The Relationship between Atmospheric Carbon Dioxide Concentration and Global Temperature for the Last 425 Million Years
Assessing human impacts on climate and biodiversity requires an understanding of the relationship between the concentration of carbon dioxide (CO 2 ) in the Earth's atmosphere and global temperature (T). Here I explore this relationship empirically using comprehensive, recently-compiled databases of stable-isotope proxies from the Phanerozoic Eon (~540 to 0 years before the present) and through complementary modeling using the atmospheric absorption/transmittance code MODTRAN. Atmospheric CO 2
... . Atmospheric CO 2 concentration is correlated weakly but negatively with linearly-detrended T proxies over the last 425 million years. Of 68 correlation coefficients (half non-parametric) between CO 2 and T proxies encompassing all known major Phanerozoic climate transitions, 77.9% are non-discernible (p > 0.05) and 60.0% of discernible correlations are negative. Marginal radiative forcing (∆RF CO2 ), the change in forcing at the top of the troposphere associated with a unit increase in atmospheric CO 2 concentration, was computed using MODTRAN. The correlation between ∆RF CO2 and linearly-detrended T across the Phanerozoic Eon is positive and discernible, but only 2.6% of variance in T is attributable to variance in ∆RF CO2 . Of 68 correlation coefficients (half non-parametric) between ∆RF CO2 and T proxies encompassing all known major Phanerozoic climate transitions, 75.0% are non-discernible and 41.2% of discernible correlations are negative. Spectral analysis, autoand cross-correlation show that proxies for T, atmospheric CO 2 concentration and ∆RF CO2 oscillate across the Phanerozoic, and cycles of CO 2 and ∆RF CO2 are antiphasic. A prominent 15 million-year CO 2 cycle coincides closely with identified mass extinctions of the past, suggesting a pressing need for research on the relationship between CO 2 , biodiversity extinction, and related carbon policies. This study demonstrates that changes in atmospheric CO 2 concentration did not cause temperature change in the ancient climate. Climate 2017, 5, 76 2 of 35 question for contemporary climate policy is how much of the observed global warming is attributable to the accumulation of atmospheric CO 2 and other trace greenhouse gases emitted by human activities. The purpose of this study is to explore the relationship between atmospheric CO 2 and global temperature in the ancient climate, with the aim of informing the current debate about climate change. The effect of atmospheric CO 2 on climate has been investigated for nearly two centuries (for historical reviews see    ), beginning with the insight by Fourier [6, 7] that the atmosphere absorbs longwave radiation from the Earth's surface. This insight was confirmed empirically by laboratory experiments demonstrating selective absorption of longwave radiation by both CO 2 and especially water vapor [8, 9] . The possible influences of atmospheric CO 2 on the Earth's energy balance and temperature were refined throughout the 19th century [8, 9] , presaging the first successful model of the Earth's radiation budget, the demonstration of the logarithmic dependence of radiative forcing on the atmospheric concentration of CO 2 , and the first estimate of the sensitivity of temperature to a doubling of atmospheric CO 2 concentration  . These empirical studies led to the hypothesis that past glacial cycles were regulated by changes in atmospheric CO 2 . The earliest suggestion that CO 2 emitted by human activities might warm the Earth [10,11] prompted numerous calculations and projections of anthropogenic global warming, and this hypothesis prevailed throughout most of the 20th century  . The role of CO 2 in climate was complemented by theoretical advances in the early twentieth century. Building on previous work [13, 14] , Milankovitch calculated that fluctuations in solar insolation caused by variations in the Earth's orbit around the Sun are a central cause of past global glacial cycles  . This theoretical foundation, combined with the empirical demonstration by paleoclimate scientists during the mid-20th century of past and impending "ice ages", focused renewed attention on global cooling, including any that might be induced by anthropogenic aerosols (, reviewed in ). The consensus among climate scientists in the mid-20th century remained, however, that greenhouse warming was likely to dominate climate on time scales most relevant to human societies (, reviewed in ). The role of atmospheric CO 2 in regulating global temperature came under renewed scrutiny at the turn of the 21st century in respect to the climate of the Phanerozoic Eon beginning about 540 million years before present (Mybp). One group of investigators supported the prevailing consensus that atmospheric CO 2 played the central role in forcing the Phanerozoic climate     based on what they interpreted as a "pervasive tight correlation" between temperature and CO 2 proxies that implied "strong control" of global temperature by atmospheric CO 2  (p. 5665). The posited association between atmospheric CO 2 and T was inferred from visual examination of CO 2 time series (modeled and proxy) and their relationship with stratigraphically-sourced glacial and cold periods, however, rather than computed correlation coefficients between CO 2 and T. Other investigators of the Phanerozoic climate hypothesized a decoupling of global temperature from the atmospheric concentration of CO 2 , suggesting that atmospheric CO 2 played little     or no [26, 27] role in forcing the ancient climate. One group concluded that an updated and exhaustive stable-isotope database of a range of Phanerozoic climate proxies completed in 2008 "does not provide unambiguous support for a long-term relationship between the carbon cycle [CO 2 ] and paleoclimate [T]."  (p. 132). The posited absence of coupling between atmospheric CO 2 and T during the Phanerozoic Eon was again, however, not supported by computed correlation coefficients, and the renewed debate over the role of atmospheric CO 2 in the Phanerozoic climate remained, therefore, unresolved. Contemporary investigators, particularly in the climate modeling community, have largely embraced the hypothesis that atmospheric CO 2 plays a significant if not the predominant role in forcing past and present global temperature [5,     . The role of atmospheric CO 2 in climate includes short-and long-term aspects. In the short term, atmospheric trace gases including CO 2 are widely considered to affect weather by influencing surface sea temperature anomalies and sea-ice variation, which are key leading indicators of annual and decadal atmospheric circulation and consequent rainfall, drought, floods and other weather extremes      . Understanding the role of atmospheric CO 2 in forcing global temperature therefore Climate 2017, 5, 76 3 of 35 has the potential to improve weather forecasting. In the long term, the Intergovernmental Panel on Climate Change (IPCC) promulgates a significant role for CO 2 in forcing global climate, estimating a "most likely" sensitivity of global temperature to a doubling of CO 2 concentration as 2-4 • C [29-31]. Policies intended to adapt to the projected consequences of global warming and to mitigate the projected effects by reducing anthropogenic CO 2 emissions are on the agenda of local, regional and national governments and international bodies. The compilation in the last decade of comprehensive empirical databases containing proxies of Phanerozoic temperature and atmospheric CO 2 concentration enables a fresh analytic approach to the CO 2 /T relationship. The temperature-proxy databases include thousands of measurements by hundreds of investigators for the time period from 522 to 0 Mybp [28, 38, 39] , while proxies for atmospheric CO 2 from the Phanerozoic Eon encompass 831 measurements reported independently by hundreds of investigators for the time period from 425 to 0 Mybp  . Such an unprecedented volume of data on the Phanerozoic climate enables the most accurate quantitative empirical evaluation to date of the relationship between atmospheric CO 2 concentration and temperature in the ancient climate, which is the purpose of this study. I report here that proxies for temperature and atmospheric CO 2 concentration are generally uncorrelated across the Phanerozoic climate, showing that atmospheric CO 2 did not drive the ancient climate. The concentration of CO 2 in the atmosphere is a less-direct measure of its effect on global temperature than marginal radiative forcing, however, which is nonetheless also generally uncorrelated with temperature across the Phanerozoic. The present findings from the Phanerozoic climate provide possible insights into the role of atmospheric CO 2 in more recent glacial cycling and for contemporary climate science and carbon policies. Finally, I report that the concentration of atmospheric CO 2 oscillated regularly during the Phanerozoic and peaks in CO 2 concentration closely match the peaks of mass extinctions identified by previous investigators. This finding suggests an urgent need for research aimed at quantifying the relationship between atmospheric CO 2 concentration and past mass extinctions. I conclude that that limiting anthropogenic emissions of CO 2 may not be helpful in preventing harmful global warming, but may be essential to conserving biodiversity. Methods Data Sources Temperature proxies employed here include raw, non-detrended δ 18 O measurements (sample size or n = 6680; data from ), which were multiplied by negative unity to render isotope ratios directly proportional to temperature. This operation is expressed throughout this paper as δ 18 O*(−1) and does not change the absolute values of correlation coefficients reported here. Oxygen isotope ratios are widely used as a paleoclimate temperature proxy (e.g.,      ), although this proxy also reflects salinity, ice volume and other environmental variables and encompasses variance associated with location (e.g., proximity to the ocean) and time  . It is estimated that approximately half of the δ 18 O signal reflects changes in past temperatures and numerous equations for converting δ 18 O to temperature ("paleothermometers") have been developed and are in wide use (e.g., [44, 45, 47] ). It is widely accepted that oxygen isotope ratios are proportional to past temperature, the central prerequisite for valid regression analysis. Temperature Proxies The present analysis is limited to proxy isotopic values (‰)  generally without converting to temperature. Samples used here included measurements from tropical, temperate and Arctic latitudes  in the respective proportions~20:6:1. Temperature-proxy data were therefore dominated by paleotropical data. Radiative forcing varies with latitude  , and the present MODTRAN modeling exercises (described below) therefore included tropical latitudes to enable the most accurate possible comparison of modeled with empirical climate data. Forcing of T by CO 2 computed using MODTRAN Climate 2017, 5, 76 4 of 35 was used for all correlation analyses with paleoclimate proxies contained in the empirical databases evaluated here. To estimate the integrity of temperature-proxy data, δ 18 O values were averaged into bins of 2.5 million years (My) and the coefficient of variation (CV; the standard deviation divided by the mean) was plotted against age for the updated δ 18 O database  . The Pearson correlation coefficient between age and CV is non-discernible (R = 0.08, p = 0.11, n = 427; Figure 1a ). Enhanced variance characterizes two sampling bandwidths, 0-50 Mybp and 100-200 Mybp (Figure 1 ), while older sample ages are associated with low and stable variance. The resolution of temperature-proxy measures is relatively high-6680 samples across 522 My, or a mean of 12.8 sample datapoints per My corresponding to a mean sampling interval of 78,125 thousand years (Ky)-and does not decline with sample age (Figure 2a) . Assuming that repeat-measure variance is inversely related to sample quality, these findings do not support the hypothesis that older δ 18 O data are compromised in comparison with more recent δ 18 O data by age-related degeneration of information quality from, for example, diagenetic settling [49, 50] . Analysis of the more comprehensive databases used here, therefore, supports the same conclusions about variation of data quality with age as reached earlier on the basis of more limited datasets [28, 38, 51] .