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Electronic Supplementary Material - 2
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(1) Model of relationship between Sr/Ca and pHCF
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The relationship between Sr/Ca in coral aragonite and pHCF is modeled below. In
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this model, it is assumed that coral aragonite is precipitated from calcifying fluid
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(CF). In CF, the chemical composition (pH, DIC and concentration ratio of
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Sr2+/Ca2+) is controlled by multiple processes, such as active transport and
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calcification. Active transport by Ca2+ ATPase changes calcium ion and proton
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concentration in CF. Progressive calcification in a limited volume of CF also
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changes the chemical composition in the remaining liquid phase. Thus, two
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effects on Sr/Ca, Ca2+ up-regulation and Rayleigh fractionation, are included in
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the model. As δ11B (pHCF) and Sr/Ca were measured on the bulk samples in this
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study, these data correspond to an integrated condition of CF during calcification
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period. In order to keep consistency between the bulk observation and the model,
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a steady state chemical composition in CF is assumed for modeling.
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The difference in Ca2+ concentration between CF and seawater is calculated
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considering Ca2+ up-regulation. Since each Ca2+ may be exchanged for 2 protons
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by Ca2+ ATPase, an increase in Ca2+ concentration in CF ([Ca2+]CF) linearly
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increases alkalinity in CF (ALKCF). According to this relationship, ALKCF is
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employed to calculate [Ca2+]CF using the following equation:
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Δ[Ca2+] = ∆ALK/2
(1)
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where Δ[Ca2+] and ΔALK are difference in Ca2+ concentration and ALK between
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CF and seawater ([Ca2+]CF - [Ca2+]SW and ALKCF - ALKSW), respectively. To
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calculate [Ca2+]CF, eqn. (1) becomes:
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[Ca2+]CF = (ALKCF - ALKSW)/2 + [Ca2+]SW
(2)
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Because [Ca2+]SW is proportional to salinity, [Ca2+]SW is calculated to be constant
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at 10.0 mmol mol-1 at salinity of 34.2. ALKSW measured during culturing was
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almost constant among three treatments (2324 µmol kg-1). As ALK can be
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calculated from pH and DIC (Zeebe and Wolf-Gladrow, 2001) (Fig. S1), ALKCF
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is calculated from pHCF and DICCF in the model. Because an increase in pH (at a
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given DIC) and/or DIC (at a given pH) raises ALK in the solution, ΔALK can be
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divided into two, that is, ΔALK due to pH change (ΔALKpH) and due to DIC
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change (ΔALKDIC) (ΔALK = ΔALKpH + ΔALKDIC). pHCF is higher than ambient
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seawater (Fig. 3). Possible diffusion of metabolic CO2 from the tissue to CF raises
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DIC in CF (DICCF) to values higher than that in seawater (DICSW). Thus, in the
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model, pH and DIC in CF potentially influence ALKCF and [Ca2+]CF.
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For the calculation of ALKCF, pHCF ranges from 8.0 to 8.8 with calculations made
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for every 0.1 pH change (on total scale). In order to distinguish effects of pH and
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DIC on [Ca2+]CF and Sr/Ca in aragonite, DICCF is fixed at seawater value of 1959,
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2121 and 2284 µmol kg-1 observed in CNT, MID and LOW treatments,
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respectively (DICCF = DICSW). The calculation of ALKCF is conducted using
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software of CO2-sys (Lewis and Wallace, 1998). In this point, ALKCF is
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calculated by varying pHCF at identical DICCF with DICSW to obtain ΔALKpH.
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[Ca2+]CF considering only pH effect ([Ca2+]CF-pH) is calculated from ΔALKpH
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based on eqn. (2).
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[Ca2+]CF-pH = (ALKCF-pH - ALKSW)/2 + [Ca2+]SW
(3)
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Active transport of strontium is assumed to be negligible. Then Sr2+/Ca2+ in CF
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([Sr2+/Ca2+]CF-pH), affected by only pHCF, is calculated as:
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[Sr2+/Ca2+]CF-pH = [Sr2+]SW / [Ca2+]CF-pH
(4)
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where [Sr2+]SW is proportional to salinity of seawater, being 0.0862 mmol mol-1 at
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salinity of 34.2.
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Progressive calcification gradually decreases the Sr2+/Ca2+ ratio in CF, assuming
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that CF is nearly a closed system, because the distribution coefficient of Sr/Ca
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between aragonite and parent solution is larger than unity. Rayleigh fractionation
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is applied to consider this effect in the model. Sr/Ca in coral aragonite ([Sr/Ca]CO-
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ARA)
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effect is calculated as below:
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influenced by Ca2+ up-regulation associated with pHCF, and the Rayleigh
[Sr/Ca]CO-ARA = DSr/Ca [Sr2+/Ca2+]CF-pH F’
(5)
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where DSr/Ca is the distribution coefficient of Sr/Ca between parent solution and
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aragonite (DSr/Ca = 1.15 at SST of 29.3 ˚C) (Gaetani and Cohen 2006). F’
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represents the degree of progress of calcification relative to the reservoir
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replenishment, for which values are unconstrained. We run the model using four
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fixed value of F’ (1.00, 0.98, 0.97 and 0.95) where a value of 1 would represent
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rapid renewal relative to calcification thus no Rayleigh effect, while smaller
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values of F’ indicate lower rates of renewal relative to precipitation and thus
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greater Rayleigh effects.
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In addition, Sr/Ca in aragonite ([Sr/Ca]SW-ARA) inorganically precipitated from
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seawater, is also calculated as:
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[Sr/Ca]SW-ARA = DSr/Ca[Sr2+/Ca2+]SW
(6)
where [Sr2+/Ca2+]SW represents Sr2+/Ca2+ ionic ratio in the seawater.
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(2) Estimate of DIC and Ω in CF
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Fig. S2 is schematic relationship among [Sr/Ca]SW-ARA, [Sr/Ca]CO-ARA, and the
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measured Sr/Ca ([Sr/Ca]MEAS). As described above, [Sr/Ca]CO-ARA includes effects
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by Ca2+ up-regulation (Δ[Ca2+]pH) and Rayleigh effect (F’). In contrast, [Sr/Ca]SW-
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ARA
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difference between [Sr/Ca]SW-ARA and [Sr/Ca]CO-ARA at F’ = 1.0 represents effect
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by Ca2+ up-regulation due to pH effect (Fig. S2). In addition, the difference
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among [Sr/Ca]CO-ARA of various F’ values represent Rayleigh effect on Sr/Ca (Fig.
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S2).
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Although DICCF is assumed to be the same as DICSW, it is likely that DICCF is also
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up – regulated by diffusion of CO2 into CF, influencing [Sr/Ca]MEAS. Thus,
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assuming that pH and DIC in CF are higher than ambient seawater, [Sr/Ca]MEAS is
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represented as:
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is calculated without these effects (i.e. Δ[Ca2+]pH = 0 and F’ = 1.0). Thus, the
[Sr/Ca]MEAS = (DSr/Ca ([Sr2+]SW/([Ca2+]SW + Δ[Ca2+]pH + Δ[Ca2+]DIC))) F’ (7)
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where Δ[Ca2+]DIC links to ΔALKDIC as: Δ[Ca2+]DIC = ΔALKDIC/2, according to
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eqn. (1) (see Fig. S1). Therefore, the difference between [Sr/Ca]CO-ARA (F’ = 1.0)
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and [Sr/Ca]MEAS represents the effect of DIC up – regulation (Δ[Ca2+]DIC) and
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Rayleigh effect (F’) (Fig. S2). Further, when F’ of [Sr/Ca]MEAS is identical with
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that of [Sr/Ca]CO-ARA, the difference simply corresponds to DIC up – regulation.
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Combining eqn. (4), (5) and (7), the next equation is obtained to calculate
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Δ[Ca2+]DIC.
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Δ[Ca2+]DIC = DSr/Ca[Sr2+]SWF’{([Sr/Ca]MEAS)-1 – ([Sr/Ca]CO-ARA)-1}
(8)
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It is possible to calculate Δ[Ca2+] as a sum of Δ[Ca2+]pH (eqn. (3)), and Δ[Ca2+]DIC
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(eqn. (8)) at a given F’ value. As described in the text, four values of F’ (1.00,
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0.98, 0.97 and 0.95) are used for estimates. Then, ΔALK for each sample is
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calculated from eqn. (1), and ALKCF including effects of pH and DIC is obtained
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as: ALKCF = ALKSW + ΔALK. Finally, DICCF and carbonate ion concentration in
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CF ([CO32-]CF) are calculated from ALKCF from the above equation and pHCF
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derived from δ11B, based on Zeebe and Wolf-Gladrow (2001).
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Using Ca2+ and CO32- ion concentrations in CF, aragonite saturation state in CF
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(ΩCF) is calculated as below:
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ΩCF = [Ca2+]CF [CO32-]CF /KSP
(9)
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where KSP is the solubility product of aragonite in seawater (Mucci 1983) at
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temperature of 29.3 ˚C and salinity of 34.2 (KSP = 10-6.21).
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References
Gaetani G, Cohen A (2006) Element partitioning during precipitation of aragonite from seawater:
A framework for understanding paleoproxies. Geochim Cosmochim Acta 70:4617-4634
Lewis E, Wallace D (1998) Program developed for CO 2 System Calculations. URL:
http://cdiac.esd.ornl.gov/oceans/co2rprtnbk.html
Mucci A (1983) The solubility of calcite and aragonite in seawater at various salinities,
temperatures, and one atmospheric total pressure. Am J Sci 283:780-799
Zeebe RE and Wolf-Gladrow DA (2001) CO2 in Seawater: Equilibrium, Kinetics, Isotopes.
Elsevier, Amsterdam.
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Figure captions
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Figure S1
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Relationship between pH and ALK calculated using DIC values of 1960 and 2280
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µmol kg-1 (black and dark blue line, respectively). Difference in ALK (diff-ALK)
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between black diamond (pH 8.4, DIC 1960 µmol kg-1) and dark blue diamond (pH
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8.6, DIC 2280 µmol kg-1) is divided into pH effect (ΔALKpH, light blue arrow)
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and DIC effect (ΔDICpH, amber arrow).
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Figure S2
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Schematic of relationship among [Sr/Ca]SW-ARA (light blue), [Sr/Ca]CO-ARA (dark
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blue) and [Sr/Ca]MEAS (amber circle). Light blue, dark blue and amber arrows
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indicate reduction of Sr/Ca due to pH effect, Rayleigh effect, and DIC effect,
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respectively.
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