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 19th 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 21st 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.