by Kyoji Kimoto (e-mail email@example.com)
1. History of model studies
a. Lapse rate: fixed lapse rate of 6.5K/km
( moist adiabatic lapse rate is more adequate-see [Ramanathan et al.1978])
b. Planck response: 1.3K
(0.54-0.6K is more likely-see section2 and section3)
c. Climate sensitivity: 2.4K with water vapor feedback
(0.2-0.8K is more likely-see section 5)
d. CO2 contribution in the greenhouse effect of 33K: over 10K
(3.3-6.7K is more likely based on IR absorption -see [Newell et al., 1979; Barrett, 2005])
*) Planck response is the surface temperature rise dTs due to CO2 doubling without feedbacks of lapse rate, water vapor, albedo and cloud.
*) Climate sensitivity = (Planck response)*(Feedbacks effect)
2. Fixed lapse rate of 6.5K/km versus moist adiabatic lapse rate
As to Planck response, the following RCM studies appeared after [Manabe et al., 1964/67] utilizing a fixed lapse rate of 6.5K/km, which is the first basis of IPCC scheme.
Planck response Radiative forcing for CO2 doubling
[Manabe et al., 1964/67] 1.3K 3.5 W/m2
[Hansen et al., 1981] 1.2K 4.0 W/m2
[Schlesinger, 1986] 1.3K 4.0 W/m2
IPCC AR4 GCM studies 1.2K 3.7 W/m2
In 1976, Cess obtained 0.3 K/(W/m2) for Planck response factor with the following procedure, which gives Planck response of 1.2K utilizing the radiative forcing of 4W/m2 for CO2 doubling [Cess.1976].
OLR (Outgoing Long wave Radiation) = Eeff σ Ts^4
Planck feedback parameter λ0 = -dOLR/dTs = -4Eeff σ Ts^3
= -4OLR/Ts = -3.3(W/m2)/K
Planck response factor = -1/λ0 = 0.3K/(W/m2)
Here, Eeff = the effective emissivity of the surface-atmosphere system
σ = Stefan-Boltzmann constant Ts=288K OLR= 233W/m2
Cess’s procedure has been followed by many researchers including IPCC AR4 (see Group A), which is the second basis of IPCC scheme. 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. Group B and Group C appeared in the literature to criticize the defects of Group A [Kimoto, 2009].
4. Climate sensitivity based on IPCC’s theory
According to IPCC, climate sensitivity is expressed as follows [Bony et al.,2006].
Climate sensitivity = Planck response *λ0/ (λ0 + λlr + λwv + λa + λc)
Here, Planck response = -3.7(W/m2) / λ0
λ0: Planck feedback parameter λ0 = -4OLR/Ts
λlr: lapse rate feedback parameter
λwv: water vapor feedback parameter
λa: albedo feedback parameter
λc: cloud feedback parameter
Ts: surface temperature
OLR: Outgoing Long wave Radiation
Table 2 shows the comparison of Group A, Group B and Group C of Table 1 in terms of Planck response and climate sensitivity calculated with averaged feedback parameters for IPCC AR4 obtained from 14GCMs simulation [Soden et al., 2006].
Table 2 also shows the following test results as to Ts and OLR of each group.
Test 1: Is the combination of Ts and OLR accordance with Stefan-Boltzmann law?
Test2: Is Ts surface temperature?
(Evaluation of Table 2)
Group A: Climate sensitivity is 6 times larger than 0.5K in section 5.
Stefan-Boltzmann law is not fulfilled.
Group B: Climate sensitivity is 4 times larger than 0.5K in section 5.
Ts is not the surface temperature.
Group C: Climate sensitivity is close to 0.5K in section 5.
Stefan-Boltzmann law is satisfied, and Ts is surface temperature.
5. Climate sensitivity based on the observational methods
(1) From the energy balance consideration: 0.24K [Newell et al., 1979]
(2) From the response to volcanos : 0.3-0.5K [Lindzen, 1997]
(3) From 8 natural experiments: 0.4K or less [Idso, 1998]
(4) From the data analysis of Pinatubo eruption
Climate sensitivity factor : 0.22K/(W/m2) [Douglass et al.,2006].
Climate sensitivity: 0.22K/(W/m2)*3.7W/m2=0.8K
(5)From the ERBE: 0.5K [Lindzen et al., 2009]
(6)From the CERES: 0.6K [Spencer et al., 2010]
(7)From the energy budget of the earth (adapted from Trenberth et al. 2009)
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