Simple Equation of Multi-Decadal Atmospheric Carbon Concentration Change
ABSTRACT
Surplus CO2 is removed from the atmosphere by natural sinks at rate, proportional to the surplus CO2 concentration. In other words, it undergoes exponential decay with a single decay constant. This conclusion is rigorously proven, using first principles and relatively recent observations of oceans. Historical data for CO2 concentrations and emissions from 1958–2013 are then used to calculate the half-life of the surplus concentration. This theoretically derived formula is found to be an excellent match to the historical CO2 concentrations over the measurement period. Furthermore, the “initial” CO2 concentration in the formula came out to be very close to the likely “pre-industrial” CO2 concentration. Based on the used datasets, the half-life of the surplus concentration of CO2 in the atmosphere is found to be approximately 40 years.
Full Article: defyccc.com/docs/se/MDACC-Halperin.pdf
Supporting Material (data and software as Excel file): defyccc.com/docs/se/MDACC-Halperin-Supporting-Material.xlsx
Cite as:
Halperin Ari, 2015. Simple Equation of Multi-Decadal Atmospheric Carbon Concentration Change, defyccc.com, defyccc.com/se
Article’s History
Originally published on November 24, 2015.
The article is archived at www.webcitation.org/6dJdf6BpL
The supporting material is archived at www.webcitation.org/6dJeovZD7
Author’s comment posted on December 3, 2015.
This page is archived at www.webcitation.org/6dWPiCJlD on December 4, 2015
AGU Index Terms (November 29, 2015)
1600 GLOBAL CHANGE
…. 1610 Atmosphere (0315, 0325)
…. 1616 Climate variability (1635, 3305, 3309, 4215, 4513)
…. 1620 Climate dynamics (0429, 3309)
…. 1631 Land/atmosphere interactions (1218, 1843, 3322)
…. 1635 Oceans (1616, 3305, 4215, 4513)
3300 ATMOSPHERIC PROCESSES
…. 3305 Climate change and variability (1616, 1635, 3309, 4215, 4513)
…. 3309 Climatology (1616, 1620, 3305, 4215, 8408)
…. 3322 Land/atmosphere interactions (1218, 1631, 1843, 4301)
…. 3339 Ocean/atmosphere interactions (0312, 4301, 4504)
0400 BIOGEOSCIENCES
…. 0426 Biosphere/atmosphere interactions (0315)
…. 0428 Carbon cycling (4806)
…. 4800 OCEANOGRAPHY: BIOLOGICAL AND CHEMICAL (0460)
…. 4806 Carbon cycling (0428)
…. 4928 Global climate models (1626, 3337)
Web of Science Categories (November 29, 2015): OCEANOGRAPHY, ENVIRONMENTAL SCIENCES, GEOCHEMISTRY & GEOPHYSICS, METEOROLOGY & ATMOSPHERIC SCIENCES
The article contains an estimate of the half-life of the surplus atmospheric CO2 concentration, using the official datasets. The author takes notice that these datasets are biased because of underreporting of the anthropogenic CO2 release since UNFCCC, 1992. This bias might have caused exaggerated estimate of the half-life.
The author thinks that the half-life of the surplus atmospheric CO2 concentration is between 30 and 40 years. The most likely value is 35 years. Corresponding D0 = 267 ppm.
This comment does not affect other results and conclusions of the article.
(Comment ID: H2015#1)
A half-life of 35 years implies an average effective atmospheric lifetime (a/k/a “adjustment time”) of emitted CO2 equal to 35 / ln(2) ≌ 50 years. That matches what several other authors have reported, including me:
Burton, D. A. (2024). Comment on Stallinga, P.(2023), Residence Time vs. Adjustment Time of Carbon Dioxide in the Atmosphere. https://doi.org/10.31219/osf.io/brdq9
and Dr. Roy Spencer:
Spencer, R. W. (2023). ENSO Impact on the Declining CO2 Sink Rate. J Mari Scie Res Ocean, 6(4), 163-170. https://doi.org/10.33140/jmsro.06.04.03
and Dr. Peter Dietze:
http://www.john-daly.com/carbon.htm#:~:text=The%20value%20for%20T%20can%20be%20defined%20dividing%20the%20amount%20of%20present%20excess%20by%20the%20present%20outflow%2C%20yielding%2055%20years
and Ferdinand Engelbeen:
Engelbeen F (2022).The origin of the increase of CO2in the atmosphere, http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html (section 3)
and
https://wattsupwiththat.com/2024/08/30/new-study-co2s-atmospheric-residence-time-4-yearsnatural-sources-drive-co2-concentration-changes/#comment-3962581
(“Tau = 120 ppmv / 2.25 ppmv/year = 53 years”)
and Prof. Richard Lindzen during the Q&A (3rd video) of this excellent(!) lecture:
● Part 1: https://www.youtube.com/watch?v=hRAzbfqydoY
● Part 2: https://www.youtube.com/watch?v=V-vIhTNqKCw
● Part 3 (Q&A): https://www.youtube.com/watch?v=69kmPGDh1Gs (including discussion of CO2 adjustment time / effective atmospheric lifetime):
One other note… I don’t think the “land use change emission” estimates are reliable, inasmuch as they’re from models which differ greatly in their calculated estimates. But if we simply consider land use change emissions to be a diminishment of natural CO2 removals, then we can ignore them, and subtract the rate of fossil carbon emissions from the atmospheric CO2 growth rate to find the rate of natural CO2 removals. That doesn’t affect the conclusions much, but it does yield a higher D₀.