“The present findings corroborate the earlier conclusion based on study of the Paleozoic climate that “global climate may be independent of variations in atmospheric carbon dioxide concentration.” [64] (p.198).

Climate Impact of Increasing Atmospheric Carbon Dioxide

J. Hansen, D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind, G. RussellScience: 28 August 1981, Volume 213, Number 4511

…”The major difficulty in accepting this theory has been the absence of observed warming coincident with the historic C02 increase. In fact, the temperature in the Northern Hemisphere decreased by about 0.5°C between 1940 and 1970 (9), a time of rapid C02 buildup. In addition, recent claims that climate models overestimate the impact of radiative perturbations by an order of magnitude (10, 11) have raised the issue of whether the greenhouse effect is well understood.” …

(The authors are atmospheric physicists at the NASA Institute for Space Studies, Goddard Space Flight Center. New York 10025. D. Johnson contributed to the carbon dioxide research as a participant in the Summer Institute on Planets and Climate at the Goddard Institute for Space Studies and Columbia University.)

http://www.sealevel.info/1981_Hansen_etal_1.pdf

Reference 11 from above article is found in “Science. 1980 Mar 28;207(4438):1462-3.  The following is an excerpt from reference 11.

The Climatological Significance of a Doubling of Earth’s Atmospheric Carbon Dioxide Concentration. Idso SB.1

¹U.S. Water Conservation Laboratory, 4331 East Broadway, Phoenix, Arizona 85040

Abstract: “The mean global increase in thermal radiation received at the surface of the earth as a consequence of a doubling of the atmospheric carbon dioxide content is calculated to be 2.28 watts per square meter. Multiplying this forcing function by the atmosphere’s surface air temperature response function, which has recently been determined by three independent experimental analyses to have a mean global value of 0.113 K per watt per square meter, yields a value of </= 0.26 K for the resultant change in the mean global surface air temperature. This result is about one order of magnitude less than those obtained from most theoretical numerical models, but it is virtually identical to the result of a fourth experimental approach to the problem described by Newell and Dopplick. There thus appears to be a major discrepancy between current theory and experiment relative to the effects of carbon dioxide on climate. Until this discrepancy is resolved, we should not be too quick to limit our options in the selection of future energy alternatives.”

PMID: 17779615 DOI: 10.1126/science.207.4438.1462

https://www.ncbi.nlm.nih.gov/pubmed/17779615

Sherwood Idso, PhD.  http://www.co2science.org

The Relationship between Atmospheric Carbon Dioxide Concentration and Global Temperature for the Last 425 Million Years. W. Jackson Davis 1,2

1 Environmental Studies Institute, Boulder, CO 80301, USA; JacksonDavis@EnvironmentalStudiesInstitute.org

2 Division of Physical and Biological Sciences, University of California, Santa Cruz, CA 95064, USA

Received: 8 August 2017; Accepted: 22 September 2017; Published: 29 September 2017

Abstract: “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 (~540 million years 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. … This study demonstrates that changes in atmospheric CO2 concentration did not cause temperature change in the ancient climate.”  …

…  “The absence of a discernible correlation between atmospheric CO2 concentration and T over most of the Phanerozoic, as demonstrated above, appears to contravene the widely-accepted view about the relationship between atmospheric CO2 and temperature, by which increases in atmospheric CO2 concentration cause corresponding increases in T owing to increased radiative forcing.” …

“The logarithmic RFCO2 curve, established more than a century ago [10], implies a saturation effect, or diminishing returns, in which the marginal forcing power of atmospheric CO2 declines as CO2 concentration in the atmosphere increases.” …

“Discussion and Conclusions”

“The principal findings of this study are that neither the atmospheric concentration of CO2 nor ΔRFCO2 is correlated with T over most of the ancient (Phanerozoic) climate. Over all major climate transitions of the Phanerozoic Eon, about three-quarters of 136 correlation coefficients computed here between T and atmospheric CO2 concentration, and between T and ΔRFCO2, are non-discernible, and about half of the discernible correlations are negative. Correlation does not imply causality, but the absence of correlation proves conclusively the absence of causality [63]. The finding that atmospheric CO2 concentration and ΔRFCO2 are generally uncorrelated with T, therefore, implies either that neither variable exerted significant causal influence on T during the Phanerozoic Eon or that the underlying proxy databases do not accurately reflect the variables evaluated.”

“The present findings corroborate the earlier conclusion based on study of the Paleozoic climate that “global climate may be independent of variations in atmospheric carbon dioxide concentration.” [64] (p.198). The present study shows further, however, that past atmospheric CO2 concentration oscillates on a cycle of 15–20 My and an amplitude of a few hundred to several hundreds of ppmv. A second longer cycle oscillates at 60–70 My. As discussed below, the peaks of the ~15 My cycles align closely with the times of identified mass extinctions during the Phanerozoic Eon, inviting further research on the relationship between atmospheric CO2 concentration and mass extinctions during the Phanerozoic.”

https://www.mdpi.com/2225-1154/5/4/76  (pdf)

These 3 papers are well worth reading in their entirety.