by Kyoji Kimoto
1. Comparison of climate sensitivities among three groups
Group A (IPCC AR4):
CS(NF)=1.2K mathematical error due to Cess’s calculation
CS(WF)=3K too large positive feedback since λi for IPCC AR4 are utilized
Group B (Bony):
CS(NF)=1.0K not surface value since T is 255K in Stefan-Boltzmann law
CS(WF)=2.0K large positive feedback since λi for IPCC AR4 are utilized
Group C (Ramanathan):
CS(NF)=0.52K surface value since T is 288K in Stefan-Boltzmann law
CS(WF)=2.2K too large positive feedback since GCM study is adopted
Group B’ (Lindzen,Spencer):
CS(NF)=0.9-1.1K not surface value since T is 255K in Stefan-Boltzmann law
CS(WF)=0.5-0.6K large negative feedback due to water vapor or cloud feedback
Group C’ (Kimoto):
CS(NF)=0.54K surface value since T is 288K in Stefan-Boltzmann law
CS(WF)=0.75K fairly large positive feedback since λi for IPCC AR4 are utilized
CS(WF)=0.5K slightly negative feedback
CS(WF)=0.2K large negative feedback
2．CS(NF) obtained from RCM studies with fixed lapse rate of 6.5K/km
According to IPCC, climate sensitivity (With Feedback) is expressed as follows.
CS(WF)=CS(NF) x (Feedback effects)
CS(WF): Climate Sensitivity(With Feedback)
CS(NF): Climate Sensitivity(No Feedback)
Table2 shows two RCM studies appeared after [Manabe et al., 1964/67] with fixed lapse rate of 6.5K/km obtaining CS(NF) of 1.2-1.3K (see Figure1).This constitutes the first basis of IPCC’s claim that CS(NF) is 1.2K. Radiative forcing for CO2 doubling is in the range of 3.5-4.0W/m2 at the tropopause.
However, dTs is around 0.6K when moist adiabatic lapse rate is utilized as shown in Figure2, which is better parameterization in RCM studies than fixed lapse rate of 6.5K/km [Ramanathan et al., 1978, Hummel et al., 1981].
3. CS(NF) calculation based on Stefan-Boltzmann law
In 1976, Cess obtained -3.3(W/m2)/K for Planck feedback parameter λ0 utilizing the following procedure, which gives CS(NF) of 1.2K with radiative forcing of 4W/m2 for CO2 doubling [Cess.1976].
Cess’s procedure has been followed by many researchers including IPCC AR4 [Soden et al., 2006], which constitutes the second basis of IPCC’s claim that CS(NF) is 1.2K (see Group A in Table3). However, this procedure is apparently a mathematical error since Eeff is not a constant. Furthermore, the combination of Ts and OLR is not accordance with Stefan-Boltzmann law [Kimoto, 2009]. Table3 shows the comparison of CS(NF) for three groups calculated with radiative forcing of 3.7W/m2 for CO2 doubling.
Table 4 shows CS(WF) calculated from CS(NF) of Group A and Group C’ in Table3 with averaged feedback parameters λi of lapse rate, water vapor, albedo and cloud feedback for IPCC AR4 [Soden et al., 2006].
Table 3. Planck feedback parameter L0 and CS(NF) based on Stefan-Boltzmann law
Table 5 shows the comparison of CS(NF) and CS(WF) of three groups in Table 3. CS(WF) are calculated with feedback parameters λi shown in Table4. Table 5 also shows the test results as to Ts and OLR utilized in Stefan-Boltzmann law to calculate CS(NF).
CS(NF) of Group B’ (Lindzen, Spencer) is 0.9-1.1K which is calculated with T=255K or 259K in Stefan-Boltzmann law at the effective radiation height of 5-8 km. Therefore, these CS(NF) cannot be applicable to the surface considering moist adiabatic lapse rate.
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