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I'm looking to find experiments that experimentally demonstrate the Idealized greenhouse model.

So far all the experiments I've come across do not quite demonstrate the model, but something else.

There is quite a bit of nuance here, so I will explain. As a brief recap of my understanding, the basic physics model of the atmospheric greenhouse effect is that if the Earth had no atmosphere, it would be -18°C in total equilibrium with the incoming solar radiation, i.e. absorbing as much energy as it possibly could be from the Sun. Importantly, the Sun's input is simplified to be evenly irradiating and constant and equal to the outgoing radiation of the surface, whose value due to the geometry involved is 1/4th the actual solar radiation during daytime.

If we then add greenhouse gases to the equation, which gases allow the visible light of the Sun through but absorb the infrared light the Earth re-emits as a result of being warmed by the sun, the net result is an increase of the surface temperature over and above this previously possible "max" radiative equilibrium.

A skeptic argument is that this violates the 2nd law of thermodynamics, to which the response is that it doesn't since the Sun is the ultimate source of energy, and the Earth isn't getting hotter than the Sun, i.e. that the greenhouse gases act just like insulation does (example link, note the comparisons to a blanket). It is obvious of course that if you surround a cup of hot coffee with some aluminum foil (leaving some air in between), 97% of the infrared the coffee emits will reflect back at it, which does not violate any laws of physics as the net heat flow is still from coffee to foil, i.e. the foil is not "heating up" the coffee per se, just slowing down its rate of cooling.

However, although it's true that in reality the Sun heats the Earth more during the day than at night, and as such additional radiative insulation could preserve the temperature better -- that's not what the model explaining the greenhouse effect is based on. The model is based on a constant solar irradiance, 100% of which already was fully absorbed by the Earth prior to the addition of the gases. In other words one could argue that the -18°C already was the maximum temperature that could be reached by the surface in this model, and as such it would not be possible by any means to cause this temperature to increase in a 'passive manner' (e.g. without doing work such as running a heat pump) without violating the 2nd law.

The constancy of the solar irradiance of the model is directly relevant here. To illustrate this, it will help to understand that you can't burn paper with moonlight and a magnifying glass. To put it differently, if the Sun is out and the temperature of a patch of ground is 30°C, you could still use magnifying glasses to burn a piece of paper on this patch of ground, because the magnifying glasses can 'expand' the 'small' image of the sun to look bigger, such as to surround a spot of Earth with the high-intensity sun, thus causing a paper to be able to reach 220°C+ and ignite. But if you were to instead step into a large room with an even 30°C ceiling, though the ground would be the same 30°C temperature, this would no longer be possible, because the patch of ground is already as if it were surrounded by the 30°C ceiling, and thus optics cannot make it any brighter. (It is straightforward to see that if it were possible one could then direct that higher temperature light back at the ceiling, thus being able to increase the temperature indefinitely.)

Similarly, the idealized greenhouse model is essentially saying that if we were to step into a giant vacuum chamber with a ceiling evenly radiating -18°C equivalent of visible light and a floor absorbing it all and reaching a temperature of -18°C, evenly emitted as infrared light... that if we were to separate out a piece of ground and cover it with a glass container (transparent to visible light and absorbent of infrared light), the ground in the glass cube would become warmer than the -18°C, being able to reach +15°C or so depending on the specifics.

The parallel to insulation might not quite apply since insulation only preserves the temperature of what it is insulating, and if better insulating something results in a higher temperature at a new equilibrium it's only because the heat source was already hotter in the first place. This is why it's important to use a diffuse even low-intensity light as depicted in the model vs. a spot source of light or the sun.

As the theoretical debates on the second law of thermodynamics can be endless, instead I'm looking to see if anybody has been able to actually reproduce this result experimentally. All the experiments I have found so far that purport to do so don't actually demonstrate it per se. For example:

Short of running an experiment in space, which may be doable but quite expensive, it seems one could run an experiment using vacuum chambers and a large ceiling of low-intensity light. One would have to take care that the infrared the ground is emitting doesn't come back to it from the ceiling or any other source besides the glass enclosure. Such an experiment would settle any possible skeptic counterpoints regarding the 2nd law completely as it would be experimentally evident that the atmospheric greenhouse effect works in reality and therefore of course does not violate the 2nd law.

Have any such experiments, or ones along similar lines, been done? If so, what are the references or links to them?

Please note I'm not looking for models, measurements, theories, references to consensus, etc. I'm just looking for repeatable experimental evidence that this model has been shown to be capable of happening in reality, to at least some extent yet still maintaining the fundamentals of the model.

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The best such experiment I know of to demonstrate the physics of a pure-radiative greenhouse effect in a non-convective atmosphere is the solar pond. However, it is essential to emphasise that this is not how the actual greenhouse effect works in planetary atmospheres.

I will come on to the real greenhouse effect in a moment. First, I'll talk about the solar pond. This is a set-up that has been used in hot and sunny countries to generate solar power.

Consider sunlight shining down through clear water, being absorbed at the bottom, and then re-emitted as black body infrared radiation. Liquid water is an incredibly strong greenhouse agent: it is nearly transparent to visible light, but only a few millimetres of water is enough to block all thermal infrared. The radiation comes off the bottom and immediately slams into the bottom millimetre layer of water, and is absorbed. This millimetre-thick layer warms up, and re-emits the energy both up and down. The radiation going up slams into the next layer, and then the next layer, all the way up to the surface. If the sunlight inputs power density P into the pond, the top layer has to emit power P upwards, and because the radiation is emitted in all directions, downwards too. The next layer down must emit 2P upwards into it, to ensure a net upwards power flow of P, and hence also emits 2P down. It has to be hotter to do this. The next layer emits 3P up and down, the next 4P, and so on. The power radiated is proportional to the optical depth, the number of fully-opaque layers, and the (absolute) temperature needed to emit that black body radiation rises as the fourth root of optical depth (by the Stefan-Boltzman law.) Liquid water is so strong an absorber of infrared that the greenhouse effect in a few metres of water is more than enough to boil it.

However, it is experimentally obvious that ordinary ponds of water do not boil in the sun. This is because of convection. As soon as a temperature difference arises with cool water on top of warm, the warm water immediately rises to the surface, eliminating any build up of temperature at depth.

In a solar pond, we suppress convection by dissolving salt in the water to change its density. We make the water at the bottom a dense, salty solution, and the water at the top a layer of less dense, fresher water. The haline gradient suppresses convection until the temperature gradient gets much bigger, and the bottom of the pool heats up. In ponds only a few metres deep, the water at the bottom can reach 90 C. The behaviour of the infrared can easily be checked with a thermal camera. If you want a desktop lab set-up to demonstrate that it is indeed feasible physics, this is the best example I know of.

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However, it has been known by climate scientists since the late 1950s that this is not how the greenhouse effect works in Earth's atmosphere, for the same reason it doesn't work that way in ponds of water: convection. Excess heat build-up at the surface is very rapidly eliminated because hot air rises.

As you say, the energy absorbed by the Earth has to be balanced very precisely by outgoing infrared radiation to outer space, and this happens at a black body temperature of -18 C. (Being picky, that's not quite the situation if Earth had no atmosphere, because the calculation takes into account sunlight reflected from clouds, which of course would not exist in a vacuum. But that's not critical.)

However, the surface that does so is the planetary surface visible in the infrared, which because of greenhouse gases in the bottom 10 km of atmosphere, is on average about 5 km up. Imagine looking at Earth with a thermal infrared camera, and seeing only a fuzzy opaque ball about 5 km up obscuring the solid surface entirely. This is the 'surface' that radiates to space, and so settles at -18 C.

The other part of the mechanism we need to understand is the fact that gases warm up when they are compressed, and cool down when they are allowed to expand. As atmospheric gases rise and fall, the change in pressure causes corresponding changes in temperature. The rate of change of temperature with altitude is called the adiabatic lapse rate, and is about 10 C/km for dry air.

This is modified when air contains water vapour, as when water cools it condenses, giving off heat. This reduces the adiabatic lapse rate to about 6.5 C/km (called the moist adiabatic lapse rate), meaning that for every 1000 metres you climb, the temperature drops about 6.5 C.

So when air near the surface is heated, it can only rise convectively if the gradient is bigger than the moist adiabatic lapse rate. There is a sharp transition in behaviour that tends to hold the atmosphere close to this line. Below the gradient, there is no convection and heat builds up near the surface. Above the gradient, and convection starts up and immediately removes the excess. It's like the way a pan of boiling water stays at 100 C, even if you turn the heat up.

So we have two effects that act in combination. The atmosphere at 5 km altitude is held at -18 C by the overall energy balance, and as air descends from this altitude to the surface via convective cycling, adiabatic compression warms it at a rate of 6.5 C/km. So we calculate -18 + 6.5 * 5 = 14.5 C, the temperature at the surface. This is the convective greenhouse effect.

(We can do a quick check that the adiabatic lapse rate is indeed important by looking again at liquid water. Because water is nearly incompressible, the lapse rate is close to zero and we get no boiling oceans, despite the massive downward backradiation water emits.)

More greenhouse gases raise the altitude of emission to space. More water vapour lowers the adiabatic lapse rate. More clouds reduce the temperature of radiative equilibrium. And we're averaging nonlinear effects over a wide range of circumstances with lots of other physical effects going on, so none of this is anything like as simple as I've painted the picture here.

As a final note, actual greenhouses (the buildings made of glass) have been found to work almost entirely by suppressing convection, too. Experiments were done where panes of glass and panes of rock salt (which is transparent to infrared) were used to make greenhouses, and the temperature inside was found to be nearly identical. An actual greenhouse gives us some indication of how hot the surface of the Earth would be if the idealised greenhouse effect was not short-circuited by convection. Back in the 1960s, Manabe and Strickler calculated the global average surface temperature without convection to be about 60 C.

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In summary:

  • The idealised greenhouse effect can be demonstrated with a solar pond.

  • There is no point in using it to debate with climate sceptics because it's not how the greenhouse effect in a convective atmosphere actually works.

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  • $\begingroup$ Thanks for the reply! Re: the solar pond, naive question but wouldn't enclosing the pond in glass greatly minimize the heat loss due convection? In any case, we could use a magnifying glass to boil water with the sun so this doesn't address the fundamental thermodynamic question. If a solar pond in a room with an even visible light ceiling with equivalent energy of 30°C were to get the pond to 90°C+, it would demonstrate the effect indeed, and the math appears to imply it could. Re: the lapse rate and altitude of emission, it doesn't address the fundamental question, and isn't experimental. $\endgroup$
    – Cloudyman
    Apr 3, 2023 at 9:03
  • $\begingroup$ Basically it seems at minimum an experiment to verify the atmospheric greenhouse effect would need to establish a situation with almost zero heat loss due to conduction and convection and therefore all the heat loss due to radiation -- and then demonstrate that the addition of a substance that behaves differently on different wavelengths of light, elevates the temperature of the situation to a higher point. I'm not 100% sure if it would need exactly the diffuse light source vs a hotter point, as long as it's constant and everything is totally evenly irradiated. $\endgroup$
    – Cloudyman
    Apr 3, 2023 at 14:42
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What many refer to as the 'atmospheric greenhouse effect' is actually a conflation for the Kelvin-Helmholtz gravitationally-induced lapse rate.

An actual greenhouse works primarily by blocking convective removal of energy from a space, while allowing radiative energy to enter the space. Our atmosphere convects. It is not a greenhouse... in fact, the troposphere is more akin to the evaporator section of an AC unit.

The effective emission height is ~5.105 km. That also happens to be where atmospheric pressure is ~1/2 that at sea level.

7 – 13 µm: >280 K (near-surface)

>13 - <=17 µm: ~220 K (near the tropopause)

>17 µm: ~260 – ~240 K (~5km in the troposphere)

The emission profile is equivalent to a blackbody object with a temperature of ~255 K, and thus an effective emission height of ~5.105 km.

The lapse rate is said to average ~6.5 K km-1.

6.5 K km-1 * 5.105 km = 33.1825 K. That is not the ‘greenhouse effect’, it’s the tropospheric lapse rate due to Kelvin-Helmholtz gravitational auto-compression.

Polyatomic molecules (CO2, H2O) reduce the adiabatic lapse rate (ALR), not increase it (dry ALR: ~9.81 K km-1; humid ALR: ~3.5 to ~6.5 K km-1) by dint of their higher molar heat capacity and/or latent heat capacity convectively transiting more energy (as compared to the monoatomics and homonuclear diatomics), thus attempting to reduce temperature differential with altitude (temperature differential with altitude being that aforementioned lapse rate), while at the same time radiatively cooling the upper atmosphere faster than they can convectively warm it… they increase thermodynamic coupling between heat source (surface) and sink (space)… they are coolants.

9.81 K km-1 * 5.105 km = 50.08005 K (dry adiabatic lapse rate, due primarily to homonuclear diatomics and monoatomics... remember that we've removed in this case the polyatomic with the highest contribution to lowering the lapse rate), which would give a surface temperature of 255 + 50.08005 = 305.08005 K. Sans CO2, that number would be even higher.

Water vapor (primarily) reduces that to 272.8675 K – 288.1825 K, depending upon humidity. Other polyatomics (CO2) contribute to cooling, to a lesser extent. The higher the concentration of polyatomics, the more vertical the lapse rate, the cooler the surface.

Also remember: the atmosphere is stable as long as actual lapse rate is less than Adiabatic Lapse Rate (ALR)… and a greater concentration of polyatomic molecules reduces ALR… thus convection increases.

That’s why neither CO2 nor H2O are used as a filler gas in dual-pane windows… if they were such terrific ‘heat trapping’ gases, they’d be used as such. They’re not. Low DOF (Degree of Freedom), low specific heat capacity, nonradiative monoatomics generally are.

Analogize a dual-pane window to the Earth | atmosphere | space system (flip a dual-pane window so it's horizontal)... the bottom pane (and the heat source beneath it) would be the planet's surface, the filler gas would be the atmosphere, the upper pane would be the interface between the atmosphere and space.

If one uses a monoatomic filler gas, there is comparatively less energy transfer between panes. If one uses CO2 (a radiative polyatomic) there is more energy transfer than for a monoatomic. If one uses water vapor, there is drastically more energy transfer.

So one could say that in regards to water, we live inside the equivalent of the evaporator section of a gigantic world-sized air conditioning (AC) unit, with water as the refrigerant, with other polyatomics acting as less efficient coolants, and with the monoatomics and homonuclear diatomics playing the same role as noncondensable gases would play in an AC system… a reduction in the efficiency at which energy is transported due to low molar heat capacity of those monoatomics or homonuclear diatomics and their inability to effectively radiatively emit.

Water vapor isn’t a ‘global warming’ gas… it acts as a literal refrigerant (in the strict ‘refrigeration cycle’ sense) below the tropopause.

The refrigeration cycle (Earth) [A/C system]:

A liquid evaporates at the heat source (the surface) [in the evaporator], it is transported (convected) [via an A/C compressor], it gives up its energy to the heat sink and undergoes phase change (emits radiation in the upper atmosphere, the majority of which is upwelling owing to the mean free path length / altitude / air density relation) [in the condenser], it is transported (falls as rain or snow) [via that A/C compressor], and the cycle repeats.

The same holds for other polyatomics, to a lesser extent (mainly because at prevalent Earthly temperatures, their latent heat capacity doesn't come into play, only their relatively higher DOF (as compared to monoatomics) does).

It is the monoatomics and homonuclear diatomics which are the actual ‘greenhouse’ gases… remember that an actual greenhouse works by hindering convection.

Monoatomics (Ar) have no vibrational mode quantum states, and thus cannot emit (nor absorb) IR. Homonuclear diatomics (O2, N2) have no net magnetic dipole and thus cannot emit (nor absorb) IR unless that net-zero magnetic dipole is perturbed via collision.

In an atmosphere consisting of solely monoatomics and homonuclear diatomics, the atoms / molecules could pick up energy via conduction by contacting the surface, just as the polyatomics do; they could convect just as the polyatomics do… but once in the upper atmosphere, they could not as effectively radiatively emit that energy to space, the upper atmosphere would warm, lending less buoyancy to convecting air, thus hindering convection… and that’s how an actual greenhouse works, by hindering convection.

The surface would also have to warm because that ~76.2% of energy which is currently removed from the surface via convection and evaporation would have to be removed nearly solely via radiation (there would be some collisional perturbation of N2 and O2, and thus some emission in the atmosphere)…. and a higher surface radiant exitance implies a higher surface temperature.

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