Introduction

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

The long-term carbon cycle is controlled by chemical weathering, volcanic and metamorphic degassing, and the burial of organic carbon (1, 2). Ancient atmospheric carbon dioxide levels are reflected in the isotopic content of organic carbon (3) and, less directly, strontium (4) in marine sedimentary rocks; the former because photosynthetic carbon isotope fractionation is sensitive to CO₂ levels, and the latter because weathering and degassing are associated with extreme values of the abundance ratio ⁸⁷Sr/⁸⁶Sr. However, attempts to use these geochemical signals to estimate past CO₂ levels (5-8) are hindered by the signals' additional relationships to various tectonic (9, 10) and biological (11) effects. Moreover, the strontium signal has proven especially difficult to parse (12-15).

Here, I attempt to resolve these ambiguities in the isotopic signals of carbon and strontium. First, it is shown that the last 500 million years of the strontium signal, after transformation to remove the effects of recycled sediment (16, 17), correlate significantly with the concurrent record of isotopic fractionation between inorganic and organic carbon (3). This empirical result is supplemented by the theoretical deduction that the two records are linked by their common dependence on rates of continental weathering and magmatic activity. The assumption that CO₂ levels fall with the former and rise with the latter then indicates that an appropriate average of the two records should reflect the long-term fluctuations of the partial pressure of atmospheric CO₂. The CO₂ signal derived from this analysis represents fluctuations at time scales greater than about 10 million years (My). Comparison with the geologic record of climatic variations (18) reveals no obvious correspondence.

	Strontium and Carbon Isotopic Signals

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

Fig. 1 shows the strontium and carbon isotopic signals for the last 500 My. The data for the strontium isotope ratios ⁸⁷Sr/⁸⁶Sr were compiled by Veizer et al. (4) and Walter et al. (19); the former source accounts for all ⁸⁷Sr/⁸⁶Sr data younger than 520 My, whereas the latter was used for data extending back to 608 My (not shown). Both sets of ⁸⁷Sr/⁸⁶Sr data were first averaged in nonoverlapping time windows of 10 My. The resulting unevenly spaced record was then transformed (20) to an evenly spaced record with time increments of approximately 10 My and no contributions to the power spectral density at periods less than 21 My.

View larger version (22K): [in this window] [in a new window]   Fig. 1.   Data for toc (red filled circles) (3) and 87Sr/86Sr (blue open squares) (4). The time scale for toc has been revised from the original to match the scheme (32) used for the strontium data. The capital letters correspond to the following geologic periods: Ordovician, Silurian, Devonian, Carboniferous, Permian, Triassic, Jurassic, Cretaceous, and Tertiary.

The second record in Fig. 1, compiled by Hayes et al. (3) derives from the isotopic composition of marine organic carbon and carbonate carbon. From isotopic abundance ratios R_x = (¹³C/¹²C)_x for carbon in sample x, the isotopic fractionation between sample x and a standard (STD) sample, _x = 1,000[(R_x  R_STD)/R_STD], is obtained for carbonate (_a) and organic (_o) carbon. The isotopic fractionation _toc between total organic carbon and sedimentary carbonates is then given approximately by _toc = _a  o, which is the second signal plotted in Fig. 1.

Fig. 1 shows a surprising similarity between the two records for fluctuations with periods less than about 100 My. However, the correlation between the two time series is not statistically significant [Spearman rank correlation coefficient (21) R_s = 0.40, P = 0.17, N = 46], because the longer-period fluctuations are not in phase. It is therefore interesting to ask why the two records appear similar at shorter time scales and dissimilar at longer time scales.

Recent work has shown that the measurements of _toc approximately fit the empirical relation (3, 22)

[ 1 ]

The parameter ₀ represents the isotopic effects of photosynthesis and secondary biological processes along with the isotopic depletion of dissolved CO₂ in surface waters relative to sedimentary carbonate. Because ₀ is approximately constant throughout the period plotted in Fig. 1, the main source of _toc's fluctuations is contained in isotopic effects due to changing algal physiologythe permeability, surface-to-volume ratio, and growth rate of algal cellsrepresented by , and the concentration  of dissolved carbon dioxide in surface waters (3, 8).

Although the mechanisms responsible for the fluctuations of s = ⁸⁷Sr/⁸⁶Sr are subject to much debate (4, 9, 10, 12-15), some aspects of the signal's evolution are nevertheless clear. Because ⁸⁷Rb decays to ⁸⁷Sr with a half-life of ~48 billion years, the supply of ⁸⁷Sr may be taken to be approximately constant over the last 500 My. However, it is not uniformly distributed: the fluvial input to the oceans is derived in part from rocksboth silicates and metamorphosed carbonates (12-15)that are relatively enriched in radiogenic Sr (s  0.712 or greater) compared to the nonradiogenic Sr of mantle origin supplied at hydrothermal vents (s  0.7035) (23). The value of s(t) at some particular time t represents, to first approximation, the relative fluxes of these two extreme values.

However, this first approximation ignores the recycling of rocks in the sedimentary cycle (16). As pointed out by Brass (17), about 75% of the strontium input to the oceans should come from the weathering of exposed carbonates of marine origin. Because these carbonates retain a memory of s at the time of deposition, their contribution to sedimentary Sr significantly damps the signal coming from hydrothermal vents (low s) and rocks containing radiogenic Sr (high s) (9).

Denoting the fluvial flux of radiogenic Sr by r, the input from hydrothermal vents by v_h, and the memory effect by m, a simple expression for the strontium isotope ratio s is

[ 2 ]

where 0  µ  1 is the fraction of sedimentary Sr deriving from the memory flux, and g is a function that depends on both r and v_h. The memory term can be approximated by assuming that sedimentary strontium is weathered at a rate proportional to its mass (16). Then m(t) is simply a weighted (exponentially decaying) average of s(),  < t (17), which we express by the convolution

[ 3 ]

The parameter  is related to the half-life t_1/2 of sedimentary Sr; i.e.,  = (ln 2)/t_1/2. Brass estimates 57 My < t_1/2 < 102 My (17). Therefore, the memory effect should strongly influence the fluctuations of s at long time scales (greater than about 100 My), whereas the short time scale fluctuations should be relatively unaffected.

The short-time correlations may be explained in part by noting the common dependence of _toc and g on the global weathering rate w (i.e., the flux of all weathered products from the continents to the oceans) and the rate of magmatic activity v associated not only with the hydrothermal flux v_h but also with volcanic degassing. Assuming that r = r(w) and v_h = v_h(v), g's dependence on w and v may be written^§

[ 4 ]

With respect to _toc, the physiological term  may likewise depend on w because of changing nutrient concentrations in the oceans.  could also depend on CO₂ levels, which in turn depend on degassing, weathering ratesbecause of the net uptake rate u = u(w) of atmospheric CO₂ associated with silicate weathering (1, 2, 24)and other processes, such as organic carbon burial, which we collectively designate by b. Aggregating these dependencies then yields

[ 5 ]

Comparison of Eqs. 4 and 5 directly reveals the joint dependence of g and _toc on v and w.

	Removal of the Effects of Sedimentary Recycling

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

Because the strontium signal s contains a memory effect, whereas _toc does not, removal of the memory effect should reveal correlations between s and _toc at both short and long time scales, thereby confirming the joint dependence on v and w. To test this hypothesis, I first assume it is true and use it to estimate g. For a given  and µ, m is calculated by discretizing Eq. 3 for  > 608 My. Eq. 2 is then solved for g:

[ 6 ]

Here the subscripts make explicit the dependencies on  and µ.

Let R_µ(_toc, g_µ) be the Pearson product-moment correlation coefficient (21) that quantifies the similarity of _toc and g_µ. From the foregoing argument, the best estimate of  and µ should be that which minimizes R_µ (because the expected correlation is negative). Fig. 2 shows contours of R as a function of µ and t_1/2 = (ln 2)/. The minimum R_µ = 0.81 occurs at t_1/2 = 54 My and µ = 0.99. However, the corresponding estimate of g_µ includes values below the hydrothermal minimum of 0.7035. Such nonphysical ratios probably derive from the amplification of any measurement noise resulting from division by the small quantity 1  µ in Eq. 6. Indeed, the dark gray region in Fig. 2 indicates that all such results occur only for µ close to unity. I therefore define the best estimates *, µ* of , µ by minimizing R_µ subject to the constraint that g_µ > 0.7035. One then finds t*_1/2 = ln 2/* = 41 My and µ* = 0.83, corresponding to R_*µ* = 0.80 (within 1% of the unconstrained minimum). These results are in reasonable accord with Brass's estimate of the half-life of sedimentary Sr (57  102 My) (17) and his conclusion that "strontium leached from limestones is about 75% of the total input" (17).

View larger version (27K): [in this window] [in a new window]   Fig. 2.   Contours of Rµ as a function of µ, the fraction of sedimentary Sr deriving from the memory flux, and t1/2 = (ln 2)/, the half-life of sedimentary Sr. R was calculated for µ = 0, 0.01, ... , 0.99 and t1/2 = 1, 2, ... , 99 My. For large half-life, the contours decrease from left to right as follow: 0.60, 0.65, 0.70, 0.75, 0.79. The symbol × marks the minimum, R*µ* = 0.80, obtained under the constraint that g(t) > 0.7035. The area shaded dark gray on the right does not satisfy the constraint. The rectangular area labeled "Brass" corresponds to previous estimates obtained by geochemical arguments (17); its horizontal extent has not been explicitly computed.

Fig. 3 shows g_*µ* compared to _toc. Compared with Fig. 1, one sees that both the long and short period fluctuations are now not only approximately equally correlated, but the correlation is also significant (R_s = 0.74, P < 10³, N = 46). The hypothesis that recycled sediment partially obscured an inherent correlation because of a shared dependence on weathering and volcanic processes is therefore confirmed.

View larger version (22K): [in this window] [in a new window]   Fig. 3.   The function g (blue squares) obtained by removing the memory flux from the 87Sr/86Sr data of Fig. 1, along with toc (red circles). Note that the range of the 87Sr/86Sr curve is approximately five times greater than in Fig. 1. The data are plotted such that the mean of both time series lies on the same horizontal line and their rms fluctuations have the same vertical extent.

	Relationship to CO2 Levels

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

To understand further the correlation, I make the following assumptions concerning the functional dependencies contained in Eqs. 4 and 5:

[ 7 ]

The first two state that the flux of radiogenic Sr to the oceans and the uptake of atmospheric CO₂ because of silicate weathering increase as the global weathering rate (of all minerals in all terranes) increases. The third formalizes the natural assumption that the hydrothermal flux of Sr varies with the same sign as all magmatic processes.

Because the Sr isotope ratios increase with increasing r (i.e., g/r > 0) and decrease with increasing v_h (i.e., g/v_h < 0), one has

[ 8 ]

Because g and _toc are negatively correlated, one expects that _toc depends on v and w in the opposite sense:

[ 9 ]

The inequalities 8 and 9 have been obtained without making any explicit assumption concerning any dependence of r on u nor  on v and w. Because they show that v and w each influence g and _toc with opposite signs, the relative fluctuations of any other quantity that also depends on v and w with opposite signs may be inferred from the shared fluctuations of g and _toc.^¶ Specifically, the concentration  of oceanic CO₂ responds positively to v while its response to weathering is negative:

[ 10 ]

Thus the shared fluctuations of g and _toc indicate the relative fluctuations of ancient CO₂ levels.

	Estimation of the CO2 Signal

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

I proceed to estimate the CO₂ signal explicitly. First, the highest measurement of _toc, at 175 My, is dropped because of its statistical insignificance (3). I then transform g(t)  _g(t), a strontium-derived estimate of _toc, by mapping the left axis of Fig. 3 to the corresponding value on the right axis. The quantities _toc and _g are then averaged to obtain

[ 11 ]

The times t_i are given by the points where _toc is specified and _g(t_i) is obtained by linear interpolation. Here it is implicitly assumed that _toc and _g contain a common signal that is enhanced by averaging. Statistical arguments suggest that 's rms signal-to-noise ratio lies between about 2 and 3.^**

Assume now that  and ₀ are constant and define the dimensionless CO₂ concentration  = ₀/ (8). In terms of  and , Eq. 1 then yields

[ 12 ]

At long time scales such that the oceans are in equilibrium with the atmosphere, the partial pressure pCO₂ is proportional to  (1). The relative fluctuations of pCO₂ are therefore given by (t)/(0), which is plotted in Fig. 4 for ₀ = 36 per mil (). The gray area surrounding the pCO₂ curve in Fig. 4 brackets this result for ₀ = 35 and 38, a range consistent with previous estimates (3).

View larger version (23K): [in this window] [in a new window]   Fig. 4.   Fluctuations of pCO2 for the last 500 My, normalized by the estimate of pCO2 obtained from the most recent value of . The solid line is obtained from Eq. 12 by using 0 = 36. The lower and upper limits of the gray area surrounding the pCO2 curve result from 0 = 38 and 35, respectively. The gray bars at the top correspond to periods when Earth's climate was relatively cool; the white spaces between them correspond to warm modes (18).

Fig. 4 reveals that CO₂ levels have mostly decreased for the last 175 My. Prior to that point they appear to have fluctuated from about two to four times modern levels with a dominant period of about 100 My. The decline for the last 175 My is also present in several previous pCO₂ reconstructions (7, 8, 26, 27), and the entire curve displays some similarity to a previous estimate derived from the geologic record of carbonate formation (26). Although the period before 175 My differs substantially from previous geochemical model calculations (7), an approximate error estimate lends considerable credence to the pCO₂ curve of Fig. 4. Specifically,  should inherit 's signal-to-noise ratio of 2-3. This correspondence would be exact if () were linear. Because () is monotonic for the observed range of , its nonlinearity does not affect the timing of the maxima and minima of the pCO₂ curve. Thus the linear error estimate remains pertinent.

	Comparison with the Climate Record

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

Using a variety of sedimentological criteria, Frakes et al. (18) have concluded that Earth's climate has cycled several times between warm and cool modes for roughly the last 600 My. Recent work by Veizer et al. (28), based on measurements of oxygen isotopes in calcite and aragonite shells, appears to confirm the existence of these long-period (~135 My) climatic fluctuations. Changes in CO₂ levels are usually assumed to be among the dominant mechanisms driving such long-term climate change (29).

It is therefore interesting to ask what, if any, correspondence exists between ancient climate and the estimate of pCO₂ in Fig. 4. The gray bars at the top of Fig. 4 correspond to the periods when the global climate was cool; the intervening white space corresponds to the warm modes (18). The most recent cool period corresponds to relatively low CO₂ levels, as is widely expected (30). However, no correspondence between pCO₂ and climate is evident in the remainder of the record, in part because the apparent 100 My cycle of the pCO₂ record does not match the longer climatic cycle. The lack of correlation remains if one calculates the change in average global surface temperature resulting from changes in pCO₂ and the solar constant using energy-balance arguments (7, 26).

Superficially, this observation would seem to imply that pCO₂ does not exert dominant control on Earth's climate at time scales greater than about 10 My. A wealth of evidence, however, suggests that pCO₂ exerts at least some control [see Crowley and Berner (30) for a recent review]. Fig. 4 cannot by itself refute this assumption. Instead, it simply shows that the "null hypothesis" that pCO₂ and climate are unrelated cannot be rejected on the basis of this evidence alone.

	Discussion and Conclusion

Top Abstract Introduction Strontium and Carbon Isotopic... Removal of the Effects... Relationship to CO2 Levels Estimation of the CO2... Comparison with the Climate... Discussion and Conclusion References

One of the principal contributions of this study is methodological. From observations of a weak correlation between strontium and carbon isotopic signals (Fig. 1) and their shared dependence on global weathering rates and magmatic activity, weathering and magmatism are deduced to be the main processes driving the signals' fluctuations. Correction for the effects of sedimentary recycling enhances the correlation (Fig. 3), indicates a strong shared signal, and strengthens this conclusion.

A second, crucial step is to note that any quantity with a similar joint dependence on weathering and magmatic processes may be expected to display similar fluctuations. Here attention has been focused on CO₂ levels; as for the strontium and carbon isotopic signals, CO₂ levels depend on weathering and magmatism with opposite signs and should therefore fluctuate roughly in sync with the isotopic signals. Because the reasoning is general, it need not be limited to CO₂. Among the many possible applications, the case of oceanic phosphate concentrations is particularly interesting. Phosphate concentrations should increase with weathering and decrease with hydrothermal activity (31); thus the methodology in this paper may be applicable to their reconstruction. Moreover, because phosphorus is a limiting nutrient, oceanic productivity may be expected to covary positively with its concentration in seawater, suggesting that CO₂ levels and productivity covary negatively at geologic time scales (8).

Such reasoning naturally raises the issue of cause and effect. This study indicates that degassing and silicate weathering were the primary controls on the carbon cycle for the last 500 My. But the results do not themselves indicate whether either of these mechanisms dominated, or whether weathering was driven by the diversification of land plants (8), continental collisions (9), or a complex combination of tectonic, biological, and geochemical processes (7). They do, however, offer a new view of the long-term fluctuations of pCO₂ that will hopefully stimulate novel approaches to the study of biogeochemical cycles at evolutionary time scales.