Kyoji Kimoto, a Japanese chemist, scientist, and fuel-cell computer modeler & inventor, has a new essay below explaining why the basic anthropogenic global warming hypothesis is wrong and leads to highly exaggerated climate sensitivity to doubled CO2. Kimoto finds climate sensitivity of only 0.14C, a factor of 21 times smaller than the IPCC canonical climate sensitivity estimate of ~3C per doubled CO2.

See prior posts by Kimoto here.

Basic global warming hypothesis is wrong

by Kyoji Kimoto

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 work 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.”

https://www.aip.org/history-programs/niels-bohr-library/oral-histories/24309-1

“Observations Not Models”

http://www.worldclimatereport.com/index.php/2004/04/14/observations-not-models/

“James Hansen Increasingly Insensitive”

http://www.worldclimatereport.com/index.php/2005/04/28/james-hansen-increasingly-insensitive/

Dr. M. Schlesinger:

Schlesinger was an AGW denier in the early 1980s as shown by Gates et al. (1981) which calculated a climate sensitivity of 0.3 K when the sea surface temperature is held in climatological values for 2xCO_2. In order to get plentiful funds, he has become the top alarmist of catastrophic AGW. He calculated the central dogma of AGW theory as follows:

(a) He obtained the zero feedback climate sensitivity of 1.3 K with the FLRA for 1xCO₂and 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 the 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 the climate sensitivities for 2xCO₂ obtained in these studies, where the climate sensitivity with the 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 the 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, for the same lapse rate maintained in the perturbed atmosphere with 2xCO₂ (Chylek & Kiehl, 1981; Sinha, 1995).

Therefore, the lapse rate for 2xCO₂ is a parameter requiring a 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.

KK Fig 1A — Fig. 1 Parameter sensitivity analysis of the lapse rate for 2xCO2. CS (FAH): Climate sensitivity with the fixed absolute humidity.

In IPCC’s AGW theory, the CS (FAH) of 1.2 ~ 1.3 K is called as Planck response (Bony et al., 2006). The FLRA in the 1DRCM is extended to the Planck response of 1.2 K with the 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 the 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 the 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 = $\epsilon$ $\sigma$ T_s⁴ (3)

$\lambda_0$ = – dOLR/dT_s= – 4 $\epsilon$ $\sigma$ T_s³= – 4 OLR/T_s= – 3.3 (W/m2)/K (4)

Planck response = – RF/ $\lambda_0$ = 4(W/m2)/ 3.3 (W/m2)/K = 1.2 K (5)

Where,

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

T_s: 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 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/ $\lambda_0$ = $\Lambda_0$ = T_s/ (1 – $\alpha$ ) S₀= 0.3 K / (W/m2) (6)

Here,

surface albedo $\alpha$ = 0.3 and solar constant S₀ = 1370 W/m2.

At the equilibrium,

OLR = (S₀/4) (1 – $\alpha$ )

From (4),

$\lambda_0$ = – 4OLR/T_s= – 4x (S₀/4) (1 – $\alpha$ )/T_s

Then,

– 1/ $\lambda_0$ = $\Lambda_0$ = T_s/ (1 – $\alpha$ ) S₀

Further, the combination of T_s=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/T_s⁴,

$\epsilon$ 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)

https://www.youtube.com/watch?v=FjE4GDC7afQ

Randall shows the following equation series in his lecture.

(1 – $\alpha$ )S $\pi$ a²= $\epsilon$ ( $\sigma$ T_s⁴) 4 $\pi$ a²

(1 – $\alpha$ )S = 4 $\epsilon$ ( $\sigma$ T_s⁴)

0 = 4( $\Delta$ $\epsilon$ ) ( $\sigma$ T_s⁴) + 4 $\epsilon$ (4 $\sigma$ T_s³ $\Delta$ T_s)

$\Delta$ Ts = – (T_s/4) ( $\Delta$ $\epsilon$ / $\epsilon$ )

$\epsilon$ ( $\sigma$ T_s⁴) = 240 W/m2

( $\Delta$ $\epsilon$ ) ( $\sigma$ T_s⁴) = – 4 W/m2

This is a mathematical error as shown below.

$\Delta$ $\epsilon$ / $\epsilon$ = – 4/240

Ts = 288 K

$\Delta$ Ts = – (T_s/4) ( $\Delta$ $\epsilon$ / $\epsilon$ ) = (- 288/4) (- 4/240) = 1.2 K

Kimoto critique:

The following equation is obtained when Cess’s eq.

OLR = $\epsilon$ ( $\sigma$ T_s⁴

is differentiated with CO2 concentration C.

$\Delta$ OLR/ $\Delta$ C = ( $\Delta$ $\epsilon$ / $\Delta$ C) ( $\sigma$ T_s⁴) + 4 $\epsilon$ ( $\sigma$ T_s³) ( $\Delta$ Ts/ $\Delta$ C)

Radiative forcing is 4 W/m2 when $\Delta$ C is 2xCO2.

– 4 W/m2 = $\Delta$ $\epsilon$ ( $\sigma$ T_s⁴) + 4 $\epsilon$ ( $\sigma$ T_s³) $\Delta$ 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 T_s1 to T_s2 in Mitchell (1989) and Held & Soden (2000). However, it is erroneous since the FLRA failed in Section 2.

KK Fig 2A — Fig. 2. Global warming theory based on the radiation height change. Physical reality: The surface temperature increase is 0.1 ~ 0.2 K with the slightly decreased lapse rate of 6.3 K/km from 6.5 K/km.

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 denies the FLRA giving the 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: E_b – E_s= 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

KK Fig 3A — Fig. 3. Energy budget of the earth adapted from Trenberth et al. (2009).

Conclusions

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.

References

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THE HOCKEY SCHTICK

Wednesday, November 11, 2015

Why the basic global warming hypothesis is wrong; CO2 climate sensitivity exaggerated 21X

Basic global warming hypothesis is wrong