Hypothetically, could a planet have a larger greenhouse effect with the same mass of greenhouse gas?

That's a great question - and thanks for asking. Please keep it open, I'd like to give it a go, but I'm busy over the weekend and, in any case, could use some thinking time.

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Four days later:

Well, I’ve had some time; not nearly enough I expect; still, here goes.

So, could a planet have a larger GHE with the same mass of GHG? If my understanding is correct, then there is a trivial mechanism that would cause a slight change with altitude. The CO2 layer would be spherical, with its centre at the centre of the planet. If the CO2 layer was the uppermost, then it would have a slightly larger radius; hence a larger surface area, than if it was nearer the surface. As such, it would radiate at a slightly lower temperature to achieve radiative equilibrium. As a lower layer, it would need to reach a slightly higher temperature which would also mean a higher surface temperature.

But that is a trivial mechanism and I’ll ignore it from now.

To try to answer your question I’ll consider two scenarios; that of the CO2 layer being the top layer, and that of it being the one in contact with the surface.

From memory, the total height of the atmosphere would be equivalent to 8 km if it was all at sea level pressure. Assuming CO2 is 400/10^6, this would give a layer thickness of 3.2m at the surface. At altitude. This would increase dramatically, with the thickness of the top layer; compressed only by its own weight, measured in km. Pressure would vary within this layer, from 1/20th of sea level pressure at the lower boundary, reducing to zero at the upper boundary with space.

Now, for both layers, and assuming the planet is in radiative equilibrium, an observer above would see a strong emission of IR at the wavelengths associated with CO2 absorption. Other wavelengths will be observed from other GH layers or directly from the surface. Both layers would show a temperature gradient between lower and upper boundaries; the lower boundary being the hotter. Both would radiate strongly downwards to warm the surface.

(Edit: These different wavelengths, when viewed together, would appear as a black body radiator for a planet in equilibrium)

The question is, would the strength (effectiveness) of the greenhouse effect be the same for both scenarios? If it is, then the temperature recorded at the surface would also be the same.

My gut feeling is that there will be differences that will mean a stronger GHE, therefore a higher surface temperature for one of the scenarios. Which one? My money is on the lower layer having a stronger effect.

You will know from my previous question that I believe there would be an increased probability of absorption when the emitting and absorbing molecules are closer together. This would mean the same GHE from fewer molecules, or a stronger effect from the same number of molecules.

http://answers.yahoo.com/question/index;_ylt=Arg6v...

However, this does require that the absorption cross section remains constant. In an answer to another question, you said: “The absorption cross section depends on the transition probabilities between quantum states and there are many things that can affect the transition probability. In ordinary circumstances, pressure is the most important.”

So the very different pressures between the two layer scenarios would be significant. How? I’ve absolutely no idea!

Another difference that occurred to me was that, in the lower layer, with molecules much closer together, the time it took for a photon to travel between them would be much less. Now I don’t know, but wouldn’t this make the greenhouse effect happen much faster? … this opposing the effect I described in my question?

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To sum up, I would say a higher surface temperature from an increased greenhouse effect would be observed in the scenario of the CO2 layer being the lowest.

I’m not confident of this though, If you told me that they would be the same, that wouldn’t surprise me at all! The trouble is that every answer I get seems to lead to even more questions. And I haven’t even begun to study all that quantum stuff!

A great question though; thought provoking and challenging. I’m looking forward to the answer.

First of all although your question is valid, your imaginary planet, I would venture to say is very much imaginary. Regional concentrations of gases are known to exist however, and the Great Red Spot on Jupiter is a primary example. The implication from your question is that all greenhouse gas is CO2. This is not true. There are many other greenhouse gases CH4 is a primary example. Some greenhouse gases are stronger than others meaning that for the same amount of gas the heating effect is larger. Since stronger greenhouse gases do exist, and you have conditioned your question on the equality of the mass, a greenhouse gas that is stronger than CO2 for the same amount of molecules, will produce great heating effect if the strength of the other greenhouse gas is greater than the ratio of a mole of the specified other greenhouse/ the mole of CO2, there would be a heating effect greater than that produced by the same mass of CO2, if the ratio of the respective moles exceeds the inverse. Given the same mass of CO2 a gas with twice the molecular weight of CO2 would contain one half as many molecules. The heating effect to be greater than that of CO2 would have to be greater than 2.

My gut instinct (which may or may not have any bearing on reality) is that the concentrated layers would be less effective than an equal mass of more diffuse greenhouse gasses, because of saturation effects. Which, given the geometry of the atmosphere, might suggest that the outermost layer would be more effective than the innermost, simply because the outer layer's relatively low pressure would reduce saturation effects. But I suspect it's not quite as simple as that, and/or I'm getting the physics wrong somewhere.

Am I correct in that the virial theorem dictates that lower layers are going to be warmer than higher layers?

I think that's true, whether for that reason or not; in either case, IF it is true, then we would expect a lower layer to radiate at a higher temperature at those wavelengths, so that means that the Earth would reach a new thermal equilibrium relatively close to the old temperature. The higher the gas, the cooler the temperature at which it will radiate in those wavelengths, so there would need to be a higher temperature increase at the surface to compensate for the increased downwards forcing.

Do I have that right? The higher the layer the stronger the greenhouse effect.

Only in theory, besides I don't think degenerate matter is readily applicable to planets. But that would be Maxwell's demon, where pressure and not temperature isolates the layers thus creating a violation.

Hypothetically... a new sun, dwarf or something to that effect?

Anything is possible if you have a Maxwell's demon...

So, let me get this straight. To illustrate the physics, we're supposed to pretend the physics doesn't work.

Okay. Hypothetically yes.

Beats me. I would guess that the lower layer would have more effect.