DIVINER’s results show that the Moon’s actual mean surface temperature is much lower than the estimate derived from the standard Stefan-Boltzmann (S-B) equation:
This means we now need to accept the following distinctions:
1) The term emission temperature (Te) is strictly reserved for estimates obtained by the above (S-B) equation. It refers to a temperature calculated using the assumption of a uniform (spatially homogeneous) distribution of the absorbed solar flux (given by the term S*(1-A)/4) over the surface of a planet. Such a uniform distribution of solar flux over a sphere implies an infinite thermal conductivity of the regolith, which is a physical impossibility. This gives rise to Holder’s inequality. Hence, Te is not related (does not refer) to the absence or presence of an atmosphere. Thus, the 197K lunar average surface temperature value is not an emission temperature, but the actual average physical surface temperature (Ts) of the Moon. The emission temperature of the Moon is Te = 270.2K as calculated by the above S-B equation assuming S = 1361.7 W m-2, A = 0.13, e = 0.98. In other words, the emission temperature is not a physical temperature, but a mathematical construct having the units of temperature. As such, Te is not theoretically compatible with any measurable real temperatures.
2) The ~255K emission temperature of Earth is produced by the same equation above using A = 0.3 and e = 1.0. The average surface temperature on Earth is 287.6K, which is an actual physical temperature obtained via direct observations. Because of that, this temperature is conceptually incompatible with any emission temperature. Hence, calculating Earth’s atmospheric greenhouse effect by subtracting the 255K emission temperature from the 287.6K physical temperature is like deducting apples from oranges to get a lemon!
3) A physical temperature may only be compared to another physical temperature. The Earth without an atmosphere would have no oceans and its surface would be no different from that of the Moon (or Mercury), i.e. covered with fine porous regolith of a similar albedo as that of the Moon (since there would be no clouds). Therefore, the size of Earth’s atmospheric greenhouse effect ought to be evaluated with respect to Moon’s actual mean surface temperature since both planets orbit at the same distance from the Sun. Thus, GE = 287.6 – 197.3 = 90.3K. Perhaps, a better measure of GE is the ratio of these temperatures, which gives the relative thermal enhancement due to the presence of atmosphere (ATE), i.e. ATE = 287.6/197.3 = 1.46.
Newer visitors may wish to refer to several previous threads. This is the main one, where you’ll find pingbacks from others with links.