However, the Earth has a tilt angle of its daily rotational axis with respect to the axis of its annual rotation in orbit about the sun of ψ = 23.44° or 0.4094 radians. The paper mistakenly calls the this the precession angle. The tilt angle does precess over tens of thousands of years, but the angle of its precession is not important for this present calculation. [Thanks to Tom Anderson for pointing out the proper identity of this angle. See the comments below.] According to Sorokhtin, Chilingar, Khilyuk and Gorfunkel in Evolution of the Earth’s Global Climate, Energy Sources, Part A, (2007), 1-19 and Sorokhtin, Chilingar and Khilyuk, Global Warming and Global Cooling: Evolution of Climate on Earth, Elsevier, Amsterdam (2007), p.313, the correction factor for the rotational tilt effect, ø, according to Chilingar, replaces the factor 4 in the divisor above with 4ø, where ø is
In addition, the less saturated effect of the infra-red active gases in absorbing solar insolation prior to its reaching the Earth's surface is in effect a cooling of the surface. This solar insolation absorbing cooling effect has gained significance with respect to the surface temperature warming effect that was due to the absorption of thermal energy emitted from the Earth's surface and which broke the surface radiative equilibrium with space. The disruption of the radiative equilibrium of the Earth's surface with space is the only important means by which infra-red active molecules warm the surface. This has nothing to do with back-radiation from the atmosphere as I have discussed here, here, and here. A small amount of radiation from the atmosphere is absorbed by the Earth's surface, but only in those local conditions when the absorbing molecule in the Earth's surface has a lower temperature than does the emitting infra-red active molecule in the atmosphere. An example is when a warm wind blows over a cool surface or when photons emitted from a molecule in the air in a sunny area are absorbed by a surface area which is shaded from the sun.
This article was updated on 6 August 2015.