Snowball Earth at low solar luminosity prevented by the oceanatmosphere coupling

Ruimin Wang·Bing Shen

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 controversy is collectively known as the‘Faint Young Sun’(FYS)paradox.Though various models have been proposed,the FYS paradox has not yet been resolved.In this study,we develop a model by considering the ocean–atmosphere 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 precipitate 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 systems,and thus the emergence of the ocean in the very beginning of Earth evolution might be the key to the subsequence 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 CO2level 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 ocean.In addition,geochemical data indicate that liquid water on the Earth might be traced back to Hadean,predating the late heavy bombardment at 4.0–3.9 Ga(Kring and Cohen 2002).High oxygen isotope values of the earliest 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 geological 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 luminosity 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 longwave 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 compensated by enhancing the greenhouse effect in the atmosphere.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 CO2might be the major greenhouse gas in the early Earth.The climate model indicates that 0.01–0.1 bar CO2in Archean and Hadean atmosphere was sufficient to keep the global mean temperature(GMT)above the freezing point(273 K),while 0.1–0.5 bar CO2would elevate GMT to the present level of 288 K(von Paris et al.2008).However,a high atmospheric CO2level 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 CO2level.It is further suggested that,based on the study of paleosols,Archean atmospheric CO2level 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 NH3has a strong absorption band at ～10 μm, the peak of the blackbody radiation from the solid Earth (Sagan and Mullen 1972).However,NH3is subject to photochemical decomposition by solar ultraviolet radiation,resulting in a short lifetime(＜10 years)in the atmosphere.High NH3flux is required to maintain the high NH3concentration in the atmosphere.However,the terrestrial supply of NH3was not sufficient to resolve the FYS paradox(Kasting 1982),and accordingly,NH3may not be the major greenhouse gas in the early Earth.

CH4has also been regarded as the possible,probably most likely,greenhouse gas in early Earth.But high CH4concentration,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 CO2level was kept at 0.01 bar(Hessler et al.2004),CH4content should be less than 1000 ppmv.The modeling result indicates that 0.01 bar CO2mixed with 100–1000 ppmv CH4would be sufficient to compensate the low solar radiation and prevent the snowball Earth condition(Kasting 2005).

High atmospheric CH4level requires either high CH4flux or slow rate of CH4degradation. CH4could 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 photolysis of H2O(Pavlov et al.2001).The formation of ozone since 2.4 Ga would further enhance CH4decomposition 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 CH4photolysis.Thus,CH4decomposition is sensitive to O2level in the atmosphere(Kasting 2005).The modeling results indicate that,in order to keep 100 ppmv CH4concentration at 0.01 PAL pO2level,CH4flux should be 10 times larger than the present level(Kasting 2005).It should be noted that further reduction of O2level would enhance CH4degradation by UV radiation,requiring even high CH4flux.Therefore,a minimum flux of 6400 Tg/yr is required to sustain 100 ppmv CH4in the atmosphere with ＜0.01 PAL O2level.

There are three CH4sources. It is estimated that cometary impacts might provide 500 and 5000 Tg/yr CH4at 3.5 and 3.8 Ga,respectively(Kress and McKay 2004),but a much smaller extraterrestrial input of 20 Tg/yr CH4is 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 CH4emission 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 CH4production by methanogens accounts for more than 90%CH4flux at present,but biogenic CH4flux 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 CH4to sustain high atmosphere CH4concentration in Archean.Nevertheless,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 CH4input could not sustain high CH4content 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 CO2was the major greenhouse gas in Archean,and explore(1)how high atmospheric CO2level could be maintained,and(2)how high CO2level and paleosol data could be reconciled.

3 Quantifying early Earth atmospheric CO2 level by the ocean-atmosphere coupling model

Unlike other greenhouse gases,CO2will not be decomposed by photolysis regardless of O2level in the atmosphere. The atmospheric CO2level is controlled by volcanic degassing(Fvol)and CO2consumptions in surface Earth(Fsink).Change of atmospheric CO2level[expressed as CO2partial pressure,p（CO2）]through time can be expressed by the following equation:

where Matmis the mass of the atmosphere.High p（CO2）implies either high volcanic degassing and/or low rate of CO2consumption (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 CO2degassing 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 CO2sink(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:

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 CO2level,precipitation(rainfall)and temperature,while the global flux of CO2removal via continental weathering is also controlled by the area of exposed continents.It is widely accepted that the size of the continent was significantly smaller than that of today(Kroner 1985),and thus the rate of CO2removal by chemical weathering might be smaller in Archean.

CO2is also removed by organic matter production and burial,which accounts for ～20%of CO2burial in present-day(Kump and Arthur 1999).Although organic carbon 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(Falkowski et al.1998).

It is widely accepted that the primary productivity was smallin the early Earth,i.e.a small organic carbon sink.Assuming asteady-state with=0,we willhave the following equation:

where Rcwis the reaction rate constant of continental weathering,which is a function of e.g.precipitation and temperature.Scontis the area of exposed continents,and Forgis the size of the organic carbon sink.Rearranging Eq.(5),the atmospheric CO2level can be expressed as:

Equation(6)indicates that high atmospheric CO2level 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.Rcwor Forg,p （CO2）cannot be quantified by Eq.(6).

Another way to estimate the atmospheric CO2level is to consider the coupling between the atmosphere and ocean systems.In the ocean–atmosphere system,atmospheric CO2is dissolved into seawater,then followed by dissociation of dissolved CO2to aqueous inorganic carbon species.

When the ocean–atmosphere system is in equilibrium,the relationship between p （CO2）and seawater dissolved inorganic carbon(DIC)can be derived from Eqs.(7)–(9),and can be expressed by the following equation:

k1and k2are the first and second-order dissociation constants of carbonic acid,respectively,while HCO2is the Henry’s constant for CO2dissolution in seawater.Equation(10)indicates that p（CO2）is positively linear correlation with seawater concentration of CO32-and the square of［H+］,i.e.with an increase of seawater pH(-log（［H+］）),p （CO2）will drop,and vice versa.Thus,given known seawater pH andorp（ CO2） can be calculated.

where Ωcalis the degree of supersaturation with respect to Ca-carbonate,and kspis the constant of solubility product.In the modern ocean,Ωcalis 5 but inorganic carbonate precipitation is kinetically inhibited by nucleation that requires higher Ωcal(Higgins et al.,2009).It is proposed that inorganic carbonate precipitation requires Ωcalof 10(Arp et al.2001).Combining Eqs.(10)and(11),we arrive at the following relationship:

Thus,p （CO2）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 weathering reactions include:

From Eqs.(13)and(14),it shows that reverse weathering 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 unsaturated with respect to opal due to effective scavenge of seawater silica by silica-secreting organisms,such as diatoms,siliceous sponges,and radiolarians(Tre′guer 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 saturation 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 （CO2）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).

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(Ωcal=10)with respect to calcite

4 What can siderite tell us?

The high atmospheric CO2level 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 equilibrium between siderite and Fe-silicate minerals,it is proposed that high atmospheric CO2level would result in siderite precipitation. Further based on the study of Archean paleosols,the estimated p （CO2）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 paleosols,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 （CO2）at 0.1 bar,Ωcalof 10,and seawater pH of 6.8–7.2(Isson and Planavsky 2018),i.e.seawater DIC concentration of 13 mM,siderite precipitation 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 seawater concentration of dissolved Fe2+implies low pO2level in Archean(Fig.2),which is consistent with widespread detrital pyrite and uraninite in Archean sediments(Holland 1984;Rasmussen and Buick 1999).This conclusion is also in accordance with the mass-independent fractionation in sulfur isotope(Farquhar et al.2000;Farquhar and Wing 2003),implying the atmospheric pO2level was lower than 10-5PAL(Kasting 2001;Pavlov and Kasting 2002).Therefore,widespread marine siderite precipitation is mainly controlled by atmospheric O2level and seawater Fe2+concentration rather than CO2level in the atmosphere.

For siderite precipitation in paleosols,in fact,modern soil contains both authigenic clays and authigenic carbonate,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 CO2level 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 CO2level,and vice versa.

Fig.2 The phase diagrams showing the pH–Eh condition for siderite precipitation in seawater at-0.1 bar pCO2 level in atmosphere

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 (Fe2+［ ］) from which siderite precipitates can be expressed by the following equation:

where αHRis the Fe concentration in bedrock,μ is the freshwater dilution factor,referring to the volume ratio between freshwater and dissolved silicate minerals.Whether siderite could precipitate is determined by the saturation of solution(Ωsiderite),which can be expressed by the following equation:

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 composition would affect Fe2+［ ］.We assume siderite precipitation at Ωsiderite=10 and at pH between 6.8 and 7.2.At 0.1 bar p（CO2）,siderite precipitation requires μ ＜250 for paleosols 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)p（CO2）,the upper bound of μ decreased to 100 and 25 for bedrock with the Fe-olivine or UCC composition, respectively (Fig.3c, d). Further decrease p（CO2）to 0.001 bar(i.e.3 PAL),in order to precipitate siderite,μ should be ＜50 and ＜5 for the Feolivine and UCC composition bedrock, respectively(Fig.3e,f).

The modeling results indicate that with a decrease of atmospheric CO2level,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 conditions(Amundson et al.2003).Furthermore,our study indicates that the atmospheric CO2level is not the only control of siderite precipitation.Siderite could precipitate from a wide range of p（CO2）(0.1–0.01 bar),given sufficient Fe2+supply and suitable humidity,i.e.smaller μ.In this case,siderite in paleosols may not be used to quantify the atmospheric CO2level.

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

5 Conclusions

Our study suggests that the FYS paradox could be resolved by the ocean–atmosphere coupling,in which high atmospheric CO2level could be sustained by low seawater pH,which was favored by intense reverse weathering in the silica saturated ocean.High atmospheric CO2level is not inconsistent with the absence of siderite deposition in Archean paleosols.We suggest that siderite precipitation in paleosols was not controlled by atmospheric CO2level alone,and thus cannot be used to reconstruct CO2content in the atmosphere.Although the new model explains how high CO2level 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).