# Do gases reflect some IR radiation?

The usual definition given for a greenhouse gas is that it absorbs infrared radiation. Of course, then the gas emits its own thermal radiation, and it does so without preference for direction (assuming homogeneity).

I was looking at the greenhouse effect heat balance and noticed a larger downward flow from the atmosphere than upward.

I can think of two ways you could explain this:

• the top of the atmosphere is colder than the bottom
• the atmosphere reflects IR from the surface

While the first point is trivially true, that doesn't rule out IR reflection. This isn't a completely pointless distinction. Since the atmosphere is cooler than the surface, the temperature of the down-coming IR radiation would be higher if there was reflection going on.

So is there some reflection? Or is the downward flow of IR radiation from the atmosphere completely from absorption and remission?

This kind of pictures is often misleading. When a paradox appears, common sense tells us that there is very likely something wrong with the assumptions. Here the bad assumption is to display the whole atmosphere as a single box what leads to an apparent paradox.

In reality the density varies with altitude and this has for consequence that the mean free path of photons varies with altitude too. Variations of all radiative parameters with altitude follow.

To see the difference with a picture where the atmosphere is represented by N layers, let us take an example for N=2. We suppose that a solid surface S is radiating F (W/m²) into an atmosphere constituted of 2 layers L1 and L2 and the system is in a steady state. We suppose farther that L1 absorbs all the radiation coming from S.

L1 must reemit all the absorbed radiation (steady state) and because of isotropy, F/2 is reemitted up and F/2 is reemitted down. A part P of the upgoing F/2 will be absorbed by the upper layer L2 and of course again reemitted P/2 up and out of the system and P/2 down. As this downgoing P/2 will be absorbed by L1 and again reemitted P/4 down and P/4 up, it is proven that the flux going from the atmosphere to the surface S is F/2 + P/4 + ... > F/2. so it is actually no paradox that the downgoing flux is more than a half of the flux emitted up by the surface. The values depend on the detailed radiation properties of the layers.

Of course N=2 is still not realistic enough and I have omitted the algebra that can be done by any interested reader but the purpose was to show that an N layer atmosphere doesn't behave like a 1 layer atmosphere. Among others I have omitted the source of energy that is necessary to make up for the difference between F that S emits and F/2 + ... etc that S absorbs from the atmosphere.

Regarding the reflection, there is none in this particular case. The infrared radiation emitted by the surface between 0°C and 30°C is mostly absorbed by the vibrational spectrum of H20 molecules (partly by CO2 too). So this radiation is indeed absorbed and exactly reemitted with the exception of a small window that goes directly to space. Obviously there is always some scattering (clouds) but the processes in the dense and warm lower atmosphere are dominated by absorption and emission in the IR spectrum.

Reflection is a collective phenomenon at an interface between two media (http://en.wikipedia.org/wiki/Reflection_(physics)) and is not a property of the individual molecules in the medium, unlike absorbtion and scattering.

The interface is defined by a change in refractive coefficient.

In this case, the refractive coefficient of the atmosphere will change with altitude (because the density is lower at higher altitude), making it plausible that some amount of the IR radiated by the earth is reflected back down by the atmosphere and included in the downwards white arrow on the graphic.

However, that difference in density (and refractive coefficient) would exist regardless of the presence of greenhouse gases, because their concentrations (390 ppm for $$\mathbf{CO_2}$$) are too small to affect the refractive coefficient. So if it were only (or mainly) reflection, there would be no climate change problem due to manmade $$\mathbf{CO_2}$$ and other greenhouse gases, since they would not enhance the greenhouse effect.

The wikipedia article on the greenhouse effect (http://en.wikipedia.org/wiki/Greenhouse_effect) seems to indicate that the mechanism of downward heat flow is indeed re-emission of absorbed IR radiation.

I realize this still doesn't answer your question of why the downward heat flow is larger than that upward into space, but I can think of two reasons why that might be the case:

1. Higher density at lower altitude

If more of the atmosphere's mass is close to the earth, the same is true for its heat content, making emission to the earth more likely.

2. The heat source is at the bottom

As explained in the greenhouse effect wiki article, since the incoming radiation comes (largely) from below, most of the radiation that gets absorbed will get absorbed in the lower parts of the atmosphere, and thus will more likely get re-emitted back to earth.

The fact that the temperature at sea level is higher than at the edge of space doesn't, I think, have any relevance to this question. Each of the heat flows in the graphic has a temperature distribution (that of its source radiator), but the graphic deals only with the magnitudes of heat flows, not their temperature.

The reasoning that the heat flow to earth is greater due to the higher temperature at low altitudes is incorrect, because the earch itself is at that same temperature (roughly), so there will be no net heat flow due to the temperature difference alone.

Also, if the temperature distribution of the heat flow was the deciding factor, the sun's contribution would dwarf all others, as its temperature (and thus the temperature of its radiation) is much higher than any of the other temperatures in this system. In actual fact it is the magnitude (in Watts) of the heat flows that matters, and since the Sun is so far away, its contribution does not dominate.

• FWIW, the heat flow in these graphics between atmosphere and surface isn't a net flow. The net flow is the downgoing minus upgoing arrows. The net heat flow shouldn't be zero because of other heat pathways. That would imply a discontinuity between the surface and atmosphere, but not in the atmosphere. Commented Jan 19, 2013 at 20:20