By Bob Irvine

The world’s climate is an immensely complex and chaotic system. Climate forcings have different efficacies depending on whereabouts on the planet they act. Massive convective forces and energy transport mitigate any warming but are nearly impossible to quantify. Even our global temperature series are unreliable. And then there is clouds!

The problems encountered by scientists trying to put a number on Equilibrium Climate Sensitivity (ECS) for CO2x2 are almost insurmountable because of this complexity and estimates, consequently, vary greatly.

The Non-Condensing Green House Gasses (NCGHG) include CO2, CH4, N2O, CFC11, and CFC12. CO2 dominates the forcing from these gasses until 1850 and was responsible for 83% of their forcing at that time. It is a reasonable assumption to say that, prior to 1850 the average climate sensitivity to all the NCGHGs combined was very close to CO2 sensitivity both historically and in 1850.

If all NCGHGs were removed from the system, the sun would still be beating into the tropical and temperate oceans creating large amounts of water vapour and clouds. The only way this can change is by expanding Earth’s orbit or turning down the sun’s intensity.

The world will always have a strong GHG Effect while the sun continues to shine and that feedback to change for all concentrations of NCGHGs, including close to zero, will always be acting in a world with an existing strong GHG component. For this reason, feedback is likely to be relatively linear.

This essay will attempt to find an estimate for Equilibrium Climate Sensitivity (ECS) based on two methods of estimating the Global Mean Surface Temperature (GMST) after all NCGHGs have been artificially removed. Both these estimates include an unknown figure for System Gain Factor (SGF). We solve for the two equations and get a System Gain Factor of about 1.09. This implies a long term ECS for CO2x2 of about1.3K (1.09 x 1.2 = 1.3K)

I’d like first to get a definition out of the way. Reference Temperature (RT) is defined here as the base temperature attributed to a forcing before any atmospheric or ocean feedback has been applied. For example, the Reference Temperature for CO2x2 is agreed at 1.2C (Hansen ’84).

Another definition is also needed at this point. The System Gain Factor (SGF) is defined here as the Equilibrium Temperature divided by the Reference Temperature (RT). For example, the IPCC central SGF of CO2x2 is their likely ECS of 3.0K divided by the Reference Temperature (RT) of 1.2K. (3.0/1.2 = 2.5). The IPCC’s likely System Gain Factor (SGF) for CO2 is 2.5.

In 1850 the global temperature was 287.5K (NASA) and the total Reference Temperature for all the NCGHGs combined was 7.9K (IPCC). This is not contested.

The approximate total GH Effect (GHE) in 1850 was 32.5K and is derive by subtracting the global emission temperature (255K, IPCC) from the surface temperature (287.5K, NASA) at that time. Of that 32.5K, 7.9K is directly attributed to and is the reference temperature for all the NCGHGs as mentioned, the rest (24.6K) being made up almost totally by the contribution from water vapour (WV) and clouds.

The IPCC position is that over half this 24.6K WV and Cloud GHE is a direct result and is feedback to the NCGHG’s 7.9K direct contribution or reference temperature. I intend to show that this position is not correct and calculate a much better estimate.

METHOD

The unknown factor here is the SGF for any reference temperature from any cause. This I will designate as “A”.

Other figures used are.

• 7.9K is the reference temperature for all the NCGHGs (IPCC).
• 287.5K is the GMST in 1850 (NASA).
• 255K is the Global Emission Temperature. (IPCC).
• 32.5K is the total GHE in 1850. (Global Temperature minus Emission temperature.)

There are two ways to calculate the GMST when all the NCGHGs have been removed.

Equation 1.

The total warming due to all the NCGHGs after all feedback has acted (7.9xA) is subtracted from the 1850 GMST (287.5K).

287.5 – 7.9A = GMST after all NCGHGs have been removed.

Equation 2.

The Emission Temperature (255K) is the approximate GMST if the sun were shining on a world without any water or GHGs. This implies a world without ice. We then add an ocean but do not add any NCGHGs. While there will be different albedo feedback initially, GHGs (water vapour and clouds) will establish relatively quickly, and equilibrium temperature will eventually depend almost totally on the System Gain Factor. The equilibrium temperature will, therefore, eventually be the emission temperature times the System Gain factor.

255 x A = Global temperature after all NCGHGs have been removed.

Combining.

287.5-7.9A = 255A

A = 1.09

This implies an ECS for CO2x2 of about 1.3K (1.09 x 1.2 = 1.3K)

CONCLUSION

If all NCGHGs were removed from the system, the Global Mean Surface Temperature (GMST) would be approximately 278K. All these gasses in 1850 had added about 9.5K (1.09 x 7.9 = 9.5K) to this initial GMST to reach a GMST in 1850 of 287.5K.

This implies an ECS for CO2x2 of approximately 1.3K (1.09 x 1.2 = 1.3K).

There are many uncertainties associated with this exercise. The GMST in 1850 is not well defined, with a possible range of (±0.5). The global emission temperature, no doubt, varies and has a range of values, and the reference temperature for the NCGHGs may not be perfect. Even after considering these uncertainties the SGF and consequent ECS as calculated will not change significantly. (The Earth’s Emissivity here is assumed to be 1.0. It is actually 0.936).

This is a theoretical exercise and does not attempt to quantify albedo changes. In the modern climate, a world with all the NCGHGs included, albedo changes are considered to be insignificant. In a world without NCGHGs, however, this may not be the case. This colder world may have ice and cloud albedo feedback that differs from today’s world. (Lacis 2010). This means that the sensitivity calculated here is likely to be relatively accurate for the modern world but may understate the climate sensitivity in a colder world without NCGHGs.

While this exercise is theoretical in nature it does capture all the long-term feedback after equilibrium has been reached and is likely a lot more accurate than trying to quantify all the complex and chaotic molecular movements that make up the modern climate of the last century, and then trying to single out the small contribution from CO2.

IPCC TEST

When we use the IPCC’s System Gain Factor (SGF) of 2.5 (3.0/1.2 = 2.5), equation 1. produces a GMST of about 268K after all NCGHGs have been removed.

When this SGF (2.5) is applied per equation 2 it gives a GMST without the NCGHGs of 638K. Very different to Equation 1. Quite obviously the IPCC’s central sensitivity is not physically possible.

Another way to look at the IPCC’s approach to this. They say that the GMST after all NCGHGs have been removed would be 267.75K (287.5 – 2.5 x 7.9 = 267.75). They are saying that 240 W/M2 of solar energy striking the earth’s surface will cause a water vapour and cloud feedback response of 12.75K (267.75 – 255 = 12.75K). They also say that the 25.32 W/M2 contributed by the NCGHGs will cause a warming through the additional water vapour and cloud response of 11.85K (2.5 x 7.9 less 7.9 = 11.85). Even the IPCC should be embarrassed by an inconsistency of that magnitude.

This essay corrects that inconsistency.

NOTE

Lacis et al. 2010, find sensitivity would be significantly higher on a colder planet due to additional ice and cloud positive feedback. If this is the case, then the estimate derived here of 1.3K (ECS for CO2x2) would be a maximum with the possibility that this figure could be significantly lower in the modern world.

Reference.

Pubs.GISS: Lacis et al. 2010: Atmospheric CO₂: Principal control knob governing Earth’s temperature (nasa.gov)