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Due to IPCC the climate sensitivity of CO₂ very likely is 3.0 ± 1.5 ℃ for each doubling of the concentration of atmospheric CO₂.

Counting on earlier global warming using the Arrhenius formula [ΔT=λ·α·㏑(C/C₀)], global mean vs emissions of atmospheric CO₂, assumed mostly depending on CO₂, gives:

  1. 1970-2018 0.9 ℃ 325ppm,408ppm: sensitivity 2.74 ℃
  2. PETM 5 ℃ 700ppm,2000ppm: sensitivity 3.30 ℃

The Paleocene–Eocene Thermal Maximum (PETM) is associated with extreme changes in Earth's carbon cycle due to volcanism about 55 million years ago. The warm period lasted for about 200,000 years. (Wikipedia)

Of course, there is an amount of uncertainty in the PETM figures and Earth wasn't quite the same since it was ice free etc, but these two examples support the information from IPCC with a most likely value of about 3 ℃.

The circumstances, the cause of PETM and the coincidence of the today emissions and observed warming, indicate that calculations like this is relevant.

My question is:

Are there other geological events that can be used to estimate the climate sensitivity?

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I did an error, the concentration of atmospheric CO₂ 1970 was 325 ppm.

The formula I use is: Climate Sensitivity = ΔT∙㏑ 2/㏑(C/C₀)].

I think that the Arrhenius formula is valid only for a solid sphere without (especially vertical) currents. Calculating the climate sensitivity for global land

https://www.ncdc.noaa.gov/cag/global/time-series/globe/land/1/6/1880-2019

from the range of the Keeling curve gives sensitivity≈3.48 ℃.

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  • $\begingroup$ On the possible role and source of carbon during the PETM: pnas.org/content/113/28/7739 and nature.com/articles/nature23646. Since the driver for the warming isn't quite clear, i am not sure if we can find analogies ... but i am ready to be tought :-) Might have been a combined seabed methane and volcanic carbon release effort ... $\endgroup$ – user18411 Dec 25 '19 at 14:40
  • $\begingroup$ This work suggest that up to 28,000petagrams (28 billion tons, hope i got all the zeros right) of carbon were released, nearly doubling earlier estimates: sciencedirect.com/science/article/pii/S092181811930534X. This could be compared to current emissionrates. $\endgroup$ – user18411 Dec 25 '19 at 17:05
  • $\begingroup$ @ebv - "Mass balance calculations indicate that the required carbon mass during the CIE interval would not exceed ~28,000 Pg, given that the carbon was released from organic matter, permafrost, thermogenic methane, methane hydrate, or any of their combinations." $\endgroup$ – Lehs Dec 25 '19 at 17:40
  • $\begingroup$ Yeah, i read it or rather scanned over it. It is the "upper end" and still below current emission rates, if i made no mistake converting numbers. $\endgroup$ – user18411 Dec 25 '19 at 17:44
  • $\begingroup$ @ebv - It makes an upper limit 0.56 Gt/y. Humans today is about 10 Gt/y. Using the upper limit for calculating sensitivity gives 1.82 ℃ beating the IPCC low limit which is 1.5 ℃. $\endgroup$ – Lehs Dec 25 '19 at 18:17

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