Lake Grevelingen, located in the southwestern delta area of the Netherlands, is a coastal marine lake with a surface area of 115 km2 and an average water depth of 5.1 m (Nienhuis, 1978; Fig. 1). The bathymetry of the lake is characterised by deep gullies intersecting extended shallow areas; half of the lake is shallower than 2.6 m, and only 12.4 % of the lake is deeper than 12.5 m. In the main gully, several deep basins are present, which are separated from each other by sills. The deepest basin extends down to 45 m water depth. Originally, Lake Grevelingen was an estuary with a tidal range of about 2.3 m. A large flooding event in 1953 was the motive for the construction of two dams. The Grevelingen estuary was closed off on the landward side in 1964 and on the seaward side in 1971. This isolation led to a freshening of the system, with vast changes in water chemistry and biology (Bannink et al., 1984). To counteract these water quality problems, a sluice extending vertically between 3 and 11 m depth was constructed on the seaward side in 1978 (Pieters et al., 1985). Exchange with saline North Sea water has dominated the water budget since, resulting in the lake approaching coastal salinity (29–32) and an estimated basin-wide water residence time of 229 days (Meijers and Groot, 2007). Upon intrusion, the denser North Sea water forms a distinct subsurface layer, which is then laterally transported into the lake. Yet it has been found that opening the sluice hardly affects water-column mixing (Nolte et al., 2008), and the water quality problems persist. Monthly monitoring carried out by the executive arm of the Dutch Ministry of Infrastructure and the Environment revealed that the main gully of Lake Grevelingen has experienced seasonal stratification and hypoxia since the start of the measurements in 1978, which have differed in extent and intensity annually (Wetsteyn, 2011).

Throughout 2012, we performed monthly sampling campaigns on board the R/V Luctor, examining water-column chemistry, biogeochemical process rates and sediment–water exchange. Sampling occurred in the Den Osse basin (maximum water depth 34 m; Fig. 2), a basin located in the main gully of Lake Grevelingen. Two sills surround the basin at water depths of 10 and 20 m at the landward and seaward sides, respectively. Due to its bathymetry, particulate matter rapidly accumulates within the deeper parts of the basin (sediment accumulation rate > 2 cm yr-1; Malkin et al., 2014). The surface area and total volume of the Den Osse basin have been estimated at 649 × 104 m2 and 655 × 105 m3, respectively (Pieters et al., 1985), resulting in an average water depth of ca. 10 m. Sampling occurred at three stations along a depth gradient within the basin (Fig. 1b): S1 at 34 m water depth and located at the deepest point of the basin (51.747∘ N, 3.890∘ E), S2 at 23 m (51.749∘ N, 3.897∘ E) and S3 at 17 m (51.747∘ N, 3.898∘ E). Each campaign, water-column sampling was performed at station S1. Discrete water-column samples were collected with a 12 L Niskin bottle at eight different depths (1, 3, 6, 10, 15, 20, 25 and 32 m) to assess the carbonate system parameters (pH, partial pressure of CO2 (pCO2), total alkalinity (TA) and DIC), concentrations of O2, hydrogen sulphide (H2S), dissolved organic carbon (DOC) and nutrients, and rates of community metabolism. All water samples were collected from the Niskin bottle with gas-tight Tygon tubing. A YSI6600 CTD probe was used to record depth profiles of temperature (T), salinity (S), pressure (p) and chlorophyll a (Chl a). To determine sediment–water exchange fluxes, intact, undisturbed sediment cores (6 cm ∅) were retrieved with a UWITEC gravity corer in March, May, August and November 2012 at the three stations S1, S2 and S3. Sampling usually took place mid-morning to minimise the influence of diurnal variability in determining the seasonal trend. The exact dates and times of sampling are provided in the online supplementary information.

From T, S and p the water density ρw (kg m-3) was calculated according to Feistel (2008) using the package AquaEnv (Hofmann et al., 2010b) in the open-source programming framework R. Subsequently, the density anomaly σT (kg m-3) was defined by subtracting 1000 kg m-3 from the calculated value of ρw. Water density profiles were also used to calculate the stratification parameter ϕ (J m-3), which represents the amount of energy required to fully homogenise the water column through vertical mixing (Simpson, 1981): ϕ=1h∫-h0ρav-ρwgzdzwithρav=1h∫-h0ρwzdz, where h is the total height of the water column (m), z is depth (m), g is gravitational acceleration (m s-2), and ρav is the average water-column density (kg m-3).

Samples for the determination of [O2] were drawn from the Niskin bottle into volume-calibrated clear borosilicate biochemical oxygen demand (BOD) bottles of ca. 120 mL (Schott). O2 concentrations were measured using an automated Winkler titration procedure with potentiometric end-point detection (Mettler Toledo DL50 titrator and a platinum redox electrode). Reagents and standardisations were as described by Knap et al. (1994).

During summer months we examined the presence of H2S in the bottom water. Water samples were collected in 60 mL glass serum bottles, which were allowed to overflow and promptly closed with a gas-tight rubber stopper and screw cap. To trap the H2S as zinc sulphide, 1.2 mL of 2 % zinc acetate solution was injected through the rubber stopper into the sample using a glass syringe and needle. A second needle was inserted simultaneously through the rubber stopper to release the overpressure. The sample was stored upside down at 4 ∘C until analysis. Spectrophotometric estimation of H2S (Strickland and Parsons, 1972) was conducted by adding 1.5 mL of sample and 0.120 mL of an acidified solution of phenylenediamine and ferric chloride to a disposable cuvette. The cuvette was closed immediately thereafter to prevent the escape of H2S and was allowed to react for a minimum of 30 min before the absorbance at 670 nm was measured. For calibration, a 2 mmol L-1 sulphide solution was prepared, for which the exact concentration was determined by iodometric titration.

For the determination of TA, two separate samples were collected in 50 mL centrifuge tubes. To determine the contribution of suspended particulate matter to TA, one sample was left unfiltered, while the other was filtered through a 0.45 µm nylon membrane syringe filter (Kim et al., 2006). TA was determined using the standard operating procedure for open cell potentiometric titration (Dickson et al., 2007; SOP 3b), using an automatic titrator (Metrohm 888 Titrando), a high-accuracy burette (1 ± 0.001 mL), a thermostated reaction vessel (T=25 ∘C) and combination pH glass electrode (Metrohm 6.0259.100). TA values were calculated by a non-linear least-squares fit to the titration data in a custom-made script in R. Quality assurance involved regular analysis of Certified Reference Materials (CRM) obtained from the Scripps Institution of Oceanography (A.G. Dickson, batches 116 and 122). The relative standard deviation of the procedure was less than 0.2 % or 5 µmol kg-1 (n=10).

Samples for DIC analysis were collected in 10 mL headspace vials, left to overflow and poisoned with 10 µL of a saturated mercuric chloride (HgCl2) solution. DIC analysis was performed using an AS-C3 analyser (Apollo SciTech) which consists of an acidification unit in combination with a LICOR LI-7000 CO2/H2O gas analyser. Quality assurance involved carrying out three replicate measurements of each sample and regular analysis of CRM. The accuracy and precision of the system are 0.15 % or 3 µmol kg-1.

Water for pCO2 analysis was collected in 50 mL glass serum bottles from the Niskin bottle with Tygon tubing, left to overflow, poisoned with 50 µL of saturated HgCl2 and sealed with butyl stoppers and aluminium caps. Samples were analysed within 3 weeks of collection by the headspace technique (Weiss, 1981) using gas chromatography (GC) with a methaniser and flame ionisation detection (GC-FID, SRI 8610C). The GC-FID was calibrated with pure N2 and three CO2 : N2 standards with a CO2 molar fraction of 404, 1018, 3961 ppmv (Air Liquide Belgium). Headspace equilibration was done overnight in a thermostated bath, and temperature was recorded and typically within 3 ∘C of in situ temperature. pCO2 data were corrected to in situ temperature. Samples were collected in duplicate and the relative standard deviation of duplicate analysis averaged ±0.8 % (n=90).

Samples for the determination of pH were collected in 100 mL glass bottles. pH measurements were done immediately after collection at in situ temperature using a glass/reference electrode cell (Metrohm 6.0259.100) following standard procedures (Dickson et al., 2007; SOP 6a). Both National Institute of Standards and Technology (NIST) and TRIS (2-amino-2-hydroxymethyl-1,3-propanediol) buffers were used for calibration. The temperature difference between buffers and samples never exceeded 2 ∘C. pH values are expressed on the total hydrogen ion scale (pHT).

Net community respiration (NCP), gross primary production (GPP) and community respiration (CR) were determined using the oxygen light–dark method (Riley, 1939; Gazeau et al., 2005a). Samples were drawn from the Niskin bottle into similar BOD bottles as described in Sect. 2.2. Bottles were incubated on-deck in a water bath, keeping them at ambient surface-water temperature by continuous circulation of surface water. Samples were incubated both under various light intensities and in the dark. Hard neutral density filters with varying degrees of shading capacity (Lee Filters) were used to mimic light conditions at different depths, while sample bottles incubated in the dark were covered with aluminium foil. Incubations lasted from the time of sampling (usually mid-morning) until sunset. Oxygen concentrations were determined before and after incubation using the automated Winkler titration procedure described in Sect. 2.2.

Samples incubated in the light were used to determine NCP by calculating the difference in oxygen concentrations between the start and end of the incubations, divided by the incubation time (5 to 13 h). CR was determined in a similar fashion from samples incubated in the dark. GPP was subsequently calculated as NCP+CR (all rates expressed in mmol O2 m-3 h-1). To determine the relationship between algal biomass (represented as Chl a concentration) and GPP, samples from all depths were incubated in triplicate at 51.2 % of surface photosynthetically active radiation (PAR). This yielded a linear relationship between [Chl a] and GPP for most months (data not shown). Samples from one depth (typically 3 m) were incubated at 10 different light intensities to determine the dependency of GPP on light availability (P/I curve). These data were normalised to [Chl a] and fitted by non-linear least squares fitting using the Eilers–Peeters function (Eilers and Peeters, 1988): GPPnorm=pmax⁡(2+ω)(I/Iopt)(I/Iopt)2+ω(I/Iopt)+1, where GPPnorm is the measured GPP normalised to [Chl a] (mmol O2 mg Chl a-1 h-1), pmax⁡ is the maximum GPPnorm (mmol O2 mg Chl a-1 h-1), I and Iopt are the measured and optimum irradiance, respectively (both in µmol photons m-2 s-1) and ω is a dimensionless indicator of the relative magnitude of photoinhibition.

Downwelling light as a function of water depth was measured using a LI-COR LI-193SA spherical quantum sensor connected to a LI-COR LI-1000 data logger. A separate LICOR LI-190 quantum sensor on the roof of the research vessel connected to this data logger was used to correct for changes in incident irradiance. Light penetration depth (LPD; 1 % of surface irradiance) was quantified by calculating the light attenuation coefficient using the Lambert-Beer extinction model. To additionally assess water-column transparency, Secchi disc depth was measured and corrected for solar altitude (Verschuur, 1997). In contrast to the measurements of downwelling irradiance, which were only taken mid-morning, Secchi depths were also determined in the afternoon. Although Secchi depths cannot directly be translated into LPD estimates, they do give an indication of the seasonal and diurnal variability in subsurface light climate.

Hourly averaged measurements of incident irradiance were obtained with a LI-COR LI-190SA quantum sensor from the roof of NIOZ-Yerseke, located about 31 km from the sampling site (41.489∘ N, 4.057∘ E). These measurements, together with the light attenuation coefficient, were used to calculate the irradiance in the water column at each hour over the sampling day in 10 cm intervals until the LPD. Measured [Chl a] was linearly interpolated between sampling depths and combined with the fitted P/I curve (Eq. 2) to calculate GPP (mmol O2 m-3 h-1) at 10 cm intervals: GPP=[Chla]pmax⁡(2+ω)(I/Iopt)(I/Iopt)2+ω(I/Iopt)+1. These GPP values were integrated over time to determine volumetric GPP on the day of sampling (mmol O2 m-3 d-1). A similar procedure using measured hourly incident irradiance was followed to calculate volumetric GPP on the days in between sampling days. Parameters of the Eilers-Peeters fit were kept constant in the monthly time interval around the day of sampling, while [Chl a] depth profiles and the light attenuation coefficient were linearly interpolated between time points. These daily GPP values were integrated over time to estimate annual GPP (mmol O2 m-3 yr-1).

Rates of volumetric CR (mmol O2 m-3 h-1) were converted to daily values (mmol O2 m-3 d-1) by multiplying them by 24 h. An annual estimate for CR (mmol O2 m-3 yr-1) was calculated through linear interpolation of the daily CR values obtained on each sampling day. Finally, CR and GPP were converted from O2 to carbon (C) units. For CR, a respiratory quotient (RQ) of 1 was used. For GPP, the photosynthetic quotient (PQ) was based on the use of ammonium (NH4+) or nitrate (NO3-) during primary production. Assuming Redfield ratios, when NH4+ is taken up, this results in an O2 : C ratio of 1:1, hence a PQ of 1. Alternatively, when the algae use NO3-, this leads to an O2 : C ratio of 138:106 and a PQ of 1.3. Since the utilisation of NH4+ is energetically more favourable than that of NO3-, the former is the preferred form of dissolved inorganic nitrogen taken up during primary production (e.g. MacIsaac and Dugdale, 1972). If [NH4+] < 0.3 µmol L-1, we supposed that GPP was solely fuelled by NO3- uptake, while above this threshold only NH4+ was assumed to be taken up during GPP. Although we are aware that this is a simplification of reality, as NO3- uptake is not completely inhibited at [NH4+] > 0.3 µmol L-1 (Dortch, 1990), we have no data to further distinguish between the two pathways. Concentrations of NH4+ and NO3- were determined in conjunction with concentrations of phosphate (PO43-), silicate (Si(OH)4) and nitrite (NO2-) by automated colorimetric techniques (Middelburg and Nieuwenhuize, 2000) after filtration through 0.2 µm filters. Water for DOC analysis was collected in 10 mL glass vials and filtered over pre-combusted Whatman GF/F filters (0.7 µm). Samples were analysed using a Formacs Skalar-04 by automated UV-wet oxidation to CO2, which concentration is subsequently measured with a non-dispersive infrared detector (Middelburg and Herman, 2007). Nutrient and DOC data can be found in the Supplement.

To determine DIC and TA fluxes across the sediment–water interface, we used shipboard closed-chamber incubations. Upon sediment core retrieval, the water level was adjusted to ca. 18–20 cm above the sediment surface. To mimic in situ conditions, the overlying water was replaced with ambient bottom water prior to the start of the incubations, using a gas-tight tube and ensuring minimal disturbance of the sediment–water interface. Immediately thereafter, the cores were sealed with gas-tight polyoxymethylene lids and transferred to a temperature-controlled container set at in situ temperature. The core lids contained two sampling ports on opposite sides and a central stirrer to ensure that the overlying water remained well mixed. Incubations were done in triplicate and the incubation time was determined in such a way that during incubation the concentration change of DIC would remain linear. As a result, incubation times varied from 6 (at S1 during summer) to 65 h (at S3 during winter).

Throughout the incubation, water samples (∼ 7 mL) for DIC analysis were collected from each core five times at regular time intervals in glass syringes via one of the sampling ports. Concurrently, an equal amount of ambient bottom water was added through a replacement tube attached to the other sampling port. About 5 mL of the sample was transferred to a headspace vial, poisoned with 5 µL of a saturated HgCl2 solution and stored submerged at 4 ∘C. These samples were analysed as described in Sect. 2.3. The subsampling volume of 7 mL was less than 5 % of the water mass, so no correction factor was applied to account for dilution. DIC fluxes (mmol m-2 d-1) were calculated from the change in concentration, taking into account the enclosed sediment area and overlying water volume: J=ΔCowΔtVowA, where ΔCowΔt is the change in DIC in the overlying water vs. time (mmol m-3 d-1), which was calculated from the five data points by linear regression, Vow is the volume of the overlying water (m3) and A is the sediment surface area (m2). To determine TA fluxes, no subsampling was performed. Instead, the fluxes were calculated from the difference in TA between the beginning and end of the incubation, accounting for enclosed sediment area and overlying water volume. TA samples were collected and analysed as described in Sect. 2.3.

The measurement of four carbonate system parameters implies that we can check the internal consistency of the carbonate system (see Appendix A). For the rest of this paper, we use DIC and pHT for the carbonate system calculations. This has been suggested to be the best choice when systems other than the open ocean are studied and measurements of TA may be difficult to interpret (Dickson, 2010; see also Appendix A). All calculations were performed using the R package AquaEnv. The main advantage of AquaEnv is that it has the possibility to include acid–base systems other than the carbonate and borate system, which is especially important in highly productive and hypoxic waters. Furthermore, it provides a suite of output parameters necessary to compute the individual impact of a process on pH, such as the acid–base buffering capacity. As equilibrium constants for the carbonate system we used those of Mehrbach et al. (1973) as refitted by Dickson and Millero (1987), which were calculated from CTD-derived T, S and p using CO2SYS (Pierrot et al., 2006). For the other equilibrium constants (borate, phosphate, ammonia, silicate, nitrite, nitrate and the auto-dissociation of water) we chose the default settings of AquaEnv.

CO2 air–sea exchange (mmol C m-2 d-1) on the day of sampling was estimated using the gradient between atmospheric pCO2 (pCO2,atm) and the calculated seawater pCO2 at 1 m depth (both in atm): F=kαpCO2-pCO2,atm, where k (m d-1) is the gas transfer velocity, which was calculated from wind speed according to Wanninkhof (1992), normalised to a Schmidt number of 660. Daily-averaged wind speed at Wilhelminadorp (51.527∘ N, 3.884∘ E, measured at 10 m above the surface) was obtained from the Royal Netherlands Meteorological Institute (http://www.knmi.nl). The quantity α is the solubility of CO2 in seawater (Henry's constant; mmol m-3 atm-1) and was calculated according to Weiss (1974). For pCO2,atm we used monthly mean values measured at Mace Head (53.326∘ N, 9.899∘,W) as obtained from the National Oceanic and Atmospheric Administration Climate Monitoring and Diagnostics Laboratory air sampling network (http://www.cmdl.noaa.gov/). To calculate CO2 air–sea exchange on the days between sampling days, we used daily-averaged wind speed and linear interpolation of the other parameters.

The acid–base buffering capacity plays a crucial role in the pH dynamics of natural waters. Many different formulations of this buffering capacity exist (Frankignoulle, 1994; Egleston et al., 2010). However, a recent theoretical analysis (Hofmann et al., 2008) has shown that, for natural waters, it is most adequately defined as the change in TA associated with a certain change in [H+], thereby keeping all other total concentrations (e.g. DIC, total borate) constant: β=-∂TA∂[H+]. Hence, when the acid–base buffering capacity of the water is high, one will observe only a small change in [H+] for a given change in TA. It should be noted that β is intrinsically different from the well-known Revelle factor (Revelle and Suess, 1957; Sundquist et al., 1979) that quantifies the CO2 buffering capacity of seawater, i.e. the resilience of the coupled ocean–atmosphere system towards a perturbation in atmospheric CO2.

In this study, β was calculated according to Hofmann et al. (2008) and subsequently used to quantify the effect of several processes on pH individually as described in Hofmann et al. (2010a). Traditionally, the carbonate system is quantified using DIC and TA. Although this approach has many advantages, it can only determine the combined effect of several concomitantly acting processes on pH. In the method proposed by Hofmann et al. (2010a), pH is calculated explicitly in conjunction with DIC. As a result, the individual contribution of each individual process on pH can be extracted, even though several processes are acting simultaneously (Hagens et al., 2014). Therefore, this method is ideally suited for the analysis of proton cycling and constructing proton budgets. Briefly, each chemical reaction takes place at a certain rate and with a certain stoichiometry; for example, aerobic respiration can be described as CH2O(NH3)γN(H3PO4)γP+O2→CO2+H2O+γNNH3+γPH3PO4, where γN and γP are the ratios of nitrogen (N) and phosphorus (P) to carbon (C) in organic matter, respectively. At first sight, this reaction equation does not seem to produce any protons. However, the CO2 (as carbonic acid, H2CO3), ammonia (NH3) and phosphoric acid (H3PO4) formed will immediately dissociate into other forms at a ratio similar to their occurrence at ambient pH. As a result, protons are produced during aerobic respiration, despite the fact they are absent in Eq. (R1). The amount of protons produced is termed the stoichiometric coefficient for the proton (νH+x) or proton release rate. This coefficient is process-specific and, for aerobic respiration, equals c2+2c3-γNn1+γP(p2+2p3+3p4) (Hofmann et al., 2010a; Table 1). Here, c2 and c3 are the ratios of bicarbonate (HCO3-) and carbonate (CO32-) to DIC, n1 is the ratio of NH4+ to total ammonia, and p2, p3 and p4 are the ratios of dihydrogen phosphate (H2PO4-), monohydrogen phosphate (HPO42-) and PO43- to total phosphate, respectively. As these ratios depend on the ambient pH, so does the value of νH+x.

In natural systems, the vast majority of protons produced during a biogeochemical process according to νH+x are consumed through immediate acid–base reactions, thereby neutralising their acidifying effect. The extent to which this attenuation occurs is controlled by the acid–base buffering capacity of the system. Hence, the net change in [H+] due to a certain process x (µmol kg-1 d-1) is the product of the process rate (Rx; µmol kg-1 d-1) and the stoichiometric coefficient for the proton of that reaction (νH+x), divided by β: d[H+]xdt=νH+xβRx. The total net change in [H+] over time is simply the sum of the effects of all relevant processes, as they occur simultaneously: d[H+]totdt=1β∑x=1nνH+xRx. A straightforward way to express the vulnerability of a system to changes in pH is to look at the proton turnover time (Hofmann et al., 2010a). For this we first need to define the proton cycling intensity, which is the sum of all proton-producing (or consuming) processes. When dividing the ambient [H+] by the proton cycling intensity, the proton turnover time (τH+) can be estimated. The smaller the proton turnover time, the more susceptible the system is to changes in pH. In a system that is in steady state, i.e. the final change in [H+] is zero, the proton cycling intensity is the same irrespective of whether the sum of the proton producing or consuming processes is used for its calculation. In a natural system like the Den Osse basin this is not the case, meaning that total H+ production and total H+ consumption are not equal. Here, we use the smaller of the two for the calculation of the proton cycling intensity. As a result, the calculated turnover times should be regarded as maximal values.

Figure 2 shows a schematic overview of the major processes affecting proton cycling in the Den Osse basin. For each of the four seasons (March, May, August and November), we estimated a proton budget for the basin by calculating the net production of protons (d[H+]xdt) for GPP, CR, nitrification, CO2 air–sea exchange, sediment–water exchange of DIC and TA and vertical water-column mixing, taking account of the effects of S and T changes (Hofmann et al., 2008, 2009). These budgets thus represent the processes influencing the cycling of protons on the day of sampling. We divided the vertical of the basin into eight depth layers, whereby the eight sampling depths represented the midpoint of each layer. Using the bathymetry of the lake, for each box we calculated the total volume of water in the layer, the area at the upper and lower boundary (planar area) and the sediment area interfacing each box. The stoichiometric coefficients for the proton (νH+x) were calculated with AquaEnv using the measured concentrations of DIC, total phosphate, total ammonia and total nitrate (Table 1). Rates of nitrification (mmol N m-3 d-1) were estimated from the measured T, [NH4+] and [O2] (in mmol m-3) using (Regnier et al., 1997): Rnitr=86400kmax⁡exp⁡T-2010ln⁡q10[NH4+][NH4+]+250[O2][O2]+15, where kmax⁡ is the maximum nitrification rate constant (3 × 10-4 mmol m-3 s-1) and q10, which is set at 2, is the factor of change in rate for a change in temperature of 10 ∘C. CO2 air–sea exchange rates were converted to mmol m-3 d-1 by first multiplying them with the total surface area of the Den Osse basin (m2) and then dividing them by the volume of the uppermost box (m3), assuming that CO2 air–sea exchange only directly affects the proton budget of this box. Similarly, DIC and TA sediment fluxes (mmol m-2 d-1) were multiplied by the corresponding sediment area of the basin (m2) and then divided by the volume of the box corresponding to their measurement depth (m3). To ensure mass conservation, vertical TA and DIC transport rates (mmol d-1) were computed by multiplying the difference in mass between two consecutive boxes (mmol), i.e. the product of concentration and volume, with a mixing coefficient ζ(d-1) that was calculated based on the entrainment function by Pieters et al. (1985), multiplied by the volume of water below the pycnocline. Then the transport rates were converted to mmol m-3 d-1 by dividing them by the volume of the corresponding box. Finally, all rates (expressed in mmol m-3 d-1) were divided by 10-3 × ρw (kg L-1) to convert them to µmol kg-1 d-1.

The sum of d[H+]xdt of all processes considered (d[H+totdt; Eq. 8) was compared with Δ[H+]obsΔt, which was calculated from the measured pHT as the weighted average of the observed change in [H+] between the previous month and the current month, and between the current month and the next month. The difference between Δ[H+]obsΔt and d[H+]totdt is represented as the closure term of the budget, which is needed because some of the proton producing and consuming processes are unknown or have not been measured. This budget closure term includes the effect of lateral transport induced by wind and/or water entering Lake Grevelingen through the seaward sluice, which could not be quantified due to a lack of hydrodynamic data.

Over the year 2012, the surface-water temperature at Den Osse ranged from 1.99 to 21.03 ∘C, while bottom-water temperature showed a substantially smaller variation (1.47–16.86 ∘C; Fig. 3a). The surface water was colder than the bottom water in January, while the reverse was true between February and April. However, the temperature difference between surface and bottom water of Den Osse remained within 1 ∘C. Warming of the surface water in late spring rapidly increased the difference between surface and bottom water to 9.3 ∘C in May. This surface-to-bottom difference in temperature decreased but persisted until August. The thermocline, which was located between 10 and 15 m in May, deepened to 15–20 m in June. In July and August, on the contrary, temperature continuously decreased with depth. In September, the temperature depth profile was almost homogeneous, while in November and December surface waters were again cooler than bottom waters.

Salinity (Fig. 3b) increased with water depth at all months, but the depth of the halocline and the magnitude of the salinity gradient varied considerably over the year. This salinity gradient resulted from denser, more saline North Sea water that sank when entering Lake Grevelingen. Variations in the sluice operation, and resulting changes in North Sea exchange volumes, could therefore explain the observed month-to-month variability in salinity depth profiles. Halocline depth varied between ca. 6 m (March and from August to October) to ca. 17 m (November). The largest difference between surface (30.08) and bottom (32.21) water salinity was found in March. Lower inflow and outflow volumes, resulting from strict water level regulations in spring and early summer (Wetsteyn, 2011), led to a lower salinity throughout the water column between April and June. In July and August, a small (∼ 0.2) but noticeable decrease in salinity was recorded from 15–20 m onwards, suggesting the intrusion of a different water mass. Precipitation did not appear to exert a major control on the salinity distribution, as there was no correlation between mean water-column salinity and monthly rainfall as calculated from daily-integrated rainfall data obtained from the Royal Netherlands Meteorological Institute (http://www.knmi.nl) measured at Wilhelminadorp.

Similar to temperature, the difference in density anomaly (σT; Fig. 3c) between surface and deep water was highest in May. This density gradient was sustained until August, indicating strong water-column stratification during this period. The depth of the pycnocline decreased from ca. 15 m in May and June to ca. 10 m in July and August. This corresponded to a weakening of the stratification as indicated by the stratification parameter ϕ, which dropped from 3.34 J m-3 in May to 2.09 J m-3 in August (Fig. 3e). This weakening in stratification was presumably due to the delayed warming of bottom water compared to surface water. A week before sampling in September, weather conditions were stormy (maximum daily-averaged wind speed of 7.0 m s-1), which most likely disrupted stratification and led to ventilation of the bottom water. The resemblance in the spatio-temporal patterns of T, S and σT indicates that the water-column stratification was controlled by both temperature and salinity, where salinity was important in winter (ϕ values of ca. 1 J m-3) and temperature gradients intensified stratification in late spring and summer.

Oxygen concentrations (Fig. 3d) were highest in February as a result of the low water temperatures, increasing O2 solubility. A second peak in [O2] occurred in the surface water in July, during a period of high primary production (see Sect. 3.3.1), and led to O2 oversaturation in the upper metres. From late spring onwards, water-column stratification led to a steady decline in [O2] below the mixed-layer depth, resulting in hypoxic conditions (< 62.5 µmol L-1) below the pycnocline in July and August. Although in August the bottom water was fully depleted of O2, [H2S] remained below the detection limit (5 µM), indicating the absence of euxinia. From September onwards, water-column mixing restored high O2 concentrations throughout the water column.

Lake Grevelingen surface water is generally characterised by high water transparency and deep light penetration (Fig. 3e). LPD was 9.4 m in March and slightly increased to 10.6 m in May. Between June and August, during a period of high primary production (see Sect. 3.3.1), LPD decreased until 5.8 m. From September onwards, the surface water turned more transparent again. Accordingly, LPD increased up to 12.6 m in November, after which it stabilised at a value of 12.0 m in December. The Secchi disc data generally confirm the observed temporal pattern in the LPD, as is shown by the significant correlation between morning Secchi depths and LPD (r2 = 0.86; P< 0.001). Secchi disc depth was on average ∼ 80 % of LPD and, similar to LPD, was highest in November and lowest in July. Additionally, the Secchi depths indicate that diurnal variations in light penetration may exist. Especially in July, during an intense dinoflagellate bloom (see Sect. 3.3.1), light penetrated much deeper into the water column in the morning than in the afternoon (Secchi disc depths of 2.9 and 0.9 m, respectively). The difference between morning and afternoon Secchi disc depth was much smaller in August (3.3 and 2.5 m) and virtually absent in November (8.5 and 8.4 m).

In 2012, Lake Grevelingen experienced a major phytoplankton bloom in summer (July), a minor bloom with completely different dynamics in early spring (March), and a potential third bloom in late spring (April). The minor March bloom is reflected in a slightly elevated surface water [Chl a] and pHT, no obvious peak in GPP, but a small peak in CR. The major peak in CR in May, accompanied by a Chl a peak at 10 m depth, could result from the early spring bloom, as we might not have captured its full extent, or the potential late spring bloom (see Sect. 3.3.1). However, it most likely represents laterally transported degrading Phaeocystis globosa, the haptophyte that makes up the spring bloom in the southern part of the North Sea (Cadée and Hegeman, 1991). Highest P. globosa cell counts have been found between mid-April and mid-May, corresponding to the timing of the CR peak, at the mouth of the Eastern Scheldt (51.602∘ N, 3.721∘ E) between 1990 and 2010 (Wetsteyn, 2011), and off the Belgian coast between 1989 and 1999 (Lancelot et al., 2007). Moreover, the years with high P. globosa cell counts at the mouth of the Eastern Scheldt coincided with a large area of low-oxygen water in the entire Lake Grevelingen (Peperzak and Poelman, 2008; Wetsteyn, 2011), highlighting the connection between P. globosa blooms and O2 consumption in the lake. The high CR in May combined with the onset of stratification led to a rapid decline in bottom water [O2]. The major dinoflagellate bloom in July was short but very intense in terms of GPP and [Chl a] and appeared to contribute to the sharp increase in hypoxic water volume between June and August. Sinking P. micans from this bloom was degraded, which is reflected in higher CR in July and August compared to June, and the products of this degradation were trapped in the water below the pycnocline, as is indicated by elevated DIC levels. However, the higher CR in July and August and subsequent decline in [O2] may also result from higher water temperatures (Fig. 3a), resulting in faster degradation of allochthonous organic matter. The drawdown of bottom-water O2 is, however, not due to CR alone. The fact that [O2] declines with depth at all months indicates that sediment oxygen uptake may be an important process affecting water-column [O2]. Indeed, substantial sediment O2 uptake was found to take place year-round with rates up to 61 mmol m-2 d-1 at S1 (Seitaj et al., 2015b).

Our depth-weighted, annually averaged CR of 7.8 mmol C m-3 d-1 in the photic zone and 6.1 mmol C m-3 d-1 below the LPD are similar to estimates from the nearby located Western Scheldt, where annually averaged CR ranged from 4.7–19.1 mmol C m-3 d-1, with a mean value of 6.6 mmol C m-3 d-1 (Gazeau et al., 2005b). In the mesohaline part of the seasonally hypoxic Chesapeake Bay, summertime surface-water CR was found to vary between 9.8–53.0 mmol C m-3 d-1, while bottom-water CR varied between 0–45.6 mmol C m-3 d-1 (Lee et al., 2015). Thus, our measurements of CR are well within the range of published values, both for the Dutch coastal zone and for other seasonally hypoxic basins.

Recent modelling studies and previous measurement campaigns have presented lake-wide estimates of GPP ranging from 100 g C m-2 yr-1 (Nienhuis and Huis in 't Veld, 1984) to 572 g C m-2 yr-1 (Meijers and Groot, 2007). When integrating annual volumetric GPP over the depth of the photic zone, we arrive at an estimate of GPP for the Den Osse basin of 225 g C m-2 yr -1 in 2012. Given the different methods used and time periods considered, our estimate of GPP is consistent with these previous studies. In comparison with other coastal systems in the Netherlands, GPP in the Den Osse basin is somewhat lower than that in the adjacent Eastern Scheldt (200–550 g C m-2 yr-1; Wetsteyn and Kromkamp, 1994) and of similar magnitude to that in the western Wadden Sea between 1988 and 2003 (185 ± 13 g C m-2 yr-1; Philippart et al., 2007) and in the Western Scheldt in 2003 (150 g C m-2 yr-1; Gazeau et al., 2005b).

The fluctuations in pHT as shown in Fig. 4a result from the balance between rates and stoichiometry of proton-producing and -consuming processes, mediated by the acid–base buffering capacity of the water. Taking into account that variations in the stoichiometric coefficient for the proton are relatively minor (Table 1) compared to changes in process rates (Figs. 5 and 6) and acid–base buffering capacity (Fig. 4e), we will focus our discussion mainly on the latter two.

Any biogeochemical process will either consume or produce protons based on its stoichiometry, as the reaction always proceeds in the forward direction. The signs of νH+x in Table 1 indicate whether a process produces (positive) or consumes (negative) protons. Thus, CR and nitrification increase [H+], while GPP leads to an increase in pH. For transport processes, the direction of the flux determines whether protons are produced or consumed. For example, CO2 uptake from the atmosphere leads to an increase in [H+], while outgassing of CO2 to the atmosphere consumes protons. For vertical transport and sediment–water exchange, the direction of the net change in [H+] depends on the ratio of TA to DIC flux entering the water mass. When the flux of TA exceeds that of DIC, protons are consumed. On the contrary, when DIC fluxes are higher than TA fluxes, the net effect is an increase in [H+]. Considering the magnitude of the seasonal variability in the various process rates measured at Den Osse, they must significantly impact H+ dynamics.

Aside from this, the spatio-temporal variations in buffering capacity (Fig. 4e) also exert a major control on the proton cycling in this basin. Taking the month of August as an example, β decreases by one order of magnitude when going from surface to bottom water. When the rate of a certain process does not change with depth, the number of protons produced or consumed by this process per kg of water is 1 order of magnitude higher in the bottom water than in the surface water (see Eq. 7). This indicates that, in August, the bottom water is much more prone to changes in pH than the surface water. In line with previous studies focusing on the CO2 buffering capacity (e.g. Thomas et al., 2007; Shadwick et al., 2013), temperature was found to exert an important control on the seasonal variability of the acid–base buffering capacity in the Den Osse Basin. The fact that the contribution of acid–base systems other than the carbonate and borate system to β is highest in the anoxic bottom water is in line with previous work (e.g. Ben-Yaakov, 1973; Soetaert et al., 2007). However, their small contribution in the Den Osse basin contrasts with results from the Eastern Gotland basin in the Baltic Sea. Here, generation of TA during remineralisation under anoxic conditions by denitrification, sulphate reduction and the release of NH4+ and PO43-, and the resultant increase in buffering capacity were found to contribute significantly to the observed changes in pH (Edman and Omstedt, 2013).

To understand how variations in both process rates and acid–base buffering capacity control proton cycling in the Den Osse basin, we used Eq. (7) to calculate the change in [H+] (µmol kg-1 d-1) due to GPP at 1 m depth and CR at 1 and 25 m depth. This analysis reveals that it is the interplay between GPP (Fig. 7d) and β (Fig. 7b) that drives temporal variations in d[H+]GPPdt (Fig. 7e). The seasonal pattern of d[H+]GPPdt resembles that of GPP, but its magnitude is significantly modulated by β, especially in late summer. For example, GPP in August was 4.6 times higher than that of September (57.9 and 12.6 µmol kg-1 d-1, respectively), but d[H+]GPPdt in August was only 1.8 times higher. This difference cannot be explained by νH+GPP (Fig. 7c), which had a higher magnitude in August (-1.31) in comparison with September (-0.92), due to a switch from NO3- to NH4+ uptake (Sect. 2.4). Thus, the relatively high proton consumption in September was driven by the lower surface-water buffering capacity, which is a factor of 3.7 smaller in September compared to August (71 454 vs. 19 474). When comparing d[H+]GPPdt and d[H+]CRdt in the surface layer (Fig. 7e), we see that when GPP was higher than CR, the decrease in [H+] due to GPP was also higher than the increase in [H+] due to CR. This can simply be explained by the fact that β was the same for both processes (Fig. 7b), and the effect of νH+GPP was only minor (Fig. 7c), so that the difference between d[H+]GPPdt and d[H+]CRdt can directly be linked to the difference between GPP and CR (Fig. 7d). Some clear differences between the patterns of d[H+]CRdt at 1 and 25 m depth can be identified (Fig. 7e). With the exception of February, October and December, volumetric CR was higher at 1 m depth than at 25 m depth (Fig. 7d). Thus, the higher d[H+]CRdt in June and August at 25 m compared to 1 m depth was solely driven by the lower acid–base buffering capacity of the bottom water (Fig. 7b). In July, on the contrary, CR at 1 m depth was so much higher than at 25 m depth (30.8 vs. 2.9 µmol kg-1 d-1) that this compensated for the lower buffering capacity at depth (65 373 vs. 10 025) and led to a higher surface-water d[H+]CRdt. Again, this highlights that the magnitudes of both CR and β play a role in determining the actual change in pH.

In summary, in the Den Osse surface water we observe relatively small pH fluctuations (Fig. 7a), despite high variability in the balance between GPP and CR. In the bottom water, CR is much more constant, yet pH variability is much higher. Assuming these processes are the main biogeochemical processes producing or consuming H+ on a seasonal scale, this shows that seasonal changes in the acid–base buffering capacity play a major role in pH dynamics. Thus, our calculations clearly demonstrate that we cannot use only measured process rates to estimate the effect of a certain process on pH. Rather, it is the combined effect of variability in process rates and buffering capacity, combined with minor fluctuations in νH+x, that determines the change in pH induced by a certain process.

To further elucidate the driving mechanisms of pH fluctuations, we calculated a full proton budget for each of the four seasons in 2012. One should realise that these proton budgets are among the first of their kind based on measured data and contain many uncertainties. Figure 8 shows these budgets for 1 and 25 m depth; the budgets for the other depths can be found in the online supplementary information. This calculation illustrates that of all the measured processes, GPP and CR generally had the highest contribution to proton cycling intensity in 2012. CR always dominated the total proton production between 4.5 and 17.5 m and was usually a major contributing process above and below this interval. In the surface water GPP accounted for 34.8–99.2 % of H+ consumption, but deeper in the photic zone GPP still accounted for a significant part of the proton removal (2.7–30.3 % between 4.5 and 8 m depth). CO2 air–sea exchange usually played a minor role in the surface-water proton cycling, apart from November when outgassing of CO2 was high, and 56.6 % of the total proton consumption in the surface water was due to this process. In March, CO2 air–sea exchange contributed 14.2 % to the budget, while in May and August, its influence was less than 6 %. Nitrification accounted for 0.00–34.4 % of the total proton production and was mostly a significant proton cycling process in November and in May below 17.5 m depth. The change in temperature from one day to the next contributed 0.2–30.7 % to the proton cycling intensity and was generally a more important factor in the proton budget in March and November than in May and August. The effect of vertical mixing was even less pronounced, as it accounted for only 0.04–12.7 % of the proton cycling intensity throughout the water column.

With the exception of March, the net result of the TA and DIC fluxes from the sediment was the dominant contributor to the total H+ production in the bottom layer (62.3–99.4 %). Higher up in the basin, its contribution ranged from 2.6 to 49.2 %. In March, the net result of the sediment flux at S1 was a contribution of 24.0 % to the total proton consumption, while at S2 and S3 its effect on the budget was less than 10 %. During all months and at all depths, the absolute value of d[H+]CRdt was larger than that of Δ[H+]obsΔt. This was also usually the case for d[H+]GPPdt, d[H+]exchdt and d[H+]seddt, and in March and November for d[H+]nitrdt and d[H+]tempdt, at the depths where these processes took place. Thus, as was the case for another coastal system (Hofmann et al., 2009), the final change in [H+] resulting from all proton-producing and -consuming processes was much smaller than the change in [H+] induced by each of the separate processes.

The sum of d[H+]xdt of all measured processes (d[H+]totdt; Eq. 8) was 1–2 orders of magnitude higher than Δ[H+]obsΔt. As a result, the budget closure term dominated the proton cycling intensity, with the exception of the surface water in March and November. Its contribution ranged from 34.8 to 100 % of the total H+ production or consumption, the latter depending on the sign of the budget closure term. The dominance of the closure term highlights the uncertainties underlying the current proton cycling budget. These uncertainties arise from spatial and temporal variability, measurement error and incomplete coverage of all processes affecting proton cycling. Taking the sediment fluxes (Fig. 6b) as an example, we see that the standard deviation of both the TA and DIC fluxes, which mostly results from small-scale spatial variability, ranges up to ∼ 100 % of the measured flux. This imposes a large uncertainty on the corresponding proton flux, which may severely impact the bottom-water proton budget. Similarly, by using an empirical nitrification rate expression based on [NH4+] and [O2], we ignore temporal variability caused by, for example, changes in the microbial community. As the nitrification rate, like the other process rates, linearly correlates with the amount of protons produced, changes therein may especially impact the proton budget in November.

Since d[H+]totdt was mostly positive, the processes making up the closure term generally had to decrease [H+], i.e. remove protons from the basin. Taking account of both its order of magnitude and direction of change, we calculated that lateral transport may have accounted for the budget closure term. The average inflow in Lake Grevelingen through the seaward sluice in 2012 was 221 m3 s-1 and took place for 9.9 h per day (calculated based on sluice water levels measured at 10 min intervals; P. Lievense, personal communication, 2013). Meijers and Groot (2007) showed that 30.2 % of the water entering Lake Grevelingen through the sluice remains in the lake for a longer period of time and is not directly transported back during the consecutive period of outflow. This means that, per day, 24 × 105 m3 of North Sea water enters Lake Grevelingen. Assuming that all of this water eventually reaches the Den Osse basin and taking account of the total volume of this basin (655 × 105 m3), this means that the inflow of the seaward sluice can fully replenish the Den Osse basin in 30 days. The average density of the water in the basin in 2012 was 1023.7 kg m-3. If we assume that the pH of the inflowing water was 8.2, or [H+] was 6.31 × 10-3 µmol kg-1, then the proton flux entering the Den Osse basin was 1.55 × 107 µmol d-1. Dividing this by the total volume of the Den Osse basin, which may be a valid assumption if stratification is absent, and correcting for density led to a proton flux of 2.11 × 10-4 µmol kg-1 d-1 into the entire basin. This is in the same order of magnitude as the closure term, which, for example, for the surface water in May was -1.85 × 10-4 µmol kg-1 d-1. Note, however, that the net proton flux will be smaller as protons are also leaving the basin with outflowing water. Additionally, on both the seaward and landward sides Den Osse is surrounded by shallower waters, which are supposed to have a pH similar to that of the surface water at Den Osse. Depending on the depths at which water is entering and leaving the Den Osse basin, most likely more protons will be removed from the basin than it will receive from the adjacent water during horizontal water exchange, thus leading to a negative d[H+]closuredt. This is in line with the negative sign of the budget closure term for most months.

Over the course of the year, proton turnover time (τH+) varied substantially. In March (32.8 days) and November (35.9 days), the linearly interpolated and depth-averaged τH+ in the basin was much higher than in May (17.7 days) and August (14.4 days). For each month, different driving factors explain these patterns. The proton turnover time is linearly correlated with both ambient [H+] and β, and inversely correlated to the process rates. The high average value of τH+ in March is mostly explained by a high buffering capacity in combination with low biogeochemical activity. The decrease in May resulted from a significant increase in biogeochemical and physical process rates, since both the average [H+] and β were higher compared to March. In August, on the contrary, average β decreased a factor of 2.6 while average [H+] increased a factor 2.7, thereby almost cancelling out each other's effect on τH+. The higher turnover time in November, finally, was mostly driven by low process rates in combination with a relatively high average [H+]. To summarise, the proton turnover time in the Den Osse basin is a complex combination of variability in process rates and buffering capacity, but also depends on the ambient pH.

When the proton turnover time is divided by β, one calculates the gross proton turnover time, i.e. the turnover time without buffering (Hofmann et al., 2010a). Given that the average β in the Den Osse basin is ∼ 30 000 and τH+ varies between 14.4 and 35.9 days in the 4 months studied, the gross proton turnover time is in the order of minutes. This demonstrates that buffering reactions in active natural systems are extremely important in modulating the net change in [H+], and again highlights the fact that pH dynamics in these settings cannot be studied by measuring process rates alone.