Carnets de Géologie / Notebooks on Geology: Memoir 2005/02, Abstract 02 (CG2005_M02/02)

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[Introduction] [Basic principles of carbon cycle...]
[Modelling the Paleozoic...] [Carbon cycle modelling at...] [Conclusions]
[Bibliographic references] and ... [Figure]

Modelling atmospheric CO2 changes
at geological time scales

[Modélisation des variations du CO2 atmosphérique
à l'échelle des temps géologiques]

Louis François

Laboratoire de Physique Atmosphérique et Planétaire (LPAP), Université de Liège, Bât. B5c, 17 Allée du Six Août, B-4000 Liège (Belgium)

Aline Grard

Centre d'Étude et de Modélisation de l'Environnement (CEME), Université de Liège, Bât. B5a, 17 Allée du Six Août, B-4000 Liège (Belgium)

Yves Goddéris

Laboratoire des Mécanismes de Transfert en Géologie (LMTG), Observatoire Midi-Pyrénées, 14 Avenue Édouard Belin, 31400 Toulouse (France)
Manuscript online since December 31, 2005

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François L., Grard A. & Goddéris Y. (2005).- Modelling atmospheric CO2 changes at geological time scales. In: Steemans P. & Javaux E. (eds.), Pre-Cambrian to Palaeozoic Palaeopalynology and Palaeobotany.- Carnets de Géologie / Notebooks on Geology, Brest, Memoir 2005/02, Abstract 02 (CG2005_M02/02)

Key Words

Atmosphere; CO2; modelling; carbon cycle; climate; geochemical cycle.


Atmosphère ; CO2 ; modélisation ; cycle du carbone ; climat ; cycle géochimique.

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By trapping infrared radiation, atmospheric CO2 contributes significantly to the greenhouse warming of the planetary surface. Hence, it is thought to have played a key role in the evolution of the Earth's climate over geological time. The history of atmospheric CO2 is available only for the last few hundred thousand years from the analysis of the air trapped in cores of ice. Therefore, data regarding Pre-Pleistocene atmospheric CO2 must be derived from proxies. These provide indirect estimates of atmospheric CO2 and are much less reliable than ice-core data. The main proxies used to reconstruct atmospheric CO2 are: the 13C isotopic fractionation of marine organisms, the paleo-pH recorded in the boron isotopic composition of ancient carbonates, the stomatal density of fossil leaves and the 13C isotopic composition of paleosols. For Paleozoic times paleosols have been the main source of data but these are generally rather imprecise. Consequently, for this period geochemical models are useful to make first order estimates of atmospheric CO2 levels, as well as to help explain its temporal variation. Such models describe the geochemical cycles of several elements - the core being the carbon cycle - by writing budget equations for these elements in the framework of box models. They are often constrained by isotopic data. In the following we first summarize the basic principles of these models and then illustrate two applications: (1) changes in Paleozoic atmospheric CO2 and (2) changes in the carbon cycle across the Permo-Triassic boundary.

Basic principles of carbon cycle modelling at geological time scales

All geochemical models designed to calculate changes in atmospheric CO2 at geological time scales are based on the pioneer work of Walker et alii (1981) who postulated that, at time scales longer than ~1 Myr, atmospheric CO2 is regulated by the balance between its input from volcanism (Fvol) and its net consumption by silicate weathering followed by carbonate deposition on the seafloor (Fsw). At these lengthy time scales weathering of carbonates is unimportant because it is followed by carbonate deposition on the seafloor, so the net carbon budget of the ocean-atmosphere is zero. The global silicate weathering flux Fsw (mol yr-1) can be written as the product of the silicate rock outcrop area A (m2), the mean water runoff R (mm yr-1; i.e., liters m-2 yr-1) and the mean concentration c (mol liter-1) of divalent cations (Ca2+ and Mg2+) formed from the weathering of silicates that then enter the rivers draining the outcrop area. Because paleolithological map are generally not available, the silicate outcrop area 'A' is usually assumed to be in proportion to the continental area, which can be reconstructed over geological ages. The runoff 'R' is a function of the climate (temperature, precipitation), itself in turn dependent on atmospheric CO2 pressure pCO2, continental configuration, solar luminosity, etc. Kinetic laws of weathering derived empirically allow 'c' to be expressed as a function of climate (surface temperature), soil pCO2, orography, vegetation cover, lithology (i.e., kinds of silicate rocks), etc. Using these data for each time 't' of the geological past, the surface atmospheric CO2 pressure can be obtained by solving with respect to pCO2 the following (non linear) equation:

Fvol(t) = A(t) . R(climate) . c(climate, pCO2, orography, vegetation, lithology, )

provided that the relationship between climate and pCO2 is known. This relationship can be represented by a parametric expression or obtained from a climate model. The kinetic relationship adopted to describe the concentration 'c' is central in geochemical modelling. Walker et alii (1981) assumed an exponential dependence on surface temperature. In their view, silicate weathering is high in warm and humid climates; the effects of orography are ignored in the weathering law. Consequently, the evolution of atmospheric CO2 and climate is the direct result of changes in global volcanic activity and the area of continents. Periods of high levels of atmospheric CO2 and warm climates correspond to times of high volcanic activity and/or small continents. But, using the strontium isotopic record as a basis, Raymo et alii (1988) proposed that low CO2 and cold climates correspond to periods of orogeny. The rate of silicate weathering is high in mountainous areas because rapid uplift and erosion guarantee the existence of abundant fresh exposures to weather and runoff is usually higher in mountains. According to Raymo et alii (1988), orogeny had a more profound impact on the history of atmospheric CO2 and climate than volcanism or changes in the size of continents. More recent studies have emphasized the roles of vegetation (Berner, 1991) and lithological (Dessert et alii, 2001) changes on the evolution of atmospheric CO2.

Modelling the Paleozoic carbon cycle and climate

Over periods as long as the Paleozoic carbon cycle modelling is generally more complex than expressing the balance between volcanic CO2 release and silicate weathering. Other carbon fluxes are important in the determination of the carbon budget: transfer of organic carbon (Corg) to or from the crust (Lasaga et alii, 1985; Berner, 1991) and the weathering of seafloor basalts (François & Walker, 1992). The net transfer of Corg into the ocean-atmosphere - i.e., the difference between old Corg ('kerogen') weathering/oxidation Fow on the continents (source of C) and Corg deposition Fod on the seafloor (sink of C) - is often evaluated from an inversion of the δ13C history of ancient seawater recorded in marine limestones. For instance, Fig. 1 shows the evolution of atmospheric CO2 over Phanerozoic times calculated from the inversion of the oceanic δ13C history obtained from a moving average of the data gathered in the Ottawa-Bochum database (Veizer et alii, 1999). This inversion is based on a multi-box model describing the exchanges of carbon between the atmosphere, the ocean and the crust. It assumes that after the emergence of land plants, 50% of the organic carbon deposited on the seafloor (mostly on the shelf) originated from the land biosphere and 50% from the marine biota. A pCO2- dependent 13C fractionation (Freeman & Hayes, 1992) is adopted for marine photosynthesis. On land, photosynthetic 13C fractionation is assumed to be constant before the emergence of C4 plants at about 8 Ma. It is then modified as a result of the progressive evolution of C4 plants, assuming that the C4 contribution to organic carbon deposition from land increases from 0 to 20% between 8 and 6 Ma and remains constant after 6 Ma.

High δ13C values recorded during the Carboniferous suggest rapid rates of deposition for Corg (which removed 12C preferentially over 13C, as a result of photosynthetic fractionation) at that time. This large sink of carbon caused a low atmospheric CO2 and a cold climate during the Carboniferous, which is consistent with the glacial deposits laid down during this period. Another important event in the Paleozoic is the emergence of land plants, which enhanced weathering through the production of soil CO2 and organic acids. Land plants are not explicitly represented in long-term carbon cycle models. In any case the efficiency of continental weathering is assumed to have been altered by land plants (Berner & Kothavala, 2001), increasing when the type of vegetation changed from lichens/mosses to gymnosperms (at about 380 Ma) and from gymnosperms to angiosperms (at about 130 Ma). Combined with a relatively small land area, this factor caused very high levels of atmospheric CO2 in the early Paleozoic, prior to the existence of land plants (Fig. 1 ). Such postulated high levels of CO2 are difficult to reconcile with the observed glacial episodes during the Late Ordovician (Veizer et alii, 2000). Other factors considered in the CO2 reconstruction of Fig. 1 are the evolution of volcanic-metamorphic fluxes derived from the seafloor accretion rate (Gaffin, 1987; Entgebretson et alii, 1992), as well as the change of physical erosion through time and its impact on chemical weathering, for which proxy records are provided by the Phanerozoic history of clastic sedimentation (Wold & Hay, 1990).

It is clear that the calculated evolution of atmospheric CO2 during the Phanerozoic using an inverse model of this type is strongly dependent not only on the quality of the 13C data, but also on the various fractionation processes involved, for which large uncertainties remain today. Moreover, the 13C signal may be contaminated by the release of methane, as might have happened at the Eocene-Paleocene boundary (Zachos et alii, 2005). However, such methane bursts should have relatively short-term effects (a few 100 kyr) on the ocean-atmosphere carbon cycle. Since the 13C data are usually smoothed before being used in long-term carbon cycle models, the effect of such short-term events on the 13C inversion should be rather limited. They are more relevant to the transient models discussed in the next section.

Carbon cycle modelling at shorter time scales: the Permo-Triassic boundary

At short time scales (i.e., time scales comparable to or shorter than the residence time of carbon in the ocean-atmosphere system) non-equilibrium carbon cycle models must be used. These models must include explicit modelling of ocean biogeochemistry, including nutrients (e.g. phosphorus) limitation of ocean productivity and aragonite/calcite lysocline dynamics. Important examples are the modelling of transitions between geological periods, during which mass extinctions have been observed to occur. Huge and rapid fluctuations of marine δ13C are common during such events, but are difficult to explain with carbon cycle models. As previously discussed, many authors (e.g., Zachos et alii, 2005, and references therein) invoke methane bursts to explain such rapid and high amplitude fluctuations of the oceanic δ13C value.

Grard et alii (2005) have compared the impacts on the carbon cycle of two concurrent events that occurred during the Permo-Triassic transition: the emplacement of the Siberian traps and a mass extinction. Starting with a Late Permian atmospheric CO2 level of ~3000 ppm, the effect of the emplacement of the basaltic trap was, during the first million years, a rise in CO2 of more than 1000 ppm accompanied by a significant warming. This was followed by a drop in CO2 and a progressive cooling. After a few million years, the system reached a new steady state at which CO2 decreased by ~750 ppm and the global mean surface temperature cooled by 1.07°C, when compared to the pre-perturbation situation. The cooling is linked to the CO2 consumption associated with the weathering of the Siberian basalts, which are much more easily weathered than the average silicate crust on the continents (Dessert et alii, 2001). Combining the calculated effects of the emplacement of the trap and the extinction of a major part of the biota yields a model of oceanic δ13C changes with an amplitude of 2-3‰ that is comparable to the data. About 1‰ of this change resulted from the injection of mantle carbon (-5‰) associated with the emplacement of the traps. The rest was caused by a slowing down in the burial of organic carbon as a result of the mass extinction. The model does not elucidate the precise mechanisms leading to the extinction, but it shows that, for this Permo-Triassic transition, the observed δ13C change can be accounted for without invoking a release of methane.


Long-term carbon cycle models are still in their infancy. The major areas for improvement in these models are: (1) a better understanding of the processes governing silicate weathering, (2) a more precise and more realistic description of the organic sub-cycle, (3) a coupling of geochemical and climate models, and (4) exploitation of all available isotopic data by the inclusion of the biogeochemical cycles of many different elements and their isotopes.

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Bibliographic references

Berner R.A. (1991).- A model for atmospheric CO2 over Phanerozoic times.- American Journal of Science, New Haven, vol. 291, p. 339-376.

Berner R.A. & Kothavala Z. (2001).- GEOCARB III: A revised model of atmospheric CO2 over Phanerozoic time.- American Journal of Science, New Haven, vol. 301, p. 182-204.

Dessert C., Dupré B., François L.M., Schott J., Gaillardet J., Chakrapani G.J. & Bajpai S. (2001).- Erosion of deccan traps determined by river geochemistry: Impact on the global climate and the 87Sr/86Sr ratio of seawater.- Earth and Planetary Science Letters, Amsterdam, vol. 188, p. 459-474.

Entgebreton D.C., Kelley K.P., Cashman H.J. & Richards M.A. (1992).- 180 million years of subduction.- GSA Today, Boulder, vol. 2, p. 93-95.

François L.M. & Walker J.C.G. (1992).- Modelling the Phanerozoic carbon cycle and climate: constraints from the 87Sr/86Sr isotopic ratio of seawater.- American Journal of Science, New Haven, vol. 292, p. 81-135.

Freeman K.H. & Hayes J.M. (1992).- Fractionation of carbon isotopes by phytoplankton and estimates of ancient CO2 levels.- Global Biogeochem Cycles, Washington, vol. 6, n° 2, p. 185-198.

Gaffin S. (1987).- Ridge volume dependence of seafloor generation rate and inversion using long-term sealevel change.- American Journal of Science, New Haven, vol. 287, p. 596-611.

Grard A., François L.M., Dessert C., Dupré B. & Goddéris Y. (2005).- Basaltic volcanism and mass extinction at the Permo-Triassic boundary: environmental impact and modelling of the global carbon cycle.- Earth and Planetary Science Letters, Amsterdam, vol. 234, 207-221.

Lasaga A.C., Berner R.A. & Garrels R.M. (1985).- An improved geochemical model of atmospheric CO2 fluctuations over the past 100 million years. In: Sundquist E.T. & Broecker W.S. (eds.), The Carbon Cycle and Atmospheric CO2: Natural Variations Archean to Present.- Geophysical Monograph, Washington, vol. 32, p. 397-411.

Raymo M.E., Ruddiman W.F. & Froelich P.N. (1988).- Influence of late Cenozoic mountain building on ocean geochemical cycles.- Geology, Boulder, vol. 16, p. 649-653.

Veizer J., Ala D., Azmy K., Bruckschen P., Buhl D., Bruhn F., Carden G.A.F., Diener A., Ebneth S., Goddéris Y., Jasper T., Korte C., Pawellek F., Podlaha O.G. & Strauss H. (1999).- 87Sr/86Sr, δ13C and δ18O evolution of Phanerozoic seawater.- Chemical Geology, Amsterdam, vol. 161, p. 59-88.

Veizer J., Goddéris Y. & François L.M. (2000).- Evidence for decoupling of atmospheric CO2 and global climate during the Phanerozoic eon.- Nature, London, vol. 408, p. 698-701.

Walker J.C.G., Hays P.B. & Kasting J.F. (1981).- A negative feedback mechanism for the long-term stabilization of Earth's surface temperature.- Journal of Geophysical Research, Washington, vol. 86, p. 9776-9782.

Wold C.N. & Hay W.W. (1990).- Estimating ancient sediment fluxes.- American Journal of Science, New Haven, vol. 290, p. 1069-1089.

Zachos J.C., Röhl U., Schellenberg S.A., Sluijs A., Hodell D.A., Kelly D.C., Thomas E., Nicolo M., Raffi I., Lourens L.J., McCarren H. & Kroon D. (2005).- Rapid acidification of the ocean during the Paleocene-Eocene thermal maximum.- Science, Washington, vol. 308, p. 1611-1615.

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Figure 1: Model of the evolution of atmospheric CO2 over Phanerozoic times. CO2 levels are expressed as multiples of the Pre-industrial Atmospheric Level (P.A.L. = 280 ppm). It is a time-dependent multi-box model of the carbon cycle, containing one reservoir for the ocean-atmosphere and three reservoirs for the crust (organic carbon, shelf carbonates and pelagic carbonates). All major carbon fluxes between these reservoirs are described by the model, as well as the input/output of carbon from/to the mantle associated with seafloor accretion/subduction. The rate of deposition of organic carbon is calculated from the inversion of the δ13C evolution recorded in ocean carbonates (see text), which involves a calculation of the isotopic composition of all four model reservoirs. At each time step, the main model calls up an equilibrium sub-model, which subdivides the atmosphere-ocean reservoir into three sub-reservoirs (atmosphere, ocean surface and deep ocean). This sub-model describes the cycles of carbon, alkalinity and phosphorus within the ocean-atmosphere system. It calculates the atmospheric CO2 pressure, carbonate speciation in the ocean, aragonite and calcite compensation depths (used to evaluate shelf and pelagic carbonate depositional fluxes) and all major 13C fractionation processes in the system. Global surface temperature is evaluated from the atmospheric CO2 pressure using a simple parametric relationship and is employed in the calculation of the carbonate and silicate weathering rates in the main model. Silicates are sub-divided into basalts and other silicates, each of them with discrete weathering laws (Dessert et alii, 2001).

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