phytoplankton bloom. Through March, DIC_calc dropped from 2426.8 to 2180.7 ± 19.8 µmol kg⁻¹, presumably due to conversion of DIC into organic matter, increasing pH by ∼0.3 ± 0.06 (Soetaert et al., 2007). Analysis of the nutrient drawdown during this bloom period supports this interpretation. The C : N ratio of 6.5 : 1 closely matches the Redfield ratio of 6.6 : 1 (Redfield et al., 1963), suggesting that nitrate assimilation during the spring bloom was closely linked to the decline observed in DIC. Beyond the spring bloom, this inverse relationship between pH and DIC during short-term (days to weeks) excursions continued through the year, although on longer time scales (months), the pattern of DIC_calc was more like that of TA_pred, with a minimum DIC_calc of 2007 ± 19.8 µmol kg⁻¹ during summer and a maximum of 2426.8 ± 19.8 µmol kg⁻¹ in March 2022 (Fig. 4e). The short-term excursions in pH and DIC suggest the occurrence of smaller, secondary plankton blooms later in the year, while the longer-term similarity with TA suggests a relatively constant state of (dis)equilibrium with atmospheric CO₂ after the spring bloom (Humphreys et al., 2018), as seen from the ΔfCO₂ (Fig. 4f).

In February, FCO₂ (Fig. 4g) reached a maximum of 1.7 g-C m⁻² d⁻¹, a CO₂ source to the atmosphere, while through March and into early April, the decline in DIC caused ΔfCO₂ to become negative, driving FCO₂ to a minimum of -1.4 g-C m⁻² d⁻¹, a CO₂ sink (Thomas et al., 2005a). Throughout the year, ΔfCO₂ was predominantly controlled by changes in DIC (Fig. 4e, f), determining the direction of the flux, while the magnitude of FCO₂ was driven by wind speed (k_w ranging from 0 to 96 cm h⁻¹; Fig. S5). The cumulative FCO₂ since the start of our observations on 2 February reached a maximum of 0.1 g-C m⁻² total CO₂ released to the atmosphere on 13 March, but almost as quickly returned to zero by the beginning of May.

From May until January, FCO₂ fluctuated moderately within a range of -0.6 to 0.5 g-C m⁻² d⁻¹ while the cumulative FCO₂ remained negative, reaching a minimum of -2.2 g-C m⁻² total CO₂ taken up from the atmosphere on 10 July. The cumulative FCO₂ showed periods of increase, interspersed with two short decreases presumably linked to the secondary blooms observed in July and September. Despite these fluctuations, an overall increase in cumulative FCO₂ from May to January illustrated the Wadden Sea's role as a source of CO₂ through summer, autumn and winter, except during brief bloom-related uptake periods (Clargo et al., 2015; Thomas et al., 2005a). The positive cumulative FCO₂ by January of 4.7 g-C m⁻², despite a 21 d gap to complete a full year, indicates a net CO₂ release to the atmosphere and suggesting that the Wadden Sea acts as a CO₂ source over the entire annual cycle, consistent with previous findings (Thomas et al., 2004).

The negative correlation between TA and salinity, combined with similar TA and DIC seasonal variability, highlights an important characteristic of the Wadden Sea carbonate system. Seasonal variability in both TA and DIC was dominated by hydrological process (Sect. 4.1.1), with the additional biological effect on DIC difficult to discern. However, because the hydrological effects on TA and DIC were well correlated with each other, they mostly cancelled each other out in terms of their effects on pH. This results in biological processes being the primary driver of seasonal pH variability.

Beyond net community production (NCP) and respiration, other biological processes also influence the carbonate system in the Wadden Sea. The available nutrient data that was collected during the study (Fig. S6) exhibited similar patterns and ranges to what was observed by (Salt, 2014) in the Marsdiep channel, with high nutrient concentrations during autumn and winter and lowest concentrations during spring and summer. Salt (2014) identified nitrification and ammonia uptake as key drivers of TA consumption, whereas denitrification and sulfate reduction act as drivers of TA production. Additionally, their study highlighted the role of silicate and nitrate availability on NCP during diatom blooms.

Given the similarities (ranges and patterns) in nutrients, TA and DIC distributions with the results of Salt (2014), denitrification and sulfate reduction processes may be driving TA generation in the Wadden Sea as well. Thomas et al. (2009) estimated that these processes generate approximately 99 and 12–26 Gmol TA yr⁻¹ respectively. The importance of these sedimentary processes for the carbonate system of the Wadden Sea are well documented in many previous studies (Al-Raei et al., 2009; Brenner et al., 2016; Kieskamp et al., 1991; Norbisrath et al., 2024; Thomas et al., 2009; Voynova et al., 2019). All these processes might help explaining the observed TA and DIC distributions.

As mentioned above, both TA and DIC showed similar patterns with elevated concentrations in spring, followed by a gradual decrease through summer and autumn before increasing again in winter. The monthly variability in the slope of the linear regression between TA and DIC (δTA / δDIC) (Fig. S7) reflects the co-variability of TA and DIC within each month rather than the absolute contribution of any single biogeochemical process. These slopes provide additional insights into the dominant biogeochemical processes occurring on timescales faster than air-sea CO₂ equilibration, which restores the ratio back to approximately 1.15 in these waters (Humphreys et al., 2018). The δTA / δDIC exhibits a clear seasonality, with maximum value in winter (0.89 ± 0.01), lower values in spring and summer, and a negative ratio in September (-0.08 ± 0.01). The winter higher δTA / δDIC might coincide with TA being generated at higher rate than DIC and could result from denitrification. The peaks during winter suggest that when NCP is minimal, the influence of such sedimentary processes on the carbonate system variability becomes more apparent in the water column, as their signature is not as much obscured by NCP removal of DIC. Similar δTA / δDIC ratios near 1 driven by anaerobic mineralisation have been documented in other coastal systems including saltmarshes and estuaries (Miao et al., 2025; Yau et al., 2022). However, the lower ratios during spring and summer reflect the dominance of NCP in removing DIC faster than TA is generated, resulting in lower δTA / δDIC values. The negative δTA / δDIC in September (-0.08 ± 0.01) is consistent with a transition toward conditions dominated by respiration, approaching the stoichiometry of aerobic respiration (δTA / δDIC ∼-0.15, Chaillou et al., 2024; Wolf-Gladrow et al., 2007), representing a transitional period between the decline of NCP and an increase in organic matter remineralisation where DIC accumulates faster than TA. Future measurements to constrain the freshwater TA and DIC endmembers would help to quantify the relative contributions of mixing and biogeochemical processes.

The diel cycles of TA, salinity, and water level were distinctly different from those of temperature, pH, DIC and ΔfCO₂. Monthly-averaged hourly TA anomalies with respect to the daily mean (Figs. 7 and S8) varied between -7.2 ± 4.3 and 7.0 ± 4.3 µmol kg⁻¹. However, individual daily anomalies showed much larger variability, ranging between -43.4 ± 15.0 and 44.3 ± 9.6 µmol kg⁻¹, displaying a complex, irregular pattern without a clear day-night cycle, as the tidal cycle likely conceals any underlying biological patterns, and suggesting that tidal processes dominate over NCP and respiration in controlling daily TA variation. Changes in TA appeared to be associated with the tidal cycle, with fluctuations observed in response to both high and low tides (Fig. S9). Higher TA was observed during low tide. During high tide, North Sea water, which has lower TA than the Wadden Sea, is brought into the Wadden Sea, lowering the overall TA. During low tide, the dominance of the Wadden Sea water, which has higher TA, results in increased TA. Water level monthly anomalies (Fig. S9), which fluctuated between -27 ± 39 and 29.2 ± 45 cm (with individual daily anomalies ranging from -155±55 to 149 ± 55 cm), also showed a complex and irregular diel pattern driven by the tides, and consistent with a dominant M2 tidal constituent (Ridderinkhof et al., 2002). The Wadden Sea is characterised by asymmetrical tides, where the ebb and flood tides fluctuate in both timing and intensity (Buijsman and Ridderinkhof, 2007). This tidal asymmetry combined with the delay in TA response to changes in water level – which is typically less than 5 h – means that the minima and maxima in water level did not correspond exactly with the those in TA, and vice versa. This further complicated the overall tidal pattern by creating uneven fluctuations in water level, making it difficult to establish regularity in the tidal cycle despite the underlying tidal control.

These patterns were further examined through tidal phase analysis (Figs. 8 and S10). While several months exhibited the expected pattern of higher TA at low tide and consistent with the mixing mechanism described above, other periods displayed opposite behaviours. This variability does not follow a clear seasonal pattern, as months from different seasons exhibited similar variability, while months within the same season showed different patterns. This irregularity reflects the complexity of TA dynamics in a shallow tidal system. Tidal forcings lead to strong benthic-pelagic coupling (Huettel et al., 2003), moreover, asymmetrical tides combined with the <5 h delay in TA responses to water level changes create variable phase relationships between tidal forcing and TA responses. The combination of the tidal coupling, with varying inputs from sediments, biological processes and water types exchange can lead to irregular patterns that do not follow simple seasonal trends.

Salinity monthly anomalies (Figs. 7 and S11), which varied between -0.7±1.2 and 1.0 ± 1.9 (with individual daily anomalies ranging from -5.2 ± 0.7 to 5.4 ± 1.5), displayed a clearer 12 h periodicity compared to TA and water level. The semi-diurnal tides in the Wadden Sea (Buijsman and Ridderinkhof, 2007; van der Molen et al., 2022), consisting of two low and two high tides per day, lead to alternating shifts in TA and salinity as the system transitioned from Wadden Sea to North Sea dominance. During high tide, the influx of North Sea waters introduces higher salinity water into the Wadden Sea, resulting in a more homogeneous salinity distribution. At low tide conditions, local estuarine processes and freshwater inputs create more variable salinity conditions. However, in dry summer periods or drought conditions, particularly when freshwater discharges are reduced or completely stopped (Fig. S12), the salinity gradient between North Sea and Wadden Sea can be reversed.

Salinity also exhibited seasonal variation in the intensity of its diel fluctuations. These seasonal patterns were further examined across the tidal phase (Figs. 8 and S13), confirming the varying intensity of tidal influence on salinity variation. In March, salinity anomalies were particularly pronounced, reaching their minimum values at low tides and maximum values at high tide, and indicating strong tidal control of salinity variability. From May onward, this variability declined progressively until reaching near zero in August and September. The reduced salinity variability corresponds to a decrease in freshwater discharge from the Ijsselmeer and the Rhine during summer (Fig. S12), resulting in a weakened and more uniform salinity gradient between the Wadden Sea and the inflowing North Sea waters.

From October to December salinity anomalies increased again, likely driven by seasonal changes in freshwater input and mixing, during which tidal control of salinity variability strengthened again as the freshwater-seawater gradient was re-established.

Across the year, pH, DIC and ΔfCO₂ exhibited clearer 24 h periodicities, particularly during the warmer months (May–August). The largest monthly amplitude pH anomalies (Figs. 7 and S14), occurred in June, with a night-time minimum of -0.03 ± 0.03 and a daytime maximum of 0.03 ± 0.04. In winter, variations were smaller, often near zero. The diel pH cycle displayed a characteristic day-night pattern, consistent with biologically driven CO₂ dynamics associated with NCP and respiration. During the day, photosynthesis processes consume CO₂, reducing the concentration of CO₂ and therefore increasing pH. At night, respiration and remineralisation are the dominant biological process releasing CO₂ back in the seawater, and lowering pH (Bates et al., 2009; Falkowski, 1994). These mechanisms have been widely documented in coastal systems (Baumann and Smith, 2018; Cai, 2011; Gattuso et al., 1998), particularly in shallow tidal systems (Bauer et al., 2013; Baumann and Smith, 2018; Cai, 2011).

The magnitude of diel pH fluctuations varied seasonally, with greater amplitude in spring and summer compared to winter. This was particularly evident in July and August where the daily peak of pH occurred several hours later compared to June, and potentially reflected the effect of temperature. In wintertime, the daily variation in pH was weaker, likely due to diminished NCP and lower sea surface temperatures. In addition, mixing between the Wadden Sea and the southern North Sea likely altered pH and obscured an already reduced biological signal.

Tidal phase analysis (Figs. 8 and S15) revealed seasonal patterns in pH variability. During winter (February, November–January), pH anomalies varied minimally across tidal phases, consistent with reduced biological activity. However, from March through July, pH anomalies displayed a more complex pattern with a distinctive w-shaped pattern across the tidal cycle. This pattern developed gradually from March, suggesting a strengthening of the biological processes during this period and creating increasing biogeochemical differences between the North Sea and Wadden Sea during the high productive season. This seasonal transition was further supported by a Fourier analysis (Fig. S16), which revealed that from June to September the 24 h frequency dominated the 12 h frequency, suggesting a much stronger influence of biological processes on the daily cycle. However, during the rest of the year, particularly in winter when NCP is lower, the 24/12 h ratio was smaller, suggesting that the tidal forcing played a more prominent role in timing pH variability as result of the mixing between the different water masses in the Marsdiep Channel.

The diel cycle of temperature anomalies also varied seasonally (Figs. 7 and S17). Day-night temperature differences were most pronounced from March through August, reaching a maximum in May with monthly anomaly amplitudes of 0.6 ± 0.2 °C (daily anomalies amplitude of 3.7 ± 0.4). These fluctuations decreased until reaching a minimum in January with anomaly amplitudes of 0.2 ± 0.04 °C.

Although temperature influences pH by altering CO₂ solubility, with warmer waters generally characterised with higher pH due to reduced CO₂ solubility (Zeebe and Wolf-Gladrow, 2001), this mechanism alone cannot explain the observed patterns. While the carbonate system equilibration timescale is on the order of minutes or faster (Mojica Prieto and Millero, 2002), the exchange of CO₂ between the atmosphere and sea reaches equilibrium over much longer timescales, from weeks to months (Jones et al., 2014). Therefore, if temperature were the main driver, pH would be expected to closely follow the temperature pattern. To assess the influence of temperature, pH was recalculated using varying temperature and monthly means of TA, DIC and salinity (pH_temp) using PyCO2SYS v1.8.2 (Humphreys et al., 2023) (Fig. S18). The observed pH variations appeared to be primarily driven by processes other than temperature change, as key variations often occurred independently of temperature fluctuations. Additionally, pH deviated from pH_temp for most of the year, especially during the warmer months. For instance, pH often reached its daily maximum several hours before temperature, as observed in June (Figs. 7, S14 and S18). However, in the beginning of February, then December and January, pH tracked closely pH_temp, indicating that temperature's influence on pH became more prominent during the colder months, during which biological activities were reduced (Fig. S18).

If temperature were the primary driver, pH should consistently rise and fall with temperature fluctuations through the year, but this was not observed during this study. This strongly suggests that biological activities played a more dominant role in influencing pH variations. The mismatch between temperature and pH peaks is more consistent with light-driven NCP, during which CO₂ is consumed and results in a pH increase during periods of maximum light availability rather than maximum temperatures. This biological control may also (partly) explain the seasonal variation in pH amplitudes, with higher variability in spring and summer and coinciding with periods of increased NCP.

The diel cycle of DIC anomalies (Figs. 7 and S19) was opposite to that of pH. In winter, DIC monthly anomalies were smaller and ranged between -6.6±3.2 and 5.9 ± 4.0 µmol kg⁻¹ (with daily anomalies ranging from -43.4 ± 12.6 µmol kg⁻¹ to 50.4 ± 12.7 µmol kg⁻¹ ), consistent with weaker biological activities. Whereas, in spring and summer, these anomalies increased up to 17.6 ± 13.3 and 22.2 ± 13.3 µmol kg⁻¹ (with daily anomalies ranging from -90.5 ± 26.8 to 103.1 ± 18.1 µmol kg⁻¹). These results suggest intensified respiration during the night and NCP during the day. During these periods, pH changes closely followed DIC fluctuations, with nighttime increases in DIC corresponding to decreases in pH, and daytime DIC decreases aligning with pH increases. For instance, in June a decrease of 39.9 ± 13.3 µmol kg⁻¹ in DIC anomalies over 7 h during the day corresponded to a pH increase of 0.06 ± 0.02 during the same period, suggesting a link between DIC and pH variability that is answering to NCP and respiration. Tidal phase analysis of DIC (Figs. 8 and 20) revealed similar complexity as TA which suggests that, like TA, DIC is controlled by multiple mechanisms including water mass mixing, biological processes and potentially benthic fluxes that can mask the expected tidal signal, creating a complex DIC-tidal phase relationship.

ΔfCO₂ (Figs. 7 and S21) mirrored the diel pattern of DIC. ΔfCO₂ anomalies were typically negative during daytime as the sea acted as a CO₂ sink and shifted to positive anomalies at night, likely due to respiration. This diel ΔfCO₂ cycle became more pronounced from March to October, with monthly anomalies ranging from -37±49 to 43 ± 47 µatm (with individual daily anomalies ranging from -143 ± 48 to 196 ± 48), while in winter, the diel variation was minimal and close to zero. Together, these patterns in ΔfCO₂, DIC and pH suggest that biological processes, rather than abiotic factors, were the primary driver of their diel variability, with stronger day-night differences during warmer months when both extended daylight hours and higher temperatures enhance photosynthesis and respiration (Regaudie-de-Gioux and Duarte, 2012). This interpretation is further supported by the dominance of the 24 h frequency in the Fourier analysis (Fig. S16), which is characteristic of biologically controlled cycles.

There were periods across the year when tidal influences on DIC became more pronounced (Fig. S19), particularly in autumn and winter (February, November to January), when biological processes are generally weaker. During these months, DIC anomalies showed minimal day-night variation and followed a semi-diurnal cycle, closely resembling that of TA and water level. This suggests that during the colder months, hydrological processes exerted a stronger influence on DIC fluctuations than biological processes, and this was demonstrated by the 24/12 h ratio (Fig. S16),where the tidal component was dominant in winter and autumn. While the influence of these fluctuations on pH was smaller compared to the biologically driven DIC changes, pH monthly anomalies varied slightly, ranging between -0.003 ± 0.001 and 0.004 ± 0.002 (with daily anomalies ranging between -0.04 ± 0.009 and 0.03 ± 0.008).

Changes in both TA and DIC influence pH, although the underlying drivers differ. While TA was mainly driven by hydrological processes, DIC was driven by both biological and hydrological factors. The relative influence of these processes varied seasonally, with a higher biological influence during warmer months and more hydrological processes during the colder months. To quantify the influence of biological and hydrological processes on DIC, and their subsequent influence on pH, we calculated the Wasserstein distance for the two components of DIC, DIC_bio and DIC_hydro which represents the influence of biological and hydrological processes on DIC, respectively. The results (Fig. 9) show a clear seasonal pattern where the Wasserstein distance between DIC_bio over DIC_hydro was lower during winter indicating that hydrological processes exerted a stronger influence on DIC during winter period, which was also demonstrated by the Fourier analysis (Fig. S16). Conversely, the greater distance observed for the rest of the year suggests a stronger divergence between biological and hydrological influences on DIC, reinforcing then the observed seasonal differences in TA and DIC variability.

These results are consistent with seasonal scale variations discussed in Sect. 4.1.2 and highlight that pH is ultimately controlled by biological processes through DIC during most of the year.