From about 11,000 to 9,000 years ago the summer solar irradiance absorbed by the Earth’s surface has been estimated to be 40-60 W/m² greater than today from latitudes 40°N to 70°N (Ullman et al., 2015). These values seriously undermine the claim CO2 is the driver of climate change.
Image Source: Ullman et al., 2015
Despite these much higher insolation values, surface temperatures have been estimated to be only a few degrees warmer than today at these latitudes during the Early Holocene.
At 77°N in High Arctic Svalbard, for example, summers were estimated to be 7°C warmer than today from 10,000 to 9,000 years ago due to this higher radiative forcing (van der Bilt et al., 2019).
Image Source: van der Bilt et al., 2019
So if an additional 60 W/m² radiative forcing only elicits a 7°C surface temperature change, the effective sensitivity of a 1 W/m² perturbation to the surface energy imbalance would be about 0.12°C.
This formula (1 W/m² produces 0.12°C surface warming) has been reproduced by NASA and other scientists using satellite observations.
For example, the Mount Pinatubo eruption produced a surface temperature drop of -0.5°C to -0.6°C associated with a -4 W/m² decline in radiative forcing (Self et al., 1993). This is amounts to a 0.12°C to 0.15°C temperature sensitivity per W/m².
Image Source: Self et al., 1993
Other scientists (Douglass and Knox, 2005) have also computed a “0.15 ± 0.06 K/(W/m²)” radiative forcing-temperature sensitivity.
Image Source: Douglass and Knox, 2005
Anthropogenic global warming advocates suggest it takes an increase of 22 ppm CO2 (about 10 years) to produce a surface forcing change of 0.2 W/m² (Feldman et al., 2015).
Image Source: Feldman et al., 2015
So, using this formula, it would take 110 ppm (40-50 years) to produce a positive 1 W/m² surface forcing imbalance. This would only produce a temperature change of, at most, 0.15°C.
Bellamy and Barrett (2007) have likewise suggested the doubling of CO2 could only represent a temperature change of “0.6 – 0.8°C” with the addition of 280 ppm CO2 since the pre-industrial era. This estimate uses the assumption that doubling CO2 produces a 3.7 W/m² top-of-atmosphere (TOA) forcing.
Image Source: Bellamy and Barrett, 2007
Dr. Kimoto (2015), in contrast, suggests using the the surface radiative forcing value (1.1 W/m²) for doubling CO2 from 280 to 560 ppm rather than the TOA value (3.7 W/m²) due to the physical reality of water vapor, not CO2, dominating the infrared absorption in the lower atmosphere. He also computes a surface climate sensitivity of 0.13°C per 1 W/m².
Consequently, with doubled CO2 only yielding a 1.1 W/m² surface forcing perturbation to Earth’s energy imbalance, the climate sensitivity from doubling CO2 from 280 to 560 ppm may only be 0.14 to 0.17°C
Image Source: Kimoto, 2015
In sum, none of these values even remotely suggest CO2 can be a driver of climate change.