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 CO

_{2}mixing ratio of 300 ppm (1xCO_{2}) and that of 600 ppm (2xCO_{2}) 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 1xCO

_{2}and 2xCO_{2}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) 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 1xCO

_{2 }and 2xCO_{2}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 1xCO

_{2}and 2xCO_{2}(Manabe & Strickler, 1964; Manabe & Wetherald, 1967; Hansen et al., 1981).
Table 1 shows the climate sensitivities for 2xCO

_{2}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 2xCO

_{2}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 1xCO

_{2}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 2xCO_{2}(Chylek & Kiehl, 1981; Sinha, 1995).
Therefore, the lapse rate for 2xCO

_{2}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 2xCO_{2}, 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 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 2xCO

_{2}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 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 2xCO

_{2}as follows (Cess, 1976).
OLR = T

_{s}^{4}(3)
= – dOLR/dT

_{s }= – 4 T_{s}^{3 }= – 4 OLR/T_{s }= – 3.3 (W/m2)/K (4)
Planck response = – RF/

_{ }= 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

: the effective emissivity of the surface-atmosphere system

: 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/

_{ }= = T_{s}/ (1 – ) S_{0 }= 0.3 K / (W/m2) (6)
Here,

surface albedo = 0.3 and solar constant S

_{0}= 1370 W/m2.
At the equilibrium,

OLR = (S

_{0}/4) (1 – )
From (4),

= – 4OLR/T

_{s }= – 4x (S_{0}/4) (1 – )/T_{s}
Then,

– 1/

_{ }= = T_{s}/ (1 – ) S_{0}
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
= OLR/T

_{s}^{4},
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 equation series in his lecture.

(1 – )S a

^{2 }= ( T_{s}^{4}) 4 a^{2}
(1 – )S = 4 ( T

_{s}^{4})
0 = 4( ) ( T

_{s}^{4}) + 4 (4 T_{s}^{3}T_{s})
Ts = – (T

_{s}/4) ( /)
( T

_{s}^{4}) = 240 W/m2
( ) ( T

_{s}^{4}) = – 4 W/m2
This is a mathematical error as shown below.

/ = – 4/240

Ts = 288 K

Ts = – (T

_{s}/4) ( / ) = (- 288/4) (- 4/240) = 1.2 K
Kimoto critique:

The following equation is obtained when Cess’s eq.

OLR = ( T

_{s}^{4}
is differentiated with CO2 concentration C.

OLR/ C = ( / C) ( T

_{s}^{4}) + 4 ( T_{s}^{3}) ( Ts/ C)
Radiative forcing is 4 W/m2 when C is 2xCO2.

– 4 W/m2 = ( T

_{s}^{4}) + 4 ( T_{s}^{3}) Ts
Randall lecture (2011) neglects the second term to obtain the tricky equation above.

5. Physical reality of the response to 2xCO

_{2}
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 CO

_{2}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 2xCO

_{2}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.
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 2xCO

_{2}.
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 2xCO

_{2}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

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

Bony, S., Colman, R., Kattsov, V.M., Allan, R.P., Bretherton, C.S., Dufresne, J.L., Hall, A., Hallegatte, S., Holland, M.M., Ingram, W., Randall, D.A., Soden, B.J., Tselioudis, G., Webb, M.J., 2006. Review article: How well do we understand and evaluate climate change feedback processes? J. Climate 19, 3445-3482.

Cess, R.D., 1976. An appraisal of atmospheric feedback mechanisms employing zonal climatology. J.Atmospheric Sciences 33, 1831-1843.

Cess, R.D., Potter, G.L., Blanchet, J.P., Boer, G.J., Ghan, S.J., Kiehl, J.T., Le Treut, H., Li, Z.X., Liang, X.Z., Mitchell, J.F.B., Morcrette, J.J., Randall, D.A., Riches, M.R., Roeckner, E., Schlese, U., Slingo, A., Taylor, K.E., Washington, W.M., Wetherald, R.T., Yagai, I., 1989. Interpretation of cloud-climate feedback as produced by 14 atmospheric general circulation models. Science 245, 513-516.

Cess, R.D., Potter, G.L., Blanchet, J.P., Boer, G.J., DelGenio, A.D., Deque, M., Dymnikov, V., Galin, V., Gates, W.L., Ghan, S.J., Kiehl, J.T., Lacis, A.A., LeTreut, H., Li, Z.X., Liang, X.Z., McAvaney, B.J., Meleshko, V.P., Mitchell, J.F.B., Morcrette, J.J., Randall, D.A., Rikus, L., Roeckner, E., Royer, J.F., Schlese, U., Sheinin, D.A., Slingo, A., Sokolov, A.P., Taylor, K.E., Washington, W.M. and Wetherald, R.T., 1990. Intercomparison and interpretation of climate feedback processes in 19 Atmospheric General Circulation Models. J. Geophysical Research 95, 16,601-16,615.

Chylek, P., Kiehl, J.T., 1981. Sensitivities of radiative-convective climate models. J. Atmospheric Sciences 38, 1105-1110.

Gates, W.L., Cook, K.H., Schlesinger, M.E., 1981: Preliminary analysis of experiments on the climatic effects of increased CO2 with an atmospheric general circulation model and a climatological ocean. J. Geophysical Research 86, 6385-6393.

Hansen, J., Johnson, D., Lacis, A., Lebedeff, S., Lee, P., Rind, D., Russell, G., 1981. Climate impact of increasing atmospheric carbon dioxide. Science 213, 957-966.

Hansen, J., Lacis, A., Rind, D., Russell, G., Stone, P., Fung, I., Ruedy, R., Lerner, J., 1984. Climate sensitivity: Analysis of feedback mechanisms. in Climate Processes and Climate Sensitivity, J.E. Hansen and T. Takahashi, Eds. (American Geophysical Union, Washington, D.C., 1984), pp. 130-163.

Held, I.M., Soden, B.J., 2000. Water vapor feedback and global warming. Annu. Rev. Energy Environ. 25, 441-475.

Kiehl, J.T., Ramanathan, V., 1982. Radiative heating due to increased CO

_{2}: The role of H_{2}O continuum absorption in the 12-18 micron region. J. Atmospheric Sciences 39, 2923-2926.
Kimoto, K., 2009. On the confusion of Planck feedback parameters. Energy & Environment 20, 1057-1066.

Manabe, S., Strickler, R.F., 1964. Thermal equilibrium of the atmosphere with a convective adjustment. J. Atmospheric Sciences 21, 361-385.

Manabe, S., Wetherald, R.T., 1967. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmospheric Sciences 24, 241-259.

Mitchell, J.F.B., 1989. The greenhouse effect and climate change. Reviews of Geophysics 27, 115-139.

Newell, R.E., Dopplick, T.G., 1979. Questions concerning the possible influence of anthropogenic CO

_{2}on atmospheric temperature. J. Applied Meteorology 18, 822-825.
Ramanathan, V., Coakley, Jr.J.A., 1978. Climate modeling through radiative-convective models. Reviews of Geophysics and Space Physics 16, 465-489.

Ramanathan, V., 1981. The role of ocean-atmosphere interactions in the CO

_{2}climate problem. J. Atmospheric Sciences 38, 918-930.
Schlesinger, M.E., 1986. Equilibrium and transient climatic warming induced by increased atmospheric CO

_{2}. Climate Dynamics 1, 35-51.
Sinha, A., 1995. Relative influence of lapse rate and water vapor on the greenhouse effect. J. Geophysical Research 100, 5095-5103.

Soden, B.J., Held, I.M., 2006. An assessment of climate feedbacks in coupled ocean-atmosphere models. J. Climate 19, 3354-3360.

Trenberth, K.E., Fasullo, J.T., Kiehl, J., 2009. Earth’s global energy budget. BAMS March 2009, 311-323.

Tsushima, Y., Abe-Ouchi, A., Manabe, S., 2005. Radiative damping of annual variation in global mean temperature: comparison between observed and simulated feedbacks. Climate Dynamics 24, 591-597.

Wetherald, R.T., Manabe, S., 1988. Cloud Feedback Processes in a General Circulation Model. J. Atmospheric Science 45, 1397-1415.

This provides a more detailed description of the effect of lapse rate variability:

ReplyDeletehttp://joannenova.com.au/2015/10/for-discussion-can-convection-neutralize-the-effect-of-greenhouse-gases/

Abive my head - regardless, it is off message, so will be ignored. I have to keep reminding myself that the climate is simply a battle in a much larger war between control freaks and free thinkers.

DeleteAs Tony Heller has pointed out, NASA scientists declared already in 1971 that runaway greenhouse effect due to CO2 is not possible:

ReplyDeletehttp://realclimatescience.com/2015/11/nasa-has-known-since-1971-that-co2-is-not-dangerous-yet-lied-to-the-public-continuously/

somehow, they seem to have forgotten that.

" Also, the Fukushima nuclear disaster might not have occurred without the Kyoto protocol that promoted nuclear power."

ReplyDeleteWhat disaster?? There have been no deaths or illnesses from radiation sickness. There have been a large number of deaths from suicide by people uprooted and scared to death by radiation danger propaganda.

Look into the results of Chernobyl, unquestionably the WORST nuclear disaster ever. The predictions were 10's to hundreds of thousands of deaths from radiation. The reality has been that they have only found about 6,000 deaths that can be reasonably ascribed to the radiation. The idea that the tiny amount of radiation spread around the world is causing deaths is ludicrous with the much higher levels locally having so few.

Hormesis is a reality that mainstream needs to start accepting and Linear No Threshold assumptions are crap.

David Evans considers that the GCMs rely on the flawed architecture of the basic model and are similarly flawed as a result.

ReplyDeleteWhen one applies his revised architecture to both the basic model and the GCMs the issue of climate sensitivity to CO2 fades into insignificance.

Not to complain, but I am surprised to see this website copied my original post I did for Kimoto here:

ReplyDeletehttp://edberry.com/blog/authors-climate/kyoji-kimoto/basic-global-warming-hypothesis-is-wrong/

without even the courtesy to link to the original. The copyright is Kyoji Kimoto's. I did a lot of formatting and editing for Kyoji Kimoto in order to make his post readable for reviewers.

This post does link to your post- simply click upon the title which is linked to your site.

DeleteEd, were you looking for fame? Good luck with that.

Deletehttp://www.tech-know-group.com/papers/sensitivity.pdf

ReplyDeleteI put your suggestion in the stack model.

CONCLUSION: the sensitivity study with a variation of the lapse rate make too big variations necessary.

Forget it!

And here is yet another important and illuminating post. I can't understand how so many of our "luke-warm" friends can't see real skepticism of "CO2 warms the planet". I can see the politically motivated, rent-seeking alarmists not listening to truth, but why the luke-warmers?

ReplyDeleteBy the way, have you seen this one? "How AGW isn’t happening in the real Earth system" … by okulaer https://okulaer.wordpress.com/2015/11/15/how-agw-isnt-happening-in-the-real-earth-system/

Stop The Global Warming Swindel. Antarctic with ice volume higher than average 1978-2010. No temperature increase since 1997. Polar bears 32000 six tinder population in 1950 5000 bears. Ocean level negligible well within Natural variations...

ReplyDeleteJust one more stake in the heart of the AGW zombie that refuses to die!

ReplyDeleteAs Mark Stoval alludes to above, it is as if the only thing now keeping the zombie alive is the effort from lukewarmers.

Engineering science demonstrates CO2, in spite of being a ghg, has no effect on climate. Identification of the two factors that do cause reported average global temperature change (sunspot number is the only independent variable) are at http://agwunveiled.blogspot.com (97% match since before 1900). Everything not explicitly included (such as aerosols, volcanos, non-condensing ghg, ice changes, uncertainty in measurements, heating from earth’s core, heat stored in ocean depths, etc.) must find room in the unexplained 3%.

ReplyDeleteThe last 500 million years of substantial CO2 with no sustained temperature change is compelling evidence CO2, in spite of being a ghg, has no effect on climate. This is documented in a peer reviewed paper at Energy & Environment, Volume 26, No. 5, 2015, 841-845 and also in the AGWunveiled document.

Very interesting article on corrections in the basic global warming hypothesis.

ReplyDeleteModulation of Ice Ages via Precession and Dust-Albedo Feedbacks

ReplyDeleteA new paper proving that CO2 is a minor player in the drama that is the Earth’s climate.

(The article I produced has turned into a science paper).

Abstract

We present here a simple and novel proposal for the modulation and rhythm of ice ages and interglacials during the late Pleistocene. While the standard Milankovitch-precession theory fails to explain the long intervals between interglacials, these can be accounted for by a novel forcing and feedback system involving CO2, dust and albedo. During the glacial period, the high albedo of the northern ice sheets drives down global temperatures and CO2 concentrations, despite subsequent precessional forcing maxima. Over the following millennia CO2 is sequestered in the oceans and atmospheric concentrations eventually reach a critical minima of about 200 ppm, which causes a die-back of temperate and boreal forests and grasslands, especially at high altitude. The ensuing soil erosion generates dust storms, resulting in increased dust deposition and lower albedo on the northern ice sheets. As northern hemisphere insolation increases during the next Milankovitch cycle, the dust-laden ice-sheets absorb considerably more insolation and undergo rapid melting, which forces the climate into an interglacial period. The proposed mechanism is simple, robust, and comprehensive in its scope, and its key elements are well supported by empirical evidence.

https://www.academia.edu/20051643/Modulation_of_Ice_Ages_via_Precession_and_Dust-Albedo_Feedbacks

Sincerely,

Ralph Ellis