Empirical Validation of the Exponential Decay for Surplus CO2

Guest essay by Leo Goldstein

My new scientific paper Empirical Validation of the Exponential Decay for Surplus CO₂ further validates the conclusion that surplus CO₂ in the air decays exponentially. The half-life is re-estimated down to 30-35 years. Further, if the CO₂ sink rate has changed in the last 100 years, it has increased rather than decreased (i.e., the half-life has decreased). The paper uses pre-1958 concentrations, which were obtained by C.D. Keeling by re-analyzing certain 19^th century instrumental measurements and merging them with the ice core measurements.

This pre-1958 data indicates that atmospheric CO₂ concentrations steadily increased from 288 ppm in 1860 to 315 ppm in 1958. Thus, the IPCC opinion on atmospheric CO₂ concentrations since 1860 is in a good agreement with the empirical data. I do not agree with criticism pointing to some pre-1958 measurements showing significantly higher concentrations. Such high readings were likely caused by local sources of CO₂, such as industry, buildings, or even scientists’ own breath. The IPCC’s distortion of the carbon cycle was addressed in a recent article on WUWT.

A summary of the new paper and two relevant graphs appear below.

Surplus CO₂ is naturally removed from the atmosphere by natural sinks at a rate proportional to the surplus CO₂ concentration, on the multi-decadal scale. This result, analytically derived in (Halperin, Simple Equation of Multi-Decadal Atmospheric Carbon Concentration Change, 2015) is verified here by applying it to the pre-1958 data, which was not used in the original paper. The excellent match confirms the validity of the theoretical result. This paper also presents a more accurate estimate of the half-life of the surplus CO₂ concentration: 30-35 years. The correspondent equilibrium concentration is estimated to be in the range of 267-285 ppm (larger equilibrium concentrations correspond to lower half-lives). Also, the paper finds that if the natural sink rate did change in the past 150 years, it increased at least during the period prior to 1958. The paper uses CO₂ emissions data, corrected for some inaccuracies, introduced since 1992.

Fig. 1. Comparison of the measured concentration of CO₂ in the atmosphere (Keeling curve) to that computed using formula (2) with the same constant half-life from 1860-2013. From Halperin, Empirical Validation of the Exponential Decay for Surplus CO₂

Fig. 2. Comparison of the concentrations of CO₂ in the atmosphere, based on historic measurements from 1872-1882 (Keeling & From, 1986) and computed using formula (2) with the same constant half-life, from 1860-1957. From Halperin, Empirical Validation of the Exponential Decay for Surplus CO₂

Thus, the natural exponential decay of the surplus (over ~280 ppm) CO₂ concentration with a half-life of about 30-35 years is established now for a multi-decadal timescale. The significance of this result is that the atmospheric CO₂ concentration is unlikely to exceed 550 ppm in the 21^st century, despite current exponential growth in the use of the fossil fuels. In the unlikely case that elevated atmospheric CO₂ becomes undesirable, it will be possible to lower it significantly by decreasing emissions, although the exponential decay formula should be used in such a case with great caution, because this scenario has not been encountered before.