Then one simply measures the forcing due to all atmospheric so-called greenhouse trace gases: Correlation between CO2 climate forcing and temperature Grant Foster aka Tamino 2022 May 05 Open Mind tamino.wordpress.com/2022/05/05/correlation-between-co2-climate-forcing-and-temperature/ and then noting, as in the comments, that CO2 is about 0.83 of the total forcing, resulting in the actual TCR, ‘actual’ transient climate response, due to CO2 is close to 2.0 K. Then the CO2-only ECS, equilibrium climate sensitivity, is close to 3.3 K. However, with the rest of the current crop of global warming trace gases, ECS is more like 4 K. (See the comments section for the source of these latter remarks.)
Note that the usual definition of TCR requires an increase off 1% per annum in atmospheric CO2. Hence using the observed increase provides an ‘actual’ TCR. Also note that the logarithm is to the base 2.
Post by David B. Benson on May 23, 2022 12:17:51 GMT 9.5
The atmospheric CO2 record is extended into the past to before the beginning of the modern measurements, the Keeling curve, by the use of the high quality data from Law Dome, Antarctica. This is possible due to the exceptional snowfall rate at this site. The most recent analysis of the data is
Edited to add: The Wikipedia page en.wikipedia.org/wiki/Svante_Arrhenius#Greenhouse_effect now contains a quote from the paper from Arrhenius which, in effect, gives the logarithmic form, but directly for the temperature, not for the forcing, calling it a ‘rule’. That is a suitable term as this is an approximation to the atmospheric physics acting over the entire globe, so not a ‘law’.
So I will henceforth call
Δt = τ*lg(c/c0)
the Arrhenius-Wigley rule, as I think that Tom Wigley deserves some credit for this as well. In the now-named Arrhenius-Wigley rule, Δt is the increment of temperature attributed to atmospheric carbon dioxide, the other long-lived trace heat-trapping gases just coming along for the ride, i.e., ignored, τ is the aTCR, actual transient climate response as determined by the slope of the correlation, as by Grant Foster, c is the current atmospheric carbon dioxide concentration in ppm and c0 is the base concentration, typically taken to be 280 ppm for the pre-industrial times. In addition, note that the logarithm is lg=log_2, the logarithm to base 2 so that a doubling of CO2 gives the increase in temperature of exactly the aTCR.