Kyoji Kimoto reviews the basic global warming hypothesis. This hypothesis claims doubling atmospheric carbon dioxide in the absence of feedbacks will warm the Earth by about 1.2 degrees C.
All IPCC’s global warming predictions are based on this basic hypothesis.
Kyoji Kimoto shows why the basic global warming hypothesis may be wrong. He shows doubling carbon dioxide in the absence of feedbacks will warm the Earth by only 0.14 degrees C.
Kimoto’s paper is now open to scientific review.
by Kyoji Kimoto [latexpage]
1. Activities of four eminent modelers
The central dogma in anthropogenic global warming (AGW) theory is that zero feedback climate sensitivity (Planck response) is 1.2~1.3 K. This gives climate sensitivity when multiplied by feedbacks (Hansen et al., 1984).
Until Kimoto (2009), theoretical discussions concentrated on the feedback issue. However, it is impossible to accurately determine the feedbacks caused by the variable nature of water in the perturbed atmosphere with CO2 doubling. This problem has resulted in speculative discussions for a long time.
However, rigorous discussions are possible for the zero feedback climate sensitivity (Planck response) based on mathematics and physics. The Planck response of 1.2 K for GCMs comes from one-dimensional radiative convective equilibrium models (1DRCM) that assume the fixed lapse rate of 6.5 K/km (FLRA) and use the mathematical method of Cess (1976), equation (3).
The works of the following eminent modelers are mainly concerned with the central dogma of the AGW theory.
Dr. S. Manabe:
Manabe & Wetherald (1967) used the FLRA for the CO2 mixing ratio of 300 ppm (1xCO2) and that of 600 ppm (2xCO2) in the atmosphere, and obtained the zero feedback climate sensitivity CS(FAH) of 1.3 K in their 1DRCM study. Regarding lapse rate, Manabe & Strickler (1964) wrote,
“The observed tropospheric lapse rate of temperature is approximately 6.5 K/km. The explanation for this fact is rather complicated. It is essentially the result of a balance between (a) the stabilizing effect of upward heat transport in moist and dry convection on both small and large scales and (b), the destabilizing effect of radiative transfer. Instead of exploring the problem of the tropospheric lapse rate in detail, we here accept this as an observed fact and regard it as a critical lapse rate for convection.”
In the farewell lecture held on October 26, 2001, in Tokyo, Manabe told about his research,
“Research funds have been 3 million dollars per year and 120 million dollars for the past 40 years. It is not clever to pursue the scientific truth. Better way is choosing the relevant topics to the society for the funds covering the staff and computer cost of the project.”
Dr. J. Hansen:
(a) Hansen obtained the zero feedback climate sensitivity CS(FAH) of 1.2 K with the FLRA for 1xCO2 and 2xCO2 in his 1DRCM study.
(b) Although Hansen alarmed society about tipping points of catastrophic AGW many times, he showed no confidence in his model studies:
“The 1DRCM study is a fudge because obtained results strongly depend on the lapse rate assumed.”
“Observations Not Models”
“James Hansen Increasingly Insensitive”
Dr. M. Schlesinger:
Schlesinger was an AGW denier in the early 1980s as shown by Gates et al. (1981) who calculated a climate sensitivity of 0.3 K when the sea surface temperature is held in climatological values for 2xCO2. In order to get research funds, he became the top alarmist of catastrophic AGW. He calculated the central dogma of AGW theory as follows:
(a) He obtained a zero feedback climate sensitivity of 1.3 K with the FLRA for 1xCO2 and 2xCO2 in his 1DRCM study (Schlesinger, 1986).
(b) Unfairly, he utilized the Cess method without referring to Cess (1976) to obtain his equation (6) for the Planck response of 1.2 K (Schlesinger, 1986). Kimoto (2009) pointed out that it is only a transformation of Cess equation (4) as shown in Section 3.
Dr. D. Randall:
Randall obtained a zero feedback climate sensitivity of 1.2 K utilizing equation (3) in his lecture (2011) here. https://www.youtube.com/watch?v=FjE4GDC7afQ
However, his calculation contains a mathematical error as shown in Section 4.
2. Failure of the fixed lapse rate assumption of 6.5 K/km (FLRA)
Modern AGW theory began from the 1DRCM studies with fixed absolute and relative humidity utilizing the FLRA for 1xCO2 and 2xCO2 (Manabe & Strickler, 1964; Manabe & Wetherald, 1967; Hansen et al., 1981).
Table 1 shows climate sensitivities for 2xCO2 obtained in these studies, where the climate sensitivity with fixed absolute humidity CS (FAH) is 1.2 to 1.3 K (Hansen et al., 1984).
Schlesinger (1986) confirmed these results by obtaining the CS (FAH) of 1.3 K and radiative forcing of 4 W/m2 for 2xCO2 in his 1DRCM study.
The ratio of the climate sensitivity with fixed relative humidity CS (FRH) to the zero feedback climate sensitivity CS (FAH) is water vapor feedback WVF by (1), which is 1.6 ~ 1.8 as shown in Table 1.
CS (FRH) = CS (FAH) x WVF=CS (FAH) x 1.6 ~ 1.8 (1)
In the 1DRCM studies, the most basic assumption is the FLRA. The lapse rate of 6.5 K/km is defined for 1xCO2 in the U.S. Standard Atmosphere (1962) (Ramanathan & Coakley, 1978). There is no guarantee, however, the same lapse rate would be obtained in a perturbed atmosphere with 2xCO2 (Chylek & Kiehl, 1981; Sinha, 1995).
Therefore, the lapse rate for 2xCO2 is a parameter that requires sensitivity analysis to check the validity of the modeled results as shown in Fig.1. In the figure, line B shows the FLRA gives a uniform warming for the troposphere and the surface. Since CS (FAH) greatly changes with a minute variation of the lapse rate for 2xCO2, the results of the 1DRCM studies in Table 1 are theoretically meaningless.
Further, Fig.1 shows the failure of the FLRA in 1DRCM studies, which were initiated by Manabe & Strickler (1964) who used an invalid assumption about how doubling CO2 perturbs the atmosphere, shown in Section 1.
In IPCC’s AGW theory, the CS (FAH) of 1.2 ~ 1.3 K is called the Planck response (Bony et al., 2006). The FLRA in the 1DRCM is extended to the Planck response of 1.2 K with uniform warming throughout the troposphere in the GCMs studies (Hansen et al., 1984; Soden & Held, 2006; Bony et al., 2006). Climate sensitivity for 2xCO2 is expressed by (2) in the 14 GCMs studies for the IPCC AR4 as the extension of (1) (Soden & Held, 2006; Bony et al., 2006).
Climate sensitivity = Planck response x Feedbacks (wv, al, cl, lr)
= 1.2 K x 2.5 = 3 K (2)
Feedbacks are water vapor, ice albedo, cloud and lapse rate feedback.
The theoretical 1DRCM studies with the FLRA have failed, as shown in Fig. 1. Therefore, the canonical climate sensitivity of 3 K claimed by the IPCC is theoretically meaningless since it is used the 1DRCM studies in Table 1 in its GCMs.
Therefore, the cause of the AGW debate for the past 50 years is the lack of parameter sensitivity analysis in the 1DRCM studies by Manabe & Wetherald (1967), Hansen et al. (1981) and Schlesinger (1986). Such sensitivity analysis is a standard scientific procedure to check the validity of obtained results.
If sensitivity analysis were performed in the above studies, the result would show AGW will cause no huge economic loss. Also, the Fukushima nuclear disaster might not have occurred without the Kyoto protocol that promoted nuclear power.
3. Mathematical error in Cess (1976)
In 1976, Cess obtained – 3.3 (W/m2)/K for the Planck feedback parameter $\lambda_0$ utilizing the modified Stefan-Boltzmann equation (3), which gives the Planck response of 1.2 K with the radiative forcing RF of 4 W/m2 for 2xCO2 as follows (Cess, 1976).
OLR = $\epsilon$ $\sigma$ Ts4 (3)
$\lambda_0$ = – dOLR/dTs = – 4 $\epsilon$ $\sigma$ Ts3 = – 4 OLR/Ts = – 3.3 (W/m2)/K (4)
Planck response = – RF/$\lambda_0$ = 4(W/m2)/ 3.3 (W/m2)/K = 1.2 K (5)
OLR (Outgoing long wave radiation at the top of the atmosphere) = 233 W/m2
$\epsilon$: the effective emissivity of the surface-atmosphere system
$\sigma$: Stefan-Boltzmann constant
Ts: the surface temperature of 288 K
Coincidently, the Planck response of 1.2 K in (5) is the same as the zero feedback climate sensitivities of 1.2 to 1.3 K obtained from the 1DRCM studies in Table 1. Therefore, many researchers followed the Cess method. Their results are in the 14 GCMs studies for the IPCC AR4. AR4 shows the theoretical basis of IPCC’s claim that the Planck response is 1.2 K (Schlesinger, 1986; Wetherald & Manabe, 1988; Cess et al., 1989; Cess et al., 1990; Tsushima et al., 2005; Soden & Held, 2006; Bony et al., 2006).
However, the above derivation is apparently a mathematical error since it (emissivity) is not a constant enabling us to differentiate (3) as shown in (4) (Kimoto, 2009). Schlesinger (1986) proposed a different equation (6) to give the Planck response of 1.2 K, which is only a transformation of (4) as follows (Kimoto, 2009).
– 1/$\lambda_0$ = $\Lambda_0$ = Ts/ (1 – $\alpha$ ) S0 = 0.3 K / (W/m2) (6)
surface albedo $\alpha$ = 0.3 and solar constant S0 = 1370 W/m2.
At the equilibrium,
OLR = (S0/4) (1 – $\alpha$)
$\lambda_0$ = – 4OLR/Ts = – 4x (S0/4) (1 – $\alpha$)/Ts
– 1/$\lambda_0$ = $\Lambda_0$ = Ts/ (1 – $\alpha$) S0
Further, the combination of Ts=288 K and OLR=233 W/m2 is not in accordance with Stefan-Boltzmann law in (4) (Bony et al., 2006; Kimoto, 2009). Since (3) can be rewritten as
$\epsilon$ = OLR/Ts4,
$\epsilon$ is the ratio of OLR to the radiation flux at the surface. There are, however, fluxes from evaporation and thermal conduction in addition to the radiation flux at the surface in Fig. 3. Therefore, (3) cannot be a theoretical basis of the AGW theory because it is against the physical reality of nature.
4. Mathematical error in Randall lecture (2011)
Randall shows the following equations in his lecture.
(1 – $\alpha$)S $\pi$ a2 = $\epsilon$ ($\sigma$ Ts4) 4 $\pi$ a2
(1 – $\alpha$)S = 4 $\epsilon$ ($\sigma$ Ts4)
0 = 4($\Delta$ $\epsilon$) ($\sigma$ Ts4) + 4 $\epsilon$(4 $\sigma$ Ts3 $\Delta$ Ts)
$\Delta$ Ts = – (Ts/4) ($\Delta$ $\epsilon$/$\epsilon$)
$\epsilon$ ($\sigma$ Ts4) = 240 W/m2
($\Delta$ $\epsilon$) ($\sigma$ Ts4) = – 4 W/m2
This is a mathematical error as shown below.
$\Delta$ $\epsilon$/$\epsilon$ = – 4/240
Ts = 288 K
$\Delta$ Ts = – (Ts/4) ($\Delta$ $\epsilon$ / $\epsilon$ ) = (- 288/4) (- 4/240) = 1.2 K
The following equation is obtained when Cess’s eq.
OLR = $\epsilon$ ($\sigma$ Ts4
is differentiated with CO2 concentration C.
$\Delta$ OLR/$\Delta$ C = ($\Delta$ $\epsilon$/$\Delta$ C) ($\sigma$ Ts4) + 4 $\epsilon$ ($\sigma$ Ts3) ($\Delta$ Ts/ $\Delta$ C)
Radiative forcing is 4 W/m2 when $\Delta$ C is 2xCO2.
– 4 W/m2 = $\Delta$ $\epsilon$ ($\sigma$ Ts4) + 4 $\epsilon$ ($\sigma$ Ts3) $\Delta$Ts
Randall lecture (2011) neglects the second term to obtain the tricky equation above.
5. Physical reality of the response to 2xCO2
In the orthodox AGW theory based on the radiation height change by Mitchell (1989) and Held & Soden (2000), the radiation height increases from point a to point b in Fig. 2 due to the increased opaqueness when CO2 is doubled. This decreases the temperature at the effective radiation height of 5 km which causes an energy imbalance between the absorbed solar radiation (ASR) of 239 W/m2 and the outgoing long wave radiation (OLR) in Fig. 3.
In order to recover the balance of energy, the radiation temperature increases from point b to point c. A 1 K warming at the effective radiation height is enough to recover the energy imbalance caused by the radiative forcing of 3.7 W/m2 for 2xCO2 from Stefan-Boltzmann law as shown in Fig.2. Under the FLRA, the surface temperature increases in the same degree of 1 K from Ts1 to Ts2 in Mitchell (1989) and Held & Soden (2000). However, it is erroneous since the FLRA failed in Section 2.
In reality, the bold line in Fig.2 shows the surface temperature increases as much as 0.1~0.2 K with the slightly decreased lapse rate from 6.5 K/km to 6.3 K/km. Since the zero feedback climate sensitivity CS(FAH) is negligibly small at the surface, there is no water vapor or ice albedo feedback which are large positive feedbacks in the GCMs studies of the IPCC. The following data support the above picture.
(A) Kiehl & Ramanathan (1982) show the following radiative forcing for 2xCO2.
Radiative forcing at the tropopause: 3.7 W/m2.
Radiative forcing at the surface: 0.55 ~ 1.56 W/m2 (averaged 1.1 W/m2).
The surface radiative forcing is greatly reduced by the IR absorption overlap with water vapor plentifully existing at the surface. This does not allow the FLRA to give uniform warming throughout the troposphere in the 1DRCM and the GCMs studies.
(B) Newell & Dopplick (1979) obtained a climate sensitivity of 0.24 K considering the evaporation cooling from the surface of the ocean.
(C) Ramanathan (1981) shows the surface temperature increase of 0.17 K with the direct heating of 1.2 W/m2 for 2xCO2 at the surface.
(D) The surface climate sensitivity is calculated from the energy budget of the earth in Fig. 3 and the surface radiative forcing of 1.1W/m2 as follows.
Natural greenhouse effect: 289 K – 255 K = 34 K
Natural greenhouse energy: Eb – Es = 333 – 78 (W/m2) = 255 (W/m2)
Climate sensitivity factor : 34 K/255 (W/m2) = 0.13 K/ (W/m2)
Surface radiative forcing: 0.55 ~ 1.56 W/m2 (averaged 1.1 W/m2 )
Surface climate sensitivity: 0.13K/(W/m2) x 1.1 (W/m2) = 0.14 K
Four eminent modelers formed the central dogma of the IPCC AGW theory. Their theory claims the zero feedback climate sensitivity (Planck response) is 1.2 ~ 1.3 K for 2xCO2. When multiplied by the feedback factor of 2.5, this gives the canonical climate sensitivity of 3 K claimed by the IPCC .
However, this IPCC dogma fails due to the lack of parameter sensitivity analysis of the lapse rate for 2xCO2 in the one dimensional model (1DRCM). The dogma also contains a mathematical error in its derivation of the Planck response by Cess (1976). Therefore, the IPCC AGW theory and its canonical climate sensitivity of 3 K for 2xCO2 are invalid.
This study derives a climate sensitivity of 0.14 K from the energy budget of the earth.
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