Using Earth’s Moon as a Testbed for Quantifying the Effect of the Terrestrial Atmosphere

In the past, the planetary radiation balanceserved to quantify the atmospheric greenhouse effect by the difference between the globally averaged near-surfacetemperature of and the respective effective radiation temperature of the Earth withoutatmosphere of resulting in . Since such a “thought experiment” prohibits any rigorous assessment ofits results, this study considered the Moon as a testbed for the Earth in theabsence of its atmosphere. Since the angular velocity of Moon’s rotation is27.4 times slower than that of the Earth, the forcing method, the force-restoremethod, and a multilayer-force-restore method, used in climate modeling duringthe past four decades, were alternatively applied to address the influence ofthe 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 thedifferences are marginal. Assuming a solar albedo of , a relative emissivity , and a solar constant of and applying themultilayer-force-restore method yielded and for the Moon. Using the same values for α, e, and S, but assuming the Earth’sangular velocity for the Moon yielded and quantifying the effect of the terrestrial atmosphere by . A sensitivity study for asolar albedo of commonly assumed for the Earth in the absence of its atmosphereyielded , , and . This means that the atmospheric effect would be more than twice aslarge 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 thesolar radiation in dependence of the actual orbit position and the tilt angleof the corresponding rotation axis to the ecliptic were considered. The case ofMoon’s true angular velocity yielded and . Whereas Earth’s 27.4 times higher angular velocity yielded , and . In both cases, theeffective radiation temperature is , because the computed global albedo is . Thus, the effective radiation temperature yields flawed results whenused for quantifying the atmospheric greenhouse effect.