Abstract
In the past, the planetary radiation balance served to quantify the atmospheric greenhouse effect by the difference between the globally averaged near-surface temperature of and the respective effective radiation temperature of the Earth without atmosphere of resulting in . Since such a “thought experiment” prohibits any rigorous assessment of its results, this study considered the Moon as a testbed for the Earth in the absence of its atmosphere. Since the angular velocity of Moon’s rotation is 27.4 times slower than that of the Earth, the forcing method, the force-restore method, and a multilayer-force-restore method, used in climate modeling during the past four decades, were alternatively applied to address the influence of the angular velocity in determining the Moon’s globally averaged skin (or slab) temperature, . The multilayer-force-restore method always provides the highest values for , followed by the force-restore method and the forcing method, but the differences are marginal. Assuming a solar albedo of , a relative emissivity , and a solar constant of and applying the multilayer-force-restore method yielded and for the Moon. Using the same values for α, ε, and S, but assuming the Earth’s angular velocity for the Moon yielded and quantifying the effect of the terrestrial atmosphere by . A sensitivity study for a solar albedo of commonly assumed for the Earth in the absence of its atmosphere yielded , , and . This means that the atmospheric effect would be more than twice as large as the aforementioned difference of 33 K. To generalize the findings, twelve synodic months (i.e., 354 Earth days) and 365 Earth days, where , a Sun-zenith-distance dependent solar albedo, and the variation of the solar radiation in dependence of the actual orbit position and the tilt angle of the corresponding rotation axis to the ecliptic were considered. The case of Moon’s true angular velocity yielded and . Whereas Earth’s 27.4 times higher angular velocity yielded , and . In both cases, the effective radiation temperature is , because the computed global albedo is . Thus, the effective radiation temperature yields flawed results when used for quantifying the atmospheric greenhouse effect.
Highlights
The “thought experiment” of a planetary radiative equilibrium for the Earth in the absence of its atmosphere is considered to quantify the atmospheric effect
RE ≅ 6371 km is the mean radius of the Earth considered as a sphere, S is the solar constant, i.e., the total solar irradiance reaching the Earth’s surface for a mean distance between the Sun’s center and the Earth’s orbit of r0 ≅ 149.6 ×106 km (e.g., [2, 3]), and αE is the planetary albedo of the Earth
In case of the Moon his formula would provide Ts ≅ 267 K, a value close to its effective radiation temperature of Te ≅ 270 K, but much higher than the result of Monstein’s [30] observations of the Moon’s mean disk temperature. Because of this large discrepancy in the results of the globally averaged surface temperature and the consequence in evaluating the atmospheric effect, it is indispensable to assess whether the result of Gerlich and Tscheuschner [33] or that of Smith [34] is more relevant
Summary
The “thought experiment” of a planetary radiative equilibrium for the Earth in the absence of its atmosphere is considered to quantify the atmospheric effect (spuriously called the atmospheric greenhouse effect). In 2009, Gerlich and Tscheuschner [33] derived a globally averaged surface temperature of Ts ≅ 144 K for the Earth in the absence of its atmosphere using the same assumptions commonly considered in deriving the effective radiation temperature except for the distribution of the surface temperature Instead, they calculated surface temperatures for local radiative equilibrium. In case of the Moon his formula would provide Ts ≅ 267 K (or somewhat lower), a value close to its effective radiation temperature of Te ≅ 270 K , but much higher than the result of Monstein’s [30] observations of the Moon’s mean disk temperature Because of this large discrepancy in the results of the globally averaged surface temperature and the consequence in evaluating the atmospheric effect, it is indispensable to assess whether the result of Gerlich and Tscheuschner [33] or that of Smith [34] is more relevant. We adopted Budyko’s [27] suggestion that prior to the formation of the terrestrial atmosphere, the Earth’s surface and soil properties would probably be similar to those of the Moon
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