Modelling the global carbon cycle for the past and future evolution of the earth system

Chemical Geology 159 Ž1999. 305–317

Modelling the global carbon cycle for the past and future evolution of the earth system Siegfried Franck a

a,)

, Konrad Kossacki b, Christine Bounama

a

Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, D-14412 Potsdam, Germany b Warsaw UniÕersity, Institute of Geophysics, Pasteura 7, 02-093 Warsaw, Poland Received 4 November 1997; received in revised form 9 April 1998; accepted 15 June 1998

Abstract The Earth may be described as a global system consisting of the components solid Earth, hydrosphere, atmosphere, and biosphere. This system evolves under the external influence of increasing solar luminosity. In spite of this changing external forcing, the Earth’s climate has been stabilized by negative feedbacks against global freezing in the past Žfaint young Sun paradox.. The future long-term trend of further increasing solar luminosity will cause a further atmospheric CO 2 decrease. Atmospheric CO 2 will fall below the critical level for photosynthesis and the plant based biosphere will die out. In the present paper we propose a modelling study of the evolution of the carbon cycle from the Archaean to the planetary future. Our model is based on a paper published previously by Caldeira and Kasting wCaldeira, K., Kasting, J.F., 1992. The life span of the biosphere revisited. Nature 360, 721–723x. The difference of the current study with respect to this work resides in the forcing function used for the silicate weathering rate. While Caldeira and Kasting used a constant weathering rate over time, we calculate the time evolution of this rate by assuming a balance between the weathering flux and the CO 2 release flux by volcanism and metamorphism. We use the geodynamics theory to couple the two internal forcing functions continental area Žfor weathering. and spreading Žfor CO 2 release flux. which were generally considered as independent in previous models. This coupling introduces an additional feedback in the system. We find a warmer climate in the past and a shortening of the life span of the biosphere up to some hundred million years. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Carbon cycle; Earth system; Geodynamics; Biosphere

1. Introduction Recent investigations have provided an increasingly detailed scenario of the processes that formed the Earth and other terrestrial planets Žsee, e.g., Newson and Jones, 1990.. A steam atmosphere was )

Corresponding author. Tel.: q49-331-288-2659; fax: q49331-288-2660; e-mail: [email protected]

probably formed by impact degassing during accretion of the Earth and the Earth’s surface was covered with a magma ocean ŽMatsui and Abe, 1986; Zahnle et al., 1988; Franck, 1992.. With a decrease in the impact energy flux the steam atmosphere became unstable and the water condensed to form the protoocean ŽAbe and Matsui, 1988.. Therefore, the composition of the Earth’s atmosphere after the formation of the ocean was mainly CO 2 because we know

0009-2541r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 5 4 1 Ž 9 9 . 0 0 0 4 3 - 1

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S. Franck et al.r Chemical Geology 159 (1999) 305–317

from the composition of the chondritic meteorites that it is the second most abundant volatile in the accreting material. CO 2 is a greenhouse gas and the variation of its content in the atmosphere influences the surface temperature. Hence, it is very important to study the carbon cycle among various reservoirs at the surface and in the interior of the Earth. On planetary time scales the variation of the CO 2 content in the atmosphere is very important in investigating the relation between the evolution of the Sun as a main-sequence star and the stabilization of the Earth’s surface temperature. Such stars increase their burning rate as they age ŽGough, 1981.. During the history of the Earth the luminosity of the Sun has increased to the present level starting with a 30% lower value. If the atmospheric composition and its planetary albedo had been the same as today, the surface temperature of the Earth would have been below 08C until about 2 Ga ago. This is the so-called ‘Faint Young Sun Paradox’ first described by Sagan and Mullen Ž1972.. However, there is no geological and biological evidence that there was a global freezing at that time. Even if the solar luminosity was lower probably the mean temperature of the Earth has never been lower than about 58C ŽOwen et al., 1979; Walker, 1982; Kasting, 1987.. Various solutions for the faint young Sun paradox have been proposed ŽSagan, 1977; Sagan and Mullen, 1972; Walker et al., 1981; Kasting, 1987; Henderson-Sellers and Henderson-Sellers, 1988.. The most accepted one is that in the geological past more greenhouse gases were in the atmosphere than today. Sagan and Mullen Ž1972. proposed that the early terrestrial atmosphere was rich in ammonia and other reduced gases. Other scientists suggested that ammonia is photochemically unstable. In a geologically short period it would be photolysed to N2 ŽKuhn and Atreya, 1979; Kasting, 1982.. Shielded from solar ultraviolet radiation by a layer of photochemically generated organic haze Sagan suggested that ammonia may have been stable ŽSagan and Chyba, 1997.. Another greenhouse gas is CO 2 . It is photochemically stable and one of the most abundant gases in the Earth system. In this case there must be a mechanism that provides a feedback generating a high concentration of atmospheric CO 2 in the past while solar luminosity was lower and a progressively

lowering of CO 2 concentration with an increasing solar luminosity. Such a negative feedback regulation of the amount of CO 2 in the atmosphere through the carbon cycle among surface reservoirs of carbon Žatmosphere, ocean, crust. has been first proposed by Walker et al. Ž1981.. The main idea of this abiotic feedback mechanism is the interplay between the weathering rate, the surface temperature, and the atmospheric CO 2 partial pressure. Nowadays, there have been placed some geochemical constraints on early atmospheric CO 2 pressure that fall well below the levels needed to warm up the Earth’s surface in the geological past ŽRye et al., 1997; Kasting, 1997.. On the other side, there are the so-called daisy world models of Watson and Lovelock Ž1983.. According to these models the stabilization of the planetary surface temperature is caused by the albedo change due to vegetation with a certain parabolic growth rate. Despite the simplification in such toy-models, there is no doubt that even in so-called abiotic regulation models the biosphere plays the main role in weathering ŽBerner et al., 1983; Schwartzman and Volk, 1989. and in making the partial pressure of CO 2 in the soil up to three orders of magnitude higher than in the atmosphere. But there are also discussions about the correctness of data used for the derivation of this 1000 fold effect ŽCochran and Berner, 1992, 1993.. The above mentioned models for the regulation of the atmospheric carbon content against an increase of the solar insolation ŽWalker et al., 1981; Berner, 1993; Berner et al., 1983; Lasaga et al., 1985. are based on the so-called carbonate–silicate geochemical cycle between the atmosphere, the ocean, and the continents. The carbonate–silicate geochemical cycle consists of the following processes: –continental weathering of Ca–Mg-silicates, –precipitation of Ca–Mg-carbonates in the ocean, –subduction of oceanic lithosphere, –metamorphism of carbonates, –degassing of CO 2 via back-arc or andesitic volcanism. In some of these studies, the cycling of carbon is related to the present tectonic activities and the present continental area. But starting with the famous paper of Walker et al. Ž1981. there have been some authors using variable seafloor spreading rates and

S. Franck et al.r Chemical Geology 159 (1999) 305–317

continental area ŽBerner, 1991, 1992; Berner and Rye, 1992; Berner et al., 1983; Lasaga et al., 1985; Marshall et al., 1988; Kuhn et al., 1989; Franc¸ois and Walker, 1992; Godderis ´ and Franc¸ois, 1995. and independent forcing functions in the carbon cycle. This is reasonably because in geological time scales, the deeper parts of the Earth are considerable sinks and sources for carbon and the tectonic activity as well as the continental area have changed markably. Therefore, Tajika and Matsui Ž1992. have favoured the so-called ‘global carbon cycle’. In addition to the usual carbonate–silicate geochemical cycle it also contains the subduction of large amounts of carbon into the mantle with descending slabs and the degassing of carbon from the mantle at mid-ocean ridges. The BLAG carbonate–silicate cycle ŽBerner et al., 1983; Lasaga et al., 1985. also includes all degassing sources. A simple numerical model for an Earth system was developed by Caldeira and Kasting Ž1992.. This model investigates the reaction of the Earth system to a growing solar luminosity S( . In that way the Earth warms up and the surface temperature Ts increases. This temperature increase accelerates the weathering of silicate rock Žwith the weathering rate Fwr .. High temperatures Žnear 508C. have a negative feedback on the biological productivity P . Because of the enhanced silicate-rock weathering, the atmospheric CO 2 partial pressure Patm is reduced and this lowers Ts , Fwr , and P . In this way there is a strong feedback between silicate-rock weathering and atmospheric CO 2 partial pressure. At future high solar luminosity atmospheric CO 2 partial pressure may become so low that it is under the critical level for the photosynthesis. Then the biological productivity would go to zero and the biosphere would die out. This important problem of the life span of the biosphere was first discussed by Lovelock and Whitfield Ž1982.. The diagram illustrating the positive and negative feedback mechanisms described above is shown in Fig. 1. In the present paper we calculate the past and future evolution of the Earth system consisting of the components solid Earth, hydrosphere, atmosphere, and biosphere. Therefore, in Section 2 we describe models for the thermal and degassing history of terrestrial planets. In Section 3 we investigate the influence of geodynamical phenomena on the sce-

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Fig. 1. Positive and negative feedbacks in the Caldeira and Kasting Ž1992. Earth system model Žslightly modified..

nario and in Section 4 we present our model. The results of our calculations are presented and discussed in Section 5.

2. Models for the thermal and degassing history in the parameterized convection approximation Parameterized convection models provide important results for the thermal history of the Earth and other planets Že.g., Stevenson et al., 1983.. These models demonstrate the so-called ‘thermostat effect’, i.e., the self-regulation of the mantle temperature via temperature dependent viscosity. The basic equation of the parameterized convection model is the equation of the conservation of the energy in terms of the time rate of change of the average mantle temperature T˙m : 4 3

pD c Ž R 3m y R 3c . T˙m s y4p R m2 qm 4 q p Q Ž R 3m y R 3c . 3

Ž 1.

where r is the density, c is the specific heat at constant pressure, qm is the heat flow from the mantle, and R m and R c are the outer and the inner

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radii of the mantle, respectively. For simplicity our model does not include core heat flow which at present is about 10% of the surface heat flow. Parameterized convection models including the core heat flow Žsee, e.g., Franck and Orgzall, 1988. show no qualitative different behavior. The quantity Q describes the energy production rate by decay of radiogenic heat sources in the mantle: Q s Q0 eyl t

Ž 2.

where Q 0 and l are constants and t is the time. The Rayleigh number Ra for a convecting mantle is: Ra s

g a Ž Tm y Ts . Ž R m y R c .

kn

3

Ž 3.

where g is the acceleration due to gravity, a is the coefficient of thermal expansion, Ts is the surface temperature, k is the thermal diffusivity, and n is the viscosity. It is well known that the kinematic viscosity of the mantle depends on the temperature, the pressure, and the volatile content. Franck and Bounama Ž1995a,b, 1997. are the first introducing experimental results of the effect of water fugacity on the olivine creep rate to this general modeling problem. The mantle heat flow qm is parameterized in terms of Ra: k Ž Tm y Ts .

Ra

ž /

b

and the present-day viscosity of the mantle. Jackson and Pollack Ž1984. have investigated in detail the sensitivity of parameterized convection to the rate of decay of internal heat sources. The first self-consistent model that couples the thermal and degassing history of the Earth was proposed by Mc Govern and Schubert Ž1989.. In this model volatiles from the mantle degas at mid-ocean ridges from a certain volume Ždegassing volume. that depends on the areal spreading rate S and the melt generation depth d m ŽFig. 2.. The degassing rate of volatiles at mid-ocean spreading centers w M˙ mv xd is given by: M˙ mv

d

s Dmv d m Sf H 2 O

Ž 6.

where Dmv is the density of volatiles in the mantle Žmass of mantle volatiles per mantle volume., d m is the melt generation depth, and S is the areal plate spreading rate. The melt generation depth d m is defined by the depth where ascending mantle material intersects the basalt eutectic and extensive melting and melt segregation occur. f H 2 O is the degassing fraction of water. The rate of regassing at subduction zones w M˙ mv x r is: M˙ mv r s f bas D bas d bas SR H 2 O

Ž 7.

where k is the thermal conductivity, Ra cr is the critical value of Ra for the onset of convection, and b is an empirical constant. The parameterized convection approximation is based on using a dependence between Nusselt number Nu Žwhich is the ratio of the total heat flow and the conductive transported heat. and the Rayleigh number Ra:

where f bas , D bas , and d bas are the mass fraction volatile content, the average density, and the thickness of the seafloor crust and sediments before subduction, respectively. R H 2 O is an efficiency factor representing the fraction of volatiles that actually enter the deep mantle instead of returning to the surface through arc and back-arc volcanism or offscraping ŽFig. 2.. The balance equation for the mass Mmv of mantle volatiles is given by:

Nu A Ra b

M˙ mv s M˙ mv r y M˙ mv

qm s

Ž R m y R c . Ra cr

Ž 4.

Ž 5.

This approximation has been used in many thermal history models if you are not interested in the complexities of the flow pattern and the temperature field of the convection cells. Christensen Ž1985. has discussed in detail the influence of the empirical constant b on the results. In our calculations we have fitted the initial heat source density Q 0 so that the numerical models provide the present-day heat flow from the mantle

d

Ž 8.

The initial value of Mmv is the number n of ocean masses Mocean originally in the mantle: Mmv Ž t s 0 . s nMocean

Ž 9.

The global carbon cycle is a part of the general process of volatile exchange during the Earth’s history. In models of Jackson and Pollack Ž1987., Mc Govern and Schubert Ž1989., Williams and Pan Ž1992. and Franck and Bounama Ž1995a,b, 1997.

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309

Fig. 2. Global volatile cycle with a parameterized mantle convection model ŽFranck and Bounama, 1995b.. S is the seafloor spreading rate and d m the depth of partial melting from which volatiles are released. Regassing occurs at subduction zones after the loss of some volatiles via arc and back-arc volcanism Ž qm : mean heat flow from the mantle, Ts : global mean surface temperature, R c : core radius, R m : mantle radius..

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310

this volatile exchange has been studied in detail. The main idea is the coupling of the thermal Ž1. – Ž5. and degassing Ž6. – Ž9. history of the Earth with the help of simple relations from boundary layer theory. The starting point is the relation between heat flow qm and the average age of oceanic crust t ŽTurcotte and Schubert, 1982.. qm s

2 k Ž Tm y Ts .

'pkt

Ž 10 .

where t is given by

ts

A0 Ž t .

Ž 11 . S and A 0 Ž t . is the area of the ocean basins at time t. Combining Ž10. and Ž11. we find the relation between heat flow qm and the average age of the subducting oceanic crust which as well is a function of the spreading rate S: qm s

'S 2 k Ž Tm y Ts .

(pk A Ž t .

Ž 12 .

Berner et al. Ž1983. found that the weathering rate, the seafloor spreading rate, and the continental area have a very strong influence on the global climate. He also emphasized ŽBerner, 1992, 1993, 1997. the rise of land plants and their effect on weathering and atmospheric CO 2 . In the framework of a steady state approximation for the global carbon cycle at longer time scales Ž) 10 5 a. originally Walker et al. Ž1981. proposed an equilibrium between the CO 2 sink in the system atmosphererocean and the metamorphic Žplate tectonic. source. This approximation has been discussed in detail by Kasting Ž1984.. The sources of bringing CO 2 into the global carbon cycle to the system atmosphererocean are seafloor spreading at mid-ocean ridges and back-arc or andesitic volcanism Žsee Fig. 2.. Both processes are dependent on the spreading rate S. The sink of CO 2 in the system atmosphererocean is related to the weathering rate Fwr and the continental area A c Žavailable for weathering.. Therefore, this equilibrium may be expressed as a relation between dimensionless quantities:

0

The area of the Earth’s surface A earth is of course the sum of A 0 Ž t . and the area of continents A c Ž t .: A earth s A 0 Ž t . q A c Ž t .

Ž 13 .

Ž12. and Ž13. can be used to introduce continental crustal growth models into the equations for parameterized convection and the volatile cycle ŽFranck and Bounama, 1997.. The mechanism of the influence of continental growth on the degassing history can be explained with the help of Ž12.. The spreading rate S for fixed temperatures and heat flow is proportional to the area of ocean basins A 0 . Because the Earth’s surface area A earth is constant Ž13. we have a decreasing S with an increasing continental area A c . The geodynamical background is that the volatile exchange Ždegassing and regassing. is stronger if there is less continental area.

3. The influence of geodynamics on the carbon cycle Caldeira and Kasting Ž1992. solved their numerical model under the assumption that the weathering rate Fwr is always equal to the present value Fwr,0 . This is clearly a rather rough approximation. Already

f wr = fA s fsr

Ž 14 .

where f wr s FwrrFwr,0 is the weathering rate normalized by the present value, fA s A crA c,0 is the continental area normalized by the present value, and fsr s SrS0 is the spreading rate normalized by the present value. The ratio fsr rfA is called ‘Geophysical Forcing Ratio’ ŽGFR.. This ratio describes the influence of the volcanic activity Žproportional to S . and the continental area A c on the global climate ŽVolk, 1987.. Fig. 3 shows the curves for the average mantle temperature Tm , the mantle heat flow qm , and the spreading rate S for the thermal and degassing history calculations ŽFranck and Bounama, 1997. with an initial average mantle temperature of 3000 K and the so-called constant linear continental growth model Žsee below. as examples for the calculation of the geodynamical quantities needed in our model. Next we want to present the continental growth models Ži.e., the functions A c s f Ž t .. implemented in our simulations. The continental crust is especially diverse and heterogeneous. Its formation is less understood than that of the geologically simple oceanic crust ŽMeißner, 1986.. Two quite different hypotheses have

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311

Fig. 3. Average mantle temperature, mantle heat flow, and spreading rate for a thermal and degassing history model with constant linear continental growth and 3000 K initial average mantle temperature ŽFranck and Bounama, 1997..

been advanced to explain the evolution of the continental crust. Ž1. The present continental crust formed very early in the Earth’s history. It has been recycled through the mantle in steadily decreasing fashion such that new additions are balanced by losses resulting in a steady state system ŽArmstrong, 1991.. Then the much lower mean age must arise from the return

of the continental material to the mantle and its replacement by the new younger additions. These processes maintain the mass of the continents constant and also reduce their mean age. Ž2. The crust grows throughout geological time without recycling into the mantle. In modern studies Že.g., Taylor and McLennan, 1995. there is a growing appreciation that the conti-

Fig. 4. Sketch of the three used continental growth models Žconstant LG, DG, R & S model..

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312

nental crust grows episodically and it is concluded that at least 60% of the crust was replaced by the late Archaean Ž2.7 Ga.. In the last decades there have been presented many different crustal growth models between the two extrema discussed above. In the present study we will not use detailed models but very simple ones: a delayed growth ŽDG. model Ž A c s 0 for t F 2.2 Ga and A c A t for t ) 2.2 Ga, a constant linear growth ŽLG. model Ž A c A t ., and a growth model proposed by Reymer and Schubert Ž1984. ŽR & S. that is based on the assumption of an approximately constant continental freeboard over the last 500 million years: A c Ž t . s A e y AU0

V0aU V0

q

U U V0b qm

V0 q m Ž t .

y1

Ž 15 .

where V0 is the total volume of the water in the U ocean Ž1.17 = 10 18 m3 ., V0a is the volume of the ocean basins above the peak ridge height Ž7.75 = 10 17 U m3 ., V0b is the volume of the ocean basins below the peak ridge height Ž3.94 = 10 17 m3 ., and asterisks denote present-day values. A detailed derivation of Ž15. is given by Reymer and Schubert Ž1984.. The different continental growth models used in our simulations are shown in Fig. 4. They have been continued to the future.

4. The model As a starting and reference model Žworking values for the parameters. in our numerical experiments we used the model of Caldeira and Kasting Ž1992.. The time dependence of the solar luminosity S(Ž t . is fitted by S(Ž t . s Ž 1 y 0.38tr4.55 Ga .

y1

= 1.368 kW my2 Ž 16 .

The energy balance between incoming radiation and outgoing radiation is

Ž 1 y a . S( r4 s s Teff4

The surface temperature Ts is related to Teff by the greenhouse warming factor DT : Ts s Teff q DT .

The greenhouse warming factor is a function of Ts Žin K. and c s log Patm Ž Patm in bar.: DT s 815.17 q Ž 4.895 = 10 7 . Tsy2 y Ž 3.9787 = 10 5 . Tsy1 y 6.7084cy2 q 73.221 cy1 y 30.882Ty1cy1 .

Ž 19 .

The planetary albedo a is a function of Ts . a s 1.4891 y 0.0065979Ts q Ž 8.567 = 10y6 . Ts2

Ž 20 . The silicate-rock weathering rate Fwr was calculated from Fwr

f wr s

s

Fwr ,0

aHq

0.5

ž / ž exp

a H q ,0

Ts y T0 13.7 K

/

Ž 21 .

where a H q is the activity of Hq in fresh soil water assuming equilibration of rain water with the soil CO 2 concentration Ž Psoil . and the atmospheric SO 2 concentration Ž0.2 p.p.b... The quantities Fwr,0 , a H q ,0 , and T0 are the present values for the weathering rate, the Hq activity, and the surface temperature, respectively. Equilibrium constants for the chemical activities of the carbon and sulfur systems have been taken from Stumm and Morgan Ž1981.. These equilibrium constants account only for the anorganic weathering process. The additional effects of accelerating the weathering by vascular plants have been described for example by Berner Ž1997.. Psoil can be parameterized as a function of the biological productivity P , the atmospheric CO 2 concentration Patm , and the corresponding present values ŽVolk, 1987..

P

Psoil

s

Psoil ,0

P0

ž

1y

Patm ,0 Psoil ,0

/

q

Patm Psoil ,0

.

Ž 22 .

The biological productivity has a maximum at Ts s 258C and is zero when Ts reaches 508C: P

Pmax

Ž 17 .

where a is the planetary albedo, s is the Stefan– Boltzmann constant, and Teff is the effective blackbody radiation temperature.

Ž 18 .

ž ž

s 1y

T y 258C 258C

2

/ /ž

Patm y Pmin P1r2 q Ž Patm y Pmin .

/

.

Ž 23 .

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The maximum possible biological productivity Pmax is twice the present productivity P 0 . The minimum CO 2 concentration down to which C 4 plants can grow Ž Pmin . was set 10 p.p.m. The value P1r2 is calculated to yield P s P 0 when Ts s T0 Žs 158C. and Patm s Patm,0 Žs 320 p.p.m... The initial value of Psoil,0 is 10 Patm,0 . In our computer model we started with the parameters for the present state of the Earth system Ž f wr s FwrrFwr,0 s 1.. From the ratio of the dimensionless midocean seafloor spreading rate and the dimensionless continental area from Franck and Bounama Ž1997. we calculated f wr via Ž14. back to the Earth’s history. We find values of f wr in the order of 2–5 in the Mesoproterozoic and about 5–10 in the late Palaeoproterozoic, depending on the continental growth model. In the planetary future f wr decreases from the present value Ž f wr s 1. to f wr f 0.5 in 500 Ma. With a trial and error method we solved the system of Eqs. Ž16. – Ž23. self consistently back to the Archaean. At this geological era life changed from anaerobic to aerobic forms and for the

Fig. 5. Positive and negative feedbacks in our Earth system model.

313

biological productivity Ž23. may be applied. Then starting from the present state again we run our model 1.5 Ga into the future. The main improvement of our model on the model of Caldeira and Kasting Ž1992. is the incorporation of spreading and continental growth as main geodynamical processes into the calculation scheme in the sense of an internal forcing on the Earth system. This is sketched in Fig. 5.

5. Results and discussion With the help of the numerical procedure described in Section 4 we solved the system of equations that is illustrated by the diagram in Fig. 5. Over a time scale from 2.3 Ga ago up to the future of 1.1 Ga and 1.5 Ga the results for the mean global surface temperature Ts , the atmospheric and soil CO 2 partial pressure Patm , Psoil , and the normalized biological productivity PrP 0 are plotted in Figs. 6–8. In Fig. 9 we show the effect of the biosphere on the mean global surface temperature for the R & S continental growth model. In the abiotic case Ža planet without biosphere. ŽR & Sa. we have solved the system of equations under the condition P ' 0 at any time. In this case there is no ‘biological pump’ increasing Psoil by about 10 times Patm and as can be seen from Ž22. Psoil and Patm are always equal in the abiotically case. Our results confirm the main idea that the global carbon cycle is the main mechanism to draw down CO 2 from the Earth’s atmosphere and to buffer the surface temperature against an increase in solar luminosity. In this process the carbonate–silicate geochemical cycle is considered to be a part of the global carbon cycle. Fig. 6 shows the stabilization of the mean global surface temperature from the Archaean up to about 1 Ga into the future for the Caldeira–Kasting model ŽC & K. and for our three models with different continental growth. In comparison to the reference model ŽC & K. our three models provide warmer climates in the past but cooler ones in the future up to about 1 Ga. This effect can be easily explained from the viewpoint of geodynamics: in the geological past we had a smaller continental area and higher spreading rates. In this way the longscale equilibrium

314

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Fig. 7. Past and future evolution of atmospheric and soil CO 2 partial pressure for the reference model C&K and the delayed continental growth model DG.

Fig. 6. Past and future evolution of the mean global surface temperature for the reference model C&K and our 3 continental growth models LG, DG, R&S.

between CO 2 sinks and sources as described by Ž14. was at a higher atmospheric CO 2-level than in the C & K-model with the present weathering rate Žpresent continental area, present spreading rate.. The additional CO 2 comes from the mantle reservoir that is orders of magnitude larger than the atmospheric reservoir and therefore it can be considered as infinitely in the framework of our model. In the planetary future we have the reverse situation: a larger continental area, smaller spreading rates, less CO 2 in the atmosphere compared to the C & K-model. We can see that the more realistic R & S continental growth model gives the best surface temperature stabilization. After about 1 Ga from now all curves converge and increase to nearby 1008C in a planetologically short time. All higher forms of life would

certainly be terminated at this time. The atmospheric and soil CO 2 partial pressure Ž Patm and Psoil . in Fig. 7 show a continuous decrease. This decrease in atmospheric CO 2 results in a decreasing greenhouse effect, which compensates for the effect of increasing solar luminosity. Up to the future when the biological productivity goes to zero and the ‘biological pump’ ceases the soil CO 2 partial pressure is always higher than the atmospheric one. In the scope of the global carbon cycle between mantle and surface reservoirs the mantle becomes the main sink of carbon. In Fig. 8 the four models for the evolution of

Fig. 8. Past and future evolution of the normalized biological productivity for the reference model C&K and our 3 continental growth models LG, DG, R&S.

S. Franck et al.r Chemical Geology 159 (1999) 305–317

the normalized biological productivity are presented. Because continental growth starts late in the model with delayed continental growth ŽDG. it shows a strong increase in the biological productivity in the Archaean. This model provides the shortest life span of the photosynthetic biosphere Žabout 0.5 Ga. — nearly 300 Ma shorter than the corresponding one of the C & K reference model. For the evolution of the mean global surface temperature ŽFig. 9. the comparison of the biotic and abiotic models ŽR & S and R & Sa, respectively. shows a stronger stabilization effect as long as the biosphere exists. On the other hand the self-regulation of the mean global surface temperature works also without a biosphere ŽR & Sa.. But in this case the stabilized mean global surface temperature is up to 5 K higher. Since we did not change the weathering rates our mechanism of

315

‘switching off’ the biosphere by setting the biological productivity to zero is only a very rough approximation. The global carbon cycle plays an important role in the long scale self-regulation in the Earth system. In the Earth’s history the mean global surface temperature has been stabilized by this cycle against the external forcing of a growing solar luminosity. The abiotic stabilization mechanism will continue to about 1–1.5 Ga. Then it breaks down and the mean global surface temperature reaches a point of about 1008C where water is lost and the state of the Earth becomes similar to that of the Venus. Because the atmospheric CO 2 partial pressure drops under the minimum pressure for photosynthesis Žabout 10 p.p.m. for C 4 plants. the photosynthetic biosphere will already break down in about 0.5–0.8 Ga. All these phenomena are strongly influenced by geodynamical processes like continental growth and tectonic activity Žspreading.. Our calculation procedure was performed in such a way that we coupled two independent systems of equations that have been solved self-consistently each for each other. For every time step we entered the data of the continental area and the spreading rate from our degassingrregassing model into the system of Eqs. Ž16. – Ž23. for the Earth system. This is only a first step towards the development of a completely self-consistent Earth system model. In this sense our results are highly speculative and they present only a general qualitative picture of the evolution of atmospheric CO 2 , climate, mantle temperature, continental area, spreading, and biosphere. Additional processes like the organic carbon subcycle might also be important in the self-regulation of the Earth system Žfor a recent review see Schneider and Boston, 1993..

Acknowledgements

Fig. 9. Past and future evolution of the mean global surface temperature for the R&S model and for the abiotic R&S model ŽR&Sa., i.e., with zero biological productivity.

The authors want to thank Prof. Yuri Svirezhev, Prof. Wolfgang Cramer, Dr. Arthur Block, and Dipl.-Phys. Werner von Bloh for helpful discussions. Furthermore, the authors benefited greatly from constructive reviews of the manuscript by R.A. Berner ŽYale University., L.M. Franc¸ois ŽUniversite´ de Liege ` ., and H.N. Pollack ŽUniversity of Michigan..

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