Benthic Alkalinity fluxes from coastal sediments of the Baltic and North Seas: Comparing approaches and identifying knowledge gaps

. Benthic alkalinity production is often suggested as a major driver of net carbon sequestration 15 in continental shelf ecosystems. However, information and direct measurements of benthic alkalinity fluxes are limited and are especially challenging when biological and dynamic physical forcing causes surficial sediments to be vigorously irrigated. To address this shortcoming, we quantified net sediment-water exchange of alkalinity using a suite of complementary methods, including 1) 224 Ra budgeting, 2) incubations with 224 Ra and Br - as tracers, and 3) numerical modelling of porewater profiles. We choose 20 a set of sites in the shallow southern North Sea and western Baltic Sea, allowing us to incorporate frequently occurring sediment classes ranging from coarse sands to muds, and sediment-water interfaces ranging from biologically irrigated and advective to diffusive into the investigations. Sediment-water irrigation rates in the southern North Sea were approximately twice as high as previously estimated for the region, in part due to measured porewater 224 Ra activities higher than previously assumed. Net 25 alkalinity fluxes in the Baltic Sea were relatively low, ranging from an uptake of -35 µmol m -2 hr -1 to a release of 53 µmol m -2 hr -1 , and in the North Sea from 1 to 34 µmol m -2 hr -1 . Lower than expected apparent nitrate consumption (potential denitrification), across all sites, is one explanation for our small measured net alkalinity fluxes. Carbonate mineral dissolution and potentially precipitation, as well as sulfide re-oxidation also appear to play important roles shaping net sediment-water fluxes at locations in 30 the North Sea and Baltic Sea. North Sea sites, and 3) carbonate mineral precipitation. Our findings suggest that coastal sediments of the Southern North Sea and Western Baltic Sea are currently not major sources of TA to the water column. This is because TA production in deeper anaerobic sediments is counter-balanced by re-oxidation and TA consumption in overlying oxic sediment, causing net TA fluxes to be small and variable. The seasonality of these TA fluxes and their impact on water-column carbonate chemistry and ultimately air-water CO 2 exchange was not assessed in this study but should be a topic of future research.


Introduction
Continental shelf systems are considered to act as sinks for atmospheric CO2 (Borges et al., 2005;Laruelle et al 2010;Rutherford et al., 2021), with an important but currently uncertain role in the global carbon budget (Lacroix et al., 2021). Current trends in shelf CO2 uptake are highly variable 35 (Laruelle et al., 2018), in response to a variety of factors, including: regional trajectories in primary production, acid-base buffering (Thomas et al., 2007), the underlying geology, mixing with riverine and open-ocean waters, and wind patterns (Meyer et al., 2018). Where water depths are relatively shallow, there is an increased potential for benthic-pelagic coupling to affect the net shelf CO2 uptake. In regions like the shallow southern North Sea, persistent wind and tidal-driven mixing strongly impacts both the 40 benthic and pelagic ecosystems. This mixing ventilates surface sediments, supplying oxidants for the respiration of organic matter and flushing out the reduced products, thereby affecting net sedimentwater exchange of dissolved inorganic carbon (DIC) and total alkalinity (TA). Aerobic remineralization is a key DIC source in physically or biologically ventilated surface sediments (Neumann et al., 2021;Rassmann et al., 2020), followed by microbial sulfate reduction (MSR; Al-Raei et al., 2009;Werner et 45 al., 1999Werner et 45 al., , 2001. These DIC sources may be further enhanced to varying extents by anaerobic processes like denitrification, as well as iron and manganese reduction, which, like MSR also produce TA and DIC (e.g., Zeebe & Wolf-Galdrow, 2001). While intense biological reworking limits net organic carbon storage in North Sea sediments (Diesing et al., 2020;de Haas et al., 1997), net carbon uptake from the atmosphere may be possible through a combination of the shelf CO2 pump (Thomas et al., 2004), as 50 facilitated by large oceanic inflows (Lacroix et al., 2021), as well as a long-term increase in the DIC inventory driven by combined biological and anthropogenic CO2 (Clargo et al., 2015). Additionally, there is a suite of geochemical processes which may also affect net shelf CO2 uptake. For example, the precipitation and dissolution of calcium carbonate (CaCO3) and silicate minerals, pyrite formation and oxidation, dissolution and formation of silicate minerals, and reverse weathering 55 may substantially affect net sediment-water fluxes of DIC and TA, and, hence, the carbonate chemistry of the overlying water column (Berelson et al., 2019;Hagens et al., 2015;Pätsch et al., 2018;Rassmann et al., 2020;Thomas et al., 2009;Winde et al., 2017;Schwichtenberg et al., 2020). While these dissolution and precipitation processes are largely abiotic, their rates are shaped by the redox and acidbase setting, which itself is strongly biologically mediated (Morse and Mackenzie, 1990). Therefore, a 60 strong interplay exists in shelf sediments, between biogeochemical cycling of macro and minor nutrients, and benthic (bio)geochemical solid-solution interactions, all of which is further mediated by wind-and tidal-driven physical mixing. Figure 1. Map of sampled stations, with points colored by sediment type.
Substantial prior work in the coastal North Sea shows that these sediment (bio)geochemical processes exert a strong cumulative effect on water-column carbonate chemistry (Brenner et al., 2016;Burt et al., 2014) and ultimate CO2 exchange with the atmosphere (Thomas et al., 2009). Recent 70 modelling and experimental efforts point to benthic denitrification of riverine nitrate as a dominant TA source to the southern North Sea, but also imply a substantial role of benthic carbonate mineral dissolution (Winde et al., 2014;Pätsch et al., 2018;Burt et al., 2016;Schwichtenberg et al., 2020). In addition to these processes, metal (Fe and Mn) reduction can also be an important TA source, especially in depositional centers with finer-grained sediment and greater organic carbon loads (Lenstra et al.,75 2019; Reithmaier et al., 2021). However, rapid sediment accumulation may decouple net Fe reduction from sediment-water TA fluxes (Rassmann et al., 2020) and reaction kinetics of carbonates under impact by dissolved Fe and Mn may be slowed down substantially (Dromgoole and Walter, 1990;Böttcher & Dietzel, 2010 The Baltic and North Seas form a continuum of water and material transport (Gustafsson 1997;Kuliński et al., 2022;Maar et al., 2011), deeply linking the carbon cycles of these two ocean basins. While the nearshore regions of the southern North and western Baltic Seas are located at a similar latitude, have a similar water depth, and contain similar sediment types, they experience very different physical forcing. While tidal forcing dominates in the southern North Sea, the western Baltic is 85 instead characterized by negligible tidal forcing, estuarine mixing and associated salinity variability. For example, large tidal forcing combined with coarse-grained sediments in the southern North Sea, could promote advective over diffusive fluxes, and increase the oxygen penetration depth (Werner et al., 1999(Werner et al., , 2003Billerbeck et al. 2006;Al-Raei et al., 2009). Bioturbation and bioirrigation are also especially important in the coastal North Sea and can explain how sediment-water fluxes of oxygen and 90 other elements vary across season and sediment type Gogina et al., 2018;Neumann et al., 2021;Bratek et al., 2020). In contrast, limited tidal forcing combined with finer-grained sediments in the western Baltic Sea could promote stronger biogeochemical zonation and a relatively greater importance of anaerobic over aerobic processes (Böttcher et al., 2000). While we know that these factors shape benthic biogeochemical processing, sediment-water fluxes in these shallow coastal 95 environments are still poorly-constrained, limiting our understanding of their role in the regional carbon cycle (Kuliński et al., 2022).
In this study, we present new results quantifying sediment-water DIC and TA fluxes in the southern North Sea, considering a variety of methods, including Ra budgets and core incubations. This dataset is augmented by archived porewater data from the Baltic Sea and some additional sites in the 100 North Sea, in order to further understand the differential impacts of physical and biogeochemical forcing in these two nearby basins. Benthic TA, DIC, and element fluxes were modelled from these porewater profiles, aimed at predicting net sediment-water fluxes of DIC and TA across a broad range in sediment types. The relationships of especially SO4 2-, DIC, TA, Fe, and PO4 3were utilized as a first approach on the potential role of secondary (bio)geochemical processes described above, which are so 105 far only poorly represented in regional carbon budgets Schwichtenberg et al., 2020), in the context of the coupled physical and biological drivers of net benthic-pelagic coupling. Each applied method has its own advantages and disadvantages to emphasize advection, diffusion, or bioirrigation to varying degrees. The differences between the approaches are partially related to methodological limits, but may also indicate real differences between the consequences of physical and 110 biological drivers on biogeochemical processes such as net CO2 uptake and, therefore, require further investigations.

Dataset description
Samples collected for this study come from a set of 19 stations in the southern North Sea (10 115 sites) and the western Baltic Sea (9 sites) that were visited during cruises between 2015 and 2020 ( Figure 1). Here we present results from four cruises where sampling and experimental approaches are comparable; these were HE541 (Sept 2019) and MSM50a (Jan 2016) in the North Sea, and EMB111 (Aug-Sept 2015) and EMB238 (May 2020) in the Baltic Sea. Parts of the experimental results from MSM50 and EMB111 have previously been published by Lipka et al. (2018) and Gogina et al. (2018), 120 and these sites were chosen to be complementary in terms of water depth, distance from shore, and sediment type. Only results from HE541 in the southern North Sea are used for the Ra budget and core incubations, while porewater profile modelling and constituent ratio analyses are given for all sites. The water depth at these sites is shallow at 23.6 +/-8.5 m (mean +/-S.D.), with a maximum of 46.0 m (Site AB) and minimum of 11.2 m (Site 52). Of the 19 stations considered here, 10 are classified as sandy 125 sediments, 8 as muds, and one as silt sediment (Lipka, 2017;Lipka et al., 2018). At each site, a multicoring device was used to collect 10 cm diameter cores which contained approximately 20 cm of sediment. Sediment porewaters were extracted within 6 hrs after core collection using Rhizons (nominal pore size of 0.15 μm) at 1-2 cm intervals for the first 10 cm, and with a typical interval of 5 cm below that. Table S1 in the Supporting Information lists the preservation techniques  130 and measurement methods for each analyzed parameter.

Lab Analyses
The samples taken during the HE541 cruise were analyzed according to the following protocols: TA was determined at the Leibniz-Institut für Ostseeforschung Warnemünde (IOW) via a small volume (400-800 μL), two-point potentiometric titration according to van den Berg and Rogers, 1987. The 135 sample was transferred into a vial with a pre-set volume of HCl on board, assuming that all weak acids in solution would be protonated (pH < 3). The sample was cooled at 4 °C until further analysis. Back in the lab, the sample was allowed to equilibrate to room temperature and the first potentiometric point was measured using a pH meter (SevenMulti, Mettler-Toledo, Gießen, Germany). After the addition of HCl (75 μL, 0.1 M), the second point was recorded (pH ≈ 2). Taking these two points, the slope of the 140 electrode response was determined (van den Berg and Rogers, 1987). The measurements were calibrated against certified reference materials (CRMs), from batch 142 provided by Prof Andrew Dickson (Scripps Institution of Oceanography, San Diego, USA). DIC and δ 13 C-DIC were also analyzed at IOW with a continuous-flow isotope-ratio-monitoring mass spectrometry (CF-irmMS) using a gas mass spectrometer (Finnigan MAT 253,Thermo Fisher 145 Scientific, Waltham, USA) coupled to a gas bench (GasBench II, Thermo Fisher Scientific, Waltham, USA) via a continuous flow interface (ConFlo IV, Thermo Fisher Scientific, Waltham, USA) (Winde et al., 2014a). A calibration of the instrument was performed against CRMs provided by Prof Andrew Dickson (Scripps Institution of Oceanography, San Diego, USA). Sulfide concentrations were measured at IOW using the methylene blue technique (Cline, 1969) on a Specord 40 a spectrophotometer 150 (Analytik Jena, Germany). Determination of elemental concentrations (Ca, Fe, Mn, P, S) was performed at Hereon using an ICP-MS/MS (Agilent 8800, Agilent Technologies, Tokyo, Japan) coupled to an ESI SC-4 DX FAST autosampler (Elemental Scientific, Omaha, Nebraska, USA) equipped with a discrete sampling system with a loop volume of 1.5 mL (Zimmermann et al., 2020). Measurements were validated with a 155 seawater standard (S = 35, IAPSO Standard Seawater, Ocean Scientific International Ltd, Hampshire, United Kingdom) with the addition of Fe and Mn (c = 1 mg/L). Calibrations were prepared from either single or multi element solutions traceable to NIST CRMS. Nutrient concentrations were determined using an automated continuous flow system (AA3, Seal Analytical, Norderstedt, Germany) and standard colorimetric techniques (Graßhoff and Almgren, 1983). Dissolved metals, S, P, and Si results from the 160 Baltic Sea samples were measured at IOW via ICP-OES as described by Winde et al. (2014a) and Lipka et al. (2018).

Sediment-water flux determinations
In this study, we applied three independent methods to estimate sediment-water fluxes of major, minor, and trace elements. This is a conservative approach, because each individual method emphasizes 165 advective or diffusive processes to a different degree, ensuring that our calculated sediment-water fluxes span a complete range in possible rates. First, a water-column 224 Ra decay balance, used to derive porewater irrigation rates, which are in turn used to parameterize bulk sediment-water fluxes based on measured concentrations in the upper porewaters. The second approach is similar to the first, but with irrigation rates derived from ship-board 170 core incubation experiments, with both bromide and 224 Ra employed as tracers. We also used PROFILE models to assess sediment-water fluxes for all sites, which uses the shape of porewater profiles to balance internal production and consumption with a vertical diffusive transport (Berg et al., 1998).

224 Ra decay balance
Samples for 224 Ra were collected exclusively during the HE541 cruise in the southern North Sea, 175 following the methods of Moore et al. (2011) and Burt et al., 2016 ( 224 Ra determinations were not made during the other cruises). Briefly, approximately 100 L of water from the ship's seawater line was passed through a cascade of 10 and 1 µm filters, then pumped slowly (1 L/min) through a cartridge containing manganese oxide-coated fibers which quantitatively adsorb Ra (confirmed with efficiency samples). After rinsing and drying, samples were counted first within 24 hours of collection on board 180 the ship with a Radium Delayed Coincidence Counting (RaDeCC) system (Moore and Arnold 1996). A second count was executed after 7-14 days, allowing us to apply the error propagation technique of Burt et al., 2016 to derive uncertainty statistics for the final 224 Ra activities given in section 3.1. In addition to the bulk seawater samples, porewaters were also collected from all sites during the HE541 cruise using Rhizons, with water from all core depths combined into a single sample (~100-200 mL) that was 185 treated and counted on a RaDeCC as described above. Because 224 Ra is not a gas and has a relatively short half-life (3.7 days), its activity in surface waters is a relatively simple balance between advective-diffusive inputs from the sediments (where it decays from its longer-lived parent isotope 228 Th), lateral exchange in surface waters, and radioactive decay (Garcia-Orellana et al., 2021). We assume that lateral exchange is a small term in this budget, 190 allowing us to calculate the benthic advective-diffusive input term (net irrigation) as the balance between radioactive decay and the measured surface water activity. These irrigation rates derived from the 224 Ra decay balance (mean = 81 L m -2 d -1 ) were then used to calculate net sediment-water fluxes by multiplying by the average concentration difference between the pore water and the overlying water concentration. For "sandy" sites, we applied the average porewater concentration of each parameter 195 from the upper 5 cm in each core, while a single concentration from the top sediment layer of each core was used for the "muddy" and "silty" sites. Sign convention is that positive fluxes indicate a flux out of the sediment and vice versa.

Ship-board incubations
Benthic fluxes were measured on intact sediment cores from Multicorer by means of whole core 200 batch incubations. Typically, 3 to 4 intact sediment cores in transparent plastic liners (PMMA, 10 cm inner diameter, 60 cm length) per station were selected, which had no visible perturbations such as cracks, voids, or injured animals. The sediment cores were typically 15 -30 cm in length. The incubation was enclosed with a gas-tight lid that was adjusted to a resulting supernatant height of 15 cm (approximately 1 L volume). The water column was constantly stirred by horizontal propellers. The 205 stirring intensity was adjusted to the highest intensity that did not result in sediment resuspension to ensure vigorous mixing of the supernatant and prevent suspended particles from settling. Incubations were executed aboard the research vessel in a temperature-controlled lab set to in-situ temperature. Primary production was excluded by wrapping the cores in aluminum foil. At the beginning of each incubation, a NaBr solution was injected into the supernatant, which resulted in a final Brconcentration 210 of 1.6 mmol / L. During incubation, oxygen was monitored continuously to assess the progress, and the incubation was terminated when the oxygen saturation dropped below approximately 80 % (typically after 12 to 24 h). Water samples for nutrient and Branalyses were drawn from the core supernatant in 3 -6 h intervals (typically 10 time steps) by means of syringes connected to PVC-tubing. Water samples were then filtered through 0.45 µm syringe filters and stored frozen until analysis in the land-based 215 laboratory. After incubations, additional samples from the supernatant were immediately taken for measurements of Radium and DIC. The incubation method is described in detail in Neumann et al. .

PROFILE Modelling
We first employed the one-dimensional numerical model tool, PROFILE, to derive sediment-220 water fluxes and internal rates of production and consumption for most measured constituents (Berg et al., 1998). PROFILE builds a best-fit model from measured porewater profiles, assuming they are representative of steady state conditions. This model is then split into several equidistant zones (typically 5 to 10 discrete intervals), each of which is fit with a specific net production rate. We then set a first boundary condition as the calculated diffusive flux out the bottom of the model domain, using the 225 concentration gradient in the two deepest porewater samples, as well as the sediment porosity and calculated the molecular diffusion coefficient (Table 1). The final sediment-water flux is then determined through conservation of mass between net internal production and the bottom diffusive flux. Further parameters needed to inform PROFILE include: sediment porosity (φ), biodiffusivity, irrigation, diffusivity, statistical terms, and others given in Table 1. Biodiffusivity and irrigation coefficients were 230 chosen through an iterative process, changing one variable at a time and comparing model performance for each sediment class.

North Sea Irrigation rates (decay balance and incubation)
Surface water 224 Ra activities were consistent throughout the southern North Sea, ranging from 248 ± 11.6 dpm m -3 (Site 33) to 384 ± 21.3 dpm m -3 (Site 90). This is approximately twice as high as found in previous studies in the region (Burt et al 2014;2016), but similar to activities for the Wadden Sea (Moore et al., 2011). Our observation of high surface water 224 Ra is consistent with early fall wind-240 driven vertical mixing causing an enhanced exchange between porewater high in 224 Ra and the surface water. The wind-driven water column mixing also had the effect of breaking down any vertical stratification that may have developed during the summer (not shown). Our porewater 224 Ra activities (8.4 ± 0.89 to 44 ± 3.0 dpm L -1 ; average of 19.9 dpm L -1 (or 19,946 dpm m -3 )) were also approximately double compared to previous measurements in the German Bight (Burt et al., 2014), and the Wadden 245 Sea (Moore et al., 2011). These high 224 Ra activities yield calculated irrigation rates (mean = 81 L m -2 d -1 ; red bars in Figure 2) that were about twice the levels found by Burt et al., (2014). Solute fluxes for these sites are derived using PROFILE modelling, as discussed later. The high variability in porewater 224 Ra activity (8.4 to 44 dpm L -1 ) also shows that care should be taken when deciding on endmember activities for 224 Ra-based budgets aimed at assessing porewater irrigation rates (Cook et al., 250 2018;Garcia-Orellana et al., 2021). Irrigation rates derived from Brand 224 Ra measurements during the ship-board incubation experiments (mean = 10.5 L m -2 d -1 ; blue bars) were a factor of 8 lower than rates derived from the 224 Ra decay balance. This is consistent with prior studies in the southern North Sea, where incubationbased fluxes were 2-3 times lower than decay-balance estimates (Burt et al 2014). This difference is likely due to the fact that the decay balance implicitly represents the combined diffusive, advective, and 260 bio-irrigative processes that exist in the environment, which are incompletely captured in whole-core incubations. We must stress here that the Ra decay-balance does not necessarily represent a better estimate of the real irrigation rate, as many issues also exist with this method especially related to porewater endmember determination and the assumption of steady state (Cook et al., 2018;Garcia-Orellana et al., 2021). Rather, these irrigation rates and solute fluxes presented below, simply represent 265 a most likely range in "real-world" values. The difference among approaches can also illustrate the varying importance of physical and bio-mediated forcing of net sediment-water exchange.

North Sea TA fluxes from irrigation, incubation, and PROFILE modelling
Using the range in irrigation rates shown above, we calculated net sediment-water fluxes for a 270 variety of solutes using the measured surface-pore water concentration difference (by convention, positive is out of the sediment). Average TA fluxes are tabulated in table 2. At only two sites in the North Sea was porewater TA enriched enough to reliably calculate net fluxes using the incubation or budget approaches, given the relatively low precision of the small-volume TA titration method applied here. However, at these two sites (19 and 26), our TA fluxes ( Figure 3) were 1-2 orders of magnitude 275 lower than previous estimates for this region (Brenner et al., 2016;Burt et al., 2014;Voynova et al., 2019). Excluding the PROFILE-modelled TA fluxes for the North Sea (which had very low R 2 ), net TA fluxes in the North Sea were relatively low, ranging from 1 to 6.3 µmol m -2 hr -1 across all sites and sediment types ( seasonal variations in TA) to be more than two orders of magnitude higher, at 488-1117 µmol m -2 hr -1 ( Table 1 in Voynova et al., 2019). Two recent modelling and empirical studies placed mean TA fluxes for this region at 83 µmol m -2 hr -1  and 238 -275 µmol m -2 hr -1 (Brenner et al., 2016) respectively, closer to but still greater than our results.
295 Figure 3. Average sediment-water fluxes (µmol m -2 hr -1 ) derived from Ra or Brincubation or Ra-decay from the North Sea sites only. In this figure, the error bars represent minimum and maximum fluxes calculated from replicate pore-water cores taken at each site.

Baltic Sea TA fluxes from PROFILE modelling
In the Baltic Sea muddy sites AB and LB, TA concentration in surface sediments (0-10 cm depth) 300 exceeded surface water TA by 1-10 mM, a significant excess considering the analytical precision of small-volume TA titrations. This excess TA caused PROFILE-modelled sediment-water TA fluxes in the Baltic Sea muddy sites AB and LB as high as 159 µmol m -2 hr -1 (site LB, Figure 4), while a smaller negative flux was observed at site MB. Down-core trends in TA at these sites are well within measurement precision, allowing us to discuss potential sources of this TA and implications in section 305 3.5. In contrast with the relatively large excess TA in surface sediments at the Baltic Sea muddy sites, TA was very close to the overlying water concentration in Baltic sandy and silty sites, where increases in porewater TA were not observed until depths of 10-15 cm. Resulting modelled TA flux was small and negative at the Baltic sandy and silty sites, at -4.3 and -35 µmol m -2 hr -1 respectively ( Table 2 and Figure 4). In contrast, PROFILE-modelled TA fluxes at averaged across all Baltic Sea muddy sites for 310 which fluxes could be calculated (AB, LB, MB) were 53 ± 95.3 µmol m -2 hr -1 (Table 2). This is approximately 50% of the non-resolved "nonriverine" TA source from Gustafsson et al., (2014), which was implied to be driven largely by denitrification, sulfur metabolism, and silicate weathering. The minor down-core differences in TA in the Baltic Sea sandy sites are due to enhanced mixing in sediments with relatively low microbial activity. An analysis (Sections 3.4-3.6), supporting the 315 following factors as key in sustaining low or negative net TA fluxes in sandy Baltic Sea sites: 1) low net denitrification, 2) complete re-oxidation of sulfide and Fe(II) in surface sediments.

Sediment-water fluxes of other constituents (Baltic and North Sea)
Net sediment-water fluxes are shown together in Figure 4, with the bars representing average PROFILE-modelled fluxes, while the fluxes derived from incubation experiments and 224 Ra decay 320 balances are depicted as the colored points. Typically, PROFILE-modelled fluxes were at least 10x smaller than fluxes derived from the 224 Ra decay balance. This is consistent with enhanced advective forcing that is captured by the decay-balance approach, but missed by the incubation experiment and PROFILE model, which are in closer agreement. In addition to the sediment-water fluxes described above, the PROFILE model also generates estimates of net internal production/consumption, 325 representing a superimposition of combined biological and abiotic sources/sinks in each model zone of the sediment ( Figure S2). Some solute fluxes exhibited similar trends across all sites in the North and Baltic Seas. For example, Si fluxes were consistently positive (out of sediments) for all sites, across all methods ( Figure  4). In agreement with prior work in the region Gogina et al., 2018) ammonium (NH4 + ) release was also common and positive across all locations, except for three "sandy" sites in the North Sea (52,70,90). Net H2S fluxes were not significantly different from zero in any North Sea sites, 340 while PROFILE-modelled H2S fluxes for three Baltic sites (FB2, FB13, and LB) were negative (into the sediment). We believe that these few large negative H2S fluxes were created artificially by our use of a boundary condition (flux out of the bottom) that intersects with the zone of peak H2S accumulation. In contrast, other modelled solute fluxes varied more between basins (North vs Baltic) than across sites within basins. For example, TA fluxes in the North Sea sites were close to zero (albeit with low R 2 ), 345 while PROFILE-modelled fluxes in the Baltic were larger in magnitude and more variable (Figure 4). Baltic sites were also more often sources of Ca 2+ to the water (except AB and FB13), while Ca 2+ fluxes in the North Sea were more variable and statistically less robust. PROFILE-modelled NO3fluxes are variable and close to zero across all sites, in contrast to prior studies in the region suggesting net NO3uptake by denitrification (Brenner et al., 2016). In fact, net 350 NO3fluxes derived from the incubation and Ra budget were positive (out of the sediment). This is in line with porewater NO3trends, which generally show no net depletion in porewaters relative to surface water. While canonical denitrification is likely playing some role, the small NO3fluxes in combination with larger NH4 + fluxes suggest the presence of Dissimilatory Nitrate Reduction to Ammonium (DNRA) as a secondary sink for NO3 -, with denitrification fed by internally produced NO3rather than 355  Silt allochthonous NO3 -. Low net denitrification is consistent with slurry and flow-through core incubations in the German Bight showing denitrification largely supplied internally by nitrification (Marchant et al., 2016). In contrast, net denitrification can be quite high at estuarine sites receiving "new" NO3from the Elbe river, especially during the winter when river discharge is elevated (Neumann et al., 2017). Nevertheless, DNRA is a relatively minor process in the German Bight, limited mostly to intermediate 360 (Marchant et al., 2016) and fine-grained sediment (Bratek et al., 2020). As such, it could also be that these NH4 + fluxes are a simple result of aerobic degradation of organic matter. Therefore, in contrast with prior studies in the region (Burt et al., 2014;Brenner et al., 2016;Voyanova et al., 2019), we suggest relatively low net denitrification rates, with limited potential for TA production. This is in line with De Borger et al (2021) and Pätsch et al (2018), who together indicate relatively low denitrification 365 rates roughly balanced with nitrification, a feature that is supported by our low or negative modelled net TA fluxes ( Figure S2). DIC flux was variable across sites, but most often positive. Fluxes parameterized by Ra budgets and incubations agreed well with previously modelled diffusive fluxes for the region (Lipka 2017, figure 70), but our PROFILE model generated relatively low DIC fluxes. Sites with greater DIC release 370 were also generally larger sources of Si, NH4 + , and P, in line with the breakdown of algal detritus as a source for both.

d 13 C-DIC sources: Miller-Tans plots
The stable isotope composition of DIC reflects the diagenetic impact from dissolved organic 375 matter (DOM) or methane oxidation and interactions with carbonates (e.g., Ku et al., 1999;Meister et al., 2019;Wu et al., 2017). Using measured d 13 C-DIC data, we conducted a Miller-Tans plot analysis aimed at identifying isotopic endmembers as possible DIC sources ( Figure 5). In this graphical approach, the isotopic composition of DIC multiplied by its concentration is plotted against the concentration, with the slope indicative of the δ 13 C-DIC source value, or endmember. If the 380 remineralization of particulate organic carbon (POC) is the only source of DIC to porewaters, the slope of the Miller-Tans plot should be the same as the isotopic signature of d 13 C-POC, which in these sites ranges from -20 to -25 ‰ throughout the southern North Sea (Böttcher et al., 1998(Böttcher et al., , 2000Pollmann et al., 2021;Serna et al., 2014), from -21 to -24 ‰ in the south-western Baltic Sea (Böttcher et al., unpublished data, Voß and Struck, 1997). Any deviation in the y-intercept from typical d 13 C-POC 385 values may result from calcium carbonate dissolution as an important modulator of DIC and TA fluxes (Winde, 2017). Muddy or silty sites (1, 26, AB, FB-13, FB-2, LB, MB, TW) tend to have a larger range in DIC and so allow for a more robust graphical analysis. Calculated d 13 C-DIC endmembers for these sites were generally much higher (heavier) in comparison with the d 13 C-POC references listed above, 390 ranging from -16 to -21 ‰ (Baltic Sea) and -17 to -26 ‰ (North Sea). That the d 13 C-DIC endmember at Site 1 in the North Sea (-26 ‰) is well below the d 13 C-POC source indicates a potential DIC input from methane oxidation. Elevated surface water methane concentrations have been previously observed near Site 1 in the region around Helgoland (Bussmann et al., 2021). Due to lower microbial activity (Al Raei et al., 2009) and enhanced porewater exchange (de Beer et al., 2005), the sandy sites have a smaller 395 total range in DIC concentrations and isotope compositions, decreasing the confidence in a Miller-Tans Plot approach. Some of the sandy sites (2, 33, 4, OB, and ST), however, yield a similar d 13 C-DIC endmember value when compared to the muddy sites with values ranging between -16 and -19 ‰.
Other sandy sites (19,5,52,70,90) have much heavier endmembers, and ranging from -6 to -12 ‰. This could suggest carbonate dissolution is contributing to heavier DIC values (Ku et al., 1999;Winde 400 et al., 2014a,b;Wu et al., 2017). Carbonate weathering in pore waters has previously been suggested to be an important DIC and TA source (Winde et al., 2014a,b;Winde, 2017;Pätsch et al., 2018;Brenner et al., 2016). However, evidence for this is weak in our sandy North Sea sites, where porewater Ca 2+ concentrations were low relative to overlying surface water, as seen in the generally negative Ca 2+ fluxes (Figures 3 and 4), indicating no significant net carbonate dissolution. Instead, these heavier d 13 C-405 DIC endmembers are likely reflective of CaCO3 mineral dissolution and re-precipitation cycling (Walter et. al. 2007).  Fig S1). The grey area represents a range in expected d 13 C-POC values for the North Baltic seas combined, and the error bars represent the standard error of the Miller-Tans slope.

DIC sources and sinks: Process correlations
While the d 13 C-DIC source indicated by the Miller-Tans plot approach above may help to 415 identify possible electron donors, it cannot provide information as to the terminal electron acceptors that were used to respire the organic carbon substrate. Microbial sulfate reduction (MSR) is an important mineralization process in marine sediments of this region (Jörgensen, 1989;Al-Raei et al., 2009) and leads to the production of DIC and TA (Zeebe & Wolf-Gladrow, 2001). Down-core correlations between DIC and SO4 2may indicate the relative extent by which MSR is associated with DIC (and TA) 420 production. We calculated excess DIC and sulfate as the difference between porewater and either 1) bottom water measurements, when porewater salinity, as inferred by porewater K concentration, did not change, or 2) from an empirical relationship between water-column DIC or SO4 2and K (Baltic sites FB-2 and FB-13, where salinity increased down-core).
The muddy and silty sites in the Baltic Sea (MB, AB, LB, TW) have the strongest covariation of 425 SO4 2deficit and DIC, with slopes ranging from -1 to -2.6, with r 2 between 0.86 -0.97, suggesting MSR is a key anaerobic pathway of DIC formation in sites with fine-grained sediment ( Figure 6, green points). In sandy North Sea sites, SO4 2variation is larger than for DIC, suggesting calcification as a possible sink for DIC. In most cases, SO4 2concentrations are less than bottom water, indicating net consumption by MSR (19,4,5,70,90). However, there are also sites where some SO4 2measurements 430 were greater than bottom water (52, 33), suggesting the oxidation of H2S or FeSx. This analysis is consistent with aerobic respiration as the major metabolic pathway for net DIC production in ventilated sandy sediments, likely supported by the relatively deep oxygen penetration depths. Interestingly, North Sea mud stations (1 and 26) also have DIC:SO4 2slopes close to zero (-0.3 and 0.009, respectively). At these sites, while SO4 2variation is greater than DIC variation, the net change in SO4 2is still low. This 435 suggests that, even though oxygen penetration depths are low and gross MSR rates are relatively high (Jørgensen, 1989), it is likely that MSR is coupled with internal sulfide oxidation. Potential sources of this sulfate in cases where it appears to be produced (North Sea sites 1, 33, and 52, and Baltic site ST) include sulfide oxidation and FeSx oxidation, both of which would be increased by intermittent deeper oxygen penetration. 440

TA sources and sinks: Process correlations
We can directly assess the effect of metabolic processes on net TA production for a subset of sites where porewater TA was measured with a sufficient analytical precision. In most of the sandy sites, the down-core variation in TA was less than the analytical precision of the small-volume titrations used. For the sites where porewater TA data are available, TA and DIC are strongly correlated, even in 445 some sandy sites with a much smaller range in both analytes ( Figure 6, orange points). Muddy sites in the Baltic Sea (AB, LB, MB, and the silty TW) have a larger range in both TA and DIC, with slopes (i.e., ratio of TA:DIC) between 0.78 and 1.095. The two sandy Baltic sites (OB and ST) have similar slopes (1.16 and 0.76 respectively), although the range in both variables is much smaller. North Sea Site 1 (muddy) has a slope of 1.12, while the sandy sites have a broad range of 0.13 (site 2) to 0.65 (site 5) 450 and 0.8 (site 4). Modelled DIC fluxes were much larger than TA fluxes for all North Sea sites (Figure 4; see scale), consistent with measured porewater TA:DIC slopes below 1:1 (Figure 6; orange points). This is in part due to the likely dominance of aerobic respiration in ventilated North Sea sediments, which in contrast with anaerobic respiration, produces no TA. This dominance of aerobic respiration in permeable North Sea sediment can be attributed to the 'redox seal', which describes the 455 situation in percolated sediment with mobile bed forms, where virtually the complete percolated sediment layer is oxygenized, whereas transport in the anoxic layer below is restricted to molecular diffusion (Ahmerkamp et a. 2015). Since porewater advection is several orders of magnitude more efficient in the transport of substrates and products than molecular diffusion, fluxes across the sediment surface sustained by aerobic process substantially exceed those sustained by anaerobic processes. 460 Furthermore, we observe relatively large apparent SO4 2consumption below the oxic-anoxic interface (figure 6, purple points), suggesting significant MSR even in sandy sediments. Trends between excess TA and apparent SO4 2consumption are like those for excess DIC (Figure 6; purple points). Baltic muddy sites have significant (r 2 > 0.9) slopes ranging from -1.3 to -2.1. Baltic sandy sites have slopes closer to zero, with small excess TA values, which appear disconnected 465 from apparent SO4 2reduction. North Sea sandy sites also have slopes closer to zero, and the muddy site (Site 1) has a much shallower slope of -0.3. We infer that iterative carbonate mineral dissolution and precipitation recycling is responsible for our observations of relatively high TA:DIC ratios as well as heavy d 13 C-DIC endmembers (Miller-Tans slope). Likewise, we infer microbial SO4 2reduction is also matched by sulfide oxidation, with little net impact on sediment-water TA fluxes. Together, it 470 appears that strong internal recycling of carbonate minerals and SO4 2is a major factor causing net TA fluxes to be low across all sites (Table 1).

Figure 6.
Relationships between excess DIC and excess SO4 2-(green points), excess TA and excess DIC (orange), and excess TA vs excess SO4 2-(purple). Positive values indicate a larger concentration in 475 porewater relative to surface water.

Conclusion
We combined surface water and porewater 224 Ra measurements to build a decay balance, which indicates that the irrigative exchange between porewater and surface water is much greater than previously thought. Implicit in this assessment is our finding that the porewater 224 Ra endmember was 480 more variable and ~twice as large as previously assumed, of importance for future Ra-based budgets, which are highly sensitive to endmember quantification (Cook et al., 2018;Garcia-Orellana et al., 2021). In our southern North Sea sites, net sediment-water TA fluxes were very small in comparison with previous estimates in this region (Voyanova et al., 2019;Burt et al., 2014). This is also in contrast to the 485 measured and inferred TA production rates in the Wadden Sea, which are known to be 3-5 orders of magnitude higher on an aerial basis (Santos et al., 2015), largely associated with substantial net MSR during warm seasons (Al-Raei et al., 2009). TA in ventilated North Sea surface sediments was similar to surface water concentrations, causing net sediment-water fluxes to also be very low (~10x less than for DIC). Here, TA sources and sinks are closely balanced in North Sea sediments. We ascribe this to the 490 potential influence of 1) DNRA / denitrification being fed internally by recycled, rather than "new" NO3 -, 2) MSR in close balance with sulfide oxidation, and 3) carbonate mineral precipitation in the oxic zone.
In the Baltic Sea sites, excess TA was greater in muddy regions (and close to equilibrium in silty and sandy sites), causing modelled fluxes to be generally low and positive (muddy) or negative (sands) 495 implying a sink in surficial sediments. At Baltic Sea sites with small positive TA fluxes (muds/silt), net TA production is likely due to net MSR (see sulfate consumption; Figure 6). In contrast, at sites with net modelled TA uptake (sands), modelling results indicate TA consumption in the uppermost sediment layers, which we attribute to: 1) re-oxidation of sulfide and Fe(II), 2) minimal net denitrification, as in North Sea sites, and 3) carbonate mineral precipitation. 500 Our findings suggest that coastal sediments of the Southern North Sea and Western Baltic Sea are currently not major sources of TA to the water column. This is because TA production in deeper anaerobic sediments is counter-balanced by re-oxidation and TA consumption in overlying oxic sediment, causing net TA fluxes to be small and variable. The seasonality of these TA fluxes and their impact on water-column carbonate chemistry and ultimately air-water CO2 exchange was not assessed 505 in this study but should be a topic of future research.

Data Availability
All data used in the preparation of this manuscript, including PROFILE model input and output are available at the repository figshare (https://doi.org/10.6084/m9.figshare.20134208.v1).

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Contributor roles according to the CRediT Taxonomy Conceptualization: BVD, HT, MEB