Accepted Manuscript
Generalised expressions for the response of pH to changes in ocean chemistry
Mathilde Hagens, Jack J. Middelburg
PII: S0016-7037(16)30171-5 DOI: http://dx.doi.org/10.1016/j.gca.2016.04.012 Reference: GCA 9707
To appear in: Geochimica et Cosmochimica Acta
Received Date: 9 July 2015 Accepted Date: 6 April 2016
Please cite this article as: Hagens, M., Middelburg, J.J., Generalised expressions for the response of pH to changes in ocean chemistry, Geochimica et Cosmochimica Acta (2016), doi: http://dx.doi.org/10.1016/j.gca.2016.04.012
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. 1 Generalised expressions for the response of pH to changes in
2 ocean chemistry
3 Mathilde Hagens* and Jack J. Middelburg
4 Department of Earth Sciences – Geochemistry, Utrecht University, P.O. Box 80.021, 3508 5 TA Utrecht, Netherlands
6 *Corresponding author: M.Hagens@uu.nl
7
8 Abstract
9 The extent to which oceans are capable of buffering chemical changes resulting from the
10 uptake of carbon dioxide (CO2) or other acidifying processes can be quantified using buffer
11 factors. Here, we present general expressions describing the sensitivity of pH, CO2 and other 12 acid-base species to a change in ocean chemistry. These expressions can include as many 13 acid-base systems as desirable, making them suitable for application to, e.g., upwelling 14 regions or nutrient-rich coastal waters. We show that these expressions are fully consistent 15 with previously derived expressions for the Revelle factor and other buffer factors, which 16 only included the carbonate and borate acid-base systems, and provide more accurate values.
17 We apply our general expressions to contemporary global ocean surface water and possible 18 changes therein by the end of the 21st century. These results show that most sensitivities
19 describing a change in pH are of greater magnitude in a warmer, high-CO2 ocean, indicating
20 a decreased seawater buffering capacity. This trend is driven by the increase in CO2 and 21 slightly moderated by the warming. Respiration-derived carbon dioxide may amplify or
22 attenuate ocean acidification due to rising atmospheric CO2, depending on their relative 23 importance. Our work highlights that, to gain further insight into current and future pH 24 dynamics, it is crucial to properly quantify the various concurrently acting buffering 25 mechanisms.
26
27 1. Introduction
28 The ocean provides an important service to mankind by absorbing 25-30% of the
29 anthropogenic CO2 released. This oceanic carbon uptake not only limits global warming, but
1 30 also causes changes in ocean chemistry, collectively referred to as ocean acidification. These + 31 changes include increases in CO2, dissolved inorganic carbon (DIC) and proton (H ) 2- 32 concentrations and decreases in carbonate ion (CO3 ) concentration, calcium carbonate
33 saturation states and the efficiency of ocean CO2 uptake. The latter results from a decrease in 2- 34 the ocean CO2 buffer capacity due to diminished CO3 concentrations (Sundquist et al., 35 1979; Frankignoulle, 1994). 36 Long-term observations on the inorganic carbon system and pH at a number of sites revealed 37 systematic decreases in pH and increases in DIC (Dore et al., 2009; Bates et al., 2014), 38 consistent with model simulations showing declining open-ocean surface-water pH since the 39 industrial revolution (Orr et al., 2005). Moreover, model projections indicate that pH in the 40 future ocean will be more sensitive to biogeochemical processes (Caldeira and Wickett, 2003; 41 Egleston et al., 2010; Hofmann et al., 2010a; Orr, 2011). The response of pH to these 42 processes not only depends on the sensitivity of seawater, but also on the number of protons 43 involved (reaction stoichiometry) and the process rate (Hofmann et al., 2010a; Hagens et al., 44 2014). Seawater sensitivity additionally displays spatial differences: polar regions for 45 example, are known to be relatively vulnerable to a change in pH due to their naturally low 2- 46 CO3 concentrations, and the temperature dependency of CO2 solubility and acid-base 47 dissociation constants, while the reverse holds for warmer tropical regions (Orr et al., 2005; 48 Fabry et al., 2009; Orr, 2011). This temporal and regional variability in the sensitivity of pH 49 implies that we need to advance our understanding of the factors governing pH in the ocean.
50 The sensitivity of pH to a change in driving factors is usually expressed in terms of buffering 51 capacity or buffer factors. Traditionally, the buffering capacity of a solution is defined as its 52 ability to neutralise changes in pH or [H+] upon the addition of a strong acid or base (Van 53 Slyke, 1922) and is calculated from the inverse slope of a titration curve (Morel and Hering, 54 1993; Stumm and Morgan, 1996):
∂ pH −1 55 β = (1) ∂ANC
56 where ANC, or acid neutralisation capacity, represents the difference between base and acid 57 concentrations of a solution relative to a predefined zero level of protons (Stumm and
58 Morgan, 1996). For natural waters, ANC is usually replaced by total alkalinity (AT), which is
59 defined as the ANC with a zero level of protons at the CO2 equivalence point or a pH of 4.5,
2 60 a temperature of 25ºC, standard atmospheric pressure, and zero ionic strength (Dickson, 61 1981):
−1 ∂pH 62 β = (2) ∂AT
63 The increasing awareness that ocean chemistry is changing has stimulated theoretical work 64 on pH buffering and two related buffer factors have been introduced. Similar to the 65 pioneering work of Frankignoulle (1994), Egleston et al. (2010) presented and derived an 66 explicit equation for β : AT
−1 ∂ln[H + ] 67 β = (3) AT ∂AT
68 and Hofmann et al. (2010a) introduced a proton concentration buffer factor βH :
−1 ∂[H + ] 69 β = (4) H ∂AT
70 Note that the partial derivatives in Eq. (1-4) indicate that other chemical water properties, e.g., 71 DIC and other total concentrations of acid-base species, are kept constant when determining 72 this buffering capacity (Morel and Hering, 1993). Equations (2-4) represent the most general 73 way of describing the resistance of natural waters to changes in pH. Depending on the 74 context, however, one may be interested in the way a particular biogeochemical process
75 (Zhang, 2000; Soetaert et al., 2007) or a specific acid-base system, rather than AT, influences 76 the change in pH.
77 Inspired by the work of Frankignoulle (1994), we present explicit equations for calculating 78 the sensitivity of protons to changes in ocean chemistry and apply them to several case 79 studies. These sensitivities are required if we are to better understand pH dynamics in a ∂[H + ] 80 changing world or the impact of biogeochemical processes on pH. The sensitivity as ∂AT 81 presented in this paper is identical to the inverse of the buffer factor (Eq. (4)) of Hofmann et 82 al. (2010a), and conceptually equivalent to the inverse of the buffer capacity (Morel and 83 Hering, 1993) and the buffer factor β of Egleston et al. (2010). We first derive general AT 84 explicit equations for the sensitivity of protons and acid-base species to changes in ocean 85 chemistry. Secondly, we show how the derived relationships relate to previous studies that 3 86 excluded acid-base systems other than borate (Frankignoulle, 1994; Egleston et al., 2010) and 87 we show that a similar approach applies to the well-known Revelle factor. We compare our 88 analytical approach to numerical estimates for a selection of sensitivities. Then, we show how 89 much more sensitive the pH will be in the year 2100 given projected atmospheric carbon 90 dioxide levels. Finally, we apply the sensitivities to explore ocean acidification due to the
91 combined effects of atmospheric CO2 uptake and eutrophication-stimulated organic matter 92 respiration.
93
94 2. Methods
95 2.1 Analytical derivations of buffer factors
96 To arrive at a general, complete set of buffer factors, we combined and extended several 97 earlier outlined approaches (Frankignoulle, 1994; Soetaert et al., 2007; Egleston et al., 2010). 98 If examples are used for clarification, they will be given for the carbonate system, but similar 99 derivations can be made for any other acid-base system.
100 Generally speaking, any given change in pH can be split into multiple parts representing 101 multiple processes:
∂pH ∂pH ∂pH ∂ pH 102 dpH = dT + dS + dDIC + dA + ... (5) T ∂T ∂S ∂DIC ∂AT
103 where T is temperature and S is salinity. The partial derivatives in Eq. (5) indicate that they 104 are only valid if other variables are kept constant within their derivation. The dots indicate 105 that more acid-base systems may be included, depending on the system of interest and the 106 processes taking place. Usually, only carbonate and borate systems are used in the 107 calculations, but in coastal systems, in pore-waters and in ocean oxygen minimum zones, 108 other acid-base systems such as sulphide may impact pH. Following Soetaert et al. (2007), 109 we decided to include the ammonium, phosphate, nitrate, nitrite, sulphide, silicate, fluoride 110 and sulphate acid-base systems in our derivation, and ignore the contribution of other minor
111 acid-base species and organic acids. Although the latter can substantially contribute to AT in 112 estuarine and other coastal waters (Cai et al., 1998; Kuliński et al., 2014), their acid-base 113 properties are poorly constrained (Muller and Bleie, 2008; Kim and Lee, 2009), making it 114 difficult to include them in this derivation. The selected acid-base systems should be included
115 in the definition of AT, which then becomes (Dickson, 1981; Wolf-Gladrow et al., 2007): 4 − 2− − 2− 3− AT = [HCO3 ] + 2[CO3 ]+[B(OH )4 ]+[NH 3 ]+[HPO4 ]+ 2[PO4 ] − 2− − 116 −[H 3PO4 ]−[HNO3 ]−[HNO2 ]+ [HS ]+ 2[S ]+[SiO(OH )3 ] (6) 2− − − + +2[SiO2 (OH )2 ] −[HF]− 2[H 2SO4 ]−[HSO4 ]+[OH ] −[H ]
117 This definition can be rewritten by grouping each acid-base system together:
118 A = A + A + A + A + A + A + A + A + A + A + A (7) T C B NH 4 P NO3 NO2 HS Si F SO W
119 Here, AC, AB, A , AP, A , A , AHS, ASi, AF and ASO refer to the contributions of the NH 4 NO3 NO2 120 carbonate, borate, ammonium, phosphate, nitrate, nitrite, sulphide, silicate, fluoride and
121 sulphate acid-base systems to AT respectively, while AW refers to the contribution due to the 122 auto-dissociation of water. So, taking the carbonate system as an example, we can see that
− 2− + 123 AC = [HCO3 ]+ 2[CO3 ]. Equation (7) can be differentiated with respect to [H ]:
∂A ∂A ∂A ∂A ∂A ∂A ∂A ∂A T = C + B + NH 4 + P + NO3 + NO2 + HS ∂[H + ] ∂[H + ] ∂[H + ] ∂[H + ] ∂[H + ] ∂[H + ] ∂[H + ] ∂[H + ] 124 (8) ∂A ∂A ∂A ∂A + Si + F + SO + W ∂[H + ] ∂[H + ] ∂[H + ] ∂[H + ]
125 It is important to realise that the subscripts in Eq. (8) simply represent terms belonging 126 together being grouped (as for Eq. (7)) and do not imply that total concentrations of all acid-
127 base species remain constant. However, if we also assume that AT changes only due to 128 addition or removal of [H+], then Eq. (8) is directly linked to the inverse of the well-known 129 acid-base buffering capacity (Eq. (2)) sensu Morel and Hering (1993) and identical to the 130 inverse of proton concentration buffer factor (Eq. (4)) as defined by Hofmann et al. (2010a):
k ∂A 131 β = i (9) H ∑ + i=1 ∂[H ] i
132 Here, i represents the total concentration of an acid-base system, Ai represents the
133 contribution of that acid-base system to AT, and k represents the total number of acid-base 134 systems present in the system.
135 Since we are interested in the effect of the change in the total concentration of a certain acid- + 136 base species (TotX) on [H ], we differentiate both TotX and AT with respect to changes in 137 proton concentration and the concentration of an acid-base species X that makes up part of 138 TotX:
5 ∂TotX ∂TotX 139 dTotX = d[X]+ d[H + ] (10a) + ∂[X] H + ∂[H ] X
∂A ∂A 140 dA = T d[X]+ T d[H + ] (10b) T + ∂[X] H + ∂[H ] X
141 We can convert these expressions to describe the sensitivity of [H+] to a change in TotX by 142 making use of the matrix inversion method (Egleston et al., 2010):
dTotX d[X] 143 = J (11) + dAT d[H ]
144 The Jacobian J is defined as
∂TotX ∂TotX + a b ∂[X] H + ∂[H ] X 145 J = = (12) c d ∂A ∂A T T + ∂[X] H + ∂[H ] X
146 From matrix algebra, we know that
d[X] dTotX 147 −1 (13) + = J d[H ] dAT
148 The inverse Jacobian J-1 can then be defined as
∂[X] ∂[X] -d b ∂TotX ∂AT bc - ad bc - ad 149 J -1 = = (14) ∂[H + ] ∂[H + ] c -a ∂TotX ∂AT bc - ad bc - ad
150 where a, b, c and d refer to the corresponding partial derivatives of Eq. (12).
∂A ∂TotX ∂TotX 151 The sensitivities T , and (Eq. (12)) can be analytically + ∂[X] H + ∂[X] H + ∂[H ] X ∂A 152 derived using simple differentiation (Table 3a). Combined with T , one can insert + ∂[H ] X 153 these partial derivatives into Eq. 14 to obtain the analytical expressions for the sensitivities
6 ∂[X] ∂[X] ∂[H + ] 154 , , and the two sensitivities which are of most interest to this study, and ∂AT ∂TotX ∂TotX ∂[H + ] 155 . As first identified by Frankignoulle (1994), the remaining challenge is thus to obtain ∂AT ∂A 156 a general expression for the term T , which is the change in A due to the change in + T ∂[H ] X + 157 [H ] under the assumption that species X is kept constant. It is therefore not equal to βH , 158 which implies that all total concentrations are constant, but it is tightly linked to it.
159 Specifically:
∂A ∂A ∂A 160 T X X (15) + = βH − + + + ∂[H ] X ∂[H ] TotX ∂[H ] X
∂A 161 i.e., the sought-after T equals the buffer factor ( β ) for the condition that the total + H ∂[H ] X 162 concentrations of all acid-base species remain constant, minus the term describing the 163 contribution of the acid-base system to which species X belongs, plus a term accounting for + 164 the change in AX due to a change in [H ] under the assumption that X remains constant.
165 To illustrate the procedure, we select the carbonate system as the system of interest. As an
166 example we take the addition of CO2, meaning that DIC changes while the total
167 concentrations of the other acid-base systems and AT remain constant, i.e. ocean acidification.
* 168 For this purpose, we define CO2 as the sum of aqueous CO2 and carbonic acid (H2CO3), such
* * 169 that an addition of CO2 equals an increase in CO2 . In this case, CO2 is our species of interest 170 X and DIC is our independent state variable TotX, while the other total concentrations are 171 reaction invariant, i.e., they are not affected by the chemical transformations in the systems
* + 172 (Waller and Makila, 1981). Nevertheless, the addition of CO2 affects [H ] and thus will 173 change the speciation of these acid-base systems. Therefore, to analytically derive the partial 174 derivatives of Eq. (8) that belong to the reaction invariant, it is necessary to express the 175 corresponding species of Eq. (6) in terms of their total concentration, [H+] and equilibrium 176 constants only (Park, 1969; Soetaert et al., 2007) (Table 1b). The corresponding analytical 177 expressions for the partial derivatives can be found in Table 2b. In our example, DIC is not ∂A 178 invariant, and T cannot be equal to Therefore, to analytically represent + βH . ∂[H ] * CO2 7 ∂AT ∂AC 179 + we have to remove the term + from the definition of βH , but ∂[H ] * ∂[H ] CO2 DIC
180 recall that the addition of CO2 does not affect AT. Thus, to implement the contribution of the
181 carbonate system to AT when DIC is not invariant, we can express AC, as well as its partial
+ + * 182 derivative with respect to [H ] (Eq. (8)), in terms of equilibrium constants, [H ] and [CO2 ] ∂A ∂A 183 (Tables 1a and 2a) and add C to the analytical representation of T . In + + ∂[H ] * ∂[H ] * CO2 CO2 ∂A ∂A C X 184 more general terms, + can be expressed as + , where AX represents the ∂[H ] * ∂[H ] CO2 X
185 contribution of the acid-base system associated with TotX to AT. Since βH is explicitly + 186 defined under the assumption that AT changes only due to changes in [H ], i.e., all total
187 concentrations are reaction invariant, we can find the analytical expression for βH by
188 summing all the terms from Table 2b. Then, taking again the addition of CO2 as example, we
∂AT ∂AC 189 can find the analytical expression for + by subtracting + (also from ∂[H ] * ∂[H ] CO2 DIC
∂AC 190 Table 2b) from βH and adding + (Table 2a). This yields ∂[H ] * CO2
∂AT ∂AC ∂AC 191 + = βH − + + + (16) ∂[H ] * ∂[H ] ∂[H ] * CO2 DIC CO2
192 where
* 2− − [CO2 ]− [CO3 ] [HCO3 ] ∂A −1 DIC 193 C = (17, T.2b) ∂[H + ] [H + ] * − DIC 2− 2[CO2 ]+ [HCO3 ] +2[CO3 ] DIC
194 and
∂A −1 C nA HCO− CO2− 195 + = + ()− C + ()[ 3 ]+ 4[ 3 ] (18,T.2a) ∂[H ] * [H ] CO2
196 where n stands for the charge contribution to alkalinity (Soetaert et al., 2007). In the case of
197 the carbonate system, adding or removing CO2 changes DIC but not AT, i.e. n equals 0, such
8 - 2- 198 that Eq. (18) simplifies. Addition or removal of bicarbonate (HCO3 ) or CO3 changes AT 199 and n is 1 and 2, respectively. As a result, Eq. (16) can also be applied to the addition or - 2- 200 removal of HCO3 or CO3 , with the same expression but a different result for Eq. (18). The
∂AC ∂AC ∂AC 201 relation between + and either of the terms + or + can be ∂[H ] * ∂[H ] − ∂[H ] 2− CO2 HCO3 CO3 202 generalised into:
∂A ∂A nA 203 X = X + X (19) + + + ∂[H ] X ∂[H ] X [H ] ref
204 Here, Xref is the reference species of the acid-base system associated with TotX for the total 205 alkalinity expression. This reference species is also referred to as the zero level of protons
206 (Wolf-Gladrow et al., 2007). Similarly as for CO2, a change in any Xref is equivalent to a 207 change in its corresponding TotX when other properties are held constant (MacIntyre, 1978).
208 Generally, using the appropriate combination of terms expressing AT from Table 1a and 1b 209 for the state variable of interest, we can write the analytical expression for Eq. (7) that is 210 applicable to the situation. Thus, with the carbonate system as the acid-base system of
211 interest, one would take AC from Table 1a and the other terms of Eq. (7) from Table 1b. For 212 each of the terms in Table 1a and 1b, the derivatives with respect to [H+] (Eq. (8)) are given 213 in Table 2. The derivatives of Table 2a, which are valid in case of an independent state 214 variable TotX, are written in such a general way that they can also be applied whenever a 215 change in any of the species contributing to TotX is specified.
216
217 2.2 Linking generalised expressions to prior work limited to the carbonate and borate acid- 218 base systems
219 The expressions presented in Tables 1 and 2 are generally applicable to any combination of 220 acid-base systems, any number of state variables, and for any total concentration or any of 221 species contributing to the total concentration as independent state variable. The expressions ∂A 222 in Table 3a are also generally applicable, as long as the conditions under which T + ∂[H ] X 223 is valid are correctly taken into account for the specific situation. As Egleston et al. (2010) 224 pointed out, more than one acid-base system can be added as an independent state variable, 225 yielding an m by m Jacobian matrix (Eq. (12)) where m equals the number of acid-base 9 ∂AT 226 systems of interest plus 1 (due to the inclusion of AT). In such cases, (Eq. ∂[H + ] X1,X2 ...Xm 227 (15)) is built up from (m-1) parts of Table 2a.
228 The resulting expressions in Table 3b are valid for any combination of acid-base systems and 229 any total concentration, or any species contributing to the total concentration, as independent 230 state variable. The main difference with the expressions in Tables 2 and 3a is that the former
231 are only valid in the case of two independent state variables: AT and the total concentration, 232 or either of its species, of the acid-base system of interest. That is simply because the matrix
233 inversion given in Eq. (13) is only valid for a 2 x 2 matrix. As the number of state variables 234 increases, the inverse of the Jacobian matrix becomes significantly more complex, meaning ∂[H + ] 235 that it is difficult to analytically derive the sensitivities , ∂AT X1,X2 ...Xm−1,Xm + ∂[H ] ∂[Xm ] ∂[Xm ] 236 , and . In such cases it is ∂TotXm ∂TotXm + ∂AT + X1,X2 ...Xm−1,Xm H ,X1,X2 ...Xm−1 H ,X1,X2 ...Xm−1 237 recommended to numerically perform the matrix inversion. One might question how useful 238 the expressions in Table 3b may be as they only have a limited validity. However, often such 239 partial derivatives are used to partition the contributions of separate processes to the total 240 change in pH sensu Eq. (5), both in modelling studies (McNeil and Matear, 2007; Hauri et al., 241 2013) and when analysing time series (Takahashi et al., 2014). For such analyses, the buffer 242 factors of Table 3b are very well suited as each property is purportedly individually studied 243 while the other properties are kept constant.
244 The implicit assumption that the partial derivatives in Table 3b are homogeneous, i.e., they 245 are only valid when all other properties are kept constant, has another consequence. A careful ∂[H + ] 246 comparison of Eq. (19) with in Table 3b shows that, in case of a change in DIC, the ∂TotX ∂[H + ] ∂A 247 factor will be the same irrespective of whether T is defined with X being + ∂DIC ∂[H ] X
* - 2- 248 CO2 , HCO3 or CO3 . Conceptually this makes sense, as this is implied in the definition of ∂[H + ] ∂[H + ] 249 . In other words, for the analytical derivation of it is only of importance to ∂DIC ∂TotX
10 ∂[H + ] 250 specify TotX; the choice for X is free and will not affect the outcome of . Since a ∂TotX
+ ∂[H ] + 251 change in TotX is equivalent to a change in Xref, in fact describes the response of [H ] ∂TotX ∂[H + ] 252 to a change in either TotX or Xref. Similarly, the factor will produce the same value ∂AT 253 irrespective of which total concentration, or even which species, is used in its calculation. So ∂[H + ] 254 as long as X is defined as a species contributing to TotX, can be calculated. These ∂AT 255 generalisations can, for obvious reasons, not be made for the sensitivities describing a change 256 in X. As a result, the subscripts presented in Table 3a have been dropped in Table 3b.
257 Finally, all buffer factors presented so far consider the change in [H+]. Since we usually work 258 with pH, rather than [H+], it is convenient to convert them to factors describing the change in 259 pH. To convert the factors in Table 3a from [H+] to pH, we use Eq. (20) (Frankignoulle, 260 1994; Stumm and Morgan, 1996):
∂Y ∂[H + ] ∂Y ∂Y 261 = = −ln(10)[H + ] (20) + + ∂pH X ∂pH ∂[H ] X ∂[H ] X
262 where Y may refer to either TotX or AT.
263 Similarly, for the factors in Table 3b,
∂pH ∂ pH ∂[H + ] −1 ∂[H + ] 264 = = (21) ∂Y ∂[H + ] ∂Y ln(10)[H + ] ∂Y
265 The generalised expressions for the buffer factors presented in this paper are fully consistent ∂[H + ] 266 with those presented by Frankignoulle (1994) and Egleston et al. (2010), where was ∂AT 267 determined with DIC as state variable, while assuming that total borate was invariant and 268 neglecting the contribution of other acid-base systems except the auto-dissociation of water. 269 For example, the equation given by Egleston et al. (2010) for β is as follows: AT
−1 ∂ln[H + ] A2 270 β = = C −σ (22) AT ∂A DIC T
271 with, taking into account the correction identified by Álvarez et al. (2014), 11 + − − 2− [H ][B(OH )4 ] + − 272 σ = [HCO3 ]+ 4[CO3 ]+ + +[H ]+ [OH ] (23) K B + [H ]
∂[H + ] 273 This equation is equivalent to our expression for under the conditions defined in their ∂AT 274 paper. Egleston et al. (2010) only included the carbonate and borate acid-base systems and
275 auto-dissociation of water in their definition of AT. The proton concentration buffer factor
276 βH is thus also only built up from these three components:
∂A ∂A ∂A 277 β = C + B + W (24) H ∂[H + ] ∂[H + ] ∂[H + ] DIC TotB H2O
* 278 Since a change in DIC is equivalent to a change in CO2 , we define DIC as the independent
279 state variable TotX, so that the contribution of the independent state variable to AT is AC and
* ∂AT 280 the species of interest is CO2 . The expression for + (Eq. (16)) then becomes: ∂[H ] * CO2
∂AT ∂AC ∂AB ∂AW 281 + = + + + + + (25) ∂[H ] * ∂[H ] * ∂[H ] ∂[H ] CO2 CO2 TotB H2O
282 Taking the relevant factors of Tables 2a and 2b, and recalling that n equals 0 in the case of a 283 DIC addition, with some rearranging we define
[B(OH ) ] [HCO− ]+ 4[CO2− ]+[B(OH )− ] 3 ∂AT −1 3 3 4 284 + = + TotB (26) ∂[H ] * [H ] − + CO2 +[OH ]+[H ]
+ − [H ][B(OH )4 ] − [B(OH )3 ] 285 It can mathematically be shown that + is equal to [B(OH )4 ] , from KB +[H ] TotB 286 which it follows that:
∂AT −1 287 + = + σ (27) ∂[H ] * [H ] CO2
∂[H + ] 288 Now we insert this definition into our expression for (Table 3b) and adapt it to A ∂ T X
* 289 include our previously defined parameters X = CO2 , n = 0, TotX = DIC and AX = AC:
12 ∂[H + ] DIC[H + ] 290 = (28) ∂A −1 T A2 H + DIC C + [ ] + σ [H ]
291 This can be rearranged to yield
∂[H + ] DIC[H + ] 292 = 2 (29) ∂AT AC −σ ⋅ DIC
293 Dividing both numerator and denominator on the right hand side by DIC and dividing the left 294 and right hand sides by [H+] gives:
1 ∂[H + ] 1 295 = (30) [H + ] ∂A A2 T C −σ DIC
296 from which it can easily be seen that:
−1 −1 1 ∂[H + ] ∂ln[H + ] A2 297 = = C −σ (31) + [H ] ∂AT ∂AT DIC
298 The factors that Egleston et al. (2010) derived are valid for a change in DIC without taking 299 into account which species of DIC is changed, although they are also applicable in case of a 300 change in the reference species CO* . Thus, their factors β and β are equivalent to our 2 AT DIC ∂[H + ] ∂[H + ] 301 factors and , respectively, as presented in Table 3b. Their factors γ and AT ∂AT ∂TotX ∂[X] ∂[X] 302 γ DIC are equivalent to our factors and , but only in the special case where X ∂AT ∂TotX
* 303 equals Xref, since their γ and γ are defined for the addition of CO (which is Xref for AT DIC 2
304 the carbonate system) and lack a term describing the charge contribution to alkalinity. ∂[X] 305 Interestingly though, their factors ω and ω are also similar to our factors and AT DIC ∂AT
∂[X] 2- 306 , but with X = CO3 . This is further detailed in part A of the Supplementary ∂TotX 307 Information.
308 The factors β and β of Egleston et al. (2010) are also equivalent to the factors ΦD and DIC AT
309 ΦH derived by Frankignoulle (1994), which describe the change in pH due to change in 13 310 dissolved CO2 and AT, respectively. Frankignoulle (1994), however, additionally derived 311 chemical, heterogeneous buffer factors that describe the change in pH resulting from changes - 2- 312 in [HCO3 ] and [CO3 ]. By specifically inducing a change in either of these species, both + 313 DIC and AT are affected. After converting from pH to [H ], his results can be summarised as:
∂[H + ] ∂[H + ] ∂[H + ] 314 = + n (32) ∂X ∂TotX ∂AT
∂[H + ] ∂[H + ] 315 Thus, if CO* is added or removed, equals , in line with what has been 2 ∂X ∂TotX
316 discussed above. Part B of the Supplementary Information shows the derivation of Eq. 32.
317 The generalised expression for the buffer factors can, in principle, also be used to elucidate 318 and quantify the salinity, temperature and pressure (p) dependencies of pH (Hofmann et al., 319 2009). However, the resulting expressions are rather complex and it is therefore 320 recommended to calculate the sensitivities numerically (see part C of the Supplementary 321 Information).
322 The acid-base buffer factor ( βH ) and underlying terms are also linked to the well-known
323 Revelle factor (RF) expressing the sensitivity of pCO2 to changes in DIC (Revelle and Suess, 324 1957; Bolin and Eriksson, 1959; Sundquist et al., 1979):
∂ln[CO ] DIC ∂[CO ] 325 RF 2 2 (33) = = ∂ln DIC [CO2 ] ∂DIC
∂[X] 326 From the expression for in Table 3b, and defining that TotX = DIC, X = CO2 (from ∂TotX
* 327 now on denoted CO2 for consistency) and, since it is homogeneous, n equals 0, we can ∂[CO* ] 328 define 2 : ∂DIC
∂A [CO* ][H + ] T * 2 + ∂[CO ] ∂[H ] * 329 2 = CO2 (34) ∂DIC 2 + ∂AT AC +[H ] + DIC ∂[H ] * CO2
∂AT 330 The factor + is defined as in Eq. (16). From Eq. (34) it easily follows that: ∂[H ] * CO2
14 + ∂AT [H ] + DIC ∂[H ] * 331 RF = CO2 (35) 2 + ∂AT AC +[H ] + DIC ∂[H ] * CO2
332 This generalised Revelle factor includes all acid-base systems relevant for the system of 333 interest and it can easily be shown that it is fully consistent with the homogeneous RF 334 derived by Sundquist et al. (1979) and Zeebe and Wolf-Gladrow (2001). The work done by 335 Sundquist et al. (1979) only includes the carbonate and borate acid-base systems and neglects
∂AT 336 the auto-dissociation of water. In this specific case, + is defined as: ∂[H ] * CO2
∂AT ∂AC ∂AB 337 + = + + + (36) ∂[H ] * ∂[H ] * ∂[H ] CO2 CO2 TotB
338 Assuming for this purpose that proton activity and concentration are equal, the expression 339 given by Sundquist et al. (1979) reads:
−1 G[HCO− ]− 4[CO2− ]2 340 2− 3 3 (37) RF = DIC [H 2CO3]+[CO3 ]+ − 2− [HCO3 ]+ 4[CO3 ]+G
341 with:
+ TotB⋅ KB[H ] 342 G = + 2 (38) (K B +[H ])
343 The work by Zeebe and Wolf-Gladrow (2001) also includes the auto-dissociation of water. In
∂AT 344 this case, + is defined as in Eq. (25). Their expression for RF reads: ∂[H ] * CO2
−1 DIC ∂DIC 345 RF = * * (39) [CO2 ] ∂[CO2 ]
346 with:
15 4K K K (K )2 K + C1 C2 C1 C1 C2 [H ] + 2 + + + + 3 + * ⋅ [H ] [H ] [H ] [CO2 ] K K K C1 C2 C1 KW TotB ⋅ K B 1+ + 2 + + 1+ + 2 + + 2 ∂DIC [H ] [H ] [H ] (K + [H ]) 347 = B (40) ∂[CO* ] 4K K K + 2 C1 C2 C1 [H ] KW TotB ⋅ K B + 2 + + + * 1+ + 2 + + 2 [H ] [H ] [CO2 ] [H ] (K B +[H ])
348 Part D of the Supplementary Information shows that Eqs. (37) and (39) are both equivalent to 349 Eq. (35).
350
351 3. Applications
352 3.1 Sensitivities in contemporary global ocean surface water
353 We have now derived all partial derivatives of Eq. (5) and are thus able to attribute changes
354 in pH to different factors. To make these buffer factors more tangible, and to get a feeling for 355 the importance of each of the factors, we will take the global ocean surface water as a model ∂pH 356 system and apply changes in each of the factors discussed in Sect 2.1 and 2.2. Since ∂TotX ∂pH 357 and are independent of the species of the acid-base system that is added or removed ∂AT 358 (Table 3b), we will only consider changes in TotX, rather than the individual species. All 359 calculations were performed on the free pH scale (see part C of the Supplementary 360 Information for a discussion on the various pH scales) using the R package AquaEnv 361 (Hofmann et al., 2010b). To highlight that the free scale is used in this paper, from now on
362 we will denote pH as pHF. As carbonate dissociation constants we used those of Lueker et al. 363 (2000) as recommended by Dickson et al. (2007). For the other acid-base dissociation
364 constants and the CO2 solubility constant, we chose the default settings of AquaEnv.
365 The initial conditions of our model system were chosen to represent the global open-ocean 366 surface-water mean of the year 2000 (Table E.1 of the Supplementary Information). We
367 calculated the sensitivities of pHF to changes in TotX, AT, T and S for 2000 and 2100,
368 assuming that temperature and atmospheric pCO2 (pCO2,atm) change according to the highest
369 Representative Concentration Pathway, RCP8.5. The increase in pCO2,atm until 2100 was
370 taken from Meinshausen et al. (2011), thereby assuming that seawater pCO2 increases by the 371 same magnitude. The increase in global average SST from the 1990s to the 2090s has been 16 372 estimated at 2.73±0.72ºC (Bopp et al., 2013). All other parameters were kept constant. If 373 necessary, nutrient concentrations were converted from µmol L-1 to µmol kg-1.
374 Table 4 shows the sensitivities for the contemporary global open ocean surface water and 375 how these may change by the end of the 21st century. A negative sensitivity, as for DIC,
376 indicates that adding this species to the system leads to a decrease in pHF, consistent with our 377 general knowledge of the carbonate system. The reverse holds for the positive sensitivities, ∂ pH 378 such as , where an increase in AT leads to an increase in pHF. The signs of the ∂AT 379 sensitivities do not change in the range of conditions we consider here and, in fact, do not
380 change over the whole range of pHF values in oceanic and coastal waters, since the 381 denominator in the sensitivities of Table 3b always has a negative sign, i.e., the term
∂A 382 [H + ] T − nA TotX is always negative and exceeds A2 . Therefore, the sign of + X X ∂[H ] X ∂pH 383 depends on the sign of A ; if the contribution of an acid-base system to TA is ∂TotX X ∂pH 384 positive, then is by definition negative. The magnitude of a sensitivity with respect to ∂TotX
385 a total concentration of an acid-base species mainly depends on two factors: (1) AX , which ∂pH ∂pH 386 controls the numerator in , and (2) TotX, which controls the denominator in as ∂TotX ∂TotX ∂A 387 it is much more variable than [H + ] T − nA and much larger than A2 , the other two + X X ∂[H ] X ∂A 388 terms appearing here. The factor T only deviates substantially from β when A + H X ∂[H ] X ∂A 389 contributes substantially to A ; in these cases, the absolute value of T exceeds that T + ∂[H ] X
390 of βH by up to 1 order of magnitude (in the case of AC). It varies per species whether TotX ∂pH ∂ pH 391 or A mainly controls the magnitude of . For example, the denominators of X ∂TotX ∂DIC ∂ pH 392 and have a similar order of magnitude, but since AB is 1 order of magnitude smaller ∂TotB ∂ pH ∂pH 393 than AC, the absolute value of is much higher than that of . In contrast, AB is 1 ∂DIC ∂TotB 17 394 order of magnitude higher than ASi, but due to the much smaller total concentration of silicate ∂ pH 395 in comparison to borate, the absolute value of is higher. ∂TotSi
∂pH 396 Table 4 shows that has the highest absolute value, and for this reason TotPO4, ∂TotPO4 397 together with TotSi, is by default included in the most common programs for calculating the 398 carbonate chemistry, such as CO2SYS (Lewis and Wallace, 1998), SWCO2 (Hunter, 2007) 399 and seacarb (Lavigne et al., 2014). The units of the sensitivities with respect to changes in the -1 -1 -1 400 total concentrations are in (mol kg ) . This means that adding 1 µmol kg TotPO4 to this -1 401 system leads to a decrease in pHF of 0.00180, while the addition of 1 µmol kg DIC, under
402 these conditions equivalent to a ∆pCO2 of 1.59 ppmv, lowers pHF by 0.00175. However, in
403 natural systems DIC changes are about two orders of magnitude higher than those in TotPO4 404 because of the Redfield ratio. Hence, as displayed in Eq. (5), it is ultimately the combination
405 of the change in TotX combined with the sensitivity that determines the actual change in pHF.
406 Increasing T, S and p all lead to a decrease in pHF. Under constant DIC and AT, the increase 407 in K resulting from an increase in temperature exceeds that of K , resulting in a shift of C2 C1
* 408 the carbonate system towards CO2 . A warming of 1ºC lowers pH by 0.0137, while the effect 409 of changing pressure is much smaller; increasing p by 1 bar (which implies an increase in ∂pH 410 depth of ca. 10 m) leads to a decrease in pH of 0.000417. Our estimate of F is in ∂T 411 reasonable agreement with the -0.016±0.001 estimated by Takahashi et al. (2014), who use a
412 more extensive data set and report pH on the total scale (from now on denoted as pHT). Note 413 that Pilson (2014), in contrast to these results, calculated an increase in pH (displayed on the
414 NIST scale, from now on denoted as pHNIST) with an increase in T. This different result can, 415 however, be explained by the different approaches used. In our approach we keep the total
416 concentrations of the acid-base species and AT constant when calculating the sensitivity of
417 pH with respect to an increase in T. This leads to an increase in pCO2 while keeping DIC
418 constant, and thus a lowering in pH. Pilson (2014), however, kept the atmospheric [CO2] and
419 AT constant when increasing T. Since an increase in T leads to lower CO2 solubility (Weiss,
420 1974), less atmospheric CO2 is absorbed by the water, resulting in a decrease of both DIC
421 and the fugacity of CO2 (fCO2), and thus an increase in pH. Increasing S by 1 leads to a 422 lowering in pH of 0.0099. By also including the effect of S on TotB, Takahashi et al. (2014)
18 ∂ pH 423 estimated a value for T of -0.0125±0.0005. If we assume that an increase in S of 1 units ∂S 424 leads to an increase in TotB of 12.358 µmol kg-1 (Lee et al., 2010), then we can calculate a 425 combined sensitivity of increasing S and TotB of -0.0142. Taking into account the different 426 pH scale, this is not far from the estimate of Takahashi et al. (2014).
427
428 3.2 Sensitivities in the future ocean
429 When comparing the sensitivities of the contemporary ocean and a warmer, high-CO ocean, 2 430 it becomes clear that not all sensitivities respond in a similar way to these processes. The
431 majority of sensitivities becomes greater when pCO2 increases, indicating larger pH change 432 associated with a certain increment of TotX. Taking DIC as an example, an increase of 1 -1 433 µmol kg DIC in a high-CO2 ocean (pCO2 = 891 ppmv, DIC increase equivalent to ∆pCO2 = + 434 6.14 ppmv) lowers pHF by 0.00270. This is equivalent to an increase in [H ] that is 3.71 435 times higher compared to the increase in [H+] when adding 1 µmol kg-1 of DIC to the 436 contemporary ocean. This factor of 3.71 is significantly higher than the ca. 1.4 found by
437 Riebesell et al. (2009), who used a more conservative increase in pCO2,atm. Also the -1 438 sensitivity of pH to a change in AT increases; an increase of 1 µmol kg AT, caused by e.g. 439 0.5 µmol kg-1 of calcite dissolution, raises pH by 0.00263, equivalent to a 3.93 times higher + 440 decrease in [H ]. In addition, the high-CO2 ocean is less sensitive to changes in S and T, the 441 latter of which is consistent with Riebesell et al. (2009), who found the same trend in both 442 cold and warm surface waters.
443 In contrast to ocean acidification, ocean warming lowers most sensitivities, because of an 2- 444 increase in buffering capacity due to a higher [CO3 ] (Sunda and Cai, 2012). Taking DIC as -1 445 an example, an increase of 1 µmol kg DIC in a warmer ocean (equivalent to ∆pCO2 = 1.54 + 446 ppmv) lowers pHF by 0.00167, i.e., the increase in [H ] is 93.9% of the increase in the 447 contemporary ocean. Similarly, the decrease in [H+] in a warmer ocean is 93.1% of the -1 448 current decrease resulting from an increase in AT of 1 µmol kg . While most sensitivities 449 related to TotX show an opposite response to warming and acidification, this is not the case 450 for the sensitivities related to S and T changes.
451 When ocean acidification and warming are combined, the response of the sensitivities largely 452 reflects that of ocean acidification alone, but somewhat attenuated because of opposing
453 effects of increases in T and pCO2. Taking again DIC and AT as examples, in this scenario a 19 -1 + 454 1 µmol kg addition of DIC (equivalent to ∆pCO2 = 5.88 ppmv) leads to an increase in [H ] 455 that is 3.43 times higher compared to the increase in [H+] when adding 1 µmol kg-1 of DIC to -1 + 456 the contemporary ocean, while an increase in AT of 1 µmol kg causes a decline in [H ] that
457 is 3.62 times higher in a warmer, high-CO2 ocean. Both of these values are lower than the
458 factors mentioned for an increase in pCO2 only. The values of the sensitivities for warming 459 and acidification combined cannot be calculated by summing the separate changes of a higher
460 T and pCO2. The reason for this is that our assumption that pCO2 is the same in both the high 461 and the low T scenarios implies that DIC is slightly lower in the scenario where T is higher.
462 If we had kept DIC, rather than pCO2, the same in the high and low T scenarios, then this 463 would have been possible.
464 When comparing the relative changes in sensitivity between the contemporary and a warmer, ∂pH ∂ pH 465 high-CO2 ocean, it can be seen that increases more than the absolute value of . ∂AT ∂DIC
466 This is important when considering a process that influences both AT and DIC, such as calcite
467 dissolution or precipitation where the AT:DIC production or consumption ratio is 2:1. In the + -1 468 contemporary ocean, the increase in [H ] by adding 1 µmol kg AT is 91.1% of the decrease + -1 469 in [H ] by adding 1 µmol kg DIC. In a warmer, high-CO2 ocean, this fraction will increase
470 to 96.0%. Thus, the change in AT becomes relatively more important for the observed pHF 471 change.
472 Future carbon dioxide emission scenarios will determine the direction and magnitude of ∂ pH ∂ pH 473 changes in ocean buffer factors. Figure 1 shows the projected changes in , , ∂DIC ∂AT ∂pH 474 and the Revelle factor based on four emission scenarios of the 5th IPCC assessment ∂pCO2
475 (2013). The atmospheric CO2 trajectories of Meinshausen et al. (2011) were combined with 476 average ocean surface water composition (Table E.1) and no temperature increase was 477 assumed because of its limited effect. The impact of biogeochemical processes and ocean 478 acidification on ocean pH will increase in proportion to the projected atmospheric 479 perturbation. The business-as-usual scenario (RCP8.5) will result in an ocean that is less 480 buffered and can take up less carbon dioxide than an ocean subject to the scenario with early 481 measure to reduce carbon emissions (RCP3D). The average Revelle factor will change from
482 9.9 in the year 2000 to 15.0 for RCP8.5 and 10.5 for RCP3D. These different CO2 trajectories
20 483 also have a major impact on the sensitivity of ocean pH to biogeochemical processes such as 484 calcification and primary production.
485 In the context of ocean acidification due to atmospheric pCO2 it instructive to separate the
486 changes in pH with respect to pCO2 and DIC (Orr, 2011):
∂pH ∂pH ∂pCO 487 = 2 (41) ∂DIC ∂pCO2 ∂DIC
∂pH ∂ pH ∂pCO 488 To analytically calculate , we take the quotient of and 2 . The latter term ∂pCO ∂DIC ∂DIC 2 489 is derived from Eq. (34):
∂A pCO [H + ] T * 2 + ∂pCO 1 ∂[CO ] ∂[H ] * 490 2 2 CO2 (42) = = ∂DIC K0 ∂DIC 2 + ∂AT AC +[H ] + DIC ∂[H ] * CO2
* 491 where [CO2 ]= K0 pCO2 and assuming that K0 does not change as temperature remains 492 constant during these calculations. The resulting expression then becomes:
Ac ∂pH 493 ln(10) (43) = ∂pCO2 + ∂AT pCO2[H ] + ∂[H ] * CO2
∂ pH 494 As can be seen in Figs. 1a-c, the increased sensitivity is affected by changes in both ∂DIC ∂pH ∂pCO 495 and 2 . Throughout the 21st century, the latter term increases by factors of 3.84 ∂pCO2 ∂DIC ∂pH 496 and 1.21 for RCP8.5 and RCP3D, respectively, while increases from -0.00110 in the ∂pCO2 497 year 2000 to -0.000442 for RCP8.5 and -0.000966 for RCP3D, respectively. Under these + 498 conditions, an increment of 1 ppmv pCO2 leads however to [H ] increases which are only 499 marginally smaller than that of the contemporary ocean (96.3 and 99.1% for RCP8.5 and 500 RCP3D, respectively). These small differences indicate, in line with Orr (2011), that the ∂ pH ∂pCO 501 response of to ocean acidification is largely due to the 2 term. ∂DIC ∂DIC
21 502
503 3.3 Elucidating interactions between ocean pH perturbations
504 The future ocean, and in particular the coastal zone, is subject to multiple stressors including 505 ocean acidification, global warming, atmospheric deposition of sulphur and nitrogen, and 506 eutrophication. The combined effects of these human perturbations on ocean pH have not yet 507 been fully explored. In the previous section, we showed that ocean acidification has a much 508 stronger effect on future pH than global warming. Doney et al. (2007), Hunter et al. (2011) 509 and Hagens et al. (2014) showed that acid generation due to deposition of atmospheric
510 sulphur and nitrogen adds to ocean acidification, but that its impact on ocean pH depends on 511 the buffer capacity. Eutrophication, the excess production of organic matter, due to human 512 nutrient inputs can lead to enhanced respiration and eventually to oxygen depletion in coastal 513 waters. Respiration of organic matter also leads to an increase in DIC and thus might 514 eventually lead to a decrease in pH (Frankignoulle et al., 1998; Cai et al., 2011; Mucci et al., 515 2011). The combined effect of ocean acidification due to dissolution of atmospheric carbon 516 dioxide and that due to eutrophication-induced respiration might be additive and result in 517 highly corrosive waters (Cai et al., 2011; Mucci et al., 2011; Melzner et al., 2013; Wallace et 518 al., 2014).
519 Figure 2 shows the relationships between pH and dissolved oxygen in seawater subjected to 520 both DIC additions from respiration and atmospheric carbon dioxide. Mean ocean surface 521 water was subjected to the four carbon dioxide trajectories of the 5th IPCC assessment and 522 respiration of Redfield organic matter. The figure also shows the relationship in the pre-
523 industrial ocean when pCO2,atm was 285 ppm. The DIC generated during respiration adds to 524 the ocean acidification due to increasing atmospheric carbon dioxide levels, but the additional 525 pH decline is not constant, consistent with earlier work (Cai et al., 2011; Sunda and Cai, 526 2012). Comparing year 2100 projections based on RCP8.5 with the pre-industrial ocean 527 shows that without respiration the pH decline would be 0.486 unit (equivalent to ∆[H+] = 528 0.0100 µmol kg-1), while it would be maximally 0.622 unit (equivalent to ∆[H+] = 0.0274 529 µmol kg-1) at an oxygen concentration of 114 µmol kg-1 At very low oxygen levels, the 530 additional pH decline due to respiration would be only 0.376 unit; however, the equivalent + -1 531 ∆[H ] (0.0293 µmol kg ) is higher than at the point of maximum pH difference. At O2 = 49 532 µmol kg-1, the absolute [H+] change is highest (0.0335 µmol kg-1); here, the pH difference 533 between both simulations is 0.539. This non-linear behaviour relates directly to changes in
22 534 the sensitivities of pH and [H+] to DIC changes under altered ambient conditions. Moreover, 535 since both sensitivities are related through −ln(10)[H + ] (Eq. (21)), it is the ambient [H+] that 536 controls their different responses to respiration. The decrease in both sensitivities at lower 537 oxygen levels can be attributed to an increase in buffering at these lower pH values (e.g. 538 Egleston et al., 2010), but this response is system-specific and depends on the initial 539 conditions. Therefore, the results of Figure 2 agree in pattern with those of Cai et al. (2011) 540 and Sunda and Cai (2012) but show different points of minimum buffering capacity. Waters 541 that currently have a high buffering capacity, such as the Gulf of Mexico, require a higher
542 pCO2 increase before their maximum sensitivity to respiration is reached than poorly 543 buffered waters such as the Baltic Sea (Sunda and Cai, 2012). Accordingly, DIC added by 544 respiration will lower pH in the future ocean but not necessarily more than it does now and 545 the other eutrophication problem (Wallace et al., 2014) will thus either stimulate or attenuate 546 pH decline depending both on the intensity of oxygen depletion and the current buffering 547 capacity.
548
549 3.4 Analytical versus numerical calculation of buffer factors
550 It has recently been pointed out that differences between analytical expressions for the 551 Revelle factor that only include the carbonate system and treat the borate system as invariant 552 (Sundquist et al., 1979; Frankignoulle, 1994; Zeebe and Wolf-Gladrow, 2001), and the
553 numerical approximation of CO2SYS and mocsy 2.0, which use the full definition of AT as
554 given by Dickson (1981), are highest when nutrients contribute significantly to AT (Orr and 555 Epitalon, 2015). We can use the generic expressions from this paper to show that the 556 analytical and numerical solutions yield similar results when the approach of Frankignoulle
557 (1994) is expanded to include all relevant acid-base systems contributing to AT. For this, we dpH 558 numerically estimated both RF and (where Y can refer to either TotX or AT) for the dY 559 contemporary ocean (Table E.1 in the Supplementary Information). A centred-finite- 560 difference approach was used in which small (1 and 0.1%) in- and decrements were applied
561 to the variable of interest (AT or TotX), after which both resulting pH values (in the case of dpH 562 ) or CO2 values (in the case of RF) were taken and used to calculate the corresponding dY
563 sensitivity. TotF and TotSO4 were discarded from this analysis, as with this numerical
23 564 estimation it is not possible to distinguish between the actual change in pH resulting from a dpH dpH 565 change in concentration ( and ), and the effects related to pH scale dTotF dTotSO4 566 conversion (see part C of the Supplementary Information). In addition, we also analytically
567 calculated the factors βD, ΦD and ΦH of Frankignoulle (1994), which are equivalent to RF, ∂ pH ∂pH 568 and , respectively. The results of both calculations were compared with the ∂DIC ∂AT 569 analytically-calculated sensitivities using the generalised expressions of this work.
570 This comparison (Table 5) shows that Frankignoulle’s factors βD, ΦD and ΦH, without all 571 acid-base systems included, deviate most from the analytically-derived factors and the 572 numerical estimates with smallest disturbance (0.1%), which may be assumed to be more 573 accurate than the estimate using a higher disturbance. This shows that our method is indeed 574 capable of analytically calculating sensitivities more accurately than previously. It is thus 575 possible to analytically calculate RF and other sensitivities at high accuracy even in nutrient- 576 rich waters. Table 5 also shows that when under these initial conditions the variable of dpH ∂pH 577 interest is changed by 1%, in most cases equals . Exceptions here are AT and dY ∂Y 578 DIC, the two variables with highest concentrations, where a smaller disturbance (0.1%) is 579 required to arrive at a result identical up to 5 significant digits. Note that it is not the focus of 580 this paper to determine which disturbance is preferentially used for each factor; this may be 581 system-specific and has been previously discussed for the Revelle factor (Orr and Epitalon, 582 2015). We rather encourage the use of analytically-calculated sensitivities using this novel 583 approach.
584
585 4 Conclusions and implications
586 Inspired by Frankignoulle (1994), we derived generic expressions describing the change in
587 pHF or an acid-base species due to changes in AT or the total concentration of that particular 588 acid-base system. These sensitivities are valid for any combination of acid-base systems and 589 any total concentration, or any of the species contributing to the total concentration, as 590 independent state variable, assuming that all other factors remain constant. They are therefore 591 ideal when attributing which factors drive a change in pH or X. Most sensitivities in a 592 warmer, more acidified ocean increase, thus decreasing the ocean’s capacity to buffer
24 593 changes in pH. This decrease is mostly driven by the increase in pCO2 and slightly tempered 594 by the increase in T.
595 Previous studies have shown that seawater buffering capacity will decrease in a warmer,
596 high-CO2 ocean (e.g. Hofmann et al., 2010a; Egleston et al., 2010; Hagens et al., 2014). Our 597 work supports this finding, but additionally is the first to give a comprehensive overview of 598 all sensitivities and shows which of these factors are most affected by global change. The 599 lower capacity of the global ocean to buffer changes in TA and most total concentrations of 600 acid-base species by the end of the 21st century has important implications. For example, we 601 may expect more pronounced diurnal (Schulz and Riebesell, 2013) and seasonal pH 602 variabilities resulting from photosynthesis and subsequent organic matter remineralisation. 603 This effect may be amplified if productivity were to increase in the future ocean (Low- 604 Décarie et al., 2014), though whether this will happen is subject of debate (Joint et al., 2011; 605 Eichner et al., 2014).
606 Both Frankignoulle (1994) and Egleston et al. (2010) discussed some useful applications of 607 the buffer factors derived in their papers. Among these are estimating the ratio of organic 608 matter production to calcification in, e.g., coral reefs, aiding experimental designs, testing 609 model parameter sensitivities, as well as error propagation (Dickson and Riley, 1978). The 610 sensitivities derived in this paper can be applied to the same questions and are particularly 611 useful in waters where the contribution of acid-base systems other than the carbonate and
612 borate systems to AT is high. Examples of these are pore waters, upwelling regions, the deep 613 ocean, high-nutrient-low-chlorophyll regions, and anoxic bottom waters in stratified seas or 614 rivers (Gaines Jr and Pilson, 1972; Ben-Yaakov, 1973; Dugdale et al., 1977; Ulfsbo et al., 615 2011).
616
617 Acknowledgements
618 This research is supported by a Sea and Coastal Research fund (83910502) of the 619 Netherlands Organisation for Scientific Research (NWO) and by the Netherlands Earth 620 System Science Centre (NESSC). We thank Alfonso Mucci, Wei-Jun Cai, James Orr and an 621 anonymous reviewer for valuable comments that improved the quality of this manuscript.
622 623 References
25 624 Álvarez M., Sanleón-Bartolomé H., Tanhua T., Mintrop L., Luchetta A., Cantoni C., 625 Schroeder K. and Civitarese G. (2014) The CO2 system in the Mediterranean Sea: a 626 basin wide perspective. Ocean Sci. 10, 69–92. 627 Bates N. R., Astor Y. M., Church M. J., Currie K., Dore J. E., González-Dávila M., 628 Lorenzoni L., Muller-Karger F., Olafsson J. and Santana-Casiano J. M. (2014) A time- 629 series view of changing ocean chemistry due to ocean uptake of anthropogenic CO2 and 630 ocean acidification. Oceanography 27, 126–141. 631 Ben-Yaakov S. (1973) pH buffering of pore water of recent anoxic marine sediments. Limnol. 632 Oceanogr. 18, 86–94. 633 Bolin B. and Eriksson E. (1959) Changes in the carbon dioxide content of the atmosphere and 634 sea due to fossil fuel combustion. In The Atmosphere and the Sea in Motion pp. 130–141.
635 Bopp L., Resplandy L., Orr J. C., Doney S. C., Dunne J. P., Gehlen M., Halloran P., Heinze 636 C., Ilyina T., Séférian R., Tjiputra J. and Vichi M. (2013) Multiple stressors of ocean 637 ecosystems in the 21st century: projections with CMIP5 models. Biogeosciences 10, 638 6225–6245. 639 Cai W.-J., Hu X., Huang W.-J., Murrell M. C., Lehrter J. C., Lohrenz S. E., Chou W.-C., 640 Zhai W., Hollibaugh J. T., Wang Y., Zhao P., Guo X., Gundersen K., Dai M. and Gong 641 G.-C. (2011) Acidification of subsurface coastal waters enhanced by eutrophication. Nat. 642 Geosci. 4, 766–770. 643 Cai W.-J., Wang Y. and Hodson R. E. (1998) Acid-base properties of dissolved organic 644 matter in the estuarine waters of Georgia, USA. Geochim. Cosmochim. Acta 62, 473– 645 483. 646 Caldeira K. and Wickett M. E. (2003) Oceanography: anthropogenic carbon and ocean pH. 647 Nature 425, 365. 648 Dickson A. G. (1981) An exact definition of total alkalinity and a procedure for the 649 estimation of alkalinity and total inorganic carbon from titration data. Deep Sea Res. 650 Part A. Oceanogr. Res. Pap. 28, 609–623. 651 Dickson A. G. and Riley J. P. (1978) The effect of analytical error on the evaluation of the 652 components of the aquatic carbon-dioxide system. Mar. Chem. 6, 77–85. 653 Dickson A. G., Sabine C. L. and Christian J. R. eds. (2007) Guide to Best Practices for 654 Ocean CO2 Measurements., PICES Special Publication 3. 655 Doney S. C., Mahowald N., Lima I., Feely R. A., Mackenzie F. T., Lamarque J.-F. and Rasch 656 P. J. (2007) Impact of anthropogenic atmospheric nitrogen and sulfur deposition on 657 ocean acidification and the inorganic carbon system. Proc. Natl. Acad. Sci. U. S. A. 104, 658 14580–14585. 659 Dore J. E., Lukas R., Sadler D. W., Church M. J. and Karl D. M. (2009) Physical and 660 biogeochemical modulation of ocean acidification in the central North Pacific. Proc. 661 Natl. Acad. Sci. U. S. A. 106, 12235–12240. 662 Dugdale R. C., Goering J. J., Barber R. T., Smith R. L. and Packard T. T. (1977) 663 Denitrification and hydrogen sulfide in the Peru upwelling region during 1976. Deep 664 Sea Res. 24, 601–608. 665 Egleston E. S., Sabine C. L. and Morel F. M. M. (2010) Revelle revisited: buffer factors that 26 666 quantify the response of ocean chemistry to changes in DIC and alkalinity. Global 667 Biogeochem. Cycles 24, GB1002. 668 Eichner M., Rost B. and Kranz S. A. (2014) Diversity of ocean acidification effects on 669 marine N2 fixers. J. Exp. Mar. Bio. Ecol. 457, 199–207. 670 Fabry V., McClintock J., Mathis J. and Grebmeier J. (2009) Ocean acidification at high 671 latitudes: the bellwether. Oceanography 22, 160–171.
672 Frankignoulle M. (1994) A complete set of buffer factors for acid/base CO2 system in 673 seawater. J. Mar. Syst. 5, 111–118. 674 Frankignoulle M., Abril G., Borges A. V., Bourge I., Canon C., Delille B., Libert E. and 675 Théate J.-M. (1998) Carbon dioxide emission from European estuaries. Science 282, 676 434–436. 677 Gaines Jr A. G. and Pilson M. E. Q. (1972) Anoxic water in the Pettaquamscutt River. 678 Limnol. Oceanogr. 17, 42–50. 679 Hagens M., Hunter K. A., Liss P. S. and Middelburg J. J. (2014) Biogeochemical context 680 impacts seawater pH changes resulting from atmospheric sulfur and nitrogen deposition. 681 Geophys. Res. Lett. 41, 935–941. 682 Hauri C., Gruber N., Vogt M., Doney S. C., Feely R. A., Lachkar Z., Leinweber A., 683 McDonnell A. M. P., Munnich M. and Plattner G.-K. (2013) Spatiotemporal variability 684 and long-term trends of ocean acidification in the California Current System. 685 Biogeosciences 10, 193–216. 686 Hofmann A. F., Middelburg J. J., Soetaert K. and Meysman F. J. R. (2009) pH modelling in 687 aquatic systems with time-variable acid-base dissociation constants applied to the turbid, 688 tidal Scheldt estuary. Biogeosciences 6, 1539–1561. 689 Hofmann A. F., Middelburg J. J., Soetaert K., Wolf-Gladrow D. A. and Meysman F. J. R. 690 (2010a) Proton cycling, buffering, and reaction stoichiometry in natural waters. Mar. 691 Chem. 121, 246–255. 692 Hofmann A. F., Soetaert K., Middelburg J. J. and Meysman F. J. R. (2010b) AquaEnv: An 693 aquatic acid–base modelling environment in R. Aquat. Geochemistry 16, 507–546.
694 Hunter K. A. (2007) XLCO2 – Seawater CO2 equilibrium calculations using Excel. , 1–18. 695 Hunter K. A., Liss P. S., Surapipith V., Dentener F., Duce R., Kanakidou M., Kubilay N., 696 Mahowald N., Okin G., Sarin M., Uematsu M. and Zhu T. (2011) Impacts of 697 anthropogenic SOx , NOx and NH3 on acidification of coastal waters and shipping lanes. 698 Geophys. Res. Lett. 38, L13602. 699 IPCC (2013) Climate Change 2013: The Physical Science Basis. Contribution of Working 700 Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate 701 Change. eds. T. F. Stocker, D. Qin, G.-K. Plattner, M. Tignor, S. K. Allen, J. Boschung, 702 A. Nauels, Y. Xia, V. Bex, and P. M. Midgley, Cambridge University Press, Cambridge. 703 Joint I., Doney S. C. and Karl D. M. (2011) Will ocean acidification affect marine microbes? 704 ISME J. 5, 1–7. 705 Kim H.-C. and Lee K. (2009) Significant contribution of dissolved organic matter to seawater 706 alkalinity. Geophys. Res. Lett. 36, L20603.
27 707 Kuliński K., Schneider B., Hammer K., Machulik U. and Schulz-Bull D. (2014) The 708 influence of dissolved organic matter on the acid–base system of the Baltic Sea. J. Mar. 709 Syst. 132, 106–115. 710 Lavigne H., Epitalon J.-M. and Gattuso J.-P. (2014) seacarb: seawater carbonate chemistry 711 with R. , 1–100. 712 Lee K., Kim T.-W., Byrne R. H., Millero F. J., Feely R. A. and Liu Y.-M. (2010) The 713 universal ratio of boron to chlorinity for the North Pacific and North Atlantic oceans. 714 Geochim. Cosmochim. Acta 74, 1801–1811.
715 Lewis E. L. and Wallace D. W. R. (1998) CO2SYS: Program developed for CO2 system 716 calculations., Oak Ridge, Tennessee, United States of America. 717 Low-Décarie E., Fussmann G. F. and Bell G. (2014) Aquatic primary production in a high- 718 CO2 world. Trends Ecol. Evol. 29, 223–232.
719 Lueker T. J., Dickson A. G. and Keeling C. D. (2000) Ocean pCO2 calculated from dissolved 720 inorganic carbon, alkalinity, and equations for K1 and K2: validation based on laboratory 721 measurements of CO2 in gas and seawater at equilibrium. Mar. Chem. 70, 105–119.
722 MacIntyre F. (1978) Toward a minimal model of the world CO2 system. I. Carbonate- 723 alkalinity version. Thalass. Jugoslavica 14, 63–98. 724 McNeil B. I. and Matear R. J. (2007) Climate change feedbacks on future oceanic 725 acidification. Tellus B 59, 191–198. 726 Meinshausen M., Smith S. J., Calvin K., Daniel J. S., Kainuma M. L. T., Lamarque J.-F., 727 Matsumoto K., Montzka S. A., Raper S. C. B., Riahi K., Thomson A., Velders G. J. M. 728 and Vuuren D. P. P. (2011) The RCP greenhouse gas concentrations and their 729 extensions from 1765 to 2300. Clim. Change 109, 213–241. 730 Melzner F., Thomsen J., Koeve W., Oschlies A., Gutowska M. A., Bange H. W., Hansen H. 731 P. and Körtzinger A. (2013) Future ocean acidification will be amplified by hypoxia in 732 coastal habitats. Mar. Biol. 160, 1875–1888. 733 Morel F. M. M. and Hering J. G. (1993) Principles and Applications of Aquatic Chemistry., 734 Wiley-Interscience, New York, NY. 735 Mucci A., Starr M., Gilbert D. and Sundby B. (2011) Acidification of Lower St. Lawrence 736 Estuary bottom waters. Atmosphere-Ocean 49, 206–218. 737 Muller F. L. L. and Bleie B. (2008) Estimating the organic acid contribution to coastal 738 seawater alkalinity by potentiometric titrations in a closed cell. Anal. Chim. Acta 619, 739 183–191. 740 Orr J. C. (2011) Recent and future changes in ocean carbonate chemistry. In Ocean 741 Acidification (eds. J.-P. Gattuso and L. Hansson). Oxford University Press, Oxford. pp. 742 41–66. 743 Orr J. C. and Epitalon J.-M. (2015) Improved routines to model the ocean carbonate system: 744 mocsy 2.0. Geosci. Model Dev. 8, 485–499. 745 Orr J. C., Fabry V. J., Aumont O., Bopp L., Doney S. C., Feely R. A., Gnanadesikan A., 746 Gruber N., Ishida A., Joos F., Key R. M., Lindsay K., Maier-Reimer E., Matear R., 747 Monfray P., Mouchet A., Najjar R. G., Plattner G.-K., Rodgers K. B., Sabine C. L., 748 Sarmiento J. L., Schlitzer R., Slater R. D., Totterdell I. J., Weirig M.-F., Yamanaka Y. 28 749 and Yool A. (2005) Anthropogenic ocean acidification over the twenty-first century and 750 its impact on calcifying organisms. Nature 437, 681–686.
751 Park P. K. (1969) Oceanic CO2 system: An evaluation of ten methods of investigation. 752 Limnol. Oceanogr. 14, 179–186. 753 Pilson M. E. Q. (2014) Changing pH in the surface ocean. Oceanography 27, 120–125. 754 Revelle R. and Suess H. E. (1957) Carbon dioxide exchange between atmosphere and ocean 755 and the question of an increase of atmospheric CO2 during the past decades. Tellus 9, 756 18–27. 757 Riebesell U., Körtzinger A. and Oschlies A. (2009) Sensitivities of marine carbon fluxes to 758 ocean change. Proc. Natl. Acad. Sci. U. S. A. 106, 20602–9. 759 Schulz K. G. and Riebesell U. (2013) Diurnal changes in seawater carbonate chemistry 760 speciation at increasing atmospheric carbon dioxide. Mar. Biol. 160, 1889–1899. 761 Van Slyke D. D. (1922) On the measurement of buffer values and on the relationship of 762 buffer value to the dissociation constant of the buffer and the concentration and reaction 763 of the buffer solution. J. Biol. Chem. 52, 525–570. 764 Soetaert K., Hofmann A. F., Middelburg J. J., Meysman F. J. R. and Greenwood J. (2007) 765 The effect of biogeochemical processes on pH. Mar. Chem. 105, 30–51. 766 Stumm W. and Morgan J. J. (1996) Aquatic Chemistry: Chemical Equilibria and Rates in 767 Natural Waters. 3rd ed., John Wiley & Sons, Inc., New York, NY.
768 Sunda W. G. and Cai W.-J. (2012) Eutrophication induced CO2-acidification of subsurface 769 coastal waters: interactive effects of temperature, salinity, and atmospheric pCO2. 770 Environ. Sci. Technol. 46, 10651–10659. 771 Sundquist E. T., Plummer L. N. and Wigley T. M. (1979) Carbon dioxide in the ocean 772 surface: the homogeneous buffer factor. Science 204, 1203–1205. 773 Takahashi T., Sutherland S. C., Chipman D. W., Goddard J. G., Ho C., Newberger T., 774 Sweeney C. and Munro D. R. (2014) Climatological distributions of pH, pCO2, total 775 CO2, alkalinity, and CaCO3 saturation in the global surface ocean, and temporal changes 776 at selected locations. Mar. Chem. 164, 95–125. 777 Ulfsbo A., Hulth S. and Anderson L. G. (2011) pH and biogeochemical processes in the 778 Gotland Basin of the Baltic Sea. Mar. Chem. 127, 20–30. 779 Wallace R. B., Baumann H., Grear J. S., Aller R. C. and Gobler C. J. (2014) Coastal ocean 780 acidification: the other eutrophication problem. Estuar. Coast. Shelf Sci. 148, 1–13. 781 Waller K. V. and Makila P. M. (1981) Chemical reaction invariants and variants and their use 782 in reactor modeling, simulation, and control. Ind. Eng. Chem. Process Des. Dev. 20, 1– 783 11. 784 Weiss R. F. (1974) Carbon dioxide in water and seawater: the solubility of a non-ideal gas. 785 Mar. Chem. 2, 203–215. 786 Wolf-Gladrow D. A., Zeebe R. E., Klaas C., Körtzinger A. and Dickson A. G. (2007) Total 787 alkalinity: the explicit conservative expression and its application to biogeochemical 788 processes. Mar. Chem. 106, 287–300.
789 Zeebe R. E. and Wolf-Gladrow D. A. (2001) CO2 in seawater: equilibrium, kinetics, 29 790 isotopes., Elsevier Ltd., Amsterdam. 791 Zhang J.-Z. (2000) The use of pH and buffer intensity to quantify the carbon cycle in the 792 ocean. Mar. Chem. 70, 121–131. 793
30 794 Table 1a: Expressions for AX for the major acid-base systems present in marine waters in + 795 terms of the reference species (Xref), [H ] and dissociation constants. The reference species, 796 or the zero level of protons, is that species of an acid-base system that does not contribute to
797 AT, i.e., the stoichiometric contribution to AT (n) equals 0. These expressions are applicable 798 when the total concentration of the acid-base system TotX, or any of its species X, is the state 799 variable. Expressions are taken from Park (1969) and Stumm and Morgan (1996).
Acid-base Reference Contribution to AX AX (TotX or X is state variable)
system (TotX) species (Xref) (AX)
+ Ammonium NH4 [NH3] K NH 4 + + [NH 4 ] (TotNH4) [H ]
- Borate (TotB) B(OH)3 [B(OH)4 ] K B [B(OH ) ] [H + ] 3
- 2- Carbonate H2CO3 [HCO3 ] + 2 [CO3 ] K 2K K C1 + C1 C2 [CO* ] (DIC) [H + ] [H + ]2 2
- 2- 3- + Phosphate H2PO4 [HPO4 ] + 2[PO4 ] - K 2K K [H ] P2 P2 P3 − + + + 2 − [H 2PO4 ] (TotPO4) [H3PO4] [H ] [H ] K P1
- Nitrate NO3 - [HNO3] + −[H ] − [NO3 ] (TotNO3) K NO3
- Nitrite NO2 - [HNO2] + −[H ] − [NO2 ] (TotNO2) K NO2
- 2- Sulphide H2S [HS ] + 2[S ] K 2K K HS1 + HS1 HS2 [H S] (TotS) [H + ] [H + ]2 2
- Silicate (TotSi) Si(OH)4 [SiO(OH)3 ] + K 2K K Si1 + Si1 Si2 [Si(OH ) ] 2- + + 2 4 2[SiO2(OH)2 ] [H ] [H ]
- Fluoride (TotF) F - [HF] −[H + ] [F− ] KF
31 2- - Sulphate SO4 - [HSO4 ] - 2[H2SO4] + + 2 −[H ] 2[H ] 2− − [SO4 ] (TotSO4) K K K SO2 SO1 SO2
- + Water (auto- H2O [OH ] - [H ] - dissociation) 800 801
32 802 Table 1b: Expressions for AX for the major acid-base systems present in marine waters in 803 terms of the total concentration (TotX), [H+] and dissociation constants. These expressions 804 are applicable when the total concentration of the acid-base system (TotX) is reaction
805 invariant. The final expression for AT (Eq. (6)) for the specific situation is arrived at by 806 summing the appropriate term (a or b) for each acid-base system involved.
Acid-base Contribution to AT AX (TotX is reaction invariant)
system (TotX) (AX)
Ammonium [NH3] K NH 4 TotNH [H + ]+ K 4 (TotNH4) NH4
- Borate (TotB) [B(OH)4 ] K B + TotB [H ]+ K B
- 2- + Carbonate [HCO3 ] + 2 [CO3 ] K [H ]+ 2K K C1 C1 C2 DIC (DIC) [H + ]2 + K [H + ]+ K K C1 C1 C2
2- 3- + + 3 Phosphate [HPO4 ] + 2[PO4 ] - K K [H ]+ 2K K K −[H ] P1 P2 P1 P2 P3 + 3 + 2 + TotPO4 (TotPO4) [H3PO4] [H ] + K [H ] + K K [H ]+ 2K K K P1 P1 P2 P1 P2 P3
+ Nitrate - [HNO3] −[H ] TotNO [H + ]+ K 3 (TotNO3) NO3
+ Nitrite - [HNO2] −[H ] TotNO [H + ]+ K 2 (TotNO2) NO2
- 2- Sulphide [HS ] + 2[S ] K [H + ]+ 2K K HS1 HS1 HS2 TotS (TotS) [H + ]2 + K [H + ]+ K K HS1 HS1 HS2
- + Silicate (TotSi) [SiO(OH)3 ] + K [H ]+ 2K K Si1 Si1 Si2 2- + 2 + TotSi 2[SiO2(OH)2 ] [H ] + K [H ]+ K K Si1 Si1 Si2
Fluoride - [HF] −[H + ] + TotF (TotF) [H ]+ KF
- + + 2 Sulphate - [HSO4 ] - 2[H2SO4] −K [H ]−2[H ] SO1 TotSO (TotSO ) [H + ]2 + K [H + ]+ K K 4 4 SO1 SO1 SO2
33 - + Water (auto- [OH ] - [H ] KW + + −[H ] dissociation) [H ] 807 808
34 ∂A 809 Table 2a: Expressions for X for the major acid-base systems present in marine + ∂[H ] X 810 waters. These are used when the total concentration of the acid-base system (TotX), or any of 811 its species, is the state variable. The factor n corresponds to the stoichiometric factor in the
812 contribution of X to AT, which is by default 0 for the reference species. The reference species
813 (Xref) is that species of an acid-base system that does not contribute to AT. Acid-base system Reference ∂A X + (TotX) species ∂[H ] X
+ Ammonium NH4 −1 −nANH +()[NH ] H + ()4 3 (TotNH4) [ ]
Borate (TotB) B(OH)3 −1 −nA + [B(OH )− ] [H + ]()B ()4
Carbonate (DIC) H2CO3 −1 −nA + [HCO− ]+ 4[CO2− ] [H + ]()C ()3 3
- Phosphate H2PO4 −1 −nA + [H PO ]+[HPO2− ]+ 4[PO3− ] + ()P ()3 4 4 4 (TotPO4) [H ]
- Nitrate (TotNO3) NO3 −1 −nA + ()[HNO ] [H + ]()NO3 3
- Nitrite (TotNO2) NO2 −1 −nA + ()[HNO ] [H + ]()NO2 2
Sulphide (TotS) H2S −1 −nA + [HS− ]+ 4[S2− ] [H + ]()HS ()
Silicate (TotSi) Si(OH)4 −1 −nA + [SiO(OH )− ]+ 4[SiO (OH )2− ] [H + ]()Si ()3 2 2
Fluoride (TotF) F- −1 ()−nAF +()[HF] [H + ]
2- Sulphate (TotSO4) SO4 −1 −nA + 4[H SO ]+[HSO− ] [H + ]()SO ()2 4 4
35 Water (H2O) - -
814
36 ∂AX 815 Table 2b: Expressions for + for the major acid-base systems present in marine ∂[H ] TotX 816 waters. These are valid when the total concentration of the acid-base system (TotX) is ∂A 817 reaction invariant. The final expression for T for the specific situation (Eq. (15)) is + ∂[H ] X 818 arrived at by summing the appropriate term (a or b) for each acid-base system involved. Acid-base system ∂AX + (TotX) ∂[H ] TotX
Ammonium + −1 [NH 4 ] + [NH 3 ] (TotNH4) [H ] TotNH 4
Borate (TotB) −1 [B(OH ) ] [B(OH )− ] 3 [H + ] 4 TotB
Carbonate (DIC) 2− − [H 2CO3 ]−[CO3 ] [HCO3 ] DIC −1 [H + ] − 2− 2[H 2CO3]+[HCO3 ] +2[CO3 ] DIC
Phosphate − 2− 3− −[H 2PO4 ]− 2[HPO4 ]− 3[PO4 ] −[H 3PO4 ] (TotPO4) TotPO4 −1 2[H PO ]+[H PO− ]−[PO3− ] +[HPO2− ] 3 4 2 4 4 [H + ] 4 TotPO 4 − 2− 3− 3[H 3PO4 ]+ 2[H2PO4 ]+[HPO4 ] +2[PO4 ] TotPO4
Nitrate (TotNO3) − −1 [NO3 ] + −[HNO3 ] [H ] TotNO3
Nitrite (TotNO2) − −1 [NO2 ] + −[HNO2 ] [H ] TotNO2
Sulphide (TotS) 2− − −1 − [H S]−[S ] 2− 2[H S]+[HS ] [HS ] 2 + 2[S ] 2 [H + ] TotS TotS
37 Silicate (TotSi) 2− − [Si(OH )4 ]−[SiO2 (OH )2 ] [SiO(OH )3 ] −1 TotSi [H + ] − 2− 2[Si(OH )4 ]+[SiO(OH )3 ] +2[SiO2 (OH )2 ] TotSi
Fluoride (TotF) −1 [F − ] −[HF] + [H ] TotF
Sulphate (TotSO4) −[HSO− ]− 2[SO2− ] −2[H SO ] 4 4 2 4 −1 TotSO4 [H + ] 2− − [H 2SO4 ]− [SO4 ] −[HSO4 ] TotSO4
Water (auto- −1 − + + ()[OH ]+[H ] dissociation) [H ] 819
38 820 Table 3: Expressions for some sensitivities of interest when studying global change. TotX 821 refers to the total concentration of the acid-base system of interest, X to the species of interest
822 of that acid-base system (which equals the reference species for AT (Xref) in the case a change
823 in TotX is specified), n to the stoichiometric factor in the contribution of X to AT (which
824 equals 0 in the case a change in TotX or Xref is specified) and AX to the contribution of all
825 species of TotX to AT. Table 3a Sensitivity Expression
∂A ∂A ∂A T β − X + X + H + + ∂[H ] X ∂[H ]TotX ∂[H ]X
∂TotX nTotX − AX + [H + ] ∂[H ] X
∂A AX T [X] ∂[X] H +
∂TotX TotX [X] ∂[X] H +
∂AT + ∂AX ∂AX −ln(10)[H ]βH − + + + ∂pH X ∂[H ]TotX ∂[H ]X
∂TotX −ln(10)(nTotX − AX ) ∂ pH X 826
39 Table 3b Sensitivity Expression
∂[H + ] TotX[H + ]
∂A ∂A T A2 + [H + ] T − nA TotX X + X ∂[H ] X
∂[H + ] −A [H + ] X ∂TotX ∂A A2 + [H + ] T − nA TotX X + X ∂[H ] X
∂X −[X] −A + nTotX ( X ) ∂AT ∂A A2 + [H + ] T − nA TotX X + X ∂[H ] X
∂X ∂A [X][H + ] T + ∂TotX ∂[H ] X ∂A A2 + [H + ] T − nA TotX X ∂[H + ] X X
∂pH −TotX
∂AT ∂A ln(10) A2 + [H + ] T − nA TotX X + X ∂[H ] X
∂pH AX ∂TotX ∂A 2 + T ln(10) AX + [H ] + − nAX TotX ∂[H ] X 827
40 828 Table 4: Global mean values for all derived sensitivities at present and in 2100, using various 829 scenarios. Contemporary average surface seawater conditions were obtained from Table E.1 830 (Supplementary Information). Using the dissociation constants as outlined in Sect 3.1, this
831 corresponds to pHF = 8.21 and pCO2 = 324 ppmv. Changes in temperature (Bopp et al., 2013)
832 and pCO2,atm (Meinshausen et al., 2011) until 2100 (pCO2 = 891 ppmv, T = 21.0°C) were 833 considered both separately and combined.
Sensitivity Unit Present 2100 CO2 2100 T 2100 T+CO2
∂pH (mol kg-1)-1 1601.50 2622.39 1513.21 2474.51
∂AT
∂ pH (mol kg-1)-1 -65.01 -45.38 -75.46 -53.43
∂TotNH 4
∂pH (mol kg-1)-1 -349.00 -272.51 -348.33 -276.36
∂TotB
∂ pH (mol kg-1)-1 -1751.84 -2700.35 -1669.69 -2562.20
∂DIC
∂pH (mol kg-1)-1 -1801.31 -2730.96 -1728.16 -2601.70
∂TotPO4
∂pH (mol kg-1)-1 4.21·10-7 1.66·10-6 3.92·10-7 1.53·10-6
∂TotNO3
∂pH (mol kg-1)-1 6.23·10-3 2.45·10-2 5.80·10-3 2.26·10-2
∂TotNO2
∂pH (mol kg-1)-1 -1553.79 -2441.35 -1472.15 -2319.77
∂TotS
∂pH (mol kg-1)-1 -64.47 -44.99 -67.51 -47.65
∂TotSi
∂pH (mol kg-1)-1 3.72·10-3 1.46·10-2 3.64·10-3 1.42·10-2
∂TotF
∂ pH (mol kg-1)-1 7.71·10-5 3.03·10-4 7.97·10-5 3.10·10-4
∂TotSO4
41 ∂pH (ºC)-1 -1.37·10-2 -1.26·10-2 -1.34·10-2 -1.24·10-2
∂T
∂pH (bar)-1 -4.17·10-4 -4.31·10-4 -4.15·10-4 -4.27·10-4 ∂p
∂pH - -9.91·10-3 -9.14·10-3 -1.01·10-2 -9.44·10-3
∂S 834
42 835 Table 5: Comparison between analytical and numerical calculation of sensitivities as defined 836 for the contemporary average global surface ocean (see Table 4). The percentages in the 837 headings of the numerical calculation refer to the relative in- and decrements to which the 838 state variable was subjected. Sensitivity Analytical Numerical Numerical Frankignoulle -1 -1 (mol kg ) (0.1%) (1%) expression
RF 9.901 9.901 9.936 9.912 (dimensionless)
∂pH 1601.50 1601.52 1603.32 1603.62
∂AT
∂ pH -65.01 -65.01 -65.01 -
∂TotNH 4
∂pH -349.00 -349.00 -349.00 -
∂TotB
∂ pH -1751.84 -1751.86 -1753.10 -1754.16
∂DIC
∂pH -1801.31 -1801.31 -1801.31 -
∂TotPO4
∂pH 4.21·10-7 0 0 -
∂TotNO3
∂pH 6.23·10-3 0 0 -
∂TotNO2
∂pH -1553.79 -1553.78 -1553.78 -
∂TotS
∂pH -64.47 -64.46 -64.46 -
∂TotSi 839
43 δ pH δ pH
δ DIC δ AT a) d) −1800 2600
−2000 2400 1 − ) 1
− 2200 −2200
2000 (mol kg (mol −2400
1800 −2600 1600
δ pCO2 RF (dimensionless) δ DIC b) 15 e) 6 14 1 − )
1 5 − 13 4 mol kg mol µ 12 3
ppmv ppmv ( 11 2 10
δ pH
δ pCO2 − 4 10−4 c) ΡΧΠ8.5 ΡΧΠ6 ΡΧΠ4.5 − 6 10−4 RCP3D 1 −
− 8 10−4 (ppmv)
− 10 10−4
− 12 10−4 2000 2020 2040 2060 2080 2100 2000 2020 2040 2060 2080 2100 Years 840
44 ∂ pH ∂pCO ∂pH 841 Figure 1: Changes in a) ((mol kg-1)-1), b) 2 (ppmv (µmol kg-1)-1), c) ∂DIC ∂DIC ∂pCO 2 ∂pH 842 (ppmv-1), d) ((mol kg-1)-1) and e) the Revelle factor in the 21st century according to the ∂AT
843 four emission scenarios defined by IPCC (2013). Changes in pCO2,atm were taken from 844 Meinshausen et al. (2011), while temperature was kept constant.
45 pHF ∆pH = −0.486 8.4 ∆[H+] = 0.0100 µmol kg-1
8.2 ∆pH = −0.539 ∆[H+] = 0.0335 µmol kg-1 -1 8.0 O2 = 49 µmol kg
7.8
7.6
7.4 1850 ∆pH = −0.622 ∆[H+] = 0.0274 µmol kg-1 2000 O = 114 µmol kg-1 2100 − RCP8.5 7.2 ∆pH = −0.376 2 ∆[H+] = 0.0293 µmol kg-1 2100 − RCP6 2100 − RCP4.5 7.0 2100 − RCP3D
0 50 100 150 200 250 −1 O2 (µmol kg ) 845
846 Figure 2: Changes in pH due to O2 consumption in the pre-industrial (1850 AD), 847 contemporary (2000 AD) and future ocean (2100 AD). For the future ocean, all four emission
848 scenarios as defined by IPCC (2013) were modelled, with changes in pCO2,atm taken from 849 Meinshausen et al. (2011). Similarly to Table 4, the effect of an increased temperature was 850 tested for both the RCP8.5 emission scenario and the contemporary ocean. 851 852
46