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Supplementary Information for “Gas-hydrate dissociation prolongs acidification
of the Anthropocene oceans” - GRL
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Bernard P. Boudreau1, Yiming Luo1, Filip J.R. Meysman2, Jack J. Middelburg3 and Gerald R.
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Dickens4
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Model Equations
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[1] The equations governing the concentration of dissolved carbonate species in each
box are similar to those in Boudreau et al. [2010]. They are based on the box model
illustrated in Figs 1 and S1, the latter of which shows the mass flows.
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Figure S1.
Flows and their symbols
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[2] In the oceans, we model the total dissolved CO2 (ΣCO2) (in Gmol/km3) and
carbonate alkalinity (CAlk) (in Geq/km3):
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[ΣCO2] = [CO2] + [HCO3-] + [CO32-]
(S1)
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[CAlk] = [HCO3-] + 2 [CO32-]
(S2)
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[3] The conservation equations for these quantities are, respectively:
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Box L (low-latitude surface ocean)
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(S3)
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(S4)
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Box H (high-latitude ocean)
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(S5)
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(S6)
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Box D (deep ocean)
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(S7)
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(S8)
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where VL, VH, VD are the volumes of the oceanic boxes
(km3)
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P is the export of organic matter to the deep ocean
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B is the export of CaCO3 to the deep ocean
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(Gmol/a)
(Gmol/a)
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BD is the dissolution of CaCO3 in the deep ocean, which includes BDS and
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BPDC, and two other terms as defined in Boudreau et al. [2010]
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(Gmol/a)
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Falk is the flux of alkalinity from rivers to the oceans
(Gmol/a)
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Bburial is the flux of CaCO3 to the sediment surface that is buried
(Gmol/a)
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EH and EL are the net CO2 gas exchanges with the atmosphere
(Gmol/a)
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Note that the concentration units of Gmol/km3 and Geq/km3 are numerically equivalent
to mM and meq/L, respectively. The forms of the components of BD are explained in
detail in Boudreau et al. [2010] and not repeated here, but they include BDS, which is
the dissolution of CaCO3 arriving at the sediment due to overlying water
undersaturation, and BPDC, which is the dissolution of previously deposited carbonate,
as calculated via eq (S12) below.
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[4] In addition all the dissolved carbonate species in each box are assumed to be at
thermodynamic equilibrium:
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(S9)
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where Keq is the equilibrium constant (in (Gmol/km3)2 = mM2) for the reaction
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[5] In the atmosphere we only model CO2 gas:
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(S10)
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where VA is the volume of the atmosphere
Fanth accounts for the anthropogenic emission of fossil-fuel derived CO2
(Gmol/a)
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(km3)
The EH and EL are calculated in the form:
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Ei = EX ([CO2]i – ECO2)
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where subscript i is either H or L, EX is an exchange function calculated as the mean
gas transfer coefficient multiplied by the area of the ocean-atmosphere interface
(km3/a), and ECO2 is the equilibrium concentration (Gmol/km3), obtained with the
atmospheric PCO2 and the solubility. The Ex values are obtained from modeling the
assumed pre-industrial CO2-system of the oceans and atmosphere.
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(S11)
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[6] The previously deposited CaCO3 (b) in the sediment is governed by the mass
conservation equation [Boudreau, 2013, GRL, 37]:
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db(z,t)/dt = (B/AD + kc([CO32-]D–[CO32-]sat) – (1-φ)wρCaCO3b(z,t))/(ZmixρCaCO3)
(S12)
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where b(z,t) is the fraction of CaCO3 in the sediment at ocean depth z
(dimensionless)
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B is the export of CaCO3 to the deep ocean (Gmol/km3)
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AD is the area of the bottom of the ocean
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kc is the dissolution constant for CaCO3 – see Boudreau [2013]
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[CO32-]sat is the saturation concentration at depth z
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w is the burial velocity of the sediment surface
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ρCaCO3 is the density of CaCO3 (Calcite) (Gmol/km3)
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Zmix is the sediment mixed layer thickness (km)
(km2)
(km/a)
(Gmol/km3)
(km/a)
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[7] Use of eq (S12) is the main difference of the present model with the treatment in
Boudreau et al. [2010]; in that paper, the position of the snowline (the ocean depth
where the amount of CaCO3 in the sediment first falls to zero) was calculated by
assuming that the “wedge” of sediment between the saturation horizon and the
snowline moved (up or down) as a whole with changes in deep ocean saturation.
The latter is a simple and convenient approximation that greatly simplifies calculation
of the CaCO3 distribution with depth. The approximation is good if acidification is
“slow”; unfortunately, we have since found that anthropogenic acidification, and its
induced transients, are too fast to be well represented by this assumption.
Consequently, we have reverted to explicit calculation of b(z,t) with ocean depth and
time, as given by eq (S12).
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[8] Use of eq (S12) predicts a considerably smaller rise in the snowline than the
original method in Boudreau et al. [2010a]. This means that the BPDC component of
BD that depend on Zsnow, i.e., their eq (10), is larger in our present study and with more
dissolution, both Zcc and Zsat do not rise quite as much as indicated in Boudreau et al.
[2010]. These changes, in turn, engender small changes in the other components of
BD, i.e., BCC, BNS, BDS. These points account for all the differences in the results
between the original version of our model and the current version.
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[9] As stated in the paper, this model was also expanded to predict the temperature of
each oceanic box, given atmospheric forcing, as well as the dissolved oxygen of each
box. The temperature of the atmosphere was calculated from the relationship
[Sheffer et al., 2006]
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T = c*ln(P/Po) + To
(S13)
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as stated in the text, where T is in oC. Two values of c where considered, i.e., 1.7 and
4.7. Temperatures for the oceanic boxes were calculated assuming that
temperature is simply a scalar tracer and given by
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(S14)
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(S15)
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and
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(S16)
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where HL and HH (oC∗km3/a) are net heat exchanges with the atmosphere of the form
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Hi = KAi (TAi – Ti)
(S17)
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where i = H or L, TAi is the atmospheric temperature (oC) above the i ocean box, and
KAi is an total area heat transfer coefficient (km3/a), calculated from the steady state,
pre-industrial conditions.
[10] The model also can calculate the O2 content of the ocean basins, even though this
is not used in the present paper – see equation S18 and Figure S5 below. Oxygen is
assumed constant in the atmosphere, and the surface boxes are assumed in
equilibrium with that value for their calculated temperature. The deep ocean box is
then calculated as
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(S18)
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where ε is the molar ratio of O2 consumption by organic matter oxidation and FCH4 is
the flux of CH4 from hydrates if release to the deep ocean and quickly oxidized.
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[11] The above set of equations is solved numerically (simple Euler integration) and
has initial conditions set by modeling a pre-industrial steady state – see Boudreau et al.
[2010]. A FORTRAN implementation of this solution method is available by request.
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Initial Conditions
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[12] The follow were used as initial conditions in our modeling:
TCO2
(Gmol/km3)
CAlk (Geq/L)
T
(oC)
Box L
Box H
Box D
2.058
2.185
2.28
2.2739
2.3144
2.3471
21.5
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2
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As well as:
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TAL = 22oC
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TAH = 0oC
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UT = 24.2 Sv = 7.64x105 km3/a
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UM = 30 Sv = 9.47x105 km3/a
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Zsat/Zcc/Z10 = 3.890/4.762/4.739 km
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PCO2 = 2.83x10-3 atm
(respectively)
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Supplementary Results
A153
B
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Low-Latitude
Surface Water
IS92a
Ocean Release
Atm Release
o
Temperature ( C)
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0
5000
10000
15000
Time (AD)
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o
Temperature ( C)
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4
3
2
Deep-Water Temperature
IS92a
Ocean Release
Atm Release
1
0
0
5000
10000
15000
Time (AD)
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C
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Figure S2.
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deep ocean (C).
Temperature histories of the low-latitude atmosphere (A) and surface ocean (B) and the
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[13] Figure S2 illustrates the temperature evolution of the low-latitude atmospheric
and ocean boxes (panels A and B) and that of the deep ocean (panel C), for the
IS92a release of CO2 and with additional CO2 from hydrate dissociation as predicted
by Yamamoto et al. [2014] into the deep oceans or the atmosphere. The addition of
methane-derived CO2 does not lead to a higher temperature maximum, but does
delay the return to pre-industrial conditions. The location of the injection of CO2
from methane has only a small effect on the temperature history.
[14] The issue of the value of c in eq (S13) was explored in depth and the results are
displayed in Figs S3-S5. Figure S3 shows that the value of c has no effect on the
predictions for the IS92a emissions, while Fig. S4 shows the same with additional
CO2 from gas hydrate melting and oxidation.
[15] The mean oxygen in the deep ocean was calculated for the IS92a emissions
and with added CO2 from gas hydrate melting and illustrated in Figure S5. There is
a small effect on the oxygen value for different values of c, and this is to be expected,
as the solubility of O2 is a strong function of temperature.
[16] Finally, we explored the effect of the total release of CO2, given that Beaudoin et
al. [2014] advocate about twice as much carbon stored in gas hydrates than
Yamamoto et al. [2014]. Beaudoin et al. [2014] do not provide a release function,
so we simply multiplied the function in Fig. 1B by 2. Some of the resulting
predictions are given in Fig. S6. There is a significant long-term decrease in pH,
and the pH minimum in deep water is now made lower by the hydrate-sourced CO2.
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A
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B
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4
Surface Water Omega (Aragonite)
1400
IS92a
1200
C4.7
C1.7
800
P
CO2
(ppmv)
1000
600
400
3.5
3
2.5
2
IS92a
C4.7
C1.7
1.5
200
1
0
5000
10000
15000
0
5000
Time (AD)
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10000
15000
Time (AD)
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2.6
0
IS92a
C4.7
C1.7
C4.7
C1.7
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Depth (km)
2
SCO (mM)
2.5
2.4
2
3
IS92a
2.3
Z
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C4.7
C1.7
sat
Z
cc
2.2
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0
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C
5000
10000
15000
0
Time (AD)
5000
10000
15000
Time (AD)
D
192 Figure S3. Comparisons of predicted atmospheric CO2 (panel A), Omega of the low-latitude surface
193 ocean (panel B), total CO2 of the deep ocean and the positions of Zsat and Zcc (i.e., CCD) for the two
194 tested vales of c in eq (S13) and the IS92a emissions alone.
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A197
B
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Yamamoto Emissssions
C4.7
C1.7
1000
800
2
PCO (ppmv)
1200
600
400
Surface Water Omega (Aragonite)
1400
3
2.5
2
Yamamoto Emissions
C4.7
C1.7
1.5
1
200
0
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3.5
5000
10000
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15000
5000
10000
15000
Time (AD)
Time (AD)
0
Yamamoto Emissions
C4.7
C4.7
C1.7
C1.7
Depth (km)
1
2
3
Z
sat
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Z
cc
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0
5000
10000
15000
Time (AD)
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C
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D
202 Figure S4. Comparisons of predicted atmospheric CO2 (panel A), Omega of the low-latitude
203 surface ocean (panel B), total CO2 of the deep ocean and the positions of Zsat and Zcc (i.e., CCD)
204 for the two tested vales of c in eq (S13) and the IS92a plus Yamamoto et al. [2014]
205 gas-hydrate-based emissions.
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B
0.25
0.25
0.2
0.2
Deep-Water Oxygen (mM)
Deep-Water Oxygen (mM)
A
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0.15
0.1
IS92a
0.05
0.15
0.1
Yamamoto Emissions
C4.7
C1.7
0.05
C4.7
C1.7
0
0
0
5000
10000
15000
0
Time (AD)
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5000
10000
Time (AD)
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Figure S5.
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tested vales of c in equation (S13) and the IS92a plus Yamamoto et al. [2014] gas-hydrate-based
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emissions.
Comparisons of predicted mean oxygen concentrations in the deep ocean for the two
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2.8
SCO (mM)
pH
7.9
2
7.8
2.6
Surface pH
2.4
7.7
IS92a
Yamamoto et al.
2X
Deep Total CO
2.2
7.6
7.5
2
0
A
2
IS92a
Yamamoto et al.
2X
5000
10000
15000
Time (yr)
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0
5000
10000
15000
Time (yr)
B
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8
0
Deep pH
Critical Horizons
IS92a
Yamamoto et al.
2X
7.9
(km)
cc
4
7.5
7.4
5
0
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3
Z
7.6
C
2
&Z
7.7
sat
pH
7.8
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Zsat (km)
Zcc (km)
1
5000
10000
15000
0
Time (yr)
5000
10000
15000
Time (yr)
D
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Figure S6. Predicted evolution of the surface ocean pH (low latitude) – panel A, deep water ΣCO2 –
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panel B, deep water pH – panel C, and the positions of the calcite saturation horizon (Zsat) and the
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carbonate compensation depth (Zcc) as driven by a doubling of the Yamamoto et al. [2014] release.
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References
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Beaudoin, Y.C. et al. (2014), Frozen Heat: A UNEP Global Outlook on Methane Gas Hydrates, Vol. 1,
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United Nations Environmental Programme, GROD-Arendal, 77 pp.
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Boudreau, B. P., Middelburg, J. J., Hofmann, A. F. and Meysman, F. J. R. (2010), Ongoing transient
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Boudreau, B.P. (2013), Carbonate dissolution rates at the deep ocean floor, Geophys. Res. Lett., 40,
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1-5, doi:10.1029/2012GL054231.
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Scheffer, M., Brovkin, V. and Cox, P.M. (2006), Positive feedback between global warming and
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atmospheric CO2 concentration inferred from past climate change, Geophys. Res. Lett., 33, L10702,
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doi:10.1029/2005/\GL025044.
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Yamamoto, A., Yamanaka, Y. and Abe-Ouchi, A. (2014), Ocean oxygen depletion due to
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decomposition of submarine methane hydrate, Geophys. Res. Lett., 41, 5075-5083,
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doi:10.1002/2014GL060483.
in carbonate compensation, Global Biogeochem. Cycles, 24, GB4010.
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