ORIGINAL ARTICLE

Snowball Earth at low solar luminosity prevented by the ocean–atmosphere coupling

Ruimin Wang1• Bing Shen1

Received: 14 May 2019 / Revised: 17 July 2019 / Accepted: 16 August 2019 / Published online: 22 August 2019

� Science Press and Institute of Geochemistry, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract The standard solar model proposes that the solar

luminosity was 30% lower than the present level at 4.5

billion years ago (Ga). At low solar radiation, the climate

model predicts that the Earth should have been completely

covered by ice in the first 2 billion years, i.e. in the

snowball Earth climate mode, when the atmospheric CO2

content was at the present level. However, snowball Earth

condition is inconsistent with various sedimentological,

paleontological, and geochemical evidence. Such contro-

versy is collectively known as the ‘Faint Young Sun’

(FYS) paradox. Though various models have been pro-

posed, the FYS paradox has not yet been resolved. In this

study, we develop a model by considering the ocean–at-

mosphere coupling to show that high atmospheric CO2

level could be sustained at low seawater pH. The modeling

result indicates that 0.1 bar atmospheric CO2 level that was

required to prevent snowball Earth in early Archean could

be sustained at seawater pH of 6.8–7.2. Although the

absence of siderite in Archean paleosols has been used to

argue against high atmospheric CO2 level, we suggest that

siderite precipitation in paleosols was not controlled by the

atmospheric CO2 level alone. Instead, siderite could pre-

cipitate in anoxic conditions with various amount of CO2 in

the atmosphere, suggesting siderite cannot be used to

reconstruct the atmospheric CO2 level. Therefore, the new

model suggests that the snowball Earth condition could be

prevented by the coupling of atmosphere and ocean sys-

tems, and thus the emergence of the ocean in the very

beginning of Earth evolution might be the key to the sub-

sequence evolution of habitability.

Keywords Faint Young Sun paradox � Carbon dioxide �Earth system � Siderite

1 Introduction

The standard solar model predicts that the intensity of solar

luminosity increases through time, and the solar radiation

was 30% lower than the present level in the origin of the

solar system (Bahcall et al. 2001; Gough 1981; Newman

and Rood 1977; Sagan and Mullen 1972). At low solar

luminosity, climate models predict that the early Earth

should have been completely covered by ice, entering the

so-called ‘snowball Earth’ climate mode, if atmospheric

CO2 level remained at the present atmospheric level (PAL,

* 400 ppmv). It is proposed that 10%–18% reduction of

solar radiation was sufficient to bring the Earth into the

snowball Earth condition, and thus the whole Earth should

have been frozen in the first two billion years of Earth’s

history (Jenkins 1993; Longdoz and Francois 1997).

However, geological evidence indicates that the Earth

was not a snowball in Archean, and global glaciation did

not occur until Palaeoproterozoic (Bekker et al. 2008;

Brasier et al. 2013). Presence of liquid water on Earth

surface is supported by widespread Archean sedimentary or

meta-sedimentary rocks in Greenland, South Africa, and

Australia (Dymek and Klein 1988; Lowe 1980; Shen et al.

2001; Westall et al. 2006). Discoveries of early Archean

stromatolite (Allwood et al. 2006, 2007; Byerly et al. 1986;

Wacey 2010) and microfossils (Buick 1984; Schopf

1993, 2006; Schopf et al. 2018; Schopf and Packer 1987)

strongly argue for the emergence of life in the Archean

& Bing Shen

bingshen@pku.edu.cn

1 Key Laboratory of Orogenic Belts and Crustal Evolution,

MOE, School of Earth and Space Science, Peking University,

Beijing 100871, China

123

Acta Geochim (2019) 38(6):775–784

https://doi.org/10.1007/s11631-019-00373-7

ocean. In addition, geochemical data indicate that liquid

water on the Earth might be traced back to Hadean, pre-

dating the late heavy bombardment at 4.0–3.9 Ga (Kring

and Cohen 2002). High oxygen isotope values of the ear-

liest detrital zircons (ZrSiO4) from Jack Hills (Australia)

imply alteration of zircon by liquid water (Harrison et al.

2008; Mojzsis et al. 2001; Valley et al. 2002).

The contradiction between climate models and geolog-

ical observations is collectively known as the ‘Faint Young

Sun’ (FYS) paradox (Feulner 2012). In this paper, we will

first review the possible solutions to the FYS paradox.

Then we will focus on how and why CO2, as the only major

greenhouse gas in the atmosphere, could accumulate to

high concentration in the early Earth. Finally, we will

reconcile the discrepancy between the modeling result and

geological observations.

2 Resolving the FYS paradox

Based on planetary energy balance, the low solar lumi-

nosity in the early Earth could be compensated by reducing

the energy loss during its transport to the surface Earth. In

the modern Earth, about 45% of solar energy is either

reflected or absorbed by cloud or air, and 55% reaches the

surface of solid Earth (Hartmann 2015). It is proposed that

the snowball Earth condition could be prevented by

reducing the low cloud reflection or absorption, enhancing

the efficiency of solar radiation reaching the surface Earth

(Rondanelli and Lindzen 2010). Indeed, the reduction of

low cloud content in early Earth has been suggested due to

few galactic cosmic rays reaching the lower troposphere

(Shaviv 2003). On the other hand, because the high cloud

would absorb longwave radiation from the surface Earth,

the thin high cloud would reduce the absorption of long-

wave radiation, weakening the greenhouse effect of the

atmosphere (Goldblatt and Zahnle 2011). Due to the

opposite climatic effect of cloud to the shortwave and

longwave radiation, the net effect of cloud formation on the

global temperature remains controversial (Goldblatt and

Zahnle 2011; Rondanelli and Lindzen 2012).

On the other hand, low solar luminosity could be com-

pensated by enhancing the greenhouse effect in the atmo-

sphere. Greenhouse gases, including CO2, H2O, CH4, NH3,

and N2O, absorb longwave radiation from the surface

Earth, keeping the Earth warm (Byrne and Goldblatt 2014).

It is intuitive to speculate that CO2 might be the major

greenhouse gas in the early Earth. The climate model

indicates that 0.01–0.1 bar CO2 in Archean and Hadean

atmosphere was sufficient to keep the global mean tem-

perature (GMT) above the freezing point (273 K), while

0.1–0.5 bar CO2 would elevate GMT to the present level of

288 K (von Paris et al. 2008). However, a high atmospheric

CO2 level in the early Earth has been challenged by the

paleosol data. Rare siderite precipitation in Archean and

Palaeoproterozoic paleosols is used as strong evidence

arguing against high atmospheric CO2 level. It is further

suggested that, based on the study of paleosols, Archean

atmospheric CO2 level should be lower than 0.01 bar, and

thus other greenhouse gases are needed (Driese et al. 2011;

Hessler et al. 2004; Rye et al. 1995; Sheldon 2006).

Ammonium (NH3) is the first proposed greenhouse gas

that may resolve the FYS paradox, because NH3 has a

strong absorption band at * 10 lm, the peak of the

blackbody radiation from the solid Earth (Sagan and

Mullen 1972). However, NH3 is subject to photochemical

decomposition by solar ultraviolet radiation, resulting in a

short lifetime (\ 10 years) in the atmosphere. High NH3

flux is required to maintain the high NH3 concentration in

the atmosphere. However, the terrestrial supply of NH3 was

not sufficient to resolve the FYS paradox (Kasting 1982),

and accordingly, NH3 may not be the major greenhouse gas

in the early Earth.

CH4 has also been regarded as the possible, probably

most likely, greenhouse gas in early Earth. But high CH4

concentration, i.e. CH4/CO2 [ 0.1, would cause organic

haze formation, which reflects the incoming solar radiation

but is transparent to the outgoing infrared radiation,

resulting in an anti greenhouse effect (Kasting et al. 1983;

McKay et al. 1991, 1999). If the atmospheric CO2 level

was kept at 0.01 bar (Hessler et al. 2004), CH4 content

should be less than 1000 ppmv. The modeling result indi-

cates that 0.01 bar CO2 mixed with 100–1000 ppmv CH4

would be sufficient to compensate the low solar radiation

and prevent the snowball Earth condition (Kasting 2005).

High atmospheric CH4 level requires either high CH4

flux or slow rate of CH4 degradation. CH4 could be

removed from the atmosphere in two ways: photolysis by

ultraviolet radiation at 121.6 nm (the Lyman Alpha series)

and oxidation by OH radicals that derive from the pho-

tolysis of H2O (Pavlov et al. 2001). The formation of ozone

since 2.4 Ga would further enhance CH4 decomposition

via OH radical oxidation (Farquhar et al. 2000; Pavlov and

Kasting 2002), but on the other hand, the ozone would

shield ultraviolent radiation, lowering the efficiency of CH4

photolysis. Thus, CH4 decomposition is sensitive to O2

level in the atmosphere (Kasting 2005). The modeling

results indicate that, in order to keep 100 ppmv CH4 con-

centration at 0.01 PAL pO2 level, CH4 flux should be 10

times larger than the present level (Kasting 2005). It should

be noted that further reduction of O2 level would enhance

CH4 degradation by UV radiation, requiring even high CH4

flux. Therefore, a minimum flux of 6400 Tg/yr is required

to sustain 100 ppmv CH4 in the atmosphere with \ 0.01

PAL O2 level.

776 Acta Geochim (2019) 38(6):775–784

123

There are three CH4 sources. It is estimated that

cometary impacts might provide 500 and 5000 Tg/yr CH4

at 3.5 and 3.8 Ga, respectively (Kress and McKay 2004),

but a much smaller extraterrestrial input of 20 Tg/yr CH4 is

also proposed (Kasting 2005). In addition, the modern flux

of abiogenic CH4, e.g. hydrothermal alteration of oceanic

crust and volcanic degassing, is estimated to be 2.3 Tg/yr

(Emmanuel and Ague 2007; Lazar et al. 2012; Scott et al.

2004). Abiotic CH4 emission via hydrothermal alteration

and volcanic degassing might be higher than the modern

level by a factor of 5, due to higher heat flux in the early

Earth. Lastly, biogenic CH4 production by methanogens

accounts for more than 90% CH4 flux at present, but bio-

genic CH4 flux might be negligible before the evolution of

methanogens. The molecular clock indicates that the

methanogens might have evolved between 4.1 and 3.9 Ga

(Battistuzzi et al. 2004), but it is unclear whether

methanogenesis could provide sufficient CH4 to sustain

high atmosphere CH4 concentration in Archean. Never-

theless, there is no doubt that before the evolution of

methanogens in the first 0.5 billion years of Earth’s history

(Battistuzzi et al. 2004), extraterrestrial and abiotic CH4

input could not sustain high CH4 content in the atmosphere

so as to prevent the snowball Earth condition.

Other greenhouse gases, such as N2O and OCS, have

also been proposed as well, but these molecules confront

with rapid photodissociation with the absence of O2, and

thus unlikely to accumulate to high concentrations in early

Earth (Domagal-Goldman et al. 2011; Roberson et al.

2011).

Therefore, the FYS paradox has not yet resolved. In the

following sections, we will revisit the idea that CO2 was

the major greenhouse gas in Archean, and explore (1) how

high atmospheric CO2 level could be maintained, and (2)

how high CO2 level and paleosol data could be reconciled.

3 Quantifying early Earth atmospheric CO2 levelby the ocean–atmosphere coupling model

Unlike other greenhouse gases, CO2 will not be decom-

posed by photolysis regardless of O2 level in the atmo-

sphere. The atmospheric CO2 level is controlled by

volcanic degassing (Fvol) and CO2 consumptions in surface

Earth (Fsink). Change of atmospheric CO2 level [expressed

as CO2 partial pressure, pðCO2Þ] through time can be

expressed by the following equation:

dpðCO2Þdt

¼ Fvol � Fsinkð ÞMatm

ð1Þ

where Matm is the mass of the atmosphere. High pðCO2Þimplies either high volcanic degassing and/or low rate of

CO2 consumption (Kasting et al. 1984; Kiehl and

Dickinson 1987; von Paris et al. 2008). Because the mantle

is hotter in early Earth (Taylor and McLennan 2009),

volcanic CO2 degassing rate was expected to be higher

than the present. The modeling calculations indicate that

the heat flux might be 2–3 times higher than today (Taylor

and McLennan 2009), implying 2–3 times larger Fvol.

As the major sink of atmospheric CO2, continental

weathering accounts for * 80% of CO2 sink (Kump and

Arthur 1999). In continental weathering, dissolution of

silicate minerals/rocks by carbonic acid (H2CO3) generates

bicarbonate ions (CO32-), which is eventually buried as

carbonate rocks. Continental weathering and carbonate

precipitation can be expressed by the following equations:

CaSiO3 þ 2CO2 þ 3H2O ¼ Ca2þ þ 2HCO�3 þ H4SiO4

ð2Þ

Ca2þ þ 2HCO�3 ¼ CaCO3 þ H2Oþ CO2 ð3Þ

CaSiO3 þ CO2 þ 2H2O ¼ CaCO3 þ H4SiO4 ð4Þ

Equation (4) is the overall reaction of continental

weathering and carbonate precipitation in surface Earth.

The reaction rate of continental weathering is dependent on

atmospheric CO2 level, precipitation (rainfall) and tem-

perature, while the global flux of CO2 removal via conti-

nental weathering is also controlled by the area of exposed

continents. It is widely accepted that the size of the con-

tinent was significantly smaller than that of today (Kroner

1985), and thus the rate of CO2 removal by chemical

weathering might be smaller in Archean.

CO2 is also removed by organic matter production and

burial, which accounts for * 20% of CO2 burial in pre-

sent-day (Kump and Arthur 1999). Although organic car-

bon can be synthesized inorganically, for example, the

Fischer–Tropsch reaction that might be responsible for

organic carbon production before the evolution of life

(Bada 2004; Miller et al. 1976), biological process, e.g.,

photosynthesis, either oxygenic or anoxygenic, would be a

more efficient way of organic matter production (Falk-

owski et al. 1998).

It is widely accepted that the primary productivity was

small in the early Earth, i.e. a small organic carbon sink.

Assuming a steady-state withdpðCO2Þ

dt¼ 0, we will have the

following equation:

Fvol � Scont � Rcw � p CO2ð Þ � Forg ¼ 0 ð5Þ

where Rcw is the reaction rate constant of continental

weathering, which is a function of e.g. precipitation and

temperature. Scont is the area of exposed continents, and

Forg is the size of the organic carbon sink. Rearranging

Eq. (5), the atmospheric CO2 level can be expressed as:

p CO2ð Þ ¼ Fvol � Forg

Scont � Rcw

ð6Þ

Acta Geochim (2019) 38(6):775–784 777

123

Equation (6) indicates that high atmospheric CO2 level

requires high volcanic degassing, small organic carbon

sink, or small size of the continent, which might be the case

in early Earth. However, given unconstrained parameters,

e.g. Rcw or Forg, p CO2ð Þ cannot be quantified by Eq. (6).

Another way to estimate the atmospheric CO2 level is to

consider the coupling between the atmosphere and ocean

systems. In the ocean–atmosphere system, atmospheric

CO2 is dissolved into seawater, then followed by dissoci-

ation of dissolved CO2 to aqueous inorganic carbon

species.

p CO2ð Þ ¼ CO2ð Þa�HCO2ð7Þ

H2CO3 ¼ Hþ þ HCO�3 ð8Þ

HCO�3 ¼ Hþ þ CO2�3 ð9Þ

When the ocean–atmosphere system is in equilibrium,

the relationship between p CO2ð Þ and seawater dissolved

inorganic carbon (DIC) can be derived from Eqs. (7)–(9),

and can be expressed by the following equation:

CO2�3

� �¼ k1 � k2 � HCO2

� p CO2ð Þ½Hþ�2

ð10Þ

k1 and k2 are the first and second-order dissociation con-

stants of carbonic acid, respectively, while HCO2is the

Henry’s constant for CO2 dissolution in seawater. Equa-

tion (10) indicates that pðCO2Þ is positively linear corre-

lation with seawater concentration of CO32- and the square

of ½Hþ�, i.e. with an increase of seawater pH (�logð½Hþ�Þ),p CO2ð Þ will drop, and vice versa. Thus, given known

seawater pH and CO2�3

� �or ½HCO�3 �, p CO2ð Þ can be

calculated.

Furthermore, CO2�3

� �could be further constrained by

the carbonate saturation state of seawater. With the absence

of carbonate biomineralization in early Earth (Bartley and

Kah 2004), seawater should be supersaturated with respect

to Ca-carbonate, because either inorganic carbonate pre-

cipitation or biologically induced carbonate precipitation

requires a high degree of supersaturation with respect to

calcite or aragonite (Riding 2000, 2006). Predominant

inorganic carbonate precipitation in Archean is supported

by widespread inorganic carbonate deposition, such as

crystal fan and herring-bone structures in Archean car-

bonate (Bartley and Kah 2004; Grotzinger 1989; Grotzin-

ger and James 2000; Sami and James 1996). When

seawater is supersaturated with respect to Ca-carbonate, we

will have the following equation:

CO2�3

� �� Ca2þ� �

¼ Xcal � ksp ð11Þ

where Xcal is the degree of supersaturation with respect to

Ca-carbonate, and ksp is the constant of solubility product.

In the modern ocean, Xcal is 5 but inorganic carbonate

precipitation is kinetically inhibited by nucleation that

requires higher Xcal (Higgins et al., 2009). It is proposed

that inorganic carbonate precipitation requires Xcal of 10

(Arp et al. 2001). Combining Eqs. (10) and (11), we arrive

at the following relationship:

p CO2ð Þ ¼ ksp � Xcal � ½Hþ�2

k1 � k2 � HCO2� Ca2þ½ � ð12Þ

Thus, p CO2ð Þ can be quantified by given seawater pH

and Ca2? concentration in seawater. The seawater Ca2?

concentration varies between 10 and 30 mM in Earth’s

history (Hardie 1996, 2003). It is proposed that seawater

pH was affected by the intensity of reverse weathering,

which utilizes dissolved silica, bicarbonate, and divalent

ions (e.g. Mg2? and Fe2?) to synthesize authigenic clays

(Isson and Planavsky 2018). Examples of reverse weath-

ering reactions include:

3Fe2þ þ 2H4SiO4 þ 6HCO�3 ¼ Fe3Si2O5 OHð Þ4þ 6CO2

þ 5H2O

ð13Þ

4Mg2þ þ 6H4SiO4 þ 8HCO�3 ¼ Mg4Si6O15 OHð Þ2þ 8CO2

þ 15H2

ð14Þ

From Eqs. (13) and (14), it shows that reverse weath-

ering is sensitive to the concentration of dissolved silica in

seawater. In the modern ocean, reverse weathering is weak

because seawater silica concentration was low and unsat-

urated with respect to opal due to effective scavenge of

seawater silica by silica-secreting organisms, such as dia-

toms, siliceous sponges, and radiolarians (Treguer et al.

1995). In contrast, before the evolution of silica-secreting

organisms, the Archean and Proterozoic ocean could have

been supersaturated with respect to opal (with the satura-

tion concentration of 0.67 mM) (Hesse 1989; Maliva et al.

2005). Intense reverse weathering in the Archean and

Proterozoic ocean is consistent with high authigenic clays

content in Precambrian shales (Isson and Planavsky 2018).

By applying the seawater pH of 6.8–7.2 (Isson and

Planavsky 2018) and seawater Ca2? concentration of 10–

30 mM (Hardie 1996, 2003), the modeling results indicate

that p CO2ð Þ ranges from 0.05 to 0.2 bar (Fig. 1), which is

high enough to keep MGT above the freezing point and

thus prevent the snowball Earth condition (von Paris et al.

2008).

778 Acta Geochim (2019) 38(6):775–784

123

4 What can siderite tell us?

The high atmospheric CO2 level in the early Earth has been

challenged by the absence of siderite precipitation in

paleosols (Rye et al. 1995). Rather than siderite (FeCO3)

precipitation, iron silicate minerals, such as greenalite,

were observed in Archean and Palaeoproterozoic paleosols

(Driese et al. 2011; Hessler et al. 2004; Rosing et al. 2010;

Rye et al. 1995; Sheldon 2006). By considering the equi-

librium between siderite and Fe-silicate minerals, it is

proposed that high atmospheric CO2 level would result in

siderite precipitation. Further based on the study of

Archean paleosols, the estimated p CO2ð Þ was lower than

the value required for keeping the MGT above the freezing

point (Driese et al. 2011; Hessler et al. 2004; Rosing et al.

2010; Rye et al. 1995; Sheldon 2006).

In contrast to the rare occurrences of siderite in pale-

osols, siderites were abundantly precipitated in marine

deposits. For example, siderite is the major iron minerals in

many Archean banded iron formations (BIF) (Ohmoto

et al. 2004), suggesting Archean seawater might be

supersaturated with respect to siderite. To further constrain

the physio-chemical condition of siderite precipitation in

the Archean ocean, we calculate the phase diagram for

siderite precipitation at given Eh and pH conditions. By

adjusting seawater Fe2? concentration and DIC content, the

required Eh and pH for siderite precipitation are plotted in

Fig. 2. By keeping p CO2ð Þ at 0.1 bar, Xcal of 10, and

seawater pH of 6.8–7.2 (Isson and Planavsky 2018), i.e.

seawater DIC concentration of 13 mM, siderite precipita-

tion requires at least 1 mM of dissolved Fe2? in seawater,

which is six orders of magnitude higher than that in the

modern ocean (* 1 nM) (Johnson et al. 1997). High sea-

water concentration of dissolved Fe2? implies low pO2

level in Archean (Fig. 2), which is consistent with wide-

spread detrital pyrite and uraninite in Archean sediments

(Holland 1984; Rasmussen and Buick 1999). This con-

clusion is also in accordance with the mass-independent

fractionation in sulfur isotope (Farquhar et al. 2000; Far-

quhar and Wing 2003), implying the atmospheric pO2 level

was lower than 10-5 PAL (Kasting 2001; Pavlov and

Kasting 2002). Therefore, widespread marine siderite pre-

cipitation is mainly controlled by atmospheric O2 level and

seawater Fe2? concentration rather than CO2 level in the

atmosphere.

For siderite precipitation in paleosols, in fact, modern

soil contains both authigenic clays and authigenic carbon-

ate, and there is a wide range of variation in the authigenic

carbonate content in soils (Amundson et al. 2003; Zou et al.

2019). The authigenic mineral composition of the soil is

not only controlled by the atmospheric CO2 level but also

affected some local factors, such as precipitation and

evaporation (Amundson et al. 2003). Therefore, the

absence of siderite in Archean paleosols may not indicate

low atmospheric CO2 level, and vice versa.

Fig. 1 The modeling result

showing the relationship

between seawater pH and

atmospheric CO2 level, given

the equilibrium between the

ocean and atmosphere and

seawater supersaturated

(Xcal = 10) with respect to

calcite

Acta Geochim (2019) 38(6):775–784 779

123

We simulated the process of siderite precipitation in

paleosols. Assuming paleosols are developed in a silicate

bedrock, and thus ferrous iron (Fe2?) derives from the

dissolution of silicate minerals, while CO32- exclusively

sources from the atmosphere. For simplicity, we assumed,

(1) in situ silicate mineral dissolution was the only source

of Fe2?, i.e. exogenic Fe2? delivered by river water or

groundwater was not considered, (2) silicate minerals could

be dissolved in various amount of freshwater (expressed as

volume of freshwater divided by the volume of dissolved

silicate), and (3) authigenic mineral is precipitated from a

solution that is in equilibrium with atmosphere. Fe2?

concentration in solution ( Fe2þ½ �) from which siderite

precipitates can be expressed by the following equation:

Fe2þ� �¼ aHR= 1þ lð Þ ð15Þ

where aHR is the Fe concentration in bedrock, l is the

freshwater dilution factor, referring to the volume ratio

between freshwater and dissolved silicate minerals. Whe-

ther siderite could precipitate is determined by the satura-

tion of solution (Xsiderite), which can be expressed by the

following equation:

Xsiderite ¼Fe2þ½ � � CO2�

3

� �

ksideritesp

ð16Þ

Combining Eqs. (10), (15) and (16), we arrive at:

Xsiderite ¼k1 � k2 � HCO2

� p CO2ð Þ � ðaHRÞ2

½Hþ�2 � 1þ lð Þ2� ksideritesp

ð17Þ

Here we consider two scenarios with different bedrock

compositions: (1) Fe-olivine (Fe2SiO4) composition, and

(2) the upper continental crust (UCC) composition with 5.6

wt% of FeO (Rudnick and Gao 2014). Bedrock composi-

tion would affect Fe2þ½ �. We assume siderite precipitation

at Xsiderite = 10 and at pH between 6.8 and 7.2. At 0.1 bar

pðCO2Þ, siderite precipitation requires l \ 250 for pale-

osols developed on the Fe-olivine bedrock and \ 50 for

paleosols on bedrock with the UCC composition (Fig. 3a,

b). At 0.01 bar (i.e. 30 PAL) pðCO2Þ, the upper bound of ldecreased to 100 and 25 for bedrock with the Fe-olivine or

UCC composition, respectively (Fig. 3c, d). Further

decrease pðCO2Þ to 0.001 bar (i.e. 3 PAL), in order to

precipitate siderite, l should be \ 50 and \ 5 for the Fe-

olivine and UCC composition bedrock, respectively

(Fig. 3e, f).

The modeling results indicate that with a decrease of

atmospheric CO2 level, siderite precipitation requires less

dilution by freshwater, i.e. paleosols formed in more arid

conditions. This is exactly the case for the modern soil

carbonate, which preferentially precipitates in arid condi-

tions (Amundson et al. 2003). Furthermore, our study

indicates that the atmospheric CO2 level is not the only

control of siderite precipitation. Siderite could precipitate

from a wide range of pðCO2Þ (0.1–0.01 bar), given suffi-

cient Fe2? supply and suitable humidity, i.e. smaller l. In

this case, siderite in paleosols may not be used to quantify

the atmospheric CO2 level.

14121086420

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Fe - C - H2O - System at 25.00 CEh (Volts)

Fe2O3

Fe3O4

Fe(OH)2FeCO3

Fe(+3a)

Fe(+2a)

CO2: 0.1 barFe: 1 mMTIC: 13 mM

14121086420

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Fe - C - H2O - System at 25.00 CEh (Volts)

Fe2O3

Fe3O4

Fe(OH)2

Fe(+3a)

Fe(+2a) FeOH(+a)

CO2: 0.1 barFe: 1 µMTIC: 13 mM

14121086420

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0

Fe - C - H2O - System at 25.00 CEh (Volts)

FeCO3

Fe2O3

Fe3O4

Fe(OH)2

Fe(+3a)

Fe(+2a)

CO2: 0.1 barFe: 0.1 MTIC: 13 mM

pH

pH

pH

a

b

c

Fig. 2 The phase diagrams showing the pH–Eh condition for siderite

precipitation in seawater at - 0.1 bar pCO2 level in atmosphere

780 Acta Geochim (2019) 38(6):775–784

123

0.1

1.0

10.0

100.0

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Ωsi

derit

e

pH

1050

250

10001000Siderite

Fe2SiO40.1 bar

0.1

1.0

10.0

100.0

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Ωsi

derit

e

pH

10

50

250

1000

250Siderite

UCC0.1 bar

0.1

1.0

10.0

100.0

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Ωsi

derit

e

pH

1025

100

250

Siderite

Fe2SiO40.01 bar 0.1

1.0

10.0

100.0

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Ωsi

derit

e

pH

10

25

100

250

100Siderite

UCC0.01 bar

0.1

1.0

10.0

100.0

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Ωsi

derit

e

pH

5

10

50

100100Siderite

Fe2SiO40.001 bar

0.10

1.00

10.00

100.00

3.0 4.0 5.0 6.0 7.0 8.0 9.0

Ωsi

derit

e

pH

5

10

50

10Siderite

UCC0.001 bar

100

a b

c d

e f

Fig. 3 The modeling results showing siderite precipitation in paleosols at various atmospheric CO2 level. The contour lines represent different

volume mixing ratio between fresh water and dissolve silicates. UCC upper continental crust. The yellow shadowed area indicates siderite

precipitation

Acta Geochim (2019) 38(6):775–784 781

123

5 Conclusions

Our study suggests that the FYS paradox could be resolved

by the ocean–atmosphere coupling, in which high atmo-

spheric CO2 level could be sustained by low seawater pH,

which was favored by intense reverse weathering in the

silica saturated ocean. High atmospheric CO2 level is not

inconsistent with the absence of siderite deposition in

Archean paleosols. We suggest that siderite precipitation in

paleosols was not controlled by atmospheric CO2 level

alone, and thus cannot be used to reconstruct CO2 content

in the atmosphere. Although the new model explains how

high CO2 level could be sustained in the atmosphere, we

make no inference about the concentration of other

greenhouse gases. More importantly, our model implies

that the emergence of the ocean and the early coupling of

the ocean–atmosphere system would be paramount for the

subsequent evolution of habitability. Finally, this model

might be applied to other planets, such as mars, where

liquid water might have been present, although it receives

even less solar radiation in the distant past.

Acknowledgements This work is supported by the National Natural

Science Foundation of China (Grant Number 41772359).

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