How Thick is the Atmosphere?

The theoretical model of blackbody radiation as radiation through a peephole of an empty cavity (with soothed walls) is independent of the mass of the cavity (which is zero). This model property reflects a passive quality of (blackbody) radiation as emission of what is absorbed, no more no less.

A solid body like a glowing lump of iron has a full continuous blackbody spectrum covering all frequencies, while a gas has more or less thin line spectrum as discussed in a previous post on radiation of solid vs gas.

The wave model of blackbody radiation analyzed on Computational Blackbody Radiation represents a solid body consisting of a lattice of atoms capable of coordinated vibration emitting infrared radiation with a continuous spectrum of wave lengths several orders of magnitude larger than atomic dimensions. The model can be seen as a set of oscillators with small damping in equilibrium with external forcing with resonance frequencies covering all frequencies (up to a cut-off scaling with temperature).

Restricting this model to a set of oscillators with only selected resonances gives a model of a gas which does not appear to have the capacity of coordinated vibration on scales larger than atomic scales. The line width of the model is about 1 Hz.

The warming effect of 0.039% atmospheric CO2, as observed in the previous post, results from the continuous ditch in the Modtran OLR spectrum in the whole interval 550 - 800 around the main resonance at wave number 667, and is (very surprisingly so) comparable to the warming effect of 2% water vapor as the main "greenhouse gas".

The continuity of the Modtran OLR spectrum in the ditch comes from considerable broadening of the line spectrum of CO2 as an effect of a 10000 m thick troposphere. With a path length of only 1000 m the spectrum would be sparser and the CO2 warming effect maybe 10 times smaller.

So here is the question: Does a 10000 m thick atmosphere radiate like a solid with a continuous spectrum, while a 1000 m thick atmosphere radiates like a gas with a line spectrum?

Hint: If continuity of the OLR spectrum requires coordination over lengths much larger than molecular, does a 10000 m thick atmosphere offer more coordination than a 1000 m thick?

PS1 Hottel charts tabulate air emissivity using the product p x L as parameter, where p is the partial pressure of CO2 and L the path length, where thus a small partial pressure/concentration can be compensated by a large path length. In experiments the path length can be of size a few meters and the question is if the p x L dependence can be extrapolated to thousands of meters?

PS2 It is not easy as outsider to judge the validity of software like Modtran/Hitran since both models and programing is complex. But if software results contradict reason, then something may be seriously wrong and if something is seriously wrong then it may be possible to identify what it is.

PS3 Compare with How Deep is the Ocean?