ARTICLES

Snowball Earth prevention by dissolvedorganic carbon remineralizationW. Richard Peltier1, Yonggang Liu1 & John W. Crowley1

The ‘snowball Earth’ hypothesis posits the occurrence of a sequence of glaciations in the Earth’s history sufficiently deep thatphotosynthetic activity was essentially arrested. Because the time interval during which these events are believed to haveoccurred immediately preceded the Cambrian explosion of life, the issue as to whether such snowball states actuallydeveloped has important implications for our understanding of evolutionary biology. Here we couple an explicit model ofthe Neoproterozoic carbon cycle to a model of the physical climate system. We show that the drawdown of atmosphericoxygen into the ocean, as surface temperatures decline, operates so as to increase the rate of remineralization of a massivepool of dissolved organic carbon. This leads directly to an increase of atmospheric carbon dioxide, enhanced greenhousewarming of the surface of the Earth, and the prevention of a snowball state.

During the Neoproterozoic era of the Earth’s history, the carboncycle exhibited a sequence of oscillation-like variations that includeddecreases of d13C to levels that have been interpreted to imply theoccurrence of intense snowball glaciations1 during which photosyn-thetic activity essentially ceased2–4. Such events would have stronglyaffected the evolution of eukaryotic life and this has led to suggestionsthat this extreme interpretation of the observed variability in thecarbon cycle could be unwarranted5,6. We have developed a coupledmodel of the co-evolution of Neoproterozoic climate and the carboncycle that provides an alternative interpretation to the ‘hard snow-ball’ hypothesis of the origin of the observed d13C variations. Thismodel links a previously developed model of the Neoproterozoicphysical climate system7,8 to a recently developed model of the carboncycle9 for the same time interval. The coupled model is shown tosupport a limit cycle oscillation in which the temperature depen-dence of the solubility of oxygen in sea water controls the rate ofremineralization of organic carbon such that the level of atmo-spheric CO2 is prevented from becoming sufficiently low to allow ahard snowball state to occur. The model also satisfies the timescaleand continental ice volume constraints that have been inferred tocharacterize these glaciation events, as well as the magnitude of thecarbon cycle excursions when an appropriate biogeochemicaldependence of photosynthetic carbon isotopic fractionation isassumed.

The sequence of intense glaciations that occurred during theCryogenian period of the Neoproterozoic era—a period that beganapproximately 850 million years (Myr) ago and which endedapproximately 635 Myr ago with the onset of the Ediacaranperiod—is currently an intense focus of interdisciplinary activity10.Evolutionary biologists and palaeontologists11,12 are interested in thisera because it preceded the Cambrian explosion of life, during whicheukaryotic biological diversity proliferated. Climate dynamicists13–18

have been attracted by the challenge posed by the appearance in thegeological record of continental-scale glaciation that is suggested tohave reached sea level in equatorial latitudes at some locations.Sedimentologists19–21 and geochronologists22 have worked on theglobal-scale correlation of glacial units across the present-day con-tinents, during a time of intense tectonic activity involving the break-up of the supercontinent of Rodinia. However, many important

questions are still unresolved. In particular, how many glaciationsactually occurred during the Cryogenian period is currently uncer-tain. Figure 1, a revised and extended version of previously publishedsketches23–25 of the evolution of d13C over the most recent billionyears of the Earth’s history, illustrates the connection in time betweenthis measure of climate variability, major tectonic events, and periodsof intense glaciation.

The nature of Cryogenian glacial episodes

Although some recent work has championed the notion that onlythree major glaciations occurred during this period23—the Sturtianglaciation at 723z16

{10 Myr ago, the Marinoan glaciation between 659and 637 Myr ago, and the Gaskiers glaciation at approximately582 Myr ago—there remain significant issues concerning the syn-chroneity of these events as inferred on the basis of the stratigraphicrecord from different continents. The chronological control upon theSturtian glaciation, in particular, now suggests that it consisted of atleast two distinct glacial episodes22. Evidence from the HuqfSupergroup of Oman has recently been interpreted to imply thatno hard snowball glaciation event could have occurred19–21.Similarly, the duration of individual glacial episodes remainsunknown (although it has been speculated to be between 4 and 30million years4), as is the answer to the question of whether each of theglacial episodes consisted of a single ice advance and retreat or ofmultiple such events.

A previously proposed model of Neoproterozoic climate suggestedthe plausibility of a ‘‘slushball’’ solution in which a significant regionof open water could have persisted at the Equator during each ofthese events. This model has been criticized26 on the basis of the claimthat it could not explain the inferred requirement of the geologicalrecord for the occurrence of episodes of glaciation that lasted at least4 Myr. This is the point of departure for the analyses described in thispaper. Our target has been the question posed by the carbon isotopicvariability depicted qualitatively in Fig. 1. Whereas subsequent to theNeoproterozoic era the carbon cycle appears to have been operatingin a quasi-equilibrium mode9, during the Neoproterozoic it appearsto have been operating in an out-of-equilibrium mode that is pecu-liar to this interval of the Earth’s history. This mode of behaviour wasrecently suggested9 to have arisen as a consequence of a significant

1Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada.

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imbalance between the mass of carbon stored in the Neoproterozoicocean in the organic and inorganic forms. Atmospheric oxygen couldhave provided an important link between the carbon cycle and cli-mate but no detailed discussion was provided9. The purpose of theanalyses reported here is to elaborate a plausible linkage and toinvestigate the extent to which this may shed light upon the stateof the Earth’s physical climate system during this critical period forbiological evolution.

Coupled carbon cycle–climate evolution

A schematic of the model we have developed for this purpose isshown in Fig. 2, consisting of three primary elements: a model ofthe carbon cycle9, a model of the physical climate system (consistingof surface energy balance and sea-ice components8), and a detailedmodel of continental-scale glaciation (the University of TorontoGlacial Systems Model; ref. 27). The mathematical details of thecarbon cycle component of the complete coupled model, whichinvolve a significant extension of the model of ref. 9, are describedin the Supplementary Information). To link these models we expli-citly incorporated a dependence of the remineralization flux J21

(Fig. 2), through which organic carbon is converted to inorganiccarbon, upon the (temperature-dependent) solubility of oxygen insea water:

J21~J21e1{F21(T{Te)½ � ð1Þ

In this expression, T is the mean surface temperature of the planetdetermined by the physical climate model and Te is the equilibriumtemperature at which the remineralization flux J21 equals its equi-librium value. For a discussion of the physical significance of the

control parameter F21, please see Methods. A primary assumptionof the present version of the model is that the variations in

Late Quaternaryglacial era

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of Pangaea

Bitter S

pringsstage

Trezonaanom

aly

Mai eberg

anomaly

Figure 1 | The history of d13Cinorg variations over the past billion years asmeasured in sequences of carbonate rocks on land. This quantity providesan indirect measure of photosynthetic activity. High values correspond totimes of high rates of burial of organic matter, a consequence of the fact thatisotopically light carbon (12C) is preferentially partitioned into organic matterby photosynthesis. Burial of this matter leaves behind an ocean that isisotopically heavier than average, from which the carbonates are precipitated.The Neoproterozoic era was clearly characterized by extreme variability ind13Cinorg. The largest-amplitude negative anomaly that is inferred to haveexisted during the Neoproterozoic is the Shuram anomaly35, which is taken tocorrespond to the major oxidation event that eliminated the condition

required for out-of-equilibrium behaviour of the carbon cycle, namely theextreme imbalance between the masses of the inorganic and organicreservoirs. This figure is a modified version of those originally produced byKaufman2 (Fig. 2), Eyles and Januszczak25 (Fig. 9) and Halverson et al.23

(observational data used with permission). The data presented through theCryogenian interval are based upon the recently compiled composite record ofref. 23 and are reproduced here with permission. The diamond-shapedsymbols represent the times for which high-quality radiometric agedeterminations (based on the U–Pb dating of detrital zircons) are available toprovide chronological control on the sequence of Neoproterozoic events.VPDB, Vienna Pee-Dee belemnite standard.

1 2

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δ1 – ε0

δ2, τ2δ1, τ1

b1

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CO2 O2Atmosphere/cryosphere–EBM

Inorganic Ocean Organic

Figure 2 | Diagram of our carbon-cycle-coupled climate model. Its primarycomponent consists of the box model of the carbon cycle of Rothman et al.9,which is coupled to both an energy balance model of the atmosphere (EBM)and the University of Toronto Glacial Systems Model of continental-scaleice-sheet evolution. The variables d1,2 and t1,2 are the isotopic compositionsand residence times for the inorganic and organic carbon reservoirs,respectively. di is the input into the inorganic reservoir from, for example,volcanic outgassing (of flux Ji) and e0 is the isotopic fractionation that occursin photosynthesis during which inorganic carbon is converted into organiccarbon. Fluxes into and out of the two reservoirs are represented by thearrows. Output from the two reservoirs occurs directly by burial (associatedwith fluxes b1,2) as well as by exchanges between them. Crucial to the successof our coupled model of carbon-cycle-climate evolution are the fluxes of O2

and CO2 between the atmosphere and ocean components of the model.

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atmospheric oxygen that accompany system evolution will have nosignificant impact upon system dynamics.

The reason that the temperature dependence of the remineraliza-tion flux has important implications for the surface climate regime isconnected to the fact that as the climate cools and the rate of con-version of organic carbon to inorganic carbon increases, the partialpressure of carbon dioxide in the atmosphere also increases, accord-ing to the relation:

pCO2(t)

pCO2, e

~M1 tð ÞM1e

� �X

ð2Þ

in which pCO2, e 5 300 p.p.m.v. is the equilibrium concentration ofatmospheric carbon dioxide at temperature Te, M1 is the mass ofinorganic carbon in the ocean and M1e

is the equilibrium mass. Ithas been suggested28 that the parameter X in equation (2) should beequal to 2 in Phanerozoic circumstances in which the climate is notchanging too quickly. It is unclear whether the partition of carbondioxide between the ocean and the atmosphere during the rapidlychanging Neoproterozoic should obey this relationship, so we con-sider X to be a parameter of the model. As the level of atmospheric CO2

increases in response to increasing M1(t), the surface of the planet willbe increasingly heated by the increasing infrared flux of energy drad (inunits of W m22) that is due to ‘greenhouse’ warming29,30:

drad~6:0 lnpCO2

(t)

pCO2, e

� �ð3Þ

The sequence of relationships (1) to (3) together describe a nega-tive feedback process whereby the carbon cycle reacts to a tendency ofthe planet to cool by enhancing the atmospheric concentration ofcarbon dioxide and thus inhibiting the cooling. During warming thesame feedback operates so as to inhibit this tendency as well. The newcoupled model of carbon cycle–climate evolution that we havedeveloped for the Neoproterozoic is strongly controlled by this feed-back process.

Cyclic glaciation due to carbon cycle coupling

In the absence of explicit coupling to the carbon cycle, the ice-sheet-coupled energy-balance model of the process of global glaciation

produces steady-state solutions for the mean surface temperaturethat are a strong function of the concentration of carbon dioxidein the atmosphere, of the solar constant, and of the spatial distri-bution of the continents. Although the detailed palaeogeography ofthe Neoproterozoic varied appreciably during the break-up ofRodinia, there is general agreement that during the Sturtian epi-sode(s) the continental fragments were clustered around theEquator. During the Marinoan episode, however, the equatorialpositioning of the main land masses was apparently less pronounced.Here we use the same palaeogeography as was used in a previousanalysis7 of Neoproterozoic surface temperature conditions, one thatis more appropriate to the Marinoan glaciation than to theSturtian(s). For the value of the solar constant we assume a decreaseof 6% below the present value, as is appropriate to this stage of theevolution of the Sun.

In the absence of carbon cycle coupling, Fig. 3a shows the steady-state variations of mean surface temperature predicted by the ice-sheet-coupled EBM, as a function of atmospheric carbon dioxideconcentration. This model exhibits hysteresis, such that a range ofvalues of the parameter drad, and thus pCO2

, exists within which atleast two different steady states are equally acceptable solutions.Which state is physically realized depends upon the initial conditionsof integration from which the solution is approached, as indicated bythe arrows on the different branches of the diagram of steady-statesolutions. The hysteresis diagram defines a ‘hot branch’ of solutionsas well as an ‘oasis branch’, the latter being the branch on which the‘slushball’ solutions to the problem of Neoproterozoic climate wereoriginally discovered8. In this model the hard snowball solutionregime also exists, but to reach it requires that pCO2

(t) reaches suffi-ciently low values. To escape from the hard snowball state in thismodel requires approximately 0.3 bar of atmospheric carbon dioxideif the sea-ice albedo is assumed to be equal to 0.6 in the hard snowballregime7. This is somewhat lower than a more accurate estimate laterobtained with a more complex model31. Here we investigate how theclimate model will behave when coupled to the explicit model of thecarbon cycle.

The results delivered by this model in fully coupled synchronousmode are illustrated in Figs 3b–e, for which examples we haveassumed X 5 2 in equation (2). Figure 3b shows several cycles of

10

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Figure 3 | The cyclic glaciation dynamics of the coupled climate–carboncycle model. a, The steady-state (equilibrium) solutions of the energy-balance-coupled ice-sheet model are shown as a function of the atmosphericcarbon dioxide concentration, represented by the increase or decrease of theinfrared flux, drad, received at the surface. The hysteresis in the model statespace is indicated by the multiple equilibria for a wide range of values of thecarbon dioxide concentration. b, The trajectory of solutions of the coupledclimate–carbon cycle model in the space of mean surface temperature versus

surface infrared forcing. The solution simply cycles the hysteresis loop of thesteady-state solutions when the impact of the temperature dependence of thesolubility of oxygen upon the remineralization flux is introduced into thedynamical system. c–e, Time series for sea-ice area, atmospheric carbondioxide concentration and land-ice volume are shown, respectively, forseveral circuits of the hysteresis loop. The scale of the x axis depends on thecontrol parameter F21, as demonstrated in Fig. 4.

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the ‘orbit’ of the solution in the plane of mean surface temperatureversus drad. These results demonstrate that the coupled systemevolves in such a way as to continuously cycle the hysteresis loopdefined by the set of steady-state solutions. In Figs 3c–e we show timeseries for sea-ice area, atmospheric CO2 and continental ice volumerespectively, for several circuits of the hysteresis loop. These resultsdemonstrate that system evolution is governed by a limit cycle oscil-lation (a periodic solution of the nonlinear dynamical system) whichwould have a period of approximately 4 Myr for F21 5 8 3 1025 anda period of approximately 30 Myr for F21 5 1 3 1025. Detailed ana-lysis (not shown) demonstrates that the onset of the periodic beha-viour for X 5 1 occurs for F21 , F21, crit, where the critical value is inthe range 5 3 1024 , F21, crit , 6 3 1024. For values less than this, theperiod of the limit cycle oscillation continues to increase as the valueof the control variable decreases. For X 5 2, the critical value of F21 isshifted to the range 3 3 1024 , F21, crit , 4 3 1024.

Figure 4, based upon analyses for several values of the control para-meter, for which time series are shown in Supplementary Fig. 1 (forX 5 1) and Supplementary Fig. 2 (for X 5 2), shows that the period ofthe limit cycle covers the previously inferred range of durations of theNeoproterozoic glacial intervals from 4 to ,30 Myr ago. In the limitF21R0, the previous model9 is recovered and the system exhibits nodynamics, as physical climate is now uncoupled from the carbon cycle.For F21 . F21, crit, the system exits the limit cycle regime (seeSupplementary Fig. 1 for F21 5 6 3 1024) and a new steady-state solu-tion is realized, one for which the mean surface temperature is equal tothe value Te (not shown). We interpret this ‘fixed point’ to representthe in-equilibrium solution for the carbon cycle that has apparentlybeen characteristic for the Phanerozoic eon that followed theNeoproterozoic with the onset of the Cambrian. The model thereforeembodies a potential explanation not only of the apparently out-of-equilibrium behaviour characteristic of the Neoproterozoic, but alsoof the in-equilibrium behaviour that has thereafter generally been therule9. Supplementary Fig. 3 shows normalized time series for all modelfields as a means of illustrating the phase relationships between them.

Eustatic sea level and ice volume variations

Figure 5 shows the distribution of land ice and sea ice over the surfaceof the Earth that the model delivers at each of the corners (labelled I toIV on Fig. 3a) of the hysteresis loop of steady solutions onto which thesolution is entrained in the time-dependent limit cycle regime. Thisregime is essentially perfectly periodic, so this set of four solutions fullycharacterizes the extremes of system behaviour. The low-temperature,

low-carbon dioxide corner of the loop (located at III in Fig. 3a) showsthat although most of the continental fragments are covered by a thickveneer of land ice and much of the surface of the ocean is covered by seaice, there is still a substantial area of the equatorial ocean that consistsof open water. This is the ‘slushball’ regime discovered previously8. Themaximum volume of land ice that develops during a single glacial cycleis approximately 500 3 106 km3, as shown on Fig. 3e, which wouldcorrespond to a fall of eustatic sea level of approximately 1 km, a resultthat could be interpreted as consistent with the deep Neoproterozoiccanyons that have been investigated on the Australian continent32,33.Although much larger, this sea-level depression is still reasonable com-pared to the sea-level drop of about 120 m that occurred during theLast Glacial Maximum34, when polar ice sheets covered only a smallfraction of the land surface.

We therefore interpret the Cryogenian period as a time duringwhich, in an organic-carbon-rich environment, the mass of organicmatter in the Neoproterozoic ocean had reached such a large valuerelative to the mass of inorganic carbon that out-of-equilibriumbehaviour with strong coupling to the physical climate systembecame possible. In our interpretation, this coupling ceased to bepossible after the intense oxidation of the organic reservoir thatoccurred towards the end of the Ediacaran period and just beforethe onset of the Cambrian22. We interpret this oxidation event ascoinciding with the Shuram anomaly shown on Fig. 135.

The isotopic variability of inorganic carbon

The model also predicts the time series of d13C(t) for the inorganicreservoir, the primary diagnostic that has been taken to require theexistence of the hard snowball regime. Escape from this regime isassumed to have been possible only via the build-up of the atmo-spheric carbon dioxide concentration owing to the presumed slowand continuous action of volcanic degassing while the oceans wereentirely covered by sea ice. To make contact with the different iso-topic concentrations of organic and inorganic carbon that developduring a single glacial cycle, the isotopic fractionation e0 that occursduring photosynthesis (see Fig. 2) must also depend upon oceanbiogeochemistry, and thus climate. To predict the evolution of car-bon isotopes we may therefore assume:

e0~eezbfrac, M(M1 CO2(t)½ �{M1e) ð4Þ

This representation of the isotopic fractionation that occurs dur-ing photosynthesis is intended to provide a parameterization of the

0 1 2 3 4 50

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Per

iod

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he g

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Figure 4 | The period of the glacial cycle predicted by the coupledclimate–carbon cycle model as a function of the control parameter of themodel F21. Results are shown for both X 5 1(solid line) and X 5 2 (dashedline), where X determines how the atmospheric carbon dioxide concentrationchanges as the mass of inorganic carbon changes relative to the referencevalues (equation (2)). The predicted period spans the range previouslyinferred to have been characteristic of Neoproterozoic glacial intervals.

II I

III IV

Land ice thickness (km)

0.5 1.5 2.5 3.5 4.5 5.5 6.5

Figure 5 | Examples of the distribution of land ice and sea ice during theglacial cycle. These examples correspond to the climate states occupied bythe model at each of the four corners (labelled I to IV) of the hysteresis loopof steady solutions shown on Fig. 3a. Irrespective of the value of the controlparameter, in the coupled mode the dynamical system simply continues tocycle the hysteresis loop. Land-ice thickness is contoured in shades of mauve,and sea ice is shown as white.

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influence of kinetic isotope effects associated, say, with the enzyma-tically catalysed carboxylation of ribose bisphosphate (J. M. Hayes,personal communication, 2006). The mass of the inorganic reservoirM1 is expected to provide a reasonably direct representation of themain control on this catalytic process. This simple parameterizationappears to be in acceptable accord with the analyses of ref. 36 as usedin the discussion28 of the dependence of the isotopic differencebetween organic and inorganic carbon as a function of atmosphericpCO2

. Best fits of the model prediction of the time variation of d13C(t)through a typical Neoproterozoic glacial–interglacial cycle basedupon the use of equation (4) are obtained with a value of bfrac,M <0.00048% per gigaton. This value is not unreasonable given that thespecies composition of the hypothesized organic-carbon-heavyNeoproterozoic ocean, in which M2?M1, is largely unknown.

Figure 6a for X 5 2 shows the model prediction of the evolutionof d13Cinorg as a function of e 5 d1 2 d2, through a singleNeoproterozoic glacial–interglacial cycle, compared with the com-plete data set from ref. 9, inspection of which demonstrates the goodfit that the model is capable of delivering to the data. When thecomparison is limited to the interval of time from 738 to 593 Myrago that contains the Sturtian and Marinoan events (Fig. 6b), how-ever, the fit of the model to the data significantly improves. Thisdemonstrates that the carbon isotopic measurements from the inter-val containing the hypothesized hard snowball events are wellexplained by the carbon-cycle-coupled slushball model. As discussedin ref. 9, the slope of the model fit to the data in the d13Cinorg versus eplane is unity, which is highly diagnostic of the condition M2 ?M1

that is characteristic of the carbon cycle component of the model.Supplementary Fig. 4 shows equivalent results for the case X 5 1.

Future model developments

Among several further avenues of investigation as we continue todevelop this model of the coupled evolution of the carbon cycle andclimate during the Neoproterozoic, one we intend to explore concernsthe potential of the model as an explicit means of assessing the mag-nitude of the variations of atmospheric oxygen that would be expectedto accompany the glaciation–deglaciation process. Another concernswhether oxidants other than oxygen, such as sulphate, may have animportant role to play. Also, how might the drawdown of atmosphericcarbon dioxide from the atmosphere due to the weathering of calciumand magnesium silicates be expected to affect our model predictions16?Here we neglected this drawdown because of the strong temperatureand precipitation dependence that is characteristic of the silicateweathering process, such that low temperature and precipitationand the absence of vascular plants in this period of the Earth’s historywould have significantly reduced its effect37–39. In spite of this and otherremaining uncertainties, the new model strongly suggests that those

observations that have been assumed to be most diagnostic of hardsnowball conditions may not require such an extreme interpretation.In our view it is more likely that it may have been the carbon cycle, notthe physical climate system, that was operating in an extreme modebefore the onset of the Cambrian explosion of life.

METHODS SUMMARY

Our model consists of three primary components. (1) A global surface energy

balance model in spherical geometry with a specified distribution of continents

and ocean coupled to a simple thermodynamic model of sea-ice formation. This

element of the structure is time-dependent and may be subjected to orbital

insolation variations. It also resolves the annual cycle of surface temperature.

(2) A detailed model of the growth and evolution of continental ice sheets that

occurs in response to variations in the surface temperature and precipitation

regimes. In this model, precipitation forcing of the hydrological cycle is pre-

scribed. Furthermore, the glacial isostatic adjustment process that affects the

flow of ice over the surface of a continent under the action of the gravitational

force is fully incorporated. (3) A two-box model of the ocean carbon cycle that

differentiates between organic and inorganic reservoirs. Components (1) and (2)

are described in terms of coupled nonlinear partial differential equations

whereas the third component is described in terms of coupled nonlinear

ordinary differential equations. On the long timescales that are of interest to

us we may safely assume the concentration of carbon dioxide to be uniform

throughout the atmosphere at all times, because CO2 is a well-mixed atmo-

spheric trace gas. The three model components are coupled together throughthe action of an assumed temperature dependence of the remineralization flux

that converts organic carbon to its inorganic (CO2) form. The temperature

assumed to control the remineralization flux is taken to be the mean surface

temperature of the planet, a temperature that is dominated by the sea-surface

temperature of the tropical ocean.

Full Methods and any associated references are available in the online version ofthe paper at www.nature.com/nature.

Received 31 October 2006; accepted 1 October 2007.

1. Kirschvink, J. L. in The Proterozoic Biosphere: A Multi-Disciplinary Study (eds Schopf,J. W. & Klein, C.) 51–52 (Cambridge Univ. Press, Cambridge, UK, 1992).

2. Kaufman, A. J. An ice age in the tropics. Nature 386, 227–228 (1997).3. Hoffman, P. F., Kaufman, A. J., Halverson, G. P. & Schrag, D. P. A Neoproterozoic

Snowball Earth. Science 281, 1342–1346 (1998).4. Hoffman, P. F. & Schrag, D. P. The snowball Earth hypothesis: testing the limits of

global change. Terra Nova 14, 129–155 (2002).

5. Runnegar, B. Loophole for snowball Earth. Nature 405, 403–404 (2000).6. Knoll, A. H. Life on a Young Planet: The First Three Billion Years of Evolution on Earth

1–277 (Princeton Univ. Press, Princeton, New Jersey, 2003).7. Hyde, W. T., Crowley, T. J., Baum, S. K. & Peltier, W. R. Neoproterozoic ‘‘Snowball

Earth’’ simulations with a coupled climate/ice-sheet model. Nature 405,425–429 (2000).

8. Peltier, W. R., Tarasov, L., Vettoretti, G. & Solheim, L. P. in The Extreme Proterozoic:Geology, Geochemistry and Climate (eds Jenkins, G. S. et al.) Geophys. Monogr. Ser.,146, 107–124 (AGU Press, Washington DC, 2004).

9. Rothman, D. H., Hayes, J. M. & Summons, R. E. Dynamics of the Neoproterozoiccarbon cycle. Proc. Natl Acad. Sci. USA 100, 8124–8129 (2003).

10. Allen, P. A. Snowball Earth on trial. Eos 87, 495 (2006).11. Moczydlowska, M. Neoproterozoic and Cambrian successions deposited on the

east European platform and Cadomian basement area of Poland. Stud. Geophys.Geodaetica 39, 276–285 (1995).

12. Grey, K. & Corkoran, M. Late Neoproterozoic stromatolites in glacigenicsuccessions of the Kimberley region, Western Australia: evidence for a youngerMarinoan glaciation. Precambr. Res. 92, 65–87 (1998).

13. Chandler, M. A. & Sohl, L. E. Climate forcings and the initiation of low-latitude icesheets during the Neoproterozoic Varanger glacial interval. J. Geophys. Res. 105,20737–20756 (2000).

14. Goodman, J. C. & Pierrehumbert, R. T. Glacial flow of floating marine ice in‘‘Snowball Earth’’. J. Geophys. Res. 108, doi:10.1029/2002JC001471 (2003).

15. Poulsen, C. J. & Jacob, R. L. Factors that inhibit snowball Earth simulation.Paleoceanography 19, doi:10.1029/2004PA001056 (2004).

16. Donnadieu, Y., Godderis, Y., Ramstein, G., Nedelec, A. & Meert, J. A. ‘‘SnowballEarth’’ triggered by continental breakup through changes in runoff. Nature 428,303–306 (2004).

17. Pollard, D. & Kasting, J. F. Snowball Earth: a thin ice solution with flowing seaglaciers. J. Geophys. Res. 110, doi:10.1029/2004JC002525 (2005).

18. Pierrehumbert, R. T. Climate dynamics of a hard snowball Earth. J. Geophys. Res.110, doi:10.1029/2004JD0005162 (2005).

19. Leather, J., Allen, P. A., Brasier, M. D. & Cozzi, A. Neoproterozoic snowball Earthunder scrutiny: Evidence from the Fiq glaciation of Oman. Geology 30, 891–894(2002).

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ε (‰)20 3525 30

ε (‰)

Figure 6 | Model predictions of d13Cinorg(t) as a function of e(t) through asingle glacial cycle. These examples for the case X 5 2 are compared withobservations of contemporaneous samples of the isotopic ratios of organicand inorganic carbon at a large number of times through theNeoproterozoic. a, Comparison of all of the available data from Rothmanet al.9. b, The data derived from 738–593 Myr ago are shown separately andthe data points from the Sturtian and Marinoan intervals are singled out.

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20. Le Guerroue, E., Allen, P. A. & Cozzi, A. Chemostratigraphic and sedimentologicalframework of the largest negative carbon isotopic excursion in Earth history: TheNeoproterozoic Shuram formation (Nafun Group, Oman). Precambr. Res. 146,68–92 (2006).

21. Allen, P. A., Leather, J. & Brasier, M. D. The Neoproterozoic Fiq glaciation and itsaftermath: Huqf Supergroup of Oman. Basin Res. 16, 507–534 (2004).

22. Condon, D. et al. U-Pb ages from the Neoproterozoic Doushantuo formation,China. Science 308, 95–98 (2005).

23. Halverson, G. P., Hoffman, P. F., Schrag, D. P., Maloof, A. C. & Rice, A. H. N.Towards a Neoproterozoic composite carbon cycle isotopic record. Geol. Soc. Am.Bull. 117, 1181–1207 (2005).

24. Hoffman, P. F. & Schrag, D. P. Snowball Earth. Sci. Am. 282, 68–75 (2000).25. Eyles, N. & Januszczak, N. ‘‘Zipper-Rift’’: A tectonic model for Neoproterozoic

glaciations during the breakup of Rodinia after 750 Ma. Earth Sci. Rev. 65, 1–73(2004).

26. Schrag, D. P. & Hoffman, P. F. Life, geology, and snowball Earth. Nature 9, 306(2001).

27. Tarasov, L. & Peltier, W. R. Arctic freshwater forcing of the Younger-Dryas coldreversal. Nature 435, 662–665 (2005).

28. Kump, L. R. & Arthur, M. A. Interpreting carbon-isotope excursions: carbonatesand organic matter. Chem. Geol. 161, 181–198 (1999).

29. Ramanathan, V., Lian, M. S. & Cess, R. D. Increasing atmospheric CO2: zonal andseasonal estimates of the effect on the radiation energy balance and surfacetemperature. J. Geophys. Res. 84, 4949–4958 (1979).

30. Marshall, H. G., Walker, J. C. G. & Kuhn, W. R. Long-term climate change and thegeochemical cycle of carbon. J. Geophys. Res. 93, 791–801 (1988).

31. Pierrehumbert, R. T. High levels of atmospheric carbon dioxide necessary for thetermination of global glaciation. Nature 429, 646–649 (2004).

32. Christie-Blick, N., von der Borch, C. C. & Dibona, P. A. Working hypotheses for theorigin of the Wonoka canyons (Neoproterozoic), South Australia. Am. J. Sci. A290, 295–332 (1990).

33. Christie-Blick, N., Williams, G. E. & Gostin, V. A. Discussion on mantle plume upliftin the sedimentary record: Origin of kilometre-deep canyons within lateNeoproterozoic successions, South Australia. J. Geol. Soc. 158, 573–576 (2001).

34. Peltier, W. R. & Fairbanks, R. G. Global glacial ice volume and Last GlacialMaximum duration from an extended Barbados sea level record. Quat. Sci. Rev. 25,3322–3337 (2006).

35. Fike, D. A., Grotzinger, J. P., Pratt, L. M. & Summons, R. E. Oxidation of theEdiacaran ocean. Nature 444, 744–747 (2006).

36. Bidigare, R. R. et al. Consistent fractionation of 13C in nature and in the laboratory:growth-rate effects in some haptophyte algae. Glob. Biogeochem. Cycles 11,279–292 (1997).

37. Walker, J. C. G., Hays, P. B. & Kasting, J. F. A negative feedback mechanism for thelong term stabilization of earth’s surface temperature. J. Geophys. Res. 86,9776–9782 (1981).

38. Berner, R. A., Lasaga, A. C. & Garrels, R. M. The carbonate-silicate geochemicalcycle and its effect on atmospheric carbon dioxide over the past 100 million years.Am. J. Sci. 283, 641–683 (1983).

39. Berner, R. A. The Phanerozoic Carbon Cycle: CO2 and O2 1–150 (Oxford Univ. Press,Oxford, UK, 2004).

Supplementary Information is linked to the online version of the paper atwww.nature.com/nature.

Acknowledgements This paper is a contribution to the Polar Climate StabilityNetwork, which is sponsored by the Canadian Foundation for Climate andAtmospheric Science and a consortium of Canadian universities. Additionalassistance was provided by the Natural Sciences and Engineering Research Councilof Canada.

Author Information Reprints and permissions information is available atwww.nature.com/reprints. Correspondence and requests for materials should beaddressed to W.R.P. (peltier@atmosp.physics.utoronto.ca).

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METHODS

By far the most important aspect of the coupled carbon cycle–climate model that

we have developed concerns the feedback between temperature and the rate at

which organic carbon is remineralized to produce inorganic carbon, as expressed

in equation (1). This relationship is supported by the well-known dependence,

through Henry’s law of classical thermodynamics, of the solubility of a gas in a

liquid upon the temperature of the liquid. Garcia et al.40 provide detailed

information on the basis of which we justify a linear parameterization of the

solubility of oxygen in sea water:

O2, sol~O2, sole {A(T{Te) ð5ÞThis dependence is introduced into the carbon cycle model by assuming that

the remineralization flux J21 is itself linearly dependent upon the deviation of the

solubility of oxygen away from its value at an equilibrium temperature Te. An

appropriate modification of the equilibrium flux J21ethat incorporates this

dependence (see Supplementary Information) is:

J21~J21e1zB

O2, sol{O2, sole

O2, sole

� �� �ð6Þ

Incorporation of equation (5) into equation (6) then gives equation (1) in the

main text.

The primary control parameter in the new coupled carbon cycle–climate

model is therefore the parameter F21, which has the dimensions of inverse

temperature:

F21~AB

O2, sole

ð7Þ

In the low-temperature vicinity of 1 uC, A < 8 mmol kg21 uC21 (ref. 40) and

O2, sol < 400mmol kg21 (ref. 40). Thus F21 < 3 3 1024uC21 for B 5 1.5 3 1022

(the importance of this value of F21 is discussed in the main text). The strength

of the dependence of the remineralization flux upon oxygen solubility that is

determined by the parameter B is clearly affected by ocean dynamics, including

the strength of the overturning circulation that operates under glacial condi-

tions. Although some model experiments have been performed8,41 in an attempt

to estimate this strength, and it is generally agreed that the thermohaline cir-

culation will act in such a way as to inhibit descent into the hard snowball state,

thermohaline circulation behaviour during the Neoproterozoic must be consid-

ered ill-constrained at present. This requires that a range of values for the para-

meter F21 be considered. Additional inhibition to snowball Earth formation in

the actual climate system may derive from the action of the wind-driven circula-

tion15 and the detailed characteristics related to sea-ice formation in the

tropics14,15 where incoming solar radiation is especially intense. Such additional

processes have been fully incorporated in a recently published simulation8 of

Neoproterozoic climate that has been preformed using the NCAR CSM 1.4

model.

The ‘two box model’ of the carbon cycle that is assumed to respond to climate

variability in the way described by the above relationships is coupled to a global

energy balance model (EBM) that is itself coupled to a thermodynamic sea-ice

module and a detailed model of continental-scale glaciation. The global EBM is

based upon that of North et al.42 as modified by Deblonde et al.43 to include a sea-

ice component. Because carbon dioxide is a well-mixed trace gas, when an

increase of the remineralization flux occurs as a consequence of decreasing

temperature and the resulting increase in carbon dioxide dissolved in the ocean

is partly partitioned into the atmosphere, there is no need to consider atmo-spheric variations in the spatial distribution of this greenhouse gas.

The model of continental-scale glaciation is based upon the use of the stand-

ard Glen flow law for the rheology and the shallow-ice approximation for the

dynamics. Because the topography of the Neoproterozoic continents is

unknown, the ice cover on the individual continental fragments is assumed to

develop on continental masses with a fixed initial freeboard of 400 m. As ice flows

from the land to the sea under the action of the gravitational force, calving is

assumed to act so as to eliminate ice beyond the continental termini. Processes

such as fast flow which are strongly conditioned by basal hydrology and sediment

deformation are eliminated from the model we employed. The isostatic adjust-

ment process that acts to modify the surface elevation of the ice sheet and thus

affects the surface mass balance is incorporated by assuming the process to act in

a simple damped return-to-equilibrium fashion with an assumed relaxation

time of 4,000 years, in acceptable accord with that appropriate for the Earth’s

present-day radial viscoelastic structure44. This is expected to be an excellent

approximation because, although the rheology of the planetary interior is

strongly temperature-dependent, the temperature of the interior has not chan-

ged significantly since Neoproterozoic time45.The climate forcing that is assumed to drive the advances and retreats of

both continental ice sheets and sea-ice cover is obtained from the surface tem-

perature field delivered by the EBM, assuming an annually averaged precipita-

tion rate of ,0.7 m yr21, which is appropriately diminished owing to the action

of the elevation desert effect, which acts so as to reduce the precipitation rate in

regions of high topographic relief such as for continents covered by substantial

thicknesses of glacial ice. These assumptions are the same as those previously

employed in the application of this model to the climate of the Neoproterozoic7.

The physical climate component of the carbon-cycle-coupled model has been

thoroughly exercised in a number of recent analyses of climate variations

through the Phanerozoic eon46,47 and in spite of its modest degree of complexity,

compared well against expectations based upon the GEOCARB model48 of past

variations in atmospheric carbon dioxide.

40. Garcia, H. E. & Gordon, L. I. Oxygen solubility in sea water: Better fitting equations.Limnol. Oceanogr. 37, 1307–1312 (1992).

41. Poulsen, C. J., Pierrehumbert, R. T. & Jacob, R. L. Impact of ocean dynamics on thesimulation of the Neoproterozoic ‘‘snowball Earth’’. Geophys. Res. Lett. 28,doi:10.1029/2000GL012058 (2001).

42. North, G. R., Mengel, J. G. & Short, D. A. Simple energy balance model resolvingthe seasons and continents: application to the astronomical theory of the ice ages.J. Geophys. Res. 88, 6576–6586 (1983).

43. Deblonde, G., Peltier, W. R. & Hyde, W. T. Simulations of continental ice sheetgrowth over the last glacial-interglacial cycle: experiments with a one levelseasonal energy balance model including seasonal ice albedo feedback. Glob.Planet. Change 98, 37–55 (1992).

44. Peltier, W. R. Postglacial variations in the level of the sea: implications for climatedynamics and solid-earth geophysics. Rev. Geophys. 36, 603–689 (1998).

45. Butler, S. L., Peltier, W. R. & Costin, S. O. Numerical models of the earth’s thermalhistory: Effects of inner core solidification and core potassium. Phys. Earth Planet.Inter. 152, 22–42 (2005).

46. Hyde, W. T., Crowley, T. J., Tarasov, L. & Peltier, W. R. The Pangean ice-age:Studies with a coupled climate-ice sheet model. Clim. Dyn. 15, 619–629 (1999).

47. Hyde, W. T., Grossman, E. L., Crowley, T. J., Pollard, D. & Scotese, C. R. Siberianglaciation as a constraint on Permian-Carboniferous CO2 levels. Geology 34,421–424 (2006).

48. Berner, R. A. GEOCARBSULF: A combined model for Phanerozoic atmospheric O2

and CO2. Geochim. Cosmochim. Acta 70, 5653–5664 (2006).

doi:10.1038/nature06354

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