Ocean Alkalinity, Buffering and Biogeochemical Processes

Abstract Alkalinity, the excess of proton acceptors over donors, plays a major role in ocean chemistry, in buffering and in calcium carbonate precipitation and dissolution. Understanding alkalinity dynamics is pivotal to quantify ocean carbon dioxide uptake during times of global change. Here we review ocean alkalinity and its role in ocean buffering as well as the biogeochemical processes governing alkalinity and pH in the ocean. We show that it is important to distinguish between measurable titration alkalinity and charge balance alkalinity that is used to quantify calcification and carbonate dissolution and needed to understand the impact of biogeochemical processes on components of the carbon dioxide system. A general treatment of ocean buffering and quantification via sensitivity factors is presented and used to link existing buffer and sensitivity factors. The impact of individual biogeochemical processes on ocean alkalinity and pH is discussed and quantified using these sensitivity factors. Processes governing ocean alkalinity on longer time scales such as carbonate compensation, (reversed) silicate weathering, and anaerobic mineralization are discussed and used to derive a close‐to‐balance ocean alkalinity budget for the modern ocean.


Introduction
The supporting information contains three sections. The first section (S1) elaborates the differences between proton and charge balances to solve carbonate equilibria and complements section 2. The second section (S2) presents explicit links between sensitivity and buffer factors reported in the literature and provides the basis for Table 1. The third section (S3) provides details on alkalinity sources and sinks in the ocean.
Text S1: Solving carbonate equilibria via proton and charge balances.
Solving ionic equilibrium problems implies balancing the number of species in solution with the number of equilibrium relations, mass and charge balances (Butler, 1964). The two alkalinity entities (titration alkalinity and charge balance alkalinity) are rooted in the use of either a proton mass balance or charge balance to obtain the needed number of equations. Consider pure water in which the water is dissociated into protons and hydroxide ions: H2OÛ H + + OH -(eq. 1.1) This reaction occurs virtually immediately and one can thus assume equilibrium between the three species (H2O, H + , OH -): where K'w, the equilibrium constant for water self-ionisation, governs the distribution between protons and hydroxide ions. Water as the liquid medium is always present with a constant concentration of ~55.4 M (998 gr H2O L -1 /18 gr H2O mol -1 ) and implicitly included in the equilibria. Accordingly, eq. 2a becomes where Kw= 55.4* K'w= 10 -14 , ignoring activity coefficients. Besides eq. 1.2b we need one additional equation to obtain the concentration of two species (H + and OH -). There are two alternatives. The first option is the balance between positive and negative ions because water is electrically neutral: H + = OH -(eq.1.3). Alternatively, the proton condition, i.e. a proton mass balance, can be used. Selfionisation of water results in the formation of one proton and one hydroxide ion, hence eq. 1.3 is again obtained. The proton condition and charge balance are identical for this trivial case for pure water with pH=7.
Next, we consider pure water to which a known amount of carbonic acid (H2CO3) has been added. Carbonic acid is a weak diprotic acid and partly dissociates first into a bicarbonate ion (HCO3 -) and a proton and subsequently the bicarbonate is dissociated partly into a carbonate ion (CO3 2-) and a proton. The relevant reactions are: H2CO3 Û HCO3 -+ H + (eq. 1.4) HCO3 -Û CO3 2-+ H + (eq. 1.5) for which we can write equilibrium relations: where K1 and K2 are the first and second stoichiometric equilibrium constants (10 -6.35 and 10 -10.3 ).
Accordingly, for the CO2-H2O system we have five unknown species (H2CO3, HCO3 -, CO3 2-, OHand H + ) and three equilibrium relations: water self-ionisation (eq.1.2b), and the first and second equilibria of carbonic acid dissociation (eq. 1.6, 1.7). Moreover, we know the total mass of carbonic acid added (SCO2 = H2CO3 + HCO3 -+ CO3 2-). To solve the system, we need one additional relation and again two alternative routes can be followed. The first option balances the positive charge of protons with the negative charge of hydroxide, bicarbonate and carbonate ions.
Note that the carbonate ion is counted twice in the charge balance because of its double charge. Alternatively, the proton condition can be used because protons are involved in all three reactions (eq. 1.1, 1.4, 1.5) and their total mass is conserved. The proton condition is given by the sum of the protons released when water and carbonic acid dissociate to their equilibrium distribution (Butler, 1964(Butler, , 1982: H + = H + H2O + H + H2CO3 (eq.1.9a). or its equivalent H + = OH -+ HCO3 -+ 2 CO3 2-(eq.1.9b). This equation is called a proton condition because all species on the left-hand side have excess protons relative to the (reference) species of the recipe (H2O and H2CO3), while species on the right-hand side are deficient in protons. The species H2O and H2CO3 are the zero level of protons for this system and each species is multiplied with the number of protons needed to convert them to the zero-proton level. The proton condition is thus similar to the charge balance, the difference being that excess/deficiency of protons rather than electrons are counted. The proton condition is usually presented as the total proton concentration (TOTH; Morel and Hering, 1993): TOTH = H + -OH --HCO3 --2 CO3 2-(eq. 1.10). Independent whether the charge balance, proton condition or total proton concentration equation is used, the system is now fully defined with 5 unknown species linked via 5 equations.
Adding NaCl to this solution will not only increase the number of unknown species from 5 to 7, but also adds to two conservation equations, one for total Na + and one for total Cl -. Dissolution of NaCl does not impact the proton mass balance (eq. 1.9, 1.10), because Na + and Clare not involved in proton exchange. However, it does imply a revision of the charge balance (eq. 1.8) to: Na + + H + = OH -+ HCO3 -+ 2CO3 2-+ Cl -(eq. 1.11). Rearranging this charge balance for the system H2O-H2CO3-NaCl to obtain the ions Na + and Clon the left-hand side, because they are invariant to changes in pH, temperature and pressure (i.e. conservative), yields the negative of TOTH on the right-hand side: CB = Na + -Cl -= OH -+ HCO3 -+ 2CO3 2--H + = -TOH (eq. 1.12).
This equation links -TOH, the definition of titration alkalinity (Dickson, 1981;Morel and Hering, 1993), with the charge balance of conservative ions (CB). Proton mass balances are always relative to a proton reference level. Equations (1.9 and 1.10) are relative to H2CO3 (because H2CO3 has been added) and in this case, the proton condition is identical to the charge balance. However, if we had added NaHCO3 and HCO3were the reference level, the proton balance would be: TOTH = H + + H2CO3-OH --CO3 2-(eq. 1.13), and the charge balance and proton balance would differ by the total concentration of carbonic acid ((SCO2). Adding additional substances to our mixture to produce seawater will increase the number of species, equilibria among the species and mass conservation equations, but there is always the need for either a charge balance or proton condition to close the system. The (seawater) titration alkalinity definitions of Dickson (1984) and TOTH of Morel and Hering (1993) are based on the proton condition, while the explicit conservative expression of total alkalinity (Zeebe and Wolf-Gladrow, 2001;Wolf-Gladrow et al., 2007) and the excess negative charge (Soetaert et al., 2007) are based on charge balance equations.

Text S2 Relations between various sensitivity factors reported in the literature
In this section, we present the relations between sensitivity factors reported in the literature and that are listed in Table 1. (1994).

Relations among the various sensitivity factors reported (as buffer factors) by Frankignoulle
Hagens and Middelburg (2016a) derived from Frankignoulle's (1994) work that Relations between factors of Sarmiento andGruber (2006), Frankignoulle (1994) and Egleston et al. (2010) The factor H of Frankignoulle is identical to HL1 of Sarmiento and Gruber:

Relations between isocapnic quotient (Q) of Humphreys et al. (2018) and general sensitivity theory of Hagens and Middelburg (2016a)
Recently, Humphreys et al (2018) introduced another sensitivity factor, the isocapnic quotient (Q) defined as:

Q =
This isocapnic quotient is fully consistent with the general sensitivity approach of Hagens & Middelburg (2016a). Starting from their table 3: Here, TotX refers to the total concentration of the acid-base system of interest, X to the species of interest of that acid-base system (which equals the reference species for AT (Xref) in the case a change in TotX is specified), n to the stoichiometric factor in the contribution of X to AT (which equals 0 in the case a change in TotX or Xref is specified) and AX to the contribution of all species of TotX to AT.
For this specific case with DIC as state variable (i.e., X = CO2 and n = 0) and total borate concentration (TotB) as reaction invariant contributing to TA, this translates into: Section S3 Alkalinity balance of the ocean. Table 3 presents a concise, consensus budget for ocean alkalinity. Some of the individual terms have a range and others have been calculated in this study. This supplementary section provides an overview and rationale for most terms.

Riverine alkalinity supply
Estimates of riverine alkalinity supply are normally assumed to be identical to riverine DIC supply to the ocean because DIC≈TA at river pH values. Riverine DIC transport to the ocean is rather well constrained as published numbers vary from 26.6 to 36.3 Tmol y -1 : 32 Tmol y -1 (Meybeck, 1987); 26.6 Tmol y -1 (Ludwig et al., 1996) (Li et al., 2017). Some of this consistency may be simply due to the use of the same data as basis for extrapolation or calibration of the model, but various approaches have been used to obtain the final global numbers (spatially resolved or not, data driven vs. model). The average river TA flux is 32 Tmol y -1 and used in Table 3.

Submarine groundwater supply
Submarine groundwater supply of alkalinity to the ocean is poorly constrained. Combining the recent Zhou et al. (2019) estimate for global freshwater submarine discharge of 489 km 3 y -1 , i.e. ~1.3% of global river discharge of 37,288 km 3 y -1 (Berner and Berner, 2012), with the average river TA of ~ 0.85 mM (31.5 Tmol/37288 km 3 ), we estimate a TA flux of 0.4 Tmol y -1 . However, groundwaters usually have higher TA levels because of carbonate dissolution and anaerobic processes. Considering that groundwater TA is three times that of rivers (Zhang and Planavasky, 2019), we estimate a submarine groundwater supply of 1.2 Tmol y -1 . Recently, Zhang and Planavasky (2019) reported a much higher contribution ranging from 7.4 to 83 Tmol y -1 . This difference is primarily due to uncertainty in submarine groundwater discharge estimates. Our conservative estimate is based on the Zhou et al. (2019) estimate of global freshwater submarine discharge, which is lower than the often used 5% of global river discharge estimate of Slomp and van Cappellen (2005). Combining this higher discharge rate with average river TA, we obtain 1.6 Tmol y -1 . Accordingly, the global submarine groundwater supply of alkalinity to the ocean adopted for Table 3 is about 1 Tmol y -1 .

Submarine weathering
Weathering of silicates in the ocean represents a sink of carbon dioxide and a source of alkalinity. Ocean crust weathering acts a sink of carbon dioxide, but most of the alkalinity generated is removed via the precipitation of calcium carbonate (Caldeira, 1995;Berner, 2004). Submarine weathering of continental silicates coupled to anaerobic diagenesis, in particular methanogenesis, is a major source of alkalinity. Wallmann et al. (2008) reported very high rates of submarine weathering based on global methane production rates of 5 to 20 Tmol C y -1 , which are much higher than present-day estimates (2.8 Tmol C y -1 ; Egger et al., 2018;0.3-2.1 Tmol C y -1 ;Wallmann et al., 2013). Given these uncertainties we use an estimate of 2.8 Tmol y -1 in our alkalinity budget of Table 3.

Anaerobic processes
Hu and Cai (2011) summarized in detail why only riverine nitrate delivery to and reduced sulfur in the ocean should be included in the alkalinity budgets for the entire ocean. The riverine nitrate delivery is well constrained at about 21 Tg Ny -1 , corresponding to an alkalinity production of 1.5 Tmol y -1 . Berner (1982) reported a sulfur burial estimate of 1.2 Tmol S y -1 , which relates to a net alkalinity production of 2.4 Tmol y -1 . Burdige (2007) revisited organic carbon burial in the ocean to 309 Tg C y -1 , which combined with Berners' C:S ratio of 2.8 corresponds to a reduced sulfur burial of 3.4 Tmol y -1 and thus alkalinity source of about 6.9 Tmol y -1 . For table 3 we have adopted the average, i.e. the overall alkalinity production due to the reduced sulfur burial is 4.7 Tmol y -1 .

Organic matter burial in marine sediments
Organic matter production generates alkalinity because of the assimilation of anions such as nitrate, phosphate and sulfate. Most of the organic matter produced in the sunlit layer is recycled, but a small fraction is ultimately buried in marine sediments. On the basis of Burdige's (2007) burial estimate of 309 Tg C y -1 (25.75 Tmol C y -1 ) and Redfield organic matter (C106H177O37N16PS0.4;Hedges et al., 2002), we arrive at a net alkalinity production of about 4.3 Tmol y -1 , because of nitrate (3.9 Tmol y -1 ), phosphate (0.24 Tmol y -1 ) and sulfate (0.2 Tmol y -1 ) incorporation in organic matter and subsequent burial. Using a more conservative global carbon burial rate [Berner, 1982] of 126 Tg C y -1 , the alkalinity production would be about 1.7 Tmol y -1 . The average of these two estimates (3 Tmol y -1 ) is presented in Table 3 and Figure 6B.

Riverine particulate inorganic carbon input
See text.

Reversed weathering
Isson and Planavsky (2018) discussed reversed weathering in detail and derived an estimate of about 1 Tmol y -1 , which is used here.