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 I recently came across this paper by Antero Ollila

https://www.academia.edu/113644210/Radiative_Forcing_and_Climate_Sensitivity_of_Carbon_Dioxide_CO_2_Fine_tuned_with_CERES_Data

It is a lengthy report, which is an indication of how difficult the subject is. I just quote its abstract here:

‘An updated effective radiative forcing (ERF) value for constructing a simplified logarithmic forcing equation, and a transient climate response (TCR) value, are presented for CO2, CH4, and N2O. The results are based on line-by-line (LBL) calculations utilizing the HITRAN database and (using) the CERES radiation flux data for fine-tuning. The ERF value derived when doubling the CO2 concentration from 280 ppm (2xCO2) is 2.65 Wm-2 which is in line with the instantaneous radiative forcing (IRF) values of climate models referred to by the IPCC. The difference between the ERF values comes from the stratospheric cooling effect. It is a question about an essential paradigm change of the IPCC approach. In the former 2xCO2 value of 3.7 Wm -2, its portion was about 5 %, and in the present value, it is about 30 %. According to this study, the same effect is 10 %. The updated TCR value is 0.7 ±0.15 °C.’ 

End of citation.

 I have often argued that the warming effect of increased CO2 has not been properly weighed against its cooling effects. Ollila’s analyses and approach appears plausible and appears correct, or at least, in my opinion, it moves the controversy around this issue into the right direction. However, I am not certain whether he fully accounted for all shortwave (SW) cooling effects caused by CO2 absorption in the 0–5 µm range. Be that as it may, his findings suggest that doubling atmospheric CO2 from the pre-industrial level of 280 ppm to 560 ppm would produce an equilibrium warming of about 0.7 ± 0.15 °C. My chain of reasoning from this paper, assuming all his assumptions and calculations are correct, is:

(Please note:  [CO2] = CO2 concentration, GH = Green House,  W=Watt)

2 x [CO2] gives a radiative forcing of ca. 2.65 W/m2 (instead of the conventional 3.7W/m2). Climate-feedbacks are thought to be weak or even slightly negative overall.

So now I calculate the current increase in temperature due to more CO2 (according to Ollila, 2023) as follows:

Pre-Industrial (ca. 1850) = 280 ppm CO2, the doubling = 560 ppm CO2

Currently the [CO2] is 420 ppm. 420 is about 58.5% of the way onto a doubling in terms of CO2 forcing, So I calculate the result of mankind contribution as follows: 0.585 x 0.7 = 0.41K

Using the confidence levels that Ollila applies, the lower estimate is 0.585 x (0.7 -0.15) = 0.32K, the upper estimate is 0.585 x (0.7+0.15) =0.50

So, according to Ollila, the warming attributable to the increase from 280 ppm to the current 420 ppm amounts to 0.41K +/- 0.09K

The conventional way of thinking / science is that the total GH effect due to clouds, water vapor, CO2 and other GH gasses & aerosols is 33K. I am not saying that I agree with that ‘calculated’ value, but assuming it is correct we find the total effect of the extra warming of the world since 1850 by CO2 to be

0.41/33 x 100 = 1.2%.

Now, before the alarmists amongst us jump on the table because they think they are all ‘proven’ to be correct, let me just put that +0.4K into some perspective: Natural temperature change according to the Eddy cycle, which is currently at or around its peak, could be as much as +2.5K in the northern hemisphere, as shown in my report here:

 De duizendjarige Eddy-cyclus – Climategate Klimaat 

The current result from A.Ollila shows again that warming due to more GH gasses is not the major cause of the actual observed warming. This graph is a summary of the UAH satellite measurements since 1979.