SOD wrote: “And the operatic duo, in their tragedy, actually produce the equations of radiative transfer.”

G&T produce the equations of radiative transfer ASSUMING local thermodynamic equilibrium exists and question whether that assumption is valid in our atmosphere. It is a reasonable question, but it was G&T’s job as scientists to come up with some evidence that the assumption of LTE is wrong. Nevertheless, the path from the most general equation of radiation transfer (which is inherently three-dimensional) to the one dimensional fluxes in energy balance diagrams is rather obscure. None of my text (Petty, Pierrehumbert and Hobbs and Wallace) cite any primary sources demonstrating that LTE is a valid assumption, and Pierrehumbert doesn’t even index the term “local thermodynamic equilibrium”.

The best answer may be the one you provided in this post: Radiative transfer calculations are consistent with what we observe happening in our atmosphere under a wide variety of conditions.

https://scienceofdoom.com/2010/11/01/theory-and-experiment-atmospheric-radiation/

]]>Vaas: Most of G&T’s paper is about oversimplified nonsense that is used to convince the public that the GHE and enhanced GHE are simple phenomena that have been understood for more than a century: greenhouses, Arrhenius, Planck’s Law and the SB equation (which apply to radiation at equilibrium with its surroundings an equilibrium which doesn’t exist at some wavelengths and altitudes. Since professional climate scientists use radiative transfer calculations, G&T are rejecting what turn out to be strawman arguments.

However, on pages 49 and 50, G&T questions the assumption that the atmosphere is in local thermodynamic equilibrium. In other words, that the fraction of excited CO2 molecules in the atmosphere depends only on the local temperature and not on the local radiation field:

“This assumption of Local Thermodynamical Equilibrium (LTE) is ruled out by many scientists even for the extremely hot atmospheres of stars. The reader is referred to Chandrasekhar’s classical book on radiative transfer [93]. LTE does only bear a certain significance for the radiation transport calculations, if the absorption coefficients were not dependent on the temperature, which is not the case at low temperatures. Nevertheless, in modern climate model computations, this approach is used unscrupulously”

Climate scientists adjust the absorption coefficients of GHG’s for changes in temperature (Doppler line broadening) and pressure broadening. So that isn’t a problem

Hermann Harde, a very prominent climate skeptic derived the equations of radiation transfer in our atmosphere starting with Einstein coefficients and covering ALL of the details including whether an assumption of LTE is appropriate in our atmosphere. He concludes that LTE valid up to 60 km (if I understand correctly), but above absorption begins to compete with collisional excitation. If I understand correctly, for the strongest CO2 line near the surface about 3.5% of emissions come from stimulated rather than spontaneous emission. So LTE is a good, but not perfect assumption here. So he ends up with three derivations of the Schwarzschild equation for radiative transfer. Both he and the consensus use this equation when scattering is negligible to calculate radiative forcing. Harde comes out with a different result because he and the consensus calculate radiative transfer through different atmospheres. So, after carefully considering the issues G&T raised, an equally skeptical physicist endorses the use of equations 60 and 61 for radiative transfer calculation in our atmosphere

https://www.hindawi.com/journals/ijas/2013/503727/

G&T’s complain about Figure 23, which is derived by the “two stream approximation” for radiation traveling in three directions. Equal emission of photons in all directions is decomposed into three fluxes: the component of energy flux in the +z direction for photons emitted upward (even slightly}, the component of energy flux in the -z direction for photons emitted downward, and the components of both emitted in the horizontal x and y directions, which approximately cancel. This is how climate science simplifies the problem of 3D radiation transfer to a one-dimensional fluxes in the +z and -z directions. (Sect 3.7.2).

]]>And the operatic duo, in their tragedy, actually produce the equations of radiative transfer.

Apply these equations, with the absorption lines known from experimental spectroscopy on CO2, water vapor etc, and you find that more CO2 reduces the outgoing longwave radiation from the earth.

Which means the earth warms up, due to the first law of thermodynamics.

But our operatic pair don’t mention the results, they just show the equation as if to say, look, no one is using this!

This implication works on those “educated” by fantasy climate blogs, but for anyone who has studied the subject.. um, yes, this is what everyone uses, and.. did you have a point G&T?

That’s why it’s clear, they were having a laugh.

]]>Vaas: Alfred Schack appears to have believed that CO2 had negligible effect on the GHE because of the overlapping absorption with water vapor.

https://onlinelibrary.wiley.com/doi/epdf/10.1002/phbl.19720280106

The last two sentences of the abstract translate to: “Prof. Schack points out that the CO2 content of the atmosphere is practically without influence. The main reason is the water vapor content of the air.”

And Schack is correct near the surface where CO2 was/is 300-400 ppm and water vapor is 10,000+ ppm. However, the amount of water vapor in the atmosphere drops with altitude – to 3 ppm by the tropopause.

If you go to the online Modtran radiation transfer software and look down from

0.5 km, the calculated upward flux is the upward flux is 442.7 and 442.4 W/m2 with 300 and 600 ppm CO2.

If you look down from 2 km, the calculated upward flux is the upward flux is 411.0 and 410.4 W/m2 with 300 and 600 ppm CO2.

If you look down from 5 km, the upward flux is 365.2 and 363.9 W/m2 with 300 and 600 ppm CO2.

And if you look down from 70 km (the “TOA”), the fluxes are 299.9 and 296.6 W/m2.

http://climatemodels.uchicago.edu/modtran/

This provide a viable explanation for how Schack arrived at we now know is the wrong answer.

]]>The variable of interest for calculating radiative heat transfer using lookup tables or charts as in Schack is the partial pressure of the absorbing gas multiplied by the path length. So for CO2 at 400ppmv or about 0.0004 atmospheres with a path length of about 8,000m the value is 3.2 atm m. That’s quite a lot of CO2 and significantly affects heat transfer.

I had a similar discussion with someone who shall remain nameless several years ago. As the line goes, I can explain it to you, but I can’t understand it for you. If you can’t admit that you could be wrong, you’re posting in the wrong forum.

]]>Oh, and Schack was likely referring to path lengths in meters, not kilometers. It makes a difference. The effective path length at one atmosphere constant pressure from the surface to space is about 8 km.

]]>Schack’s work is for heat transfer within the atmosphere, not for the surface and the atmosphere to space. Your citation is therefore irrelevant. The greenhouse effect does not, in fact, violate the Second Law so your Clausius quote is also irrelevant.

]]>Maybe rather then ridiculing G&T, you should read their paper again, because they mention what you are supposedly missing:

“Exactly this was done wellmany years ago by an expert in this field, namely Alfred Schack, who wrote a classical text-book on this subject [95]. 1972 he showed that the radiative component of heat transfer of CO2, though relevant at the temperatures in combustion chambers, can be neglected at at-mospheric temperatures.”

and

“Clausius examines thoroughly, that the second law is relevant for radiation as well, even if image formations with mirrors and lenses are taken into account”.

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