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I am deliberately asking this question in Physics rather than Earth Sciences because I think it does come down to specific physical processes.

The background is that I recently had a discussion where someone who claimed to be an experienced physicist claimed that the greenhouse effect cannot work.

This was not for the usual reasons that involve incorrect invocation of the 2nd Law of Thermodynamics or whatever, but for the apparently straightforward reason that IR at the frequency re-emitted as "backradiation" by CO2 is not absorbed by most materials except at extremely low temperatures. The upshot is that the IR is scattered at the surface and ends up going out to space anyway.

I am not a physicist. I only have a layman's interest and I had previously worked on a hand waving assumption that upward heat loss minus downwelling IR essentially sums to reduce the rate of heat lost to space. However, I can see that if the IR is not absorbed at the surface then it does appear to argue against my very naïve view of it.

As I say, I am not a physicist and I did not have an immediate answer to what this person is saying. I am sceptical, if only because it seems to be a simple argument and, if there were any truth in it, it would surely have gained some traction by now.

My actual question is in a few parts:

  1. Is this nonsense, as I suspect? What uncontroversial physics (ideally something relatively simple) refutes the claim?
  2. Is there any possible grain of truth at all? The problem I had was that I could not even get to the bottom of what physics they were invoking so that I could look into it myself.
  3. I'm now intrigued about what actually is happening at the level of IR photons hitting the surface. Assuming that what this person claims is wrong and that the backradiation does slow heat loss, what is the actual process happening at an atomic level that results in this? I assume there has to be absorption for there to be an effect.
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  • $\begingroup$ In a non-absorbing optical setup, if a window reflects half the light it receives back into a cavity, the intensity increases in the cavity (see: etalon). We’d rather not have lots more IR in the lower atmosphere since, well, plenty of things do happily absorb it despite their beliefs. That includes you and me and any semi-reasonable black body. $\endgroup$
    – Jon Custer
    Commented Dec 2, 2022 at 14:50
  • $\begingroup$ "who claimed to be an experienced physicist claimed that the greenhouse effect cannot work." Let me guess, a solid-state physicist, e.g. an engineer? Most molecules absorb IR radiation like crazy, hence water and CO2 being the most powerful greenhouse gases in the first place. The data is easy to look up, (look for 'absorbances' or 'opacities'). Only the few infrared windows in Earth's atmosphere 'leak' infrared radiation to space (and let infrared astronomers observe the cosmos in the IR). $\endgroup$ Commented Dec 2, 2022 at 15:37

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There are two major problems with what they say: First, that IR (like any light) is straightforwardly either absorbed or reflected, depending on the colour of the material, the Earth's surface is not particularly reflective at IR wavelengths (easily measured), and temperature makes little difference. The second problem is that the greenhouse effect doesn't work that way, anyway.

I have heard this claim before, where it was then justified (supposedly) on the basis of the 2nd law of thermodynamics forbidding heat from spontaneously flowing from cold objects to hot ones. The idea was that a cold object radiating at long wavelengths (like the sky, at an effective radiative temperature of about -20 C) couldn't warm a hotter object (like the surface of the Earth at + 15 C), because that would involve heat flowing the 'wrong way'. This is a misunderstanding - the 2nd Law applies to the net heat flow. Because the hot object radiates more heat towards the cold object than vice versa, the net heat flow is still hot to cold, even though there is some heat flowing cold to hot.

The most everyday-familiar refutation of this I know is a microwave oven. The wavelength of microwaves is even longer than IR, corresponding to black body radiation from an object pretty close to absolute zero. (You can think about the cosmic microwave background from the big bang being about 2.7 C above absolute zero.) Neverthless, your dinner can absorb it, and get hot.

The second problem is that the greenhouse effect in a convective atmosphere does not work by backradiation from the atmosphere keeping the surface warm. (If that was actually the mechanism, the oceans would boil, since liquid water is an even more powerful greenhouse agent than water vapour. See below.)

To understand the greenhouse effect, you first have to understand that gases have the property that they warm up if they are compressed, and cool down if they are allowed to expand. As air circulates convectively in the atmosphere, it is constantly rising and falling, and as it rises it cools, and as it descends again it warms. This sets up a fixed temperature gradient in the atmosphere, called the adiabatic lapse rate. Taking into account the latent heat carried by water vapour, the result is that the atmosphere tends to settle with a lapse rate of 6.5 C per km altitude. For every 100 metres you climb, you find the air temperature will drop about 0.65 C. If it changes at a rate any steeper than that, the warm air near the surface rises convectively, cools, but only at 6.5 C/km so it remains warmer than the surroundings it moves into. This mixes in and warms the air aloft, eliminating the excess lapse rate. It is a bit like the way that a pan of boiling water is held fixed at 100 C. If you turn the heat up, the water just boils more vigorously, carrying heat away faster by convection/evaporation, and stays at the same temperature. The atmosphere stops the lapse rate exceeding the adiabatic limit in the same way, by convecting surface heat upwards faster until the limit is met again.

Now consider the Earth from space. Heat can only enter or leave the system by radiation. The Earth receives heat (mostly at visible wavelengths) from the sun, and emits heat (in the infrared) to outer space, and the two must balance almost exactly, or the Earth would warm up at an enormous rate. (A cumulative 1 Watt per square metre difference would dump 31 MJ/year cumulatively into every square metre of land and ocean. That's the same as 31 kettles running at 1 kW for about twenty minutes.) The Earth's temperature adjusts so that it emits black body radiation at precisely the rate needed to balance the inward flow. Given the intensity of light from the sun, and the fraction the Earth absorbs rather than reflecting back into space, this temperature turns out to be about -20 C.

However, the surface that has to approach this temperature is the visible surface of the planet at infrared wavelengths, and the atmosphere is opaque in the infrared, because of greenhouse gases and clouds. The dense, moist part of the atmosphere is about 10 km thick, and IR is radiated to space across the whole span, so the average altitude of emission of radiation to space is about 5 km. This is the part of the atmosphere that has to be at -20 C to maintain the energy balance.

If the atmosphere 5 km up is held at -20 C, then the surface will be held at roughly $-20 + 5\times 6.5=12.5$ C by the adiabatic lapse rate. Air descending from this altitude is warmed by compression. This warming is the greenhouse effect.

Backradiation does occur, is absorbed, and is required for the energy flows to balance. However, it has no effect on the surface temperature, because any excess heat it might supply is quickly convected away by the processes establishing the adiabatic lapse rate. The factors that affect greenhouse warming are the energy absorbed from sunlight, the lapse rate itself (which varies with the moisture content of the air), and the average altitude of IR emission to space (which is affected by greenhouse gases and the altitude of clouds).

I will give some references, since this being a controversial subject, I want to make clear that my version above is mainstream atmospheric physics.

Soden and Held 2000 'Water Vapour Feedback and Global Warming', Annu. Rev. Energy Environ. 2000. 25:441–75. See figure 1 and the discussion around it in particular.

Manabe and Strickler 1964 'Thermal Equilibrium of the Atmosphere with a Convective Adjustment' Journal of the Atmospheric Sciences 21 (1964): 361-385.

Sagan 1960, 'The radiation balance of Venus. Technical Report No. 32-34', Jet Propulsion Laboratory, NASA Contract No. NASW-6 (1960). In this paper, the famous Carl Sagan estimated the surface temperature of Venus using the discovery that the cloud tops were at least 30 km above the surface, and the adiabatic lapse rate for the Venusian atmosphere was about 10 C/km (page 7), predicting a massive 300 C greenhouse effect! The adiabatic lapse rate formula I use here is given as eqn 7 on page 5. The clouds are actually about 50-80 km high, and the adiabatic lapse rate about 8 C/km, giving about 500-600 C of greenhouse warming.

I have heard that Schwarzchild (of black hole fame) developed the principle in his work on stellar atmospheres in the 1930s, and it was carried across to atmospheric physics in the late 1950s and early 1960s. I don't have any references to support that, though.

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I mentioned above that the greenhouse effect applies in liquid water, too. Liquid water is opaque to IR after a few millimetres, which means we can divide the body of the water up into horizontal slices 2 mm thick, each of which radiates black body radiation both upwards and downwards into the next layer. Sunlight shines down into the water at visible wavelengths, at which water is transparent, and is absorbed at depth. This same amount of energy has to be radiated to space from the topmost surface, for energy balance. Black body radiation is isotropic - the same in all directions - so it also radiates this same amount downwards into the layer below as backradiation. The layer below therefore has to radiate twice the amount both upwards and downwards, so that we get the required net upward flow. The layer below that has to radiate three times the same amount, and so on. The radiated power of the backradiation being emitted within the body of the water therefore increases linearly with depth, and by the Stefan-Botzman law, the temperature needed to generate this additional backradiation rises with the fourth root of the depth. One metre of water contains 500 layers, so the absolute temperature increase has to vary by a factor of 4.73 between top and bottom. If it's anywhere close to ambient temperature at the top, it has to be boiling at the bottom.

This does not actually happen, because as soon as the temperature gradient exceeds the adiabatic lapse rate for water (which is tiny, because water is nearly incompressible), the water starts convecting, carrying the heat up to the surface. Radiation is extremely inefficient for transporting heat through water - convection works a lot faster, and prevents any heat building up below the surface. Despite liquid water being a greenhouse agent 20,000 times more powerful than water vapour in the air (mainly because it's denser), we do not get heat buiding up in the depths.

If you suppress convection, by dissolving salt in the water to change its density with depth, the bottom of the pool does heat up. This is the basis of the solar pond, and can achieve temperatures of 90 C at the bottom with only a few metres of water.

Likewise, actual greenhouses (the buildings made out of glass) also work by suppressing convection. As can be demonstrated by using a transparent pane of rock salt for a roof, which is transparent to IR, and so emits no backradiation, but still keeps the contents warm.

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So many things wrong here.

Ordinary materials are quite absorptive/emissive in the thermal infrared. That's what makes infrared imaging cameras useful.

However, even if the surface reflects the radiation instead of absorbing it, that radiation must make its way up through the atmosphere. Greenhouse gasses interfere with this. To get heat transport through such a medium, you must have either a temperature gradient or convection. Near the surface, convection dominates, so radiation isn't big factor. It's at the tropopause that the greenhouse gas concentration has a big effect.

If the surface was reflective, the effect of greenhouse gasses would be enhanced, since the reflected radiation would be mostly at wavelengths where the absorption/emission of the greenhouse gasses is maximum. As it is, the surface reradiates absorbed radiation at a variety of wavelengths. At some infrared wavelengths, the atmosphere is transparent, so energy at those wavelengths easily escapes.

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