Even on the realist side, the discussion always sounds like the Sun is just another "forcing" whose effect is still open to question.
Well, because the actual physics involved opens a can of worms that neither side of the debate is willing to deal with. This is why both sides ignore Gerlich and Tscheuschner, for instance.
arguments as to why the [Stefan-Boltzmann] equation doesn't apply to earth (despite the fact that it clearly does).
Okay, here are a few. Assume that the method of dividing irradiance by four to obtain the temperature of a spherical, reflective Earth is valid (although it isn’t). Thus, with 1366 watts per square meter available but with 0.7 absorption, you divide by 4 and get 239 W/m², which, via Stefan-Boltzmann, corresponds to about 255 Kelvin on a blackbody. The accepted method also assumes that this 255 K body will then emit 239 W/m². But Kirchhoff says it won’t, for emissivity is equal to absorptivity. Given an absorptivity of 0.7, then, this semi-smooth body at 255 K will emit 167 W/m². Since it can’t absorb as well as a blackbody, it can’t emit as well either. In short, the accepted method of obtaining the Earth’s base temperature incorporates absorptive but not emissive reduction. No body radiates as efficiently as a blackbody. This means that a graybody necessarily retains its heat longer than a blackbody, which thereby invalidates the initial 255 K assumption, that of dividing irradiance by four.
Moreover, whereas a blackbody radiates 100% of the thermal energy impinging on it, the maximum rate of heat loss, a real body has internal conductivity, allowing it to store heat. This too skews temperature estimates. The moon, for example, is considered an 89% blackbody. 1366 times 0.89 thus yields 1216 W/m², which corresponds to about 383 Kelvin on a blackbody, which should be close to its temperature at solar noon. Does the moon’s surface actually reach that temperature, though? No. Because, as Apollo-era measurements indicated, the moon’s regolith stores some of that heat and releases it later.
This chart shows the deviation between predicted and actual lunar surface temperatures throughout the moon’s one-month "day".
The blue zone depicts the moon's thermal handicap, the orange its advantage.
A real body exposed to the sun doesn’t heat up as fast as a blackbody because it’s busy storing heat, conducting it internally into itself rather than fully radiating it. So it never gets as hot. But then it never gets as cold. Reaching its highest temperature in the solar afternoon, it begins to cool thereafter. And as it does so, the stored heat below now creeps toward the surface. In effect, a real body is a thermal battery. A blackbody has no such attributes. And this gives the moon a higher than predicted average temperature.
As a final point, let me add that EVERY planet is warmer than predicted by a divide-by-four blackbody formula.
- 1. As one can see by the yellow band on this chart, something happens to a planet's gases at pressures above a tenth of a bar. In every case, air that had been getting cooler as it approached the planet now becomes progressively warmer, irrespective of what it’s made of -- hydrogen, helium, nitrogen, carbon dioxide... whatever.
- 2. Moreover, in every case it's apparent that air temperature would only keep rising if the planet itself (rake symbol) didn’t get in the way. As its atmospheric pressure mounts, for instance, Jupiter grows far hotter than Venus.
- 3. Finally, see how the heat lines extend beyond the red circles? Each circle’s position refers to the temperature assigned to that planet by the blackbody equation (see note). In every single case, then, even for Mars, the actual temperature exceeds the estimate, i.e., the scientifically predicted temperature for this planet.
Yet the theory of the greenhouse effect was concocted for the very purpose of explaining why the earth in particular is warmer than predicted.
Does the Stefan-Boltzmann equation apply to the Earth, then? No. There are too many other parameters (some perhaps unknown as yet) that compromise its applicability. But does this significant discrepancy bother so-called climate realists, let alone alarmists? No. In my view, both sides of the radiative forcing debate are chasing their tails, having never verified the initial assumptions of a theory they both endorse. As you say, Bob, show me the physics.
Alan Siddons