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The theory of a GHE in a planetary atmosphere is rather well known. Many claim it is no longer a theory but actually proven as a fact.

However I have been reading a lot of things Richard Feynman said about science and have decided to apply some of them to the GHE. I am going to start from an assumption this is something new I have just come across and after listening to the explanations ask: "How do we know it is like that, what can we measure or test to confirm it?"

Now Richard Feynman had a very useful piece of lab equipment which he used quite a lot. I've got one of them too, albeit a version with a lower spec and with a rusty outer casing that shows its age. However I have tested it recently and it is up to spec and passes its boot up self-test. You might have a higher spec one.

So please apply your brain to this:

Planetary Atmosphere Thought Experiment.

You have 2 identical planets, same mass, same rotational speed, same orbit around a sun. They have gaseous atmospheres of identical heat capacity and of the same height. The orbits are perfectly circular and regular. The planets have reached a thermal equilibrium. The ONLY difference between the 2 planets is that one has greenhouse gases in its atmosphere and the other does not.

What differences would the GHE make to the conditions on the 2 planets?

Well fairly obviously if there is a GHE on one its surface temperature will be higher. We will call the planet with the GHE planet G, and the one without planet N.

G will have a higher surface temperature. Now suppose we are looking from outside, from space, at G and N. Will they look different to any measuring apparatus? We know the solar input to each is the same (orbits are the same) so, as we know G and N are in thermal equilibrium it MUST be the case that quantity of radiation leaving the planets is the same. So if we measure it like we do for any celestial body we will measure the same "effective temperature" looking at G and N.

G and N will have the same effective temperature. The surface of planet G will be hotter than N. The height of the atmospheres is the same so the temperature gradient in the atmosphere will be higher on G. Its lapse rate is higher. For any given height in the atmosphere the temperature of the atmosphere on G is higher at that height, than the temperature on N.

So G has a higher surface temperature and the temperature of its atmosphere is higher. Yet, as both planets are radiating into space at the same rate their measured effective temperatures are identical.

This then leads to my main question; What physical parameter can we measure if given ONE planet, without any knowledge of what the conditions are on the other, in order to determine whether we have been given planet G or N?

EDIT 22/4/17. I am adding this edit as the answers attempted so far have all really been an explanation of the details of how the GHE works on Earth and the specifics of CO2. I would like the question properly addressed as it is in connection with the thought experiment proposed. The answer I am looking for will likely be given in general terms, applicable to the GHE from any greenhouse gas or a combination of 2 or more and also be one generally applicable to any planet you might find anywhere. Multiple parameters may be measured. You do have access to the planet's surface or any chosen point in the atmosphere. To clarify the gaseous atmospher may be any combination of gases or a single gas, the specific heat capacity of the atmosphere is the same on each planet, the height of the atmospheres is defined as the height of the troposphere so the tropospheres are the same height. Layers of atmosphere above the troposphere can vary between the 2 planets as I believe there is no claim or evidence that the presence or absence of a greenhouse gas in these upper layers is significant (if you have knowledge otherwise please state it).

EDIT 26/4/17 . This edit follows the question being put "on hold" as being too broad. The actual question posed is quite specific and narrow and is also brief and to the point. It is the "What physical parameter(s) can we measure ?" type of question. That is not broad at all, it is specific and it follows the format of what Richard Feynman suggests. The answer is expected to be in the form of "We would measure X" or "We would measure X and Y" or "We would measure X, Y and Z". Obviously the answer could be expanded via something like "We would measure X and if it is below n then that shows...". So based on a simple and specific questions, and the expected simple answers, the claim of those who put this on hold for being too broad looks erroneous and I suggest they revise their view as it does not accord with a logical examination of the situation as I have explained.

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closed as too broad by Fred, bon, arkaia, kingledion, userLTK Apr 22 '17 at 2:59

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ When you say you want to measure a physical parameter, do you mean a single scalar measurand? We can measure surface (skin) temperature and atmospheric temperature profiles. It's rather the vertical distribution of temperature that tells us about the GHE, which redistributes heat within the troposphere (upper troposphere is cooled, not heated, by GHE). We can derive (but not measure) a single parameter describing GHE from such measurements. If you really mean you want to permit only a single measurement (whatever that even means?) I think you are unnecessarily overconstraining the problem. $\endgroup$ – gerrit Apr 20 '17 at 11:52
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    $\begingroup$ Why are people voting to close this question? I think it's a perfectly good question. $\endgroup$ – userLTK Apr 20 '17 at 21:08
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    $\begingroup$ This question could be highly simplified and reworded for clarity $\endgroup$ – farrenthorpe Apr 21 '17 at 2:47
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    $\begingroup$ After reading the many comments from the OP, it is clear that this thought experiment is not properly defined, since no one answering the question apparently knows what the OP wants. I am voting to close this question as 'unclear what you are asking.' $\endgroup$ – kingledion Apr 21 '17 at 23:54
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    $\begingroup$ Maybe try world-building. If the tropospheres are the same height, and the greenhouse gas planet is warmer then it would have a less massive atmosphere and the heat capacity cannot be the same. The question now contradicts the laws of physics. $\endgroup$ – userLTK Apr 22 '17 at 2:59
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The physical parameters you need to measure to confirm the existence of the greenhouse effect are few and simple. Measure the electromagnetic properties of constituent molecules in the atmosphere. Specifically, look at absorption cross sections as a function of wavelength for solar and terrestrial emission bands.

Some molecules will be transparent at solar and terrestrial bands and some will be transparent in some bands and opaque in others.

If you can find molecules that are transparent to shortwave but opaque in longwave the you have a molecule that lets energy into the atmosphere but prevents some portion of energy from escaping. This energy that is absorbed causes local heating. This local heating is the green house effect.

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    $\begingroup$ Spoiler alert: methane, water and carbon dioxide are good places to start looking. $\endgroup$ – casey Apr 21 '17 at 0:24
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    $\begingroup$ Nice to see you back on the site! $\endgroup$ – farrenthorpe Apr 21 '17 at 2:46
  • $\begingroup$ @casey. I think what you say is actually a circular argument. You started by effectively specifying that you know that certain molecular types are greenhouse gases and that if you look for them that proves it is a GHE atmosphere. You effectively start from the assumption (you would probably say knowledge) that the GHE is caused by certain types of gaseous molecules and suggest simple measurement of their "frequency response" gives the answer because that is what you think happens in a GHE atmosphere. Fair enough maybe BUT have a look at my questions below.... $\endgroup$ – user7733 Apr 21 '17 at 19:08
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    $\begingroup$ An individual CO2 molecule absorbs infrared radiation, which adds energy to the molecule. That molecule then releases the infrared energy in what is effectively a random direction. That process is what prevents the uniform radiation of IR energy away from, say, the surface of a planet. $\endgroup$ – jeffronicus Apr 21 '17 at 23:36
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    $\begingroup$ @user7733: Not a circular argument at all. You start with lab measurements of the properties of various gasses (done back in the 19th century), note their abundance in the atmosphere, and do some calculations. That's basically how Arrhenius came up with the first estimates. If you want to go all high-tech, though, there's this: phys.org/news/2015-02-carbon-dioxide-greenhouse-effect.html $\endgroup$ – jamesqf Apr 22 '17 at 5:36
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Reality is not as simple as your thought experiment

The problem with your thought experiment is that, even though you are holding sunlight intensity identical between your two planets, there are too many factors that actually affect the planet's temperature for any one measurement to give you conclusive proof of the greenhouse effect. There are two primary factors affecting the planet's temperature, given constant sunlight energy:

  • Greenhouse gasses: Water vapor, CO$_2$, and methane are all significant greenhouse gasses, as are others. Greenhouse gasses act by absorbing the IR radiation emitted from the surface of the Earth, thereby preventing it from being emitted into space. This 'traps' more heat in the system and warms up the planet.

  • Albedo: The amount of sunlight reflected from the planet affects the total energy received from the sun. Things that are light colored, like ice and clouds will reflect more light, while things that are darker colored like dense forest will absorb more.

So those two factors are easy enough. Where this gets complicated is from all the second order effects between those two factors. These are called feedback loops, and all the feedback loops feed back into each other. Examples:

  • As temperatures rise, more water vapor enters the atmosphere, which increases the greenhouse effect (marginally), and increases the temperature. However, the increase in water vapor causes more clouds to form, which increases albedo and decreases temperatures.

  • If rising temperatures/precipitation/CO$_2$ levels cause plant density to increase, then albedo (usually) decreases, and temperatures increase. However, plants also remove CO$_2$ from the atmosphere and deposit it in the soil, which decreases the greenhouse effect and lowers temperatures.

  • If rising temperatures cause more ice to melt, then ice cover goes down and albedo goes down causing temperatures to rise. However, areas above ice sheets generally have very little moisture in the air; if the ice sheets melt there may be more cloud formation, partially offsetting the loss of albedo.

That is only a couple feedback mechanisms I could think of off the top of my head. There are many, many others. It is these feedback mechanisms that make the science of climate change harder to predict.

Therefore, we cannot point to one single parameter that will cause use to identify the greenhouse effect, which is why it has taken so long to get to a scientific consensus about if an how the greenhouse effects work. Any one parameter could have dozens of feedback processes affecting how it affects global temperature, and its is only through decades of careful study that we have been able to demonstrate with high confidence the link between increasing CO$_2$ levels and increasing temperature.

To understand more fully, you have to read the IPCC report

Here is the IPCC's Fifth assessment.

This is the holy grail of current theory that is widely accepted in the scientific community regarding anthropogenic global warming. The IPCC reports are careful to make only claims supported by evidence which is why the contents of these reports are supported by 95%+ of the scientific community. This report neatly summarizes the important factors and measurable evidence (which is what you are after).

Once you read about the measurable evidence, you will have to go to the scientific literature to get the full picture of how the evidence was collected, and its justification in supporting the IPCC's report. To be honest, the whole picture is more than any one person can manage. No one will have equal knowledge of the temperature measurement methodology, fluid mechanics of the circulation models, science of cloud related feedback, etc. It is a collaboration of researchers in all these fields and more that allows the synthesis that is the IPCC report to exist.

Conclusion

Having contributed (a decade ago) to some of the oceanic circulation models, I feel connected to a small piece of the puzzle. I am a computer scientist, not an oceanographer, chemist, geologist, physicist or any of the other specialties needed to build the full picture. I have my own criticisms of how some of the computer models implement the Navier-Stokes equations (possibly since corrected), but I can satisfy myself that there are many models that generally agree and that the results in my little part of the puzzle are generally correct. I am sure that many specialists in other fields feel the same way.

If you want to get a similar confidence about why models showing future warming are correct, you should embark on some study of your own. Pick a field that interests you and is commensurate with your math skills and investigate.


Edit for further explanation:

The greenhouse effect itself varies with more than just Carbon Dioxide level. Lets use the cases of Venus, Earth, and Mars to compare.

Venus: Surface temperature is about 735 K. By Wien's law, the maximum wavelength for IR radiation from the surface (into space) is 2.897 mm / 735 K = ~4000 $\mu\text{m}$ or 2500 cm$^{-1}$ as it is more commonly stated. Take a look at this chart of Carbon Dioxide's absorption spectrum:

enter image description here

Venus has a surface emission peak that lines up almost perfectly with one of carbon dioxide's high absorption region, and a very dense carbon dioxide atmosphere. Thus Venus as come into a temperature equilibrium with a very high temperature because of a very powerful greenhouse effect that depends specifically on the surface temperature of the planet. If Venus were 100 K cooler, its greenhouse effect would be much less...and it would continue to get cooler until it reached some new equilibrium.

Earth: On Earth the greenhouse effect is driven primarily by water vapor, not carbon dioxide. Here are the absorption spectra of the two:

enter image description here

Water vapor is blueish, carbon dioxide is reddish. Note you can see the 4000 $\mu\text{m}$ carbon dioxide absorption peak here as well. You see that water vapor absorbs more of the spectrum that carbon dioxide, but Earth's peak emissions are in the 10000 $\mu\text{m}$ range, which you will note is a big gap in both water and carbon dioxide's spectrum; the result is the Earth is relatively cooler. However, the 'water vapor window' noted in the picture shows that carbon dioxide does partially fill this window. As carbon dioxide levels increase from very low to less low, the equilibrium temperature of the Earth will rise. This in turn will bring wavelength down, and move Earth's emission spectrum away from the carbon dioxide absorption, but towards a peak of water absorption. Thus, Earth's greenhouse effect depends heavily on both carbon dioxide and water vapor concentrations in the air. (Again, this doesn't even cover albedo and other things that are critically important)

Mars: Mars has a carbon dioxide partial pressure of around 575 Pa, while Earth is about 40 Pa (at the current ~400 ppm). So Mars' should have a much more significant greenhouse effect than Earth, if CO$_2$ level were the only variable. There is a way to determine the projected surface temperature of a bare rock planet based on the Stefan-Boltzman law. Plugging into that equation, Venus' projected temperature is 228 K (low due to high albedo); Earth's is 251 K; Mars' is 212 K. Actual temperatures are Venus 735 K, Earth 287 K, Mars 210 K. While the greenhouse effect is not the only reason for these discrepancies, we can see that Venus has a very high greenhouse effect, Earth has a moderate effect and Mars has none.

Conclusion

Here are the important point from this rundown:

  • Mars has higher carbon dioxide levels than Earth but less of a greenhouse effect.

  • Earth has a wider band of greenhouse gas absorption than Venus, but Venus's greenhouse effect is much stronger due to planetary emission spectra lining up with the absorption spectra.

  • Given the Mars and Venus examples, you can see that for a planet with a primarily CO$_2$ atmosphere, variations in planetary temperature would affect the greenhouse effect more than variations in CO$_2$ concentration.

I hope you can see from these examples why the interaction between carbon dioxide and the greenhouse effect is too complicated to be modeled in a simple thought experiment.

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    $\begingroup$ @user7733 If two planets have the same solar irradiance but one has GHE and the other does no, their albedo won't stay the same long. $\endgroup$ – gerrit Apr 20 '17 at 20:04
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    $\begingroup$ @user7733 I guess you missed the point. Sorry. You can read the answer again when you want to actually why the thought experiment you proposed is nonsense. There is no greenhouse effect without the other myriad factors involved. $\endgroup$ – kingledion Apr 21 '17 at 0:19
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    $\begingroup$ @user7733 I attempted to address your comments with some additional information in an edit. The TLDR answer is: yes, in the case of Mars there is CO$_2$ with a minimal greenhouse effect. $\endgroup$ – kingledion Apr 21 '17 at 19:51
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    $\begingroup$ @user7733 One more note I just thought of that I didn't make clear before. Your thought experiment would have different results for different planets. For two Venus' or Mars', addition of CO$_2$ to one of them would have little to no effect on temperature. For two Earth's, addition of CO$_2$ would increase the temperature. Therefore, I conclude that your thought experiment is of limited utility. That's what I've been trying to say. $\endgroup$ – kingledion Apr 21 '17 at 20:04
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    $\begingroup$ Very nice answer. I love all the detail. $\endgroup$ – userLTK Apr 21 '17 at 20:30
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First things first, I think the spirit of your question, when talking about identical planets with identical solar input but with different atmospheres, you want to ignore albedo. Albedo's a key component semi-black body or, planetary equilibrium temperature calculation. Reflected light doesn't warm the object under the sun, only absorbed light.

In other words, if you have very similar planets, same gravity, same atmosphere, same distance from the same sun, but one is black and one is white, the black one would be warmer. I mention this because snow cover lowers the albedo of a planet and the snow cover is a primary feedback mechanism in the rise and fall of ice ages. Your question appears to focus primarily on the atmospheric effect, and I'm assuming you want to ignore snow-cover, which no climate model would do.

The height of the atmospheres is the same

This is a bad assumption. Gas expands when it's warmer. If you have the warmer planet "G" and the colder planet "N", you can't assume the height of the atmosphere's are the same. The troposphere, while a very thin layer of the atmosphere by size, it holds most of the mass of the atmosphere (80% on Earth). The Troposphere's height is pretty close to directly proportional to temperature. See here.

As to the height of the stratosphere and mesosphere of the 2 theoretical planets, That's a more tricky calculation.

so the temperature gradient in the atmosphere will be higher on G. Its lapse rate is higher

The lapse rate applies to the troposphere. The stratosphere has a different set of rules as it's more affected by the sun's rays than the Earth's stored and radiated heat. The troposphere grows as the planet warms. It's higher over the equator than over the poles. The theoretical planet "G" has the same lapse rate as the planet "N" and a larger troposphere.

What physical parameter can we measure if given ONE planet, without any knowledge of what the conditions are on the other, in order to determine whether we have been given planet G or N?

In other words, you're asking, without measuring the components of a planet's atmosphere, how much can we tell about the surface temperature of two similar planets, G and N by studying the radiation that comes off the planet. That's a solid question.

A problem with this question is that the components of a planet's atmosphere correspond to specific bands missing from the thermal radiation leaving the planet. This is an atmosphere's spectroscopic signature. The greenhouse gases create dark bands in the IR-spectrum of light leaving the planets, so the IR light would have distinctly different signatures. The net heat leaving planet G and planet N has to be equal but Planet G traps certain wavelengths that planet N does not, so it needs to be warmer to emit the same amount of total energy into space because it has more dark bands across it's IR spectrum leaving the planet.

More detailed explanation here.

That's a very rough answer anyway. spectroscopy and heat irradiated from a planet gets complicated. Actual models of a planet's heat trapping are much more complicated than dark bands missing from the IR spectrum leaving the planet. If anyone can provide a more detailed explanation please feel free.

@Gerrit is also right. It's a bit wonkers to run this calculation without albedo, as that's a huge factor. But the simple answer is basically the correct one. Greenhouse gas is a blanket. More heat gets trapped, and IR has a harder time leaving the surface of the "G" planet, so the planet needs to be warmer on the surface to achieve the same solar radiation into space.

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    $\begingroup$ Downvoted because planet N would have a negligible lapse rate. The presence of greenhouse gases is what enables a significant lapse rate in the troposphere to exist. The Earth's atmosphere is far from thermodynamic equilibrium, which would be an isothermal atmosphere (i.e., zero lapse rate). $\endgroup$ – David Hammen Apr 21 '17 at 16:30
  • $\begingroup$ @LTK This is a thought experiment so I am entitled to specify the constraints. It is perfectly possible even in the real world that I could find (eventually) two planets of the same size WITH THE SAME ALBEDO. You are falling into the error of thinking about the knowledge you have about how things change ON THE EARTH when the GHE increases. The specified condition are that the albedo is the same AND the height of the atmospheres. $\endgroup$ – user7733 Apr 21 '17 at 18:42
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    $\begingroup$ @DavidHammen Well, if it has no troposphere, then the lapse rate is moot. But I think you[re incorrect to say zero lapse rate. From my understanding, the lapse rate is not greenhouse gas dependent. But I will agree with you a theoretical atmosphere with zero greenhouse gas poses some unusual problems that would not be encountered in real planets. $\endgroup$ – userLTK Apr 21 '17 at 18:43
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    $\begingroup$ @user7733 I'd assumed you meant same mass. Same heat capacity implies similar mass and if we're talking two similar Oxygen-Nitrogen atmospheres for example, one with a trace of CO2 the other with none, same heat capacity means very close to the same mass. Same height is a weird parameter that needs better definition. Do you mean top of the stratosphere? mesosphere? You can't mean troposphere, that doesn't work. Most of the height of an atmosphere is the upper layers, most of the heat trapping is the lower layer. I don't see what this parameter changes. $\endgroup$ – userLTK Apr 21 '17 at 19:12
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    $\begingroup$ @user7733 but your hurting your own thought experiment by asking "what is the effect of a greenhouse gas", but "I prefer not to assume similar gaseous componants". The thought experiment approach demands you set the variables precisely and if you want to know the outcome of one thing, you change only that one thing. Your request that the components be completely variable except for greenhouse gas is unreasonable. One could by O2/N2, the other Argon or Xenon. You need to set well defined parameters or your question doesn't mean anything. $\endgroup$ – userLTK Apr 22 '17 at 2:54

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