Analysis of the Holmes Hypothesis

(c) 2023 by Barton Paul Levenson

1. Introduction.

Holmes (2019) advances the hypothesis that the greenhouse effect does not exist, or is trivial, because he can predict the temperatures of three worlds at the 1 bar level of pressure in the atmosphere, from TSI (Total Solar Irradiance) alone. Some of the figures from his main table are reproduced below. Column titles have been changed for simplicity.

2. Relative TSI.

Three mistakes are obvious in the table data, two of them rather trivial.

1. There is no consistent use of significant digits, which vary from two to four.
2. The Venus T₁ value is suspect. Logarithmic interpolation using the values in the Venus Standard Atmosphere (Seiff et al. 1986) gives 346 K rather than 340.
3. The worst error is repeated throughout the article. The relative TSI figures are relative to Earth for Venus and Titan, but relative to Venus for Earth. The column he designates "TSIrelative" should read either 1.91, 1.00, 0.0109 for Venus, Earth, and Titan, respectively, if based on Earth's solar constant; or else 1.00, 0.523, 0.0570 if based on that of Venus.

This error is not fatal, however, since his results can easily be reproduced with the equation

T_calc = 289.1 (TSI/TSI_Earth)^0.25

Holmes claims that this reproduces the temperatures at the 1 bar level "to within 1 Kelvin [sic]." This is clearly wrong since the rms error for (339, 289.1, 93) versus (340, 288, 87.5) is 3.3 K. Apparently Holmes has confused the surface temperature of Titan (actually 93.7 K; Mitri et al. 2007) for the 1-bar level temperature.

3. Applicability.

Holmes states that "[a] physical law must be universal." But his temperature algorithm fails to reproduce accurate temperatures for Mars, Triton, Pluto, any airless body whatsoever, and all the giant planets.

He dismisses Mars, etc. because they have low-pressure atmospheres, stating that these "allow Solar heating to dominate... creating a stratosphere." But in fact the Martian atmosphere is nearly all troposphere, characterized by convective activity with a lapse rate of approximately 2.5 K/km (Haberle 2015).

Holmes ignores the giant planets, suggesting in a ResearchGate post that their internal heat sources are a confounding factor. Apparently he does not understand that they are a confounding factor which is easily calculated and accounted for, since the internal heat flux density is simply the difference between the total longwave flux density emitted by the planet and that expected from the planet's radiative temperature, F_internal ≡ F_lw - F_eq.

4. Out of sample tests.

He is also wrong that all the giant planets have large internal heat sources. Uranus does not. Its internal heat flux density is actually less than half that of Earth (0.044 W m^-2 versus the terrestrial 0.087). Uranus therefore provides an out-of-sample test for the Holmes hypothesis. It fails that test egregiously, predicting T_calc = 66 K versus the actual 1-bar temperature level of 76 K (Williams 2023). This is a relative error of 13% and brings the rms error for the whole ensemble (N = 4) to 5.8 K.

Another out of sample test is provided by Earth during the Last Glacial Maximum (LGM). It is important to note that TSI during this time (approximately 18,000 years ago) was almost exactly identical to the present level. The 1-bar surface temperature at LGM was approximately 282 K (Tierney et al. 2020), and Holmes's T_calc, of course, remains at 289.1 K. This is a 2.5% relative error, and the rms error for all five cases is 6.0 K. This is a far cry from "within 1 Kelvin [sic]." Clearly, if Holmes were correct, there would have been no ice ages. Indeed, with Earth's atmospheric temperature profile set only by TSI, no climate change of any sort would be possible unless TSI or atmospheric pressure changed.

In addition, the sun 4.4 billion years ago was approximately 32.3% less luminous than today (Bahcall 2001). Holmes's equation predicts T_calc = 262 K for that case, below the freezing point of water (273 K). Yet we know from the Jack Hills zircons that there was liquid water present on the surface. One could add further cases, such as the Snowball Earth glaciations during the Huronian, Sturtian, and Marinoan periods. Holmes's equation fails all of them.

5. Conventional atmosphere physics.

It should be noted that radiative-convective column models routinely find planetary surface temperatures to within a fraction of 1 K. Bullock and Grinspoon (2001), for instance, find Ts = 735.1 K for Venus versus the actual 735.3 K, while Manabe and Strickler (1964) find Ts = 287 K for Earth, versus the actual 287.4 K. (Note the difference from the US Standard Atmosphere (NOAA et al. 1976), which Holmes apparently uses. The USSA-76 gives Ts = 288.15 K.) All these models, of course, include radiative transfer methods which account for the greenhouse effect.

6. The first law of thermodynamics.

Holmes notes that albedo can be ignored for his equation; there is "no effect from planetary albedos." This, of course, implies that an atmosphere at the 1-bar level can be heated by sunlight that never reaches it. This violates the law of conservation of energy. This mistake, in and of itself, completely vitiates Holmes's thesis.

7. Conclusion.

Holmes has found a numerical coincidence between temperatures at the 1 bar level between Earth and Venus, based on TSI, and mistaken it for a universal law (despite fitting only three worlds out of ten, badly). The inability of his model to pass any out-of-sample test, the lack of any clear physical mechanism behind the model, and the unphysical assertion that conservation of energy can be ignored, means that his hypothesis is falsified, and is of no use to climatology, planetary astronomy, or physics in general.

8. References.

Bahcall, J.N., Pinsonneault, M.H., Basu, S. 2001. Solar models: Current epoch and time dependencies, neutrinos, and helioseismological properties. Astrophys. J. 555, 990-1012.

Bullock, M.A., Grinspoon, D.H. 2001. The recent evolution of climate on Venus. Icarus 150, 19-37.

Haberle, R.M. 2015. Solar System/Sun, Atmospheres, Evolution of Atmospheres. In North, G.R., Pyle, J., Zhang, F. (eds), Encyclopedia of Atmospheric Sciences (2nd ed.). Cambridge, MA: Academic Press, pp. 168-177.

Holmes, R.I. 2020. On the apparent relationship between Total Solar Irradiance and the atmospheric temperature at 1 bar on three terrestrial planets [sic]. Earth Sci. 8, 346-351.

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

Mitri, G., Showman, A.P., Lunine, J.I., Lorenz, R.D. 2007. Hydrocarbon lakes on Titan. Icarus 186, 385–394.

NOAA, NASA, USAF 1976. US Standard Atmosphere 1976. Washington, DC: U.S. Government Printing Office.

Seiff, A., Schofield, J.T., Kliore, A.J., Taylor, F.W., Limaye, S.S., Revercomb, H.E., Sromovsky, L.A., Kerzhanovich, V.V., Moroz, V.I., Marov, M.Ya. 1986. The Venus International Reference Atmosphere. Adv. Space Res. 5, 3-32.

Tierney, J.E., Zhu, J., King, J., Malevich, S.B., Hakim, G.L. 2020. Glacial cooling and climate sensitivity revisited. Nature 584, 569-573.

Williams, D.R. 2023. Uranus Fact Sheet. https://nssdc.gsfc.nasa.gov/planetary/factsheet/uranusfact.html, accessed 11/03/2023.