Supporting information for:
Changing tectonic controls on the long term carbon cycle from Mesozoic to present.
Benjamin Mills, Stuart J. Daines & Timothy M. Lenton
College of Life and Environmental Sciences, University of Exeter, Exeter, EX4 4QE, UK.
Supporting Information 1 –COPSE model alterations.
For this work we update a number of functions and forcings in the COPSE model. Silicate
weathering is split into a ‘granite’ and ‘basalt’ contribution and an additional flux of carbon from the
ocean to the crust is added to represent seafloor weathering. New forcings (BA, GA, CA) are added
that represent the relative global area of basaltic, granitic and carbonate rocks, in order that this
may influence the split between basalt and granite weathering. The degassing rate (D) forcing is
updated in response to new data [1], and the uplift/erosion (U) forcing is modified so that it does not
rely on input of strontium isotope ratios [2]. We also add a simple strontium cycle to the model.
Full equations are documented below. Aside from the changes laid above, they follow the
original COPSE model [3]. RO2 and RCO2 denote concentrations of oxygen and carbon dioxide
relative to present day. Subscript zeros represent the present day size of fluxes and reservoirs.
Model runs were performed using the MATLAB ODE suite variable timestep solvers [4].
List of fluxes: (* denotes fluxes that have been updated for this work, ** denotes new fluxes)
2 𝑠𝑖𝑙𝑤
5 𝑐𝑎𝑟𝑏𝑤
5 𝑜𝑥𝑖𝑑𝑤
0
0
0
Phosphorus weathering:
𝑝ℎ𝑜𝑠𝑤 = 𝑘𝑝ℎ𝑜𝑠𝑤 (12 𝑠𝑖𝑙𝑤 + 12 𝑐𝑎𝑟𝑏𝑤 + 12 𝑜𝑥𝑖𝑑𝑤 )
(1)
P delivery to land surface:
𝑝𝑙𝑎𝑛𝑑 = 𝑘𝑙𝑎𝑛𝑑𝑓𝑟𝑎𝑐 ∙ 𝑉𝐸𝐺 ∙ 𝑝ℎ𝑜𝑠𝑤
(2)
Land organic carbon burial:
𝑙𝑜𝑐𝑏 = 𝑘𝑙𝑜𝑐𝑏 ∙ 𝑝𝑙𝑎𝑛𝑑 ∙ 𝐶𝑃𝑙𝑎𝑛𝑑
(3)
P delivery to oceans:
𝑝𝑠𝑒𝑎 = 𝑝ℎ𝑜𝑠𝑤 − 𝑝𝑙𝑎𝑛𝑑
(4)
Marine new production:
𝑛𝑒𝑤𝑝 = 117 ∙ min (16 , 𝑃)
𝑝𝑙𝑎𝑛𝑑
0
𝑁
1
(5)
𝑛𝑒𝑤𝑝 2
)
𝑛0
Marine organic carbon burial:
𝑚𝑜𝑐𝑏 = 𝑘𝑚𝑜𝑐𝑏 (
Marine organic phosphorus burial:
𝑚𝑜𝑝𝑏 =
Calcium-bound phosphorus burial:
𝑐𝑎𝑝𝑏 = 𝑘𝑐𝑎𝑝𝑏 𝑚𝑜𝑐𝑏
Iron-sorbed phosphorus burial :
𝑓𝑒𝑝𝑏 = 𝑘𝑓𝑒𝑝𝑏 ∙
Nitrogen fixation:
𝑛𝑓𝑖𝑥 = 𝑘𝑛𝑓𝑖𝑥 ((𝑃
Marine organic nitrogen burial:
𝑚𝑜𝑛𝑏 =
Denitrification:
(6)
𝑚𝑜𝑐𝑏
𝐶𝑃𝑠𝑒𝑎
(7)
𝑚𝑜𝑐𝑏
(8)
0
(1−𝑎𝑛𝑜𝑥)
(9)
𝑘𝑜𝑥𝑓𝑟𝑎𝑐
(𝑃−𝑁/16)
0 −𝑁0 /16)
2
)
𝑚𝑜𝑐𝑏
𝐶𝑁𝑠𝑒𝑎
(10)
(11)
𝑎𝑛𝑜𝑥
𝑑𝑒𝑛𝑖𝑡 = 𝑘𝑑𝑒𝑛𝑖𝑡 (1 + (1−𝑘
𝑜𝑥𝑓𝑟𝑎𝑐
))
(12)
Temperature dependence of basalt weathering:
𝑓𝑇𝑏𝑎𝑠 = 𝑒 0.061(𝑇−𝑇0) {1 + 0.038(𝑇 − 𝑇0 )}0.65
(13)
Temperature dependence of granite weathering:
𝑓𝑇𝑔𝑟𝑎𝑛 = 𝑒 0.072(𝑇−𝑇0 ) {1 + 0.038(𝑇 − 𝑇0 )}0.65
(14)
Temperature dependence of carbonate weathering:
𝑔𝑇 = 1 + 0.087(𝑇 − 𝑇0 )
(15)
Pre-plant silicate weathering:
𝑓𝑝𝑟𝑒𝑝𝑙𝑎𝑛𝑡 = 𝑓𝑇 ∙ √𝑅𝐶𝑂2
Plant-assisted silicate weathering:
𝑓𝑝𝑙𝑎𝑛𝑡 = 𝑓𝑇 ∙ (1+𝑅𝐶𝑂2 )
(17)
Pre-plant carbonate weathering:
𝑔𝑝𝑟𝑒𝑝𝑙𝑎𝑛𝑡 = 𝑔𝑇 ∙ √𝑅𝐶𝑂2
(18)
Plant-assisted carbonate weathering:
𝑔𝑝𝑙𝑎𝑛𝑡 = 𝑔𝑇 ∙ (1+𝑅𝐶𝑂2 )
(19)
𝑓𝐶𝑂2 = 𝑓𝑝𝑟𝑒𝑝𝑙𝑎𝑛𝑡 (1 − min(𝑉𝐸𝐺 ∙ 𝑊)) + 𝑓𝑝𝑙𝑎𝑛𝑡 ∙ min(𝑉𝐸𝐺 ∙ 𝑊)
(20)
0.4
2𝑅𝐶𝑂
2
0.4
2𝑅𝐶𝑂
2
(16)
Climate forcing for silicates:
2
fCO2gran and fCO2bas result from the fCO2 function with plant-weathering feedbacks using fTgran and fTbas
respectively.
Climate forcing for carbonates:
𝑔𝐶𝑂2 = 𝑔𝑝𝑟𝑒𝑝𝑙𝑎𝑛𝑡 (1 − min(𝑉𝐸𝐺 ∙ 𝑊)) + 𝑔𝑝𝑙𝑎𝑛𝑡 ∙ min(𝑉𝐸𝐺 ∙ 𝑊)
Vegetation feedback:
(𝐶𝑂 𝑝𝑝𝑚−10)
∙
2 𝑝𝑝𝑚−10)
2
𝑉𝐸𝐺 = 2 ∙ 𝐸 ∙ (183.6+𝐶𝑂
(21)
(𝑇−𝑇0 ) 2
(1 − (
) ) ∙ (1.5 − 0.5(𝑅𝑂2 )) ∙
𝑇
𝑘𝑓𝑖𝑟𝑒
(22)
(𝑘𝑓𝑖𝑟𝑒 −1+max(586.2𝑂2 (𝑎𝑡𝑚)−122.102 ,0))
Evolution of plants:
𝑝𝑒𝑣𝑜𝑙 = (𝑘𝑝𝑟𝑒𝑝𝑙𝑎𝑛𝑡 + (1 − 𝑘𝑝𝑟𝑒𝑝𝑙𝑎𝑛𝑡 ) ∙ 𝑊 ∙ 𝑉𝐸𝐺)
(23)
Basalt weathering**:
𝑏𝑎𝑠𝑤 = %𝑏𝑎𝑠0 ∙ 𝑘𝑠𝑖𝑙𝑤 ∙ 𝑓𝐶𝑂2𝑏𝑎𝑠 ∙ 𝑃𝐺 ∙ 𝑝𝑒𝑣𝑜𝑙 ∙ 𝐵𝐴
(24)
Granite weathering**:
𝑔𝑟𝑎𝑛𝑤 = (1 − %𝑏𝑎𝑠0 ) ∙ 𝑘𝑠𝑖𝑙𝑤 ∙ 𝑓𝐶𝑂2𝑔𝑟𝑎𝑛
∙ 𝑃𝐺 ∙ 𝑈 ∙ 𝑝𝑒𝑣𝑜𝑙 ∙ 𝐺𝐴
(25)
Silicate weathering*:
𝑠𝑖𝑙𝑤 = 𝑏𝑎𝑠𝑤 + 𝑔𝑟𝑎𝑛𝑤
(26)
Carbonate weathering:
𝑐𝑎𝑟𝑏𝑤 = 𝑘𝑐𝑎𝑟𝑏𝑤 ∙ 𝑔𝐶𝑂2 ∙ 𝑃𝐺 ∙ 𝑈 ∙ 𝑝𝑒𝑣𝑜𝑙 ∙ 𝐿𝐴𝐶𝑟𝑒𝑙
(27)
Oxidative weathering:
𝑜𝑥𝑖𝑑𝑤 = 𝑘𝑜𝑥𝑖𝑑𝑤 ∙ 𝑈 ∙ √𝑅𝑂2
(28)
Marine carbonate carbon burial:
𝑚𝑐𝑐𝑏 = 𝑠𝑖𝑙𝑤 + 𝑐𝑎𝑟𝑏𝑤
(29)
Seafloor weathering**:
𝑠𝑓𝑤 = 𝑘𝑠𝑓𝑤 ∙ 𝐷 ∙ (𝑅𝐶𝑂2 )𝛼
(30)
Pyrite sulphur weathering:
𝑝𝑦𝑟𝑤 = 𝑘𝑝𝑦𝑟𝑤 ∙ 𝑈 ∙ 𝑃𝑌𝑅 √𝑅𝑂2
Gypsum sulphur weathering:
𝑔𝑦𝑝𝑤 = 𝑘𝑔𝑦𝑝𝑤 ∙ 𝑈 ∙ 𝐺𝑌𝑃 ∙ 𝑐𝑎𝑟𝑏𝑤
Pyrite sulphur burial:
𝑚𝑝𝑠𝑏 = 𝑘𝑚𝑝𝑠𝑏 ∙ 𝑆 ∙ 𝑂 ∙ 𝑚𝑜𝑐𝑏
𝑃𝑌𝑅
(31)
0
𝑆
0
3
𝐺𝑌𝑃
𝑐𝑎𝑟𝑏𝑤
0
0
1
𝑚𝑜𝑐𝑏
0
(32)
(33)
𝑆 𝐶𝐴𝐿
∙
𝑆0 𝐶𝐴𝐿0
Gypsum sulphur burial:
𝑚𝑔𝑠𝑏 = 𝑘𝑚𝑔𝑠𝑏 ∙
Organic carbon degassing:
𝑜𝑐𝑑𝑒𝑔 = 𝑘𝑜𝑐𝑑𝑒𝑔 (𝐺 ) ∙ 𝐷
Carbonate carbon degassing:
𝑐𝑐𝑑𝑒𝑔 = 𝑘𝑐𝑐𝑑𝑒𝑔 (𝐶 ) ∙ 𝐷 ∙ 𝐵
(34)
𝐺
(35)
0
𝐶
0
(36)
Other calculations:
Following COPSE, the global average surface temperature calculation is taken from the model of
Caldeira and Kasting [5] and requires inputs of solar forcing, albedo and carbon dioxide
concentration.
Relative atmospheric O2:
𝑅𝑂2 =
𝑂
𝑂0
(37)
𝑂
+𝑘𝑂2
𝑂0
where kO2 = 3.762
𝑛𝑒𝑤𝑝
Ocean anoxic fraction:
𝑎𝑛𝑜𝑥 = 𝑚𝑎𝑥 (1 − 𝑘𝑜𝑥𝑓𝑟𝑎𝑐 (𝑅𝑂2 ) ( 𝑛𝑒𝑤𝑝0 ) , 0)
Solar forcing:
𝑆=
𝑆0
(38)
(39)
𝑡
𝜏
1+0.38( )
where S0 = 1368Wm-2, τ=4.55x109 years.
Following COPSE, the global average surface temperature calculation is taken from the model of
Caldeira and Kasting [5] and requires inputs of solar forcing and carbon dioxide concentration.
Albedo is calculated within the temperature function.
Reservoir calculations:
Ocean phosphate:
𝑑𝑃
𝑑𝑡
= 𝑝ℎ𝑜𝑠𝑤 − 𝑚𝑜𝑝𝑏 − 𝑐𝑎𝑝𝑏 − 𝑓𝑒𝑝𝑏
4
(40)
𝑑𝑁
𝑑𝑡
Ocean nitrate:
= 𝑛𝑓𝑖𝑥 − 𝑑𝑒𝑛𝑖𝑡 − 𝑚𝑜𝑛𝑏
(41)
Atmosphere/ocean carbon*:
𝑑𝐴
𝑑𝑡
= 𝑐𝑐𝑑𝑒𝑔 + 𝑜𝑥𝑖𝑑𝑤 + 𝑜𝑐𝑑𝑒𝑔 + 𝐿𝐼𝑃𝑑𝑒𝑔 − 𝑠𝑖𝑙𝑤 − 𝑚𝑜𝑐𝑏 − 𝑙𝑜𝑐𝑏 − 𝑠𝑓𝑤 + 𝑝𝑦𝑟𝑤 −
𝑚𝑝𝑠𝑏
(42)
Ocean calcium (+ magnesium):
𝑑𝐶𝐴𝐿
𝑑𝑡
= 𝑠𝑖𝑙𝑤 + 𝑐𝑎𝑟𝑏𝑤 + 𝑔𝑦𝑝𝑤 − 𝑚𝑐𝑐𝑏 − 𝑚𝑔𝑠𝑏
(43)
Ocean sulphate:
𝑑𝑆
𝑑𝑡
= 𝑝𝑦𝑟𝑤 + 𝑝𝑦𝑟𝑑𝑒𝑔 + 𝑔𝑦𝑝𝑤 + 𝑔𝑦𝑝𝑑𝑒𝑔 − 𝑚𝑝𝑠𝑏 − 𝑚𝑔𝑠𝑏
(44)
Buried organic C:
𝑑𝐺
𝑑𝑡
= 𝑚𝑜𝑐𝑏 − 𝑜𝑥𝑖𝑑𝑤 − 𝑜𝑐𝑑𝑒𝑔
(45)
Buried carbonate C *:
𝑑𝐶
𝑑𝑡
= 𝑚𝑐𝑐𝑏 + 𝑠𝑓𝑤 − 𝑐𝑎𝑟𝑏𝑤 − 𝑐𝑐𝑑𝑒𝑔
(46)
Buried pyrite S:
𝑑𝑃𝑌𝑅
𝑑𝑡
= 𝑚𝑝𝑠𝑏 − 𝑝𝑦𝑟𝑤
(47)
Buried Gypsum S:
𝑑𝑃𝑌𝑅
𝑑𝑡
= 𝑚𝑔𝑠𝑏 − 𝑔𝑦𝑝𝑤
(48)
Present day values:
Source:
Marine organic carbon burial:
kmocb=4.5x1012
mol C yr-1
COPSE
Calcium-bound P burial:
kcapb=1.5x1010 mol P yr-1
COPSE
Iron-sorbed P burial:
kfepb=6x109
mol P yr-1
COPSE
Nitrogen fixation:
knfix=8.7x1012
mol N yr-1
COPSE
Denitrification:
kdenit=4.3x1012
Pyrite sulphur burial:
kmpsb=5.3x1011 mol S yr-1
5
mol N yr-1
COPSE
COPSE
Gypsum sulphur burial:
kmgsb=1x1012
Silicate weathering*:
ksilw = 4.9x1012 mol C yr-1
for steady state
Seafloor weathering**:
ksfw = 1.75x1012 mol C yr-1
[6-8]
Oxidative weathering:
koxidw=7.75x1012 mol C yr-1
for steady state
Reactive P weathering:
kphosw=4.35x1010mol P yr-1
COPSE
Pyrite sulphur weathering:
kpyrw=5.3x1011 mol S yr-1
COPSE
Gypsum sulphur weathering:
kgypw=1x1012
mol S yr-1
COPSE
Organic carbon degassing:
kocdeg=1.25x1012 mol C yr-1
COPSE
Carbonate carbon degassing:
kccdeg=6.65x1012mol C yr-1
COPSE
Atmosphere and ocean CO2:
A0=3.193x1018 mol
COPSE
Ocean phosphate:
P0=3.1x1015
mol
COPSE
Ocean nitrate:
N0=4.35x1016
mol
COPSE
Ocean Ca (+Mg):
CAL0 = 1.397x1019 mol
COPSE
Ocean sulphate:
P0=4x1019
mol
COPSE
Atmosphere and ocean oxygen:
O0=3.7x1019
mol
COPSE
Buried organic carbon:
G0=1.25x1021
mol
COPSE
Buried carbonate carbon:
C0=6.6x1021
mol
COPSE
Buried pyrite sulphur:
PYR0=1.8x1020 mol
COPSE
Buried gypsum sulphur:
GYP0=2x1020
COPSE
6
mol S yr-1
mol
COPSE
Ocean C:P burial ratio:
CPsea = 250
mol/mol
COPSE
Ocean C:N burial ratio:
CNsea = 37.5
mol/mol
COPSE
CO2-seafloor weathering feedback
α ≈0.23
mol/mol
Follows [9, 10]
Forcings:
Attributes:
Solar forcing:
𝑆=
𝑆0
𝑡
𝜏
1+0.38( )
where S0 = 1368Wm-2, τ=4.55x109 years. (COPSE)
Relative global CO2 degassing*:
𝐷 = 1 for present day, scaling relationship from [1]
Relative uplift rate*:
𝑈 = 1 for present day, follows [2, 11]
Evolution of land plants:
𝐸 = 1 for present day (COPSE)
Weathering effect of plant evolution:
𝑊 = 1 for present day (COPSE)
Carbonate burial depth:
𝐵 = 1 for present day (COPSE)
Relative basaltic area**:
𝐵𝐴 = 1 for present day (section 4 and main paper).
Relative total land area:
LArel = 1 for present day (GEOCARB)
Relative carbonate land area:
LACrel = 1 for present day (GEOCARB)
Relative granite area:
GA = LA – LAC – BAcont
where BAcont is the total basaltic area on continents (i.e. total basaltic area minus island arc and
ocean island contributions) and LA and LAC are the total land area and carbonate land area
respectively, calculated by scaling the relative areas to the present day areas (estimated from total
land area and silicate area [12]).
7
Paleogeographical runoff effect**:
𝑃𝐺 = 1 for present day, follows [12]
Supporting Information 2 – Strontium isotope system
A simple strontium cycle is added to COPSE for this work, based on previous Sr box models
[13, 14]. The system calculates concentrations of oceanic and sedimentary strontium in order to
estimate seawater 87Sr/86Sr based on the other model parameters. Fluxes of strontium are tied to
existing model variables via first-order scaling relationships. Mantle input of Sr and metamorphism
of sediments are assumed to be proportional to the global degassing rate, D. We also assume that
the rate of strontium burial in sediments relates to the concentration of strontium in the ocean and
the rate of carbonate sediment deposition. This follows the treatment of other species in COPSE.
Sr fluxes:
𝑏𝑎𝑠𝑤
Sr input from basalt weathering:
𝑆𝑟𝑏𝑎𝑠𝑤 = 𝑘𝑆𝑟𝑏𝑎𝑠𝑤 ∙ 𝑘
Sr input from granite weathering:
𝑆𝑟𝑔𝑟𝑎𝑛𝑤 = 𝑘𝑆𝑟𝑔𝑟𝑎𝑛𝑤 ∙ 𝑘
Sr input from sediment weathering:
𝑆𝑟𝑠𝑒𝑑𝑤 = 𝑘𝑆𝑟𝑠𝑒𝑑𝑤 ∙ 𝑘
Seafloor weathering:
𝑆𝑟𝑠𝑓𝑤 = 𝑘𝑆𝑟𝑠𝑓𝑤 ∙
Burial in sediments:
𝑆𝑟𝑠𝑒𝑑𝑏 = 𝑘𝑆𝑟𝑠𝑒𝑑𝑏 ∙
Mantle input:
𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 = 𝑘𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 ∙ 𝐷
(54)
Sediment metamorphism:
𝑆𝑟𝑚𝑒𝑡𝑎𝑚 = 𝑘𝑆𝑟𝑚𝑒𝑡𝑎𝑚 ∙ 𝐷
(55)
𝑏𝑎𝑠𝑤
𝑔𝑟𝑎𝑛𝑤
𝑔𝑟𝑎𝑛𝑤
𝑐𝑎𝑟𝑏𝑤
8
𝑐𝑎𝑟𝑏𝑤
𝑠𝑓𝑤
𝑘𝑠𝑓𝑤
𝑚𝑐𝑐𝑏 𝑂𝑆𝑟
∙
𝑘𝑚𝑐𝑐𝑏 𝑂𝑆𝑟0
(49)
(50)
(51)
(52)
(53)
Other calculations
Although these is no fractionation of Sr isotopes associated with the input and output fluxes
to the ocean, decay of 87Rb to 87Sr influences the 87Sr/86Sr ratio over long timescales (and is
responsible for the differing 87Sr/86Sr values between different rock types). The decay process is
represented explicitly in the model:
87
𝑆𝑟/ 86𝑆𝑟𝑔𝑟𝑎𝑛𝑖𝑡𝑒 =
87
𝑆𝑟/ 86𝑆𝑟𝑏𝑎𝑠𝑎𝑙𝑡 =
87
𝑆𝑟/ 86𝑆𝑟0 + 87𝑅𝑏/ 86𝑆𝑟𝑔𝑟𝑎𝑛𝑖𝑡𝑒 (1 − 𝑒 −𝜆𝑡 )
87
𝑆𝑟/ 86𝑆𝑟0 + 87𝑅𝑏/ 86𝑆𝑟𝑏𝑎𝑠𝑎𝑙𝑡 (1 − 𝑒 −𝜆𝑡 )
(56)
(57)
For each rock type, the rubidium-strontium ratio is then calculated such that the observed present
day 87Sr/86Sr ratio is achieved for each rock type after 4.5 billion years:
87
𝑅𝑏/ 86𝑆𝑟 =
( 87𝑆𝑟 / 86𝑆𝑟𝑝𝑟𝑒𝑠𝑒𝑛𝑡 − 87𝑆𝑟/ 86𝑆𝑟0 )
(58)
9
(1−𝑒 −𝜆∙4.5×10 )
Sr reservoir calculations:
Ocean Sr:
𝑑𝑂𝑆𝑟
𝑑𝑡
= 𝑆𝑟𝑔𝑟𝑎𝑛𝑤 + 𝑆𝑟𝑏𝑎𝑠𝑤 + 𝑆𝑟𝑠𝑒𝑑𝑤 + 𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 − 𝑆𝑟𝑠𝑒𝑑𝑏 − 𝑆𝑟𝑠𝑓𝑤
(59)
Sr in sediments :
𝑑𝑆𝑆𝑟
𝑑𝑡
= 𝑆𝑟𝑠𝑒𝑑𝑏 − 𝑆𝑟𝑠𝑒𝑑𝑤 − 𝑆𝑟𝑚𝑒𝑡𝑎𝑚
(60)
Isotope ratios are calculated by creating reservoirs consisting of Sr concentrations multiplied by their
isotopic ratios. This method is common in isotope mass balance studies [15, 16]. Here 𝑑𝑆𝑟𝑋 denotes
the 87Sr/86Sr ratio of reservoir X.
Ocean [Sr] x 87Sr/86Sr:
𝑑𝑂𝑆𝑟_𝑑𝑆𝑟
𝑑𝑡
= 𝑆𝑟𝑔𝑟𝑎𝑛𝑤 ∙ 𝑑𝑆𝑟𝑔𝑟𝑎𝑛𝑖𝑡𝑒 + 𝑆𝑟𝑏𝑎𝑠𝑤 ∙ 𝑑𝑆𝑟𝑏𝑎𝑠𝑎𝑙𝑡 + 𝑆𝑟𝑠𝑒𝑑𝑤 ∙ 𝑑𝑆𝑟𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡 + 𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 ∙
𝑑𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 − 𝑆𝑟𝑠𝑒𝑑𝑏 ∙ 𝑑𝑆𝑟𝑜𝑐𝑒𝑎𝑛 − 𝑆𝑟𝑠𝑓𝑤 ∙ 𝑑𝑆𝑟𝑜𝑐𝑒𝑎𝑛
(61)
Crustal [Sr] x 87Sr/86Sr:
9
𝑑𝑆𝑆𝑟_𝑑𝑆𝑟
𝑑𝑡
= 𝑆𝑟𝑠𝑒𝑑𝑏 ∙ 𝑑𝑆𝑟𝑜𝑐𝑒𝑎𝑛 − 𝑆𝑟𝑠𝑒𝑑𝑤 ∙ 𝑑𝑆𝑟𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡 − 𝑆𝑟𝑚𝑒𝑡𝑎𝑚 ∙ 𝑑𝑆𝑟𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡
(62)
The isotopic ratio of 87Sr to 86Sr in the ocean is then calculated by dividing the new reservoir by the
known concentration. The 87Sr/86Sr ratio for carbonate sediments is calculated in the same way, with
an additional term to account for rubidium decay within the crust:
𝑑𝑆𝑟𝑜𝑐𝑒𝑎𝑛 =
𝑂𝑆𝑟_𝑑𝑆𝑟
𝑂𝑆𝑟
,
𝑑𝑆𝑟𝑠𝑒𝑑𝑖𝑚𝑒𝑛𝑡 =
𝑆𝑆𝑟_𝑑𝑆𝑟
𝑆𝑆𝑟
+ 87𝑅𝑏/ 86𝑆𝑟𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 (1 − 𝑒 −𝜆𝑡 )
Present day Sr fluxes:
(63)
Source:
Basalt weathering
𝑘𝑆𝑟𝑏𝑎𝑠𝑤 = 1.3 × 1010 × %𝑏𝑎𝑠0 mol/yr
[13, 17]
Granite weathering
𝑘𝑆𝑟𝑔𝑟𝑎𝑛𝑤 = 1.3 × 1010 × (1 − %𝑏𝑎𝑠0 ) mol/yr
[13, 17]
Sediment weathering
𝑘𝑆𝑟𝑠𝑒𝑑𝑤 = 1.7 × 1010 mol/yr
[13]
Mantle input
𝑘𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 = 7.3 × 109 mol/yr
[13]
Sediment metamorphism
𝑘𝑆𝑟𝑚𝑒𝑡𝑎𝑚 = 1.3 × 1010 mol/yr
[13]
Seafloor weathering
𝑘𝑆𝑟𝑠𝑓𝑤 = 3.26 × 109
mol/yr
for steady state
Burial in sediments
𝑘𝑆𝑟𝑠𝑒𝑑𝑏 = 3.404 × 1010 mol/yr
for steady state
Here the split between Sr input fluxes from basalt and granite is assumed to follow the same
apportioning as in the carbon system (35% of silicate weathering is attributed to basalts [17]). Sr
burial in carbonate sediments and burial as carbonatized basalt is assumed to also follow the same
stoichiometry as the carbon system, with the total flux dictated by assuming present day steady
state for oceanic Sr concentration.
10
Other constants:
Source:
Present day ocean Sr
𝑂𝑆𝑟0 = 1.2 × 1017
[13]
Sediment Sr
𝑆𝑆𝑟0 = 5 × 1018
[13]
87
𝑑𝑆𝑟𝑏𝑎𝑠𝑎𝑙𝑡 = 0.705
[13]
87
𝑑𝑆𝑟𝑔𝑟𝑎𝑛𝑖𝑡𝑒 = 0.715
[13, 18]
87
𝑑𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 = 0.703
[13]
87
87
0.066
for correct present day 87Sr/86Sr
87
87
0.1
for correct present day 87Sr/86Sr
87
87
0.26
for correct present day 87Sr/86Sr
87
87
Sr/86Sr basalt
Sr/86Sr granite
Sr/86Sr mantle
Rb/86Sr mantle
Rb/86Sr basalt
Rb/86Sr granite
Rb/86Sr sediments
𝑅𝑏/ 86𝑆𝑟𝑚𝑎𝑛𝑡𝑙𝑒 =
𝑅𝑏/ 86𝑆𝑟𝑏𝑎𝑠𝑎𝑙𝑡 =
𝑅𝑏/ 86𝑆𝑟𝑔𝑟𝑎𝑛𝑖𝑡𝑒 =
𝑅𝑏/ 86𝑆𝑟𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 = 0.5
for correct present day 87Sr/86Sr
(assuming crustal average 87Sr/86Sr of 0.73 [19])
Initial ocean 87Sr/86Sr is set at the model start point in accordance with data (87Sr/86Sr≈0.708 for
230Ma), initial sedimentary carbonate 87Sr/86Sr is set so that the model returns present day values
for ocean 87Sr/86Sr. This requires sediment 87Sr/86Sr = 0.714 at 230Ma.
Supporting information 3 – Additional model scenarios
Figures S1-S4 are plotted below and are referred to in the manuscript. Some discussion is added
here also.
11
Figure S1. Sensitivity to assumed present day seafloor weathering rate ksfw. Panels show the upper
(a,b) and lower (c,d) estimates for present day seafloor weathering rate [6-8]. As would be expected,
a higher rate of seafloor weathering results in lower stable CO2 concentration. Lower predicted
87
Sr/86Sr results from less radiogenic input from silicate weathering (less is required to balance CO2
degassing) and reduced carbonate weathering at lower temperatures. Here α=0.23 and uncertainty
on basalt area and degassing rate result in the upper and lower boundaries.
12
Figure S2. Model results for Hay et al. [2006] uplift scenario [20]. Sharp rise in uplift rates over the
Cenozoic result in rapid increase in 87Sr/86Sr. However this exceeds the rate shown in data. One
solution may be that uplift was between the Hay et al., estimates and those used in the main paper
(following Berner [2]).
13
Figure S3. Model runs for longer LIP emplacement times. As figure 8 but with LIP emplacement
times (assumed to correspond to duration of degassing and seafloor weathering enhancement)
taken from Courtilliot et al., [2003] [21], and shown in the LIP table below. Where emplacement
time is unknown it is assumed to follow the average of the published times (~1.7Myrs). Timing is
particularly important for the Ontong-Java plateau, which is the LIP with highest initial volume.
Published emplacement timings for this LIP range from 500kyr to 3Myr [22], which our 1.7Myr
assumption falls between. Longer emplacement times reduce the predicted CO2 perturbations as
may be expected. However the Ontong-Java may still result in up to 50% increase in CO2.
14
Figure S4. Model runs for constant degassing rate, compared to the spatial weathering results of
Lefebvre et al., [2013] (crosses) [23]. The spatial modelling of basalt weathering regimes is lacking in
our work, due to the complex GCM climate dynamics required, which limit the timeframe in which a
dynamic model can be run. Snapshots of terrestrial basalt weathering from the spatial model show
much lower values at 65 and 15Ma, when compared to our model under the same (constant)
degassing scenario. Granitic weathering follows a more similar pattern, but is lower in our model
due to consideration of the seafloor weathering CO2 sink and our different results for basalt
15
weathering. The mismatch between results suggests that both LIP area decay and paleogeographic
position are important for long term climate models.
Supporting information 4 – Basalt area forcing
The basalt area forcing as used in our model runs is attached as a .mat file. This includes the
resulting upper, middle and lower estimates from figure 5, incorporating both the instant and
delayed decay options. The time points are in Myrs.
Supporting Information 5 – Phanerozoic LIP emplacements
Estimation of terrestrial basaltic area requires information on the initial area and timings of
large igneous province emplacements. Calculation of potential CO2 degassing relies on estimates of
initial LIP volume. The attached excel table contains information on all large igneous provinces from
300Ma to present, and is based on the A10 database of the Large Igneous Provinces Commission
(http://www.largeigneousprovinces.org/). Citation numbers in the excel table relate to the
references here.
For LIP volumes, red cells denotes where volumes have been estimated based on the
volume-area relationship of the more recent, well-constrained LIPs: 𝑉 = 3.2 × 105 ∙ 𝑒 2×10
−6 𝐴
where V is volume in km3 and A is area in km2. This approximation does not give a strong fit
(r2=0.66), however the LIPs for which volume is estimated in this way to not contribute greatly to
total LIP volume. All area estimates are taken directly, or inferred from literature data. The relevant
publications are noted in the final column, where there is no reference, data comes directly from the
A10 database. CO2 release is calculated from initial volume (see manuscript and [24]).
16
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20