Trick of the radiative forcing of 3.7W/m2 at the tropopause
by Kyoji Kimoto
Radiative forcing is defined as 3.7W/m2 for 2xCO2 at the tropopause by the IPCC Third Assessment Report (2001) to avoid the usage of the surface radiative forcing of around 1W/m2. It is greatly reduced from the radiative forcing of around 4W/m2 at the tropopause due to IR absorption overlap between CO2 and water vapor plentifully existing at the surface.
Kiehl & Ramanathan (1982) developed a basic idea of the IPCC trick to overcome Newell & Dopplick (1979) claiming a climate sensitivity of 0.24K with the surface radiative forcing of around 1 W/m2 as shown by the following history of the AGW theory.
1959: Plass wrote:
In addition, nearly all water vapor remains close to the ground, while carbon dioxide diffuses more evenly through the atmosphere. Thus throughout most of the atmosphere carbon dioxide is the main factor determining changes in the radiation flux.
Wiscombe (2013) explains the Plass’s idea as follows in his lecture at NASA.
Plass also notes that CO2 greenhouse action is relatively unimpeded above 2-3km.
1967: Manabe & Wetherald obtained a climate sensitivity of 2.4K with one dimensional radiative-convective model (1DRCM) utilizing the fixed lapse rate assumption of 6.5K/km for 1xCO2 and 2xCO2 giving uniform warming throughout the troposphere and the surface. They did not mention the Plass’s idea that CO2 greenhouse effect is greatly reduced at the surface due to IR absorption overlap with water vapor because their careless assumption of the fixed lapse rate prevented their study from self-criticism of uniform warming (see Fig.2).
1975: Manabe & Wetherald obtained an averaged climate sensitivity of 2.9K and polar climate sensitivity of 7-9K with 3DGCM which is based on the 1DRCM study of Manabe & Wetherald (1967).
1979: Newell & Dopplick obtained a climate sensitivity of 0.24K with the surface radiative forcing of around 1 W/m2 to criticize Manabe & Wetherald (1975).
1979: Ramanathan et al. wrote:
For example, with a doubling of CO2, Manabe & Wetherald (1975) estimates an increase in surface temperature of 2.0-2.5K within equatorial regions. From Fig.5 the surface heating of 1.1 W/m2 at the equator, due to the radiative effects of doubled CO2, can cause a maximum surface warming of about 0.2K, and hence roughly 90% of the 2.0-2.5K surface warming obtained by Manabe & Wetherald (1975) is caused by the atmospheric feedback processes described above.
1981: Ramanathan obtained the following surface warming with the feedback mechanism shown by Fig.1 copied from his review in 1998.
1981: Hansen et al. showed a climate sensitivity of 1.9K with 1DRCM study following Manabe & Wetherald (1967) utilizing the radiative forcing of 4 W/m2.
1982: Kiehl & Ramanathan obtained the following results for 2xCO2 utilizing H2O continuum absorption in the 12-18 microns region.
But, the influence of this H2O overlap with CO2 bands is relatively smaller on the radiative heating of the joint surface/troposphere system. In particular, the effect of CO2 increase on the radiative heating of the joint surface/ troposphere system is affected very little by the presence of the water vapor continuum in the 12-18 microns region. We stress the importance of considering the troposphere/ surface system as a whole, when analyzing the effects of increasing CO2. As pointed out recently by Ramanathan (1981), results based upon surface energy balance alone can lead to incongruous conclusions.”
From Hansen et al. (1981) and Kiehl & Ramanathan (1982), the radiative forcing for
2xCO2 is 4 W/m2 at the tropopause giving the no-feedback climate sensitivity of 1.2K with the sensitivity factor of 0.3K/(W/m2) based on Cess (1976) as follows:
4 W/m2 x 0.3 K/(W/m2) = 1.2K
Soden & Held (2006) shows climate sensitivity is 3K for 2xCO2 from the 14 GCM studies for the IPCC 4th Assessment Report (2007) as follows:
Climate sensitivity = no-feedback sensitivity (Planck response) x feedbacks
= 1.2K x 2.5 = 3K
Here, feedbacks are water vapor, ice albedo, lapse rate and cloud feedback.
The no-feedback sensitivity is uniform warming throughout the troposphere and the surface, which is originated from the 1DRCM studies of Manabe & Wetherald (1967) and Hansen et al. (1981) utilizing the fixed lapse rate assumption of 6.5K/km for 1xCO2 and 2xCO2.
The 1DRCM studies, however, are fudged due to their strong dependence on lapse rate used according to Hansen’s idea expressed in an interview with Spencer Weart held on 23 October, 2000 at NASA here.
Kiehl & Ramanathan (1982) is based on the joint surface/troposphere system which is originated from Cess (1976) and is in line with the 1DRCM studies giving uniform warming throughout the troposphere and the surface due to the fixed lapse rate assumption of 6.5K/km for 1xCO2 and 2xCO2. Since it is a blanket model, the OLR decrease at the tropopause heats the troposphere and the surface as shown by their conclusion above.
On the contrary, a radiation height change model is the orthodox AGW theory as shown by Mitchell (1989) and Held & Soden (2000). In Fig.2, radiation height increases from point a to point b due to increased opaqueness when CO2 is doubled. This decreases the temperature at the effective radiation height of 5km causing an energy imbalance between the absorbed solar radiation (ASR) of 240W/m2 and the outgoing long wave radiation (OLR) in Fig. 3.
In order to restore the balance of energy, the radiation temperature increases from point b to point c. Based on the Stefan-Boltzmann law, a warming of 1K at the effective radiation height is enough to remove the energy imbalance caused by the radiative forcing of 4 W/m2 for 2xCO2 in Fig. 2.
For the Manabe method, the surface temperature increases in the same degree of 1K utilizing the fixed lapse rate assumption of 6.5K/km in Fig. 2. It, however, is erroneous since the 1DRCM studies are fudged according to the Hansen’s idea above.
In contrast, Kimoto model follows Ramanathan (1981) giving the no-feedback sensitivity of 0.17K with the direct heating of 1.2W/m2 for 2xCO2 from the Stefan-Boltzmann law at the surface. It is also in line with Newell & Dopplick (1979) giving a surface climate sensitivity of 0.24K based on the surface radiative forcing of around 1W/m2 and the evaporation cooling from the surface of the ocean.
In conclusion, the surface warming should be calculated with the surface radiative forcing of around 1 W/m2 utilizing the Stefan-Boltzmann law at the surface. The upper troposphere warming nullifies the radiative forcing at the tropopause due to CO2 increase with restoring OLR which is decreased by the opaqueness increase of the atmosphere.
Fig. 2 Comparison between Manabe method and Kimoto model.
Fig. 3 Energy budget of the earth adapted from Dorland (2006).
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