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 (CO2) 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 (similar to 540 to 0 years before the present) and through complementary modeling using the atmospheric absorption/transmittance code MODTRAN. Atmospheric CO2 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 CO2 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 (Delta RFCO2), the change in forcing at the top of the troposphere associated with a unit increase in atmospheric CO2 concentration, was computed using MODTRAN. The correlation between Delta RFCO2 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 Delta RFCO2. Of 68 correlation coefficients (half non-parametric) between Delta RFCO2 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 CO2 concentration and Delta RFCO2 oscillate across the Phanerozoic, and cycles of CO2 and D RFCO2 are antiphasic. A prominent 15 million-year CO2 cycle coincides closely with identified mass extinctions of the past, suggesting a pressing need for research on the relationship between CO2, biodiversity extinction, and related carbon policies. This study demonstrates that changes in atmospheric CO2 concentration did not cause temperature change in the ancient climate.