During two sampling campaigns from 3 to 9 August 2017 and 28 July to 3 August 2018, 11 profile casts were conducted in a single station in the Chesapeake Bay with a water depth of 25 m (station 858; 38∘58.54′ N, 076∘22.22′ W). The Susquehanna River is the main tributary of the bay representing on average two-thirds of the fresh water input (Zhang et al., 2015). Despite the similar season, the two campaigns occurred at very different river flow, with about 850 m3s-1 in 2017 versus 8500 m3s-1 in 2018 due to release of flood waters from the Conowingo Dam. The August 2018 condition corresponds to flooding which occurs on average every 3.5 years (return period of 3.5 years, USGS survey).

Each CTD (conductivity, temperature, depth) cast was performed during low or high tide slack periods. An oxygen sensor (Clark electrode, SBE Inc.; detection limit of 1 µM) and fluorescence sensor (ECO-FL Fluorometer, WET Labs) were part of the CTD Rosette to take measurements during sampling. Also, a submersible all-plastic pump profiler was attached with the pump near the sensor orifices, allowing measurement and sampling at a resolution of a few centimetres over 25 m water depth. Water was pumped to the deck within 1 min, and water passed through a flow through voltammetry system measuring O2, Mn(II), Fe(II), organically complexed Fe(III), FeS clusters, H2S and polysulfides continuously (Hudson et al., 2019). When redox interfaces were identified, samples were filtered through an acetate cartridge filter (pore size 0.45 µm) for pH and inorganic carbon parameters, which were processed onboard within a few hours after sampling in order to conserve chemical speciation. The pump profiler system was cleaned with deionised water (18 MΩ) onboard the deck of the ship after deployment. No coating effects were observed with the pump system.

For each sample, all redox species were determined in the through flow voltammetry system using cyclic voltammetry with a 100 µm diameter Au/Hg amalgam PEEK microelectrode prepared according to Luther et al. (2008) connected to a DLK-60 electrochemical analyser from Analytical Instrument Systems Inc. The detection limit of this method is 0.2 µM for sulfide and polysulfides. Discrete samples for the determination of NO2-, Fe and Mn species were filtered through nylon luer-lock syringe filters (Millipore, 0.20 µm). Iron was measured on both bulk and filtered samples using the ferrozine method (Stookey, 1970): after HCl acidification (for Fe(II)) and an optional reduction step (for Fe(III)+Fe(II)) with hydroxylamine hydrochloric (final concentration 0.7 M for 1 h), ammonium acetate (final concentration 0.5 M) and ferrozine (final concentration 1 mM). Absorbance at 562 nm was read with a diode array spectrophotometer (Hewlett Packard 8452B). Limit of detection is 100 nM for Fe(II) and Fe(III) with a 1 cm cell. Shipboard nitrite determination was performed using the method of Grasshoff (1983). To 25 mL of sample, 0.5 mL of 58 mM sulfanilamide in 10 % v/v HCl and 0.5 mL of a 4 mM N(1-naphthyl)ethylene diamine hydrochloride solution were added. Samples with added reagents were shaken and left to sit for 15 min, followed by UV–Vis analysis at 540 nm using a 10 cm cell to increase detection limits. Calibration curves were constructed using sodium nitrite. Limit of detection is 10 nM for NO2-.

Dissolved manganese was determined by displacement of a Cd(II)-porphyrin complex with Mn(II) to form the Mn(II)-porphyrin complex (Ishii et al., 1982). Mn(III) species were identified based on slower reactivity with the Cd complex (Madison et al., 2011) as modified in Thibault de Chanvalon and Luther (2019). Alternatively, Mn(III) species were identified after HCl treatment (down to pH=1.5) followed by filtration in order to flocculate and eliminate the dissolved manganese bound to humic material by filtration (Oldham et al., 2017b). Limit of detection is 50 nM for Mn(II) and Mn(III) in a 1 cm cell. MnOx was measured on 20 mL samples of suspended material retained on 0.2 µm filters by the Leucoberbelin blue (LBB) method (Jones et al., 2019). Four millilitres of a reagent solution ([LBB]=78 µM, [acetic acid]=14 mM) react with the filter, and the absorbance is read at 624 nm. KMnO4 was used to calibrate the LBB method, which allows the calculation of the electron equivalents obtained from particulate MnOx. Results are given as MnO2 equivalent, with a limit of detection of 0.1 µM and an uncertainty below 5 %.

The DIC samples were preserved in 250 mL borosilicate glass bottles with 50 µL saturated HgCl2 solution. The total alkalinity (TA) samples were not poisoned to prevent HgS precipitation and H+ release in anoxic and low-salinity waters (Cai et al., 2017). Then TA was analysed by Gran titration in an open-cell setting (AS-ALK2, Apollo SciTech) within 24 h of collection (Cai et al., 2010). The DIC samples were measured by a nondispersive infrared analyser (AS-C3, Apollo SciTech) within a week (Huang et al., 2012). The precision for DIC and TA was about 0.1 %. Both DIC and TA measurements were calibrated against certified reference materials (CRMs Batch 163 and Batch 173 provided by Andrew Dickson of the Scripps Institution of Oceanography). The pH samples were measured onboard at 25 ∘C within 1 h of collection using an Orion ROSS glass electrode and calibrated with NIST standard buffers. The pCO2, calcite saturation and TA were calculated from measured DIC and pH via the CO2SYS program using Cai and Wang (1998) constants. The measured TA was found to be highly correlated to the calculated TA (r2=0.995 and 0.998, slope=0.995 and 1.017 for the 2017 and 2018 campaign respectively), and their difference was always below 45 µM with an average of 7.5 µM for 2017 and of 22.2 µM for 2018. These results suggest a low contribution of non-carbonate species (e.g. nitrite, ammonium or organic matter; Cotovicz et al., 2016), and measured TA was used for the interpretation.

High-resolution profiles of salinity and temperature plotted in Fig. 1 show the stratified water column at station 858. Carbonate and redox chemistry are plotted against salinity in Fig. 2. These data result from the 11 CTD casts performed over 1 week during each campaign and correspond to depths ranging from 0.7 to 25 m. Plots against depth generate noisier profiles and are shown in Fig. A2, while plots against salinity follow the water masses. Despite the overall lower salinity due to a near-7-fold river flow increase in 2018 than 2017 (5800 ms-1 in 2018 versus 850 m3s-1 in 2017), similar zonation of the water column occurred.

A surface layer sampled only in 2018 is visible in the top 3 m depth (Fig. 1). It presents highly variable temperature and oxygen concentration and oversaturation of pCO2 (Fig. 2), indicating emission to the atmosphere. Below, at 3 m depth, a subsurface layer (named primary production zone or PP in Fig. 2) is characterised by a high amount of O2 (about or above 100 % saturation), high pH (about 8; 8.11 ± 0.07, n=13 in 2017 and 7.94 ± 0.08, n=14 in 2018) and high day-to-day temperature variation (above 1 ∘C between different days). The layer presents relatively low pCO2 (505 ±75 µatm, n=13 in 2017 and 770 ± 130 µatm, n=14 in 2018), with minimal values at 110 µatm in 2017 and 205 µatm in 2018 which are below the atmospheric pCO2 of 407 µatm (Chen et al., 2020). This signature corresponds to primary production (PP). Fluorescence (not shown) correlates with pH as expected for primary production (pH=Fluo(mV)×13+7.14, r2=0.8 in 2017 and r2=0.9 in 2018). DICex and TAex reach their minimal value in the surface layer. While DICex minimum is similar between the two campaigns (78 ± 17 µM, n=13 in 2017 and 76 ± 10 µM, n=14 in 2018); TAex minimum is much lower in 2017 (7 ± 3 µM, n=12) than in 2018 (48 ± 7 µM, n=14).

Below, with increasing salinity, an important increase of pCO2 accompanying the decrease of O2, pH and temperature is visible. A relatively invariable low oxygen zone (called ILO in Fig. 2) is here defined by the salinity invariance of O2 concentrations at about 24 ± 3 µM (n=15) in 2017 and 105 ± 5 µM (n=16) in 2018. Other species are also relatively stable for this depth, such as pCO2 at about 3250 ± 150 µatm (n=10) in 2017 and 2590 ± 100 µatm (n=16) in 2018 and pH at about 7.28 ± 0.01 (n=13) in 2017 and 7.37 ± 0.02 (n=16) in 2018. Deeper, where the oxygen is not detectable (≲1 µM) and in absence of free sulfide, the so-called anoxic zone corresponds to a pH minimum at 7.24 ± 0.01 (n=40), similar in 2017 and 2018, that generates a pCO2 maximum. The deepest layer is a sulfidic layer, [H2S]=11.2 ± 2.8 µM (n=36), in which the pH seems quite stable at 7.33 ± 0.01 (n=29) and 7.32 ± 0.01 (n=9) in 2017 and 2018 respectively. The Ca2+ concentrations observed by Su et al. (2021) and during the 2018 cruise (data not shown) vary linearly with salinity (calcium excess stays below 200 µM or 10 % of total Ca). Assuming similar behaviour in 2017, calculations show that the whole water column (except four samples from the PP zone) is under saturated (0.36<Ωcal<1; mean=0.68) with respect to calcite in 2018, while undersaturation is only valid below S=10 in 2017. The main changes between the two campaigns correspond to a greater oxygen penetration in 2018, especially visible in the ILO zone. Additionally, a surface layer (with salinity below 3) is visible above the primary production zone in 2018 but is related to the more superficial sampling in 2018.

The development of the anoxic zone during summer (Su et al., 2021) and the regularity of this development over the years (Sholkovitz et al., 1992; Trouwborst et al., 2006; Lewis et al., 2007; Cai et al., 2017; Oldham et al., 2017a) requires the presence of species able to rapidly oxidise the H2S mixing upward and to reduce the O2 mixing downward. The three main redox couples known to play this role, NO3-/NO2-, MnOx/Mn2+ and Fe3+/Fe2+, are described in Fig. 3 by the superimposition of all cast results against salinity. Four representative casts are plotted in Fig. A3. The primary production zone is depleted in dissolved Mn(II) and Mn(III) and shows an average value for solid MnOx (0.7 ± 0.1 µM, n=4) and NO2- (2.1 ± 0.1 µM, n=18). In 2018, iron speciation was investigated in the primary production zone, showing an important iron pool (1.6 ± 0.1 µM, n=9) dominated by solid Fe(II) (95 % ± 2 %). Below, in the ILO zone, NO2- reaches a maximum plateau at 5.3 ± 0.2 µM, n=11 in 2017 that is not visible in 2018; MnOx dominates the Mn pool in the ILO zone with a concentration of 1.8 ± 0.1 µM, n=14 in 2017 and 1.3 ± 0.2 µM, and n=3 in 2018. Fe(II) represents only 49 %± 13 %, n=4 of the iron pool (for a total iron concentration of 2.0 ± 0.4 µM, n=4) in 2017, while it represents 87 % ± 5 %, n=4 of the iron pool in 2018 (for a total concentration of 1.2 ± 0.2 µM, n=4). Just below oxygen depletion, in the anoxic zone, MnOx reaches a maximum (2.0 ± 0.1 µM, n=25 in 2017 and 2.9 ± 0.4 µM, n=12 in 2018). During both campaigns, the sulfidic layer is characterised by the absence of NO2- and MnOx, while dissolved manganese concentration increases up to 7.7 ± 0.8 µM, n=15, and the iron pool increases to 5.0 ± 0.7 µM, n=13. No Mn(III) was detected with the porphyrin kinetics method (Thibault de Chanvalon and Luther, 2019), but about 30 % of the total dissolved manganese flocculated after acidification down to pH 1.5 when analysed in 2017, indicating the existence of Mn(III).

The simultaneous and high-resolution sampling of multiple carbonate parameters and redox species gives us the rare opportunity to investigate in detail the interaction between carbonate species and redox-sensitive elements. In the Chesapeake Bay, main changes of DIC and TA can be explained by mixing between upstream and oceanic endmembers (Appendix, Fig. A1). This “endmember-driven” interpretation leads to the calculation of an excess of DIC and TA, DICex and TAex, relative to the mixing line, as shown in Fig. 4a. At station 858, the steep gradient observed, for example the pH and pCO2 gradients in the PP zone; the O2 and NO2- gradients above the anoxic zone; and the Mn, Fe and H2S gradients at depth, suggest that ongoing in situ processes control the changes of concentrations and dominate the time-dependent endmember variability or the mixing with an unknown third endmember. Additionally, the TAex versus DICex plot (Fig. 4a) shows steep changes of direction, such as in the case of straight lines between local endmembers maintained by ongoing reactions, while a preponderance of mixing would produce more progressive changes. Finally, at depth, Fig. 4a shows a similar slope for both years studied (ΔTAex/ΔDICex=2.4) rather than a similar TAex and DICex concentration, which reinforces the validity of the reaction-driven approximation.

Assuming (1) that mixing is efficiently described by vertical turbulent diffusion mixing; (2) that the measured concentrations correspond to a steady state – no changes observed over the 1 week sampling; (3) that no additional endmember contributes significantly to the excess calculation, in particular that the samples are isolated from atmospheric exchanges; and (4) that lateral mixing is negligible, which is equivalent to the lateral invariance of the system – as in the stratified water column of station 858, the reaction-driven approximation (Sect. 2.3.1) permits interpretation of the concentration changes as a linear combination of the stoichiometry of several chemical reactions (Eq. 5). The weighted coefficients of each reaction are equal to the rate of each reaction relative to the sum of the rate of all occurring reactions, vi/v (Eq. 4). Accordingly, this interpretation does not identify reactions with minor impact on the carbonate cycle (Eq. 7) or reactions that cancelled each other later during the journey. For example, ΔTAex introduced by PP is frequently cancelled by a similar amount or even higher ΔTAex by AR. The starting point corresponds to the upstream (S=1.5) endmember at DICex=0 and TAex=0. Figure 4a shows a slight DICex enrichment at TAex=0, which reflects a bias from the endmember calculation.

In oxygenated water, the ΔTAex/ΔDICex analysis can be supported and strengthened by looking also at the ΔAOU/ΔDICex ratio (Fig. 4b) and establishing a ΔTAex/ΔDICex/ΔAOU signature for each water layer. Then, a linear combination of up to three reactions can be fit to the observed ΔTAex/ΔDICex/ΔAOU signature. The main candidate reactions to be combined are aerobic respiration (AR), primary production (whose overall mass balance equation is here summarised as negative AR), carbonate dissolution (CD) and nitrification of ammonium (Nit) as presented in Table 1 and in Fig. 4c. In 2017, the whole oxygenated zone, including the PP zone and the ILO zone, is characterised by a ΔTAex/ΔDICex/ΔAOU=0.1/1/1 (Fig. 4a and b), which corresponds to the occurrence of only net aerobic respiration (AR) (theoretical values are 0.15/1/1, see Table 1 and Fig. 4c). Note (a) that “net aerobic respiration” indicates that primary production is possible at a significant rate but slower than AR and (b) that this ΔTAex/ΔDICex/ΔAOU signature indicates weak nitrification following respiration. In case of full nitrification, the theoretical slopes should be ΔTAex/ΔDICex/ΔAOU=-0.167/1/1.31, as proposed by Zeebe and Wolf-Gladrow (2001). A combination of 1 AR and 0.025 Nit (nitrification of 16 % of the produced NH3) improves the modelled value to 0.1/1/1.05. The relatively slow nitrification can be explained by slow kinetics of NH4+ oxidation, with a half-life time estimated between a few days in estuaries (Horrigan et al., 1990) to multiple years in coastal environments (Heiss and Fulweiler, 2016). As a comparison, other NH4+ fates, such as adsorption, lead to an ammonium half-life time of about a few minutes (Alshameri et al., 2018) to a few hours (Raaphorst and Malschaert, 1996) depending on the concentration of fine particles. Additionally, algae are known to use NH4+ as an N source (Raven et al., 1992), and NH4+ can be directly assimilated by heterotrophic organisms.

In 2018, fresh water masses brought by the exceptional flood modified the carbonate system equilibrium. First, a low-salinity layer with pCO2 at 1540 µatm overlays the primary production layer (Fig. 2), preventing the uptake of atmospheric CO2 by primary production as was observed in 2016 (Chen et al., 2020). Just below the surface layer, in the PP zone, the lock down of atmospheric exchange by the low-salinity layer produces supersaturation of trapped O2 (Fig. 2). In Fig. 4a and b, this process translates into a vertical distribution at DICex=40 µM with ΔTAex/ΔDICex/ΔAOU=1.37/0/-1. This original signature can be modelled by the combination of simultaneous carbonate dissolution (CD), the water column being undersaturated, and PP, no important turbidity was visible as modelled by Cerco et al. (2013), in equal proportion (second line in Table 2); the carbonate dissolution buffers the DIC consumption by the PP. Note that the ratio between ΔTAex/ΔAOU implicates an important nitrate assimilation superior or equal to the amount of N required for the PP, as modelised by negative nitrification in Table 2.

In 2018, below the PP zone down to DICex=240 µM, the beginning of the ILO zone, the TAex increases significantly with a ΔTAex/ΔDICex/ΔAOU=0.67/1/0.67 (Fig. 4a and b), incompatible with AR. To explain this signature, a contribution of CD superimposed on AR seems most likely. A linear combination fitting leads to 0.5 CD for 1 AR (third line in Table 2) and results in ΔTAex/ΔDICex/ΔAOU=0.77/1/0.67. An explanation of its occurrence solely in 2018 could be the increase in carbonate-rich suspended material at high flow conditions (Su et al., 2021). Excess of Ca2+ compared to the mixing line with oceanic end member (not shown) indicates that up to 200 µM of Ca2+ is produced in the oxygenated layer. Deeper, in the ILO zone, ΔTAex/ΔDICex/ΔAOU=0.2/1/1.25 (Fig. 4a and b), which results mainly from AR (0.15/1/1) with the possible addition of CD and Nit, the exact signature being fitted for 0.54 CD and 0.46 Nit for 1 AR (fourth line in Table 2), as a continuum of AR and CD relative rates from the overlaying layer. This important nitrification is also in good agreement with the nitrification observed in the PP zone during this campaign, the lack of nitrite build-up in the ILO zone and the relatively high oxygen concentration (at 105 µM) in the ILO zone in 2018 which is able to sustain nitrification. Overall, our results show that the higher river flow of 2018 increases carbonate dissolution for the top 5–10 m water depth that is superimposed on primary production or aerobic respiration. Additionally, in 2017 the ΔTAex/ΔDICex/ΔAOU system indicates weak nitrification, while in 2018 significant nitrification in the ILO and PP zones is suggested by the reaction-driven approximation. The role of nitrification in explaining TAex depletion is only hypothetical since no direct measurements of NH4+ and NO3- were performed. In particular, TAex depletion is particularly intense during high flow, high suspended particles season and could be produced by NH4+ adsorption to the particles rather than by nitrification.

In the absence of oxygen, the ΔTAex/ΔDICex/ΔH2S will be used for rates calculation. In the anoxic zone, the signature is similar in summer 2017 and 2018 at ΔTAex/ΔDICex/ΔH2S=2.4/1/0. The reaction-driven approximation of this signature is more difficult than in oxidised water because more reactions are known to occur simultaneously in the absence of oxygen. However, to fit with the reaction-driven approximation, it is not necessary to describe each reaction step but only the overall changes concerning the journey of a water mass over different redox conditions resulting in a combined result or reaction. This approach has recently been proposed for FeS burial by Hiscock and Millero (2006), Rassmann et al. (2020) or Su et al. (2020b). A scenario combining sulfate reduction (SR) is particularly attractive since SR represents the main carbon remineralisation pathway in absence of oxygen. However, a combination of SR with CD would result in a ΔTAex/ΔDICex between 1.15 and 2 (see Table 1 or Fig. 4c) and fails to reach the ΔTAex/ΔDICex of 2.4. Moreover, SR alone underestimates the importance of the H2S oxidation pathway that can consume all the alkalinity produced during SR. For example, SR follow by oxygenated oxidation results in a ΔTAex/ΔDICex/ΔAOU signature equal to AR only. In the Chesapeake Bay, H2S oxidation is critical since no H2S is measurable in the anoxic zone, while the gradient at the sediment–water interface indicates high H2S sedimentary efflux (Fig. 2).

Generalising these observations, recent efforts to build an alkalinity budget on the global scale (Hu and Cai, 2011; Middelburg et al., 2020) highlight that the alkalinity produced by anaerobic respiration corresponds to the uncharged species produced, mostly in solid or gaseous phases. Indeed, the alkalinity changes produced during a natural reaction equal the “charge transfer” from species having some charge at pH=4.5, such as NO3- and SO42-, to a species that would lose its charges at pH=4.5, mainly HCO3-, that is not counted in the alkalinity calculation (see Eq. 12). Although correct, this approach tends to neglect the roles of Fe and Mn oxides (Middelburg et al., 2020) since their transformation from (oxyhydr)oxides into sulfur or carbonate solid species does not involve any charge transfer. When looking in detail at these processes, the metal oxides are critical since they are the main H2S oxidation pathway that does not regenerate H2SO4 but rather produces S0, Sn2- or FeS (Findlay et al., 2014; Avetisyan et al., 2021), which limits alkalinity consumption.

To build a pool of candidate reactions for the fitting, first, dissolved species at too low a concentration (e.g. Mn2+aq, Fe2+aq) to be a net reagent to affect the carbon cycle at steady state are not taken into account. These species are usually recycled rapidly and hold the role of catalyser or electron shuttle between other redox species and did not reach 10 µM during the campaigns (Fig. 3). Second, many minerals are expected to be at low concentration or thermodynamically not favoured, and their associated reactions are neglected (e.g. iron phosphate, ferrous or manganous oxide, metal sulfur clusters, MnS, FeCO3, adsorption processes, reverse weathering). Therefore, only aqueous species with important stock concentrations (that can exceed 0.1 mM in anoxic water) are taken into account, i.e. SO42-, Ca2+, H2S and NH4+ together with gaseous (N2, CO2) and main solid phases (FeS2, FeS, S0, MnCO3, FeOOH, MnO2). Third, the combination of many carbon remineralisation reactions with re-oxidation reactions or the net result produces a net chemical equation equal to another remineralisation reaction. As an example, the chemical equation of SR followed by H2S oxidation with oxygen is equal to the equation of aerobic respiration: the proposed model confounds both pathways because the resulting chemical changes are similar.

Table 1 lists the resulting combined reactions, and the calculated ΔTAex/ΔDICex slopes are represented in Fig. 4c. For the anoxic zone, the nitrate respiration can be associated with N2 production (NR-N2) or with NH3 production (NR-NH3), and the manganese oxide respiration produces carbonate precipitation (MnR-MnC). For the sulfidic zone, SR can occur alone, producing a build-up of H2S. However, at a certain point, H2S gets significantly oxidised either by MnO2 which produces MnCO3 and S0 (SR-SMnC) or by FeOOH, producing FeS and S0 (SR-SFeS) and ultimately FeS2 (SR-FeS2). Direct respiration of FeOOH is also taken into account, but as the only final Fe product in the model is FeS or FeS2, it has to be accompanied by some SR (FeSR-FeS).

Figure 4c demonstrates that the slope of ΔTAex/ΔDICex=2.4 can be obtained for any reaction in combination with MnR-MnC. Combinations without MnR-MnC, however, lead to a negative SR, whose overall equation could be interpreted as a possible small participation of anoxygenic phototrophic (purple) bacteria (Findlay et al., 2015, 2017), but are not considered further, as the amount of ΔTAex involved would be tiny. Therefore, in the absence of nitrate, oxygen and H2S, only a combination of MnR-MnC with SR-SMnC (producing S0, fifth line in Table 2), SR-FeS (producing FeS, sixth line in Table 2) or CD (releasing Ca2+, seventh line in Table 2) gives the particularly high ΔTAex/ΔDICex of 2.4. S0 was not measured during our campaign, but it has been previously reported in this water column (Findlay et al., 2014), and the S0 produced by SR-SMnC can react with FeS to form FeS2. All the three identified combinations require a critical role of MnO2. Since Fig. 3 does not indicate any clear reaction for iron while the steep gradient of MnOx in proximity to the H2S rich layer suggests reaction between MnOx and H2S, the combination with SR-SMnC is the most likely (fifth line in Table 2). Deeper, the vertical gradient of sulfide suggests that part of the H2S came by diffusion from the sediment's porewater (Fig. 2). The assumptions required for the reaction-driven approximation are still valid as soon as steady state is maintained by ongoing reactions, even if one of the local endmembers has not been sampled, since it is probably located in the sediment. In the presence of sulfide, the ΔTAex/ΔDICex/ΔH2S signature is 2.4/1/1.2 in 2017 and 2.4/1/3.2 in 2018 (Fig. 4a and d) and can be explained by the same combination of reactions without complete oxidation of H2S from SR to take into account the build-up of H2S (Table 2).

The high observed ratio of ΔTAex/ΔDICex=2.4 seems very specific to the Chesapeake Bay. Moreover, the reaction-driven interpretation can be applied to other published datasets for which the ΔTA/ΔDIC/ΔH2S system can be calculated (Table 3). In the water column, most of the available datasets are not suitable for the reaction-driven approximation, since either they focus on surface water where DIC and TA are strongly impacted by atmospheric exchange or the water masses change too fast to consider that reactions dominate over water mixing. However, porewater measured in the Gulf of Mexico has ΔTAex/ΔDICex/ΔH2S=1.15/1/0.53 (Hu et al., 2010), as expected when sulfate reduction is associated with H2S accumulation (SR reaction; ΔTAex/ΔDICex/ΔH2S=1.15/1/0.5; Table 1). Similarly, Hiscock and Millero (2006) report ΔTAex/ΔDICex/ΔH2S=1.3/1/0.5 in the western Black Sea close to the SR signature. In the Baltic Sea sediment, ΔTAex/ΔDICex/ΔH2S=1.3/1/0.07 was reported (Lukawska-Matuszewska, 2016), which is close to the expected signature in the case of important H2S consumption by Fe oxides and consequent precipitation as pyrite (SR-FeS2 reaction; ΔTAex/ΔDICex/ΔH2S=1.2/1/0). In Rhône river prodelta sediments, the reported ΔTAex/ΔDICex/ΔH2S is 1/1/0, which can be related to the 1/1/0 signature of FeSR-FeS (Table 1) that is expected in iron-rich sediments, with high sedimentation rates preventing FeS2 formation in the pore water (Rassmann et al., 2020). In permeable, carbonate-rich sediments, the reported signature of ΔTAex/ΔDICex/ΔH2S in Hawaii sands is 0.86/1/ND (Drupp et al., 2016). The lack of salinity and oxygen datasets prevents further model fits, but the ΔTAex/ΔDICex is below 2.4. For oxygen-depleted data from the whole Chesapeake Bay described in Su et al. (2020a), the signatures are ΔTAex/ΔDICex/ΔAOU=0.2/1/1 in the presence of oxygen (typical signature of AR) and 0.8/1/ND in the absence of oxygen that could correspond to NR-N2 or a combination of CD and Nit. Overall, this bibliographic survey highlights the effectiveness of the reaction-driven approximation to identify preponderant reactions controlling the carbon cycle and puts into perspective the originality of the ΔTAex/ΔDICex/ΔAOU signature of 2.4/1/0 observed in the Chesapeake Bay.

While the reaction-driven approximation indicates a dominant role of the SR-SMnC reaction, this possibility needs to be validated by looking at the saturation state of rhodochrosite (the main MnCO3 mineral) and looking at the mass budget between MnOx consumed and TAex produced. The rhodochrosite saturation (Luo and Millero, 2003) is always below 0.3 in our samples, which stands against the occurrence of in situ SR-SMnC reaction. When inspecting the mass budget, the 88 to 155 µM of MnO2 required to produce the 100 µM TAex increase observed (Fig. 4a) is 1 order of magnitude higher than the observed MnOx or Mn2+ concentration (Fig. 3). This mass budget discrepancy cannot be solved by invoking suspended material, since the 88 µM of MnO2 would require a suspended material concentration of about 4.4 gL-1 (assuming an average concentration of 20 µmolg-1 of Mn), which is again 1 or 2 orders of magnitude higher than the 0.01–0.1 gL-1 usually found in the Chesapeake Bay (Cerco et al., 2013). However, a fast settling rate could satisfy and explain the discrepancy between water and solid concentration. But another process dephasing aqueous from solid reaction products is also possible at station 858, since the dissolved phase could have moved up, rather than the particles settling down. In this case, the SR-SMnC reaction was not happening only in the water column of the Chesapeake Bay, and part of the TAex and DICex pool could have been produced in the sediment during the previous year (e.g. Aller, 2014), then diffused out of the sediment simultaneously with other reduced elements as the summer begins. Indeed, many previous studies at station 858 (e.g. Sholkovitz et al., 1992) explained the seasonality of anoxia with an upward move of the redox front from the sediments to bottom waters during the start of summer. Important sedimentary efflux of H2S, Feaq and Mnaq were still visible during both of our August campaigns. Therefore, the 100 µM TA pool does not fit with the ambient Mn2+ or MnO2 in the water column but rather with the MnCO3 deposited in the sediment. The sedimentary solid Mn stock of the Chesapeake Bay is particularly important, up to 70 µmolg-1 at station 858 (Sinex and Helz, 1981) compared to an average value of 15 µmolg-1 for the upper continental crust (Rudnick and Gao, 2003). Indeed semi-enclosed basins are known to concentrate manganese at the deeper sediment (Thamdrup and Dalsgaard, 2000; Lenstra et al., 2020). Recent investigations at a close station (ET 5.1; 38∘48.36′ N; 75∘54.66′ W) in the Chesapeake Bay (Lenstra et al., 2021) report that about 60 % of the surface sedimentary Mn pool is MnOx (acid ascorbic extractable) and 25 % is Mn carbonate (1 M HCl extraction). Assuming a porosity of 0.8 and a bulk solid density of 2.6, the sedimentary pool corresponds to 35 mM of manganese, which largely exceeds the 88 µM required to produce the 100 µM TAex increase. Therefore, the Chesapeake Bay sediment is particularly rich in manganese and could host important SR-SMnC reactions in the surface pore water, whose soluble products diffuse up to the water column during summer and could bear with them the high ΔTAex/ΔDICex signature observed.

The assumptions detailed in Sect. 4.1 permit the reaction-driven approach to be reconsidered in regard to this sediment efflux scenario. Indeed, the sediment efflux does not need to be considered as an additional endmember; that would violate the third assumption, since its salinity and the pore water concentrations results from the upstream and oceanic endmembers superimposed to geochemical reactions. In Sect. 2.3.1, we point out that Eq. (1) was valid in between each local endmember and that the straight lines on the ΔTAex/ΔDICex plot between them indicate that the local endmembers are maintained in steady state by a chemical reaction with a similar stoichiometry. These results indicate that, even if most of the MnCO3 was produced when the local endmembers were localised in the sediment, (a) their migration does not alter the TAex/DICex signature, and (b) the chemical reaction that produced them is still ongoing at a sufficient rate to maintain a steady state characterised by the steep changes of direction observed in Fig. 4a.