Pearson and Palmer used boron isotopes to infer paleo-ocean pH, and then used this paleo-pH proxy to estimate paleo-atmospheric pCO₂ under the assumption of constant concentration of total dissolved inorganic carbon in seawater. However, carbon is continuously supplied to the atmosphere and ocean by degassing from metamorphism and magmatism and by the weathering of carbonate minerals and organic carbon, and is continuously consumed by the production of carbonate and organic carbon sediments (3). Hence, the total dissolved inorganic carbon load of the ocean could be expected to vary over time.

The carbonate chemistry of seawater is largely controlled by the twin constraints of atmospheric pCO₂ and ocean carbonate-ion concentration (3). The mean partial pressure of CO₂ in the surface ocean is nearly equal to that of the atmosphere. Because the ocean is in contact with carbonate sediments, both on shelves and in the deep sea, the ocean as a first approximation is roughly saturated with respect to calcite. If we assume that the concentration of Ca²⁺ has remained nearly constant, this is equivalent to a roughly constant carbonate-ion concentration (CO₃²).

Under this assumption we can predict pCO₂ as a function of the hydrogen-ion concentration, or pH, using:

(1)

where K_H is the Henry's law constant for CO₂, and K₁ and K₂ are the first and second dissociation constants for carbonic acid. Equation 1 scales with the square of the hydrogen-ion concentration, whereas the equation used by Pearson and Palmer roughly scales directly with the hydrogen-ion concentration (Fig. 1). Hence, the assumption of constant carbonate-ion concentration yields far greater pH sensitivity than does the assumption of constant total dissolved inorganic carbon concentration.

If we assume that the preindustrial surface ocean had a pH of 8.25, Eq. 1 yields a pCO₂ of ~2.5 times the preindustrial atmospheric value for the pH of 8.05 inferred by Pearson and Palmer for the Eocene surface ocean. If climate sensitivity to enhanced atmospheric CO₂ is 1.5° to 4.5°C per CO₂-doubling (4), then this yields 2° to 6°C CO₂-induced warming for the Eocene, which suggests that enhanced atmospheric CO₂ content could explain much or all of inferred Eocene warmth. In this calculation we have assumed that the carbonate ion concentration is constant, and therefore a large variation in calcium carbonate saturation state in the surface ocean is not implied. However, the Eocene ocean overall was probably more acidic than at present, as suggested by a distinctly shallower carbonate compensation depth at that time (5), and this in itself suggests that the Eocene atmospheric CO₂ level was higher than it is today. Factors such as biological productivity could affect the surface-ocean carbonate ion concentration and thereby affect the predicted pCO₂ in the surface ocean. Nevertheless, we have shown here that pH values inferred by Pearson and Palmer are entirely consistent with large amounts of CO₂ in the Eocene atmosphere. Therefore, reports of the death of the carbon dioxide paradigm are exaggerated.

Ken Caldeira
Climate System Modeling Group
Lawrence Livermore National Laboratory
7000 East Avenue, L-103
Livermore, CA 94550, U.S.A.
E-mail: kenc{at}LLNL.gov
Robert Berner
Department of Geology and Geophysics
Yale University
New Haven, CT 06520-8109, U.S.A.
E-mail: berner{at}hess.geology.yale.edu

REFERENCES

1. P. N. Pearson and M. R. Palmer, Science 284, 1824 (1999) [Abstract/Free Full Text] .
2. R. A. Kerr, Science 284, 1743 (1999) [CrossRef] [Medline] .
3. R. A. Berner, A. C. Lasaga, R. M. Garrels, Am. J. Sci. 283, 641 (1983) .
4. Intergovernmental Panel on Climate Change (IPCC), Climate Change 1995: The Science of Climate Change: Contribution of Working Group I to the Second Assessment Report of the Intergovernmental Panel on Climate Change, J. T. Houghton et al., Eds. (Cambridge Univ. Press, New York, 1995).
5. T. J. van Andel, Earth Planet. Sci. Lett. 26, 187 (1975) .

Pearson and Palmer (1) use boron isotope measurements to infer sea surface pH values for the middle Eocene. From these values they argue that the carbon dioxide concentration in the mid-Eocene atmosphere was similar to modern values. However, their calculation of equilibrium atmospheric pCO₂ from sea surface pH is based on the invalid assumption of a modern oceanic total CO₂ (CO₂) concentration for the middle Eocene. They conclude that a higher CO₂ value "is unreasonable because it would imply a larger variation in calcium carbonate saturation in the oceans than is compatible with the geologic record." Figure 1 [of (2)] shows that a wide range of calcite saturation states can occur at virtually any CO₂ concentration, as long as changes in CO₂ are accompanied by corresponding changes in total alkalinity (A_T). Such changes are not at all unreasonable; they are implicit in any scenario for changes in atmospheric CO₂ levels due to long-term shifts in the carbonate-silicate geochemical cycle (3-5). Changes in oceanic CO₂ have long been known as a prerequisite for the occurrence of large changes in atmospheric CO₂ in the geologic past (2, 6).

6

6

Figure 1 also shows that a wide range of equilibrium pCO₂ values can be calculated for surface waters associated with any given calcite saturation condition in the deep ocean. Pearson and Palmer's best estimate of 8.05 for mid-Eocene surface pH, combined with the shallower calcite compensation depth of the middle Eocene (7), can be shown to imply deep ocean CO₂ and A_T values that are at least 50 percent higher than modern values. This scenario would be consistent with an equilibrium atmospheric pCO₂ three to four times the preindustrial value. These calculations would vary somewhat for different assumed temperatures and salinities, but the general features of Fig. 1 would remain the same.

Estimates of past sea surface pH are a very valuable addition to the information needed to understand the geologic history of atmospheric CO₂. However, these estimates must be supplemented by careful consideration of other constraints and by testing of hypothesized changes in past oceanic chemistry.

Eric T. Sundquist
U.S. Geological Survey
384 Woods Hole Road
Woods Hole, Massachusetts 02543, U.S.A.
E-mail: esundqui{at}usgs.gov

REFERENCES

1. P. N. Pearson and M. R. Palmer, Science 284, 1824 (1999) .
2. E. T. Sundquist, in The Changing Carbon Cycle: A Global Analysis, J. R. Trabalka and D. E. Reichle, Eds. (Springer-Verlag, New York, 1986), pp. 371-402.
3. R. M. Garrels, A. Lerman, F. T. Mackenzie, Am. Scientist 64, 306 (1976) .
4. R. A. Berner, A. C. Lasaga, R. M. Garrels, Am. J. Sci. 283, 641 (1983) .
5. E. T. Sundquist, Quat. Sci. Rev. 10, 283 (1991) .
6. M. L. Bender, in Climate Processes and Climate Sensitivity, J. E. Hansen and T. Takahashi, Eds. (American Geophysical Union, Washington, DC, 1984), pp. 352-359.
7. T. H. Van Andel, Earth Planet. Sci. Lett. 26, 187 (1975) .

Response: Sundquist, and Caldeira and Berner make the important point that our best estimate of middle Eocene atmospheric pCO₂ (370 to 400 ppm) may be low because we assumed a value for total dissolved inorganic carbon (CO₂) that is equal to that today. If CO₂ was higher, then our estimate of pCO₂ would need be revised upward.

In our report we were clear that in order to calculate pCO₂, some value of CO₂ must be taken. Because the actual level of CO₂ at 43 million years ago is not well known, we provided a diagram [figure 3 in (1)] that allowed the reader to estimate pCO₂ for CO₂ values up to 250% of the modern. Readers are invited to substitute whatever value they think is most appropriate. The diagram is similar in its essentials to figure 1 of Sundquist.

The great promise of the boron isotope technique is that it will soon be possible to analyze large numbers of samples with excellent stratigraphic resolution, as is currently the case, for example, with oxygen isotopes. It is likely that pCO₂, CO₂, and the carbonate compensation depth fluctuated considerably in the Eocene, possibly even on Milankovitch time scales (<100,000 years). General statements about enhanced metamorphic and magmatic outgassing rates in the Eocene as a whole may not be relevant to the situation in a specific narrow time window in the middle Eocene (43 Ma). Thus, while it may be the case that CO₂ was 50 percent higher, as Sundquist believes, we do not feel confident enough about the evidence from generalized geological considerations to rely on this assumption.

Caldeira and Berner make the interesting suggestion that a good assumption to make in order to calculate pCO₂ from surface ocean pH might be that the total carbonate ion concentration in the surface ocean was the same as that today. A potential advantage of this is that pCO₂ can be estimated with greater sensitivity than if we assume constant CO₂. However, as Caldeira and Berner make clear, the approach relies on the assumption that the calcium ion (Ca²⁺) concentration of the ocean has not changed, which may not be the case. We know of no reliable geochemical proxy for Ca²⁺ in the surface ocean. Modeling studies [see figure 9 in (2)] suggest that Ca²⁺ concentration may have changed by a factor of 3 in the Cenozoic. Thus, while the suggestion of Caldeira and Berner may prove valuable, more work needs to be done on proxies for Ca²⁺.

These comments underline the need for the development of quantitative determinations of past CO₂ variation so that pCO₂ estimates using the boron isotope technique can be made more accurate.

Paul N. Pearson
Department of Earth Sciences
University of Bristol
Queens Road
Bristol BS8 1RJ, U.K.
E-mail paul.pearson{at}bristol.ac.uk
Martin R. Palmer
T. H. Huxley School
Royal School of Mines
Imperial College
Prince Consort Road
London SW7 2BP, U.K.
E:mail: martin.palmer{at}ic.ac.uk

REFERENCES

1. P. N. Pearson and M. R. Palmer, Science 284, 1824 (1999) .
2. R. A. Berner, A. C. Lasagna, R. M. Garrels, Am. J. Sci. 283, 641 (1983) .