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CO2 lags temperature - what does it mean?

What the science says...

Select a level... Basic Intermediate Advanced

CO2 didn't initiate warming from past ice ages but it did amplify the warming.  In fact, about 90% of the global warming followed the CO2 increase.

Climate Myth...

CO2 lags temperature

"An article in Science magazine illustrated that a rise in carbon dioxide did not precede a rise in temperatures, but actually lagged behind temperature rises by 200 to 1000 years.  A rise in carbon dioxide levels could not have caused a rise in temperature if it followed the temperature." (Joe Barton, US House of Representatives (Texas) 1985-2019) - Full Statement

At a glance

Antarctic ice-core data today provide a continuous record on temperature and atmospheric composition that goes back for some 800,000 years. The data track the last few glacial periods and their abrupt endings, with rapid transitions into mild interglacials. But in some of the ice-cores, temperature rises first and is followed, a few hundred years later, by rising carbon dioxide (CO2) levels.

Certain purveyors of climate-myths seized on this observation, claiming it to be “proof” that carbon dioxide doesn't cause climate change. Wrong, wrong, wrong. But how? The answer lies in a beer-can.

In fact, you can do this one yourself. You need two cans of any fizzy beer. On a nice summer's day, take one out of the fridge and place it outside in direct sunshine for a few hours. Leave the other where it is. Then open the two at the same time. The warm one will froth like mad, half-emptying the can and making a mess. What is left in the can will be horrible and flat. Conversely, the one straight from the fridge will just give a “pfft” noise and will be pleasant to drink, being cool and fizzy.

What's that got to do with this myth? Well, you have just demonstrated an important point about the solubility of CO2 in water. CO2 gives fizzy drinks their fizz and it is far more soluble in colder water. As the water warms, it cannot hold onto as much CO2 and it starts to degas. Hence that flat lager.

Exactly the same principle applies to the oceans. When global warming is initiated, both land and the oceans start to warm up. On land, permafrost starts to thaw out, over vast areas. Carbon dioxide (and methane) are released, having been trapped in that permafrost deep-freeze for thousands of years. At sea, that “warm beer effect” kicks in. Thanks to both processes, atmospheric CO2 levels rise in earnest, amplifying and maintaining the warmth. That rise in CO2 thereby caused more of the gas to be released, warming things up yet more in a vicious cycle, known as a positive feedback. Other feedbacks kick in too: for example as the ice-sheets shrink, their ability to reflect Solar energy back out to space likewise decreases, so that heat is instead absorbed by Earth’s surface.

The trigger for the initial warming at the end of an ice-age is a favourable combination of cyclic patterns in Earth's orbit around the Sun, leading to a significant increase in the solar energy received by Earth's Northern Hemisphere. That's no secret. Glacial-interglacial transitions are caused by several factors working in combination – triggers and feedbacks. We've understood that for a long time.

And when you think about it, saying CO2 lagged temperature during glacial-interglacial transitions so cannot possibly be causing modern warming is a bit like saying, “chickens do not lay eggs, because they have been observed to hatch from them".

Please use this form to provide feedback about this new "At a glance" section. Read a more technical version below or dig deeper via the tabs above!


Further details

That CO2 can lag behind but amplify temperature during a glacial-interglacial transition was in fact predicted as long ago as 1990. In the paper The Ice-Core Record: Climate Sensitivity and Future Greenhouse Warming by Claude Lorius and colleagues published in the journal Nature in 1990, a key passage reads:

"The discovery of significant changes in climate forcing linked with the composition of the atmosphere has led to the idea that changes in the CO2 and CH4 content have played a significant part in the glacial-interglacial climate changes by amplifying, together with the growth and decay of the Northern Hemisphere ice sheets, the relatively weak orbital forcing and by constituting a link between the Northern and Southern Hemisphere climates."

This was published over a decade before ice core records were accurate enough to confirm a CO2 lag. We now know that CO2 did not initiate the warming from past ice ages but it did amplify the warming. In fact, about 90% of the global warming followed the CO2 increase.

Antarctic ice cores reveal an interesting story, now going back for around 800,000 years. During this period, changes in CO2 levels tend to follow changes in temperatures by about 600 to 1000 years, as illustrated in Figure 1 below. This has led some to disingenuously claim that CO2 simply cannot be responsible for the current global warming. Unsurprisingly, such a claim does not tell the whole story.

Figure 1: Vostok ice core records for carbon dioxide concentration and temperature change.

The initial change in temperature as an ice-age comes to an end is triggered by cyclic changes in Earth’s orbit around the sun, affecting the amount of seasonal sunlight reaching Earth’s surface in the Northern Hemisphere. The cycles are lengthy: all of them take tens of thousands of years to complete.As both land and oceans start to warm up, they both release large amounts of CO2 into the atmosphere, from melting permafrost and from warming ocean water, since CO2 solubility in water is greater in cold conditions. That release enhances the greenhouse effect, amplifying the warming trend and leading to yet more CO2 being degassed. In other words, increasing CO2 levels become both the cause and effect of further warming. Once started, it’s a vicious, self-reinforcing cycle - an excellent example of what science refers to as a positive climate feedback.

Indeed, such positive feedbacks are necessary to complete the shifts from glacial to interglacial conditions, since the effect of orbital changes alone are too weak to fully drive such variations. Additional positive feedbacks which play an important role in this process include other greenhouse gases like methane - you may have seen videos of that gas bubbling up through icy lakes in permafrost country and being ignited. Changes in ice sheet cover and vegetation patterns determine the amount of Solar energy getting absorbed by Earth’s surface or being reflected back out to space: decrease an ice-sheet’s area and warming will thereby increase.

The detailed mechanisms for the above general pattern have of course been investigated. In a 2012 study, published in the journal Nature (Shakun et al. 2012), Jeremy Shakun and colleagues looked at global temperature changes at the commencement of the last glacial-interglacial transition. This work added a lot of vital detail to our understanding of the CO2-temperature change relationship. They found that:

1) The Earth's orbital cycles triggered warming in the Arctic approximately 19,000 years ago, causing large amounts of ice to melt, flooding the oceans with fresh water.

2) This influx of fresh water then disrupted ocean current circulation, in turn causing a seesawing of heat between the hemispheres.

3) The Southern Hemisphere and its oceans warmed first, starting about 18,000 years ago. As the Southern Ocean warms, the solubility of CO2 in water falls. This causes the oceans to give up more CO2, releasing it into the atmosphere.

4) Finally, CO2 levels may lag temperature in some ice-core records from Antarctica, but in some other parts of the world the reverse was the case: temperature and CO2 either rose in pace or temperature lagged CO2. Figure 2 demonstrates this graphically and shows how things are never as simplistic as purveyors of misinformation would wish.

Shakun Fig 2a 

Figure 2: Average global temperature (blue), Antarctic temperature (red), and atmospheric CO2 concentration (yellow dots). Source.

Last updated on 14 February 2023 by John Mason. View Archives

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Further reading

That CO2 lags and amplifies temperature was actually predicted in 1990 in a paper The ice-core record: climate sensitivity and future greenhouse warming by Claude Lorius (co-authored by James Hansen):

"Changes in the CO2 and CH4 content have played a significant part in the glacial-interglacial climate changes by amplifying, together with the growth and decay of the Northern Hemisphere ice sheets, the relatively weak orbital forcing"

The paper also notes that orbital changes are one initial cause for ice ages. This was published over a decade before ice core records were accurate enough to confirm a CO2 lag (thanks to John Mashey for the tip).

Also, gotta love this quote from Deltoid in answer to the CO2 lag argument: See also my forthcoming paper: "Chickens do not lay eggs, because they have been observed to hatch from them".

Further viewing

Denial101x video

Myth Deconstruction

Related resource: Myth Deconstruction as animated GIF

MD Lag

Please check the related blog post for background information about this graphics resource.

Fact brief

Click the thumbnail for the concise fact brief version created in collaboration with Gigafact:

fact brief

Comments

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Comments 301 to 325 out of 679:

  1. Scaddenp (303) … “Carbon-cycle feedbacks are slow. Most AR4 models ignored them as irrelevant for next 100 years. If this is incorrect, then warming would be worse.” I thought Sharkhova et al (2010) had rather clearly shown this to be incorrect. Warming will be worse as will Arctic amplification and its effects on the GIS.
  2. Agnostic, I gather you contesting whether carbon feedbacks are slow, not they will make warming worse. While I dont doubt Shakhova et al, results, what we dont have is an idea as what is "normal". This was discussed at Realclimate last year.
  3. A nice change to find a level-headed scientific discussion for a change - thank you for the time and effort involved. As a non-chemist/physicist I seek comment on a related matter. Papers, blogs and posts elsewhere (eg www.gemarsh.com/wp-content/uploads/Interglacials-and-CO2.pdf and various Wiki entries)throw Be10 variations found in ice cores and various sediment cores into the CO2/temp lag discussion. I believe cosmic ray flux a bit far fetched as an explanation for global temperature variation, but am not qualified to form an opinion.
    Response: The cosmic rays argument is covered here. In short current evidence does not support the hypothesis.
  4. 1. The Greenhouse theory is not straightforward. Absorption figures for CO2 at STP show that ALL the surface energy emitted in the CO2 band is absorbed within the first 500m of atmosphere, and the majority below 50m (0.5% of the atmosphere). Doubling CO2 has a negligible direct effect: ALL the energy is still absorbed into the atmosphere, just at half the altitude. 2. At the top of the atmosphere, using the same figures, but adjusting line shapes and amplitudes for temperature and pressure, it is clear that the greater portion of the 15-18W/m^2 emitted to space by CO2 is being emitted by the ~10% of the atmosphere lying ABOVE the Tropopause. Rough figures are: from 11-12.5km, 5%; 12.5-15km, 10%; 15-17.5km, 12%, 17.5-20km, 13%;20-25km, 20%; above 25km, 40%. If you increase CO2 concentrations, emissions are from higher levels, and an even higher proportion will be above the tropopause. IE more CO2 has a strong cooling effect. 3. Notwithstanding the above, the claimed feedback effect of CO2 on the ice-core temperatures is very shaky. I looked at the figure and note the long lag in the FALL in CO2 concentration. Why does the CO2 not hold up the temperature fall? Where is the mathematical model and its comparison with the data? At present the data does not seem to support the hypothesis. 4. The data unequivocally shows a lag between temperature and CO2 concentration. It is being claimed that CO2 makes temperatures hotter than they otherwise would be. There does not seem to be support for this in the data presented in the headline post.
  5. novandilcosid wrote: "It is being claimed that CO2 makes temperatures hotter than they otherwise would be. There does not seem to be support for this in the data presented in the headline post." That CO2 causes higher surface temperatures (aka 'the greenhouse effect') was first proven by John Tyndall more than 150 years ago. Articles explaining how this works and correcting other fundamental errors in your analysis above can be found on this site at; Has the greenhouse effect been falsified? and The greenhouse effect and the 2nd law of thermodynamics
  6. CBDunkerson wrote: "That CO2 causes higher surface temperatures (aka 'the greenhouse effect') was first proven by John Tyndall more than 150 years ago. Articles explaining how this works and correcting other fundamental errors in your analysis above can be found on this site at; Has the greenhouse effect been falsified? and The greenhouse effect and the 2nd law of thermodynamics" I thank CBD for his response to my post. I would be grateful if he would identify all the "fundamental errors" in my post rather than referring me to vague and unspecific articles. My main ponts are: 1. The undisputed absorption figures for CO2 mean that an increase in concentration cannot directly greatly (I mean by more than 0.5W/m^2) increase the absorption of surface energy by the atmosphere. 2. The increased absorption of sunlight by the upper atmosphere means a drop in insolation at the Surface of about 1W/m^2. The increased back radiation due to the decreased average altitude of the CO2 surface-bound emissions is about 0.5W/m^2, so the NET direct effect of doubled CO2 on the Surface is a cooling forcing of 0.5W/m^2. 3. At the other boundary, it is clear from the outgoing spectra that CO2 is responsible for between 15 and 18W/m^2 of the emissions to space. It is also very clear that the emissions at the stronger wavenumber 670 are stronger than the rest of the CO2 band. Because emissions to space have to get through the overlying gas, it is also clear that the more strongly absorbed wavenumber 670 emissions are coming from higher in the atmosphere than say the wavenumber 650 emissions. So in this case, Higher = hotter, ie the wavenumber 670 emissions are definitely coming from the stratosphere. 4. All very well, but what about the rest of the CO2 band? At STP 50% of wavenumber 650 emissions are absorbed in the first 25m of atmosphere. At say 17km the same number of CO2 molecules occupy about 250m. The pressure decrease over these 250m means only a small narrowing of the emission/absorption lines, so absorption rate will not be greatly affected: at 17km just under half the wavenumber 650 photons are absorbed within 250m. 5. I calculate that the published absorption data for CO2 means that the great majority of emissions from CO2 must be coming from above the Tropopause.
    Response: Your comments regarding the physics of the greenhouse effect are off-topic for this thread and are covered elsewhere. Per this site's Comment Policy, please review the appropriate posts and place your comments there. In addition to the links provided by CBD you may find the CO2 effect is saturated thread relevant. Future off-topic comments will be removed.
  7. I thank the moderator, and apologise. The headline post makes the assertion that CO2 amplifies temperature. It is my view that the ice core data shown does not support that assertion. If temperature was being amplified proportionately to CO2 concentration then we would expect to see some influence of this on falling temperatures. I don't see this effect at all in the data.
  8. novandilcosid - This thread discusses the fact that CO2 has lagged temperature changes in the past, often used as a 'skeptic' argument that changing CO2 concentration now won't be a problem. The Milankovitch cycles driving the repeated glaciation of the Earth only supply a very small forcing (both up and down), not enough to change temperatures very much by themselves. They do induce CO2 feedbacks (vegetation changes, but primarily changes in solubility of CO2 in the oceans, which is inversely related to temperature); these act as positive feedback, amplifying the Milankovitch changes. The ocean CO2 feedback takes 500-1000 years due to deep circulation - hence the lag seen in the ice cores. Both also affect water vapor (more powerful a greenhouse gas than CO2), which takes a matter of weeks or so to respond. Further amplification occurs (in both directions) with changes in ice coverage and albedo. Once a swing in base forcing occurs, that change is greatly amplified. The total effect with feedback amplification (each feedback having it's own time frame) is to produce the temperature swings seen in the glacial cycle. --- Now we're inducing a very large and very fast temperature forcing by artificially increasing CO2 levels to amounts not seen since the Pliocene, when global temps were 2-3°C higher than today, global sea level 25 meters higher than now. This forcing is larger than the Milankovitch cycle changes. And that can't be good.
  9. novandilcosid #312, I have responded to your post, and having done so noted your matching post on the CO2 is saturated thread.
  10. "If temperature was being amplified proportionately to CO2 concentration then we would expect to see some influence of this on falling temperatures. " Do I understand you correctly in that you are expecting co2 to drop as soon as the solar forcing drops the temperature, but that you don't see that? Carbon feedbacks with temperature are mostly very slow. The change in solar is the driver. Once temperatures drop it takes time for the changes in the carbon cycle to remove carbon. Putting carbon back into the atmosphere when temperatures rise can happen faster (eg methane release from thawing permafrost).
  11. Scaddenp @ 316 : "Do I understand you correctly in that you are expecting co2 to drop as soon as the solar forcing drops the temperature, but that you don't see that?" No I expect to see elevated CO2 affecting the rate of Tdrop, and also drooping CO2 to affect the low temperature base. I see neither of these effects in the graphs and they should be there. Basically once temperature has fallen it generally remains flat, even though CO2 concentration is falling. If CO2 drives temperature we sgould see a corresponding droop on the low temp but we don't.
  12. KR @ 314 "The Milankovitch cycles driving the repeated glaciation of the Earth only supply a very small forcing (both up and down), not enough to change temperatures very much by themselves." That's the problem with Milankovitch - not enough oomph. All should note that Milankovitch is not the only shot in the locker. I think those who are not aware of the cosmic theory of Ice Ages should take a dekko at Fred Hoyles "Ice". This seems to me to be a more coherent and less ambiguously weak possible cause of Ice Ages. Hoyle correctly points out that these typically happen very fast - on the order of 20 years. A second alternative is the Svensmark hypothesis, again a cosmic origin.
  13. " If CO2 drives temperature we sgould see a corresponding droop on the low temp but we don't." Sorry, but solar IS what is drives temperature here. CO2 and albedo just amplify. Together these have no problem driving the ice age cycle using standard physics. An alternative theory has to explain a vast amount of observations including isotope signatures for methane and CO2 in ice core, spatial distribution of cooling etc etc which current climate theory does quite well. I frankly find it unbelievable that anyone can look at even the original, pre-ice core data and seriously doubt that Milankovich cycles are not involved. I suspect a few seconds on google will find you the problems with Hoyle's theory. The lack of oomph is only a problem if you are determined that GHG changes cannot affect the temperature of the planet. Does your alternative model no-GHG effect correctly predict the surface temperature of venus, earth and mars?
  14. novandil#318: "Fred Hoyles "Ice" ... the Svensmark hypothesis, again a cosmic origin." Not much value in either Hoyle (debunked here) or Svensmark. See Its cosmic rays
  15. Responding to Henry Justice from another thread (and recycling comment from "models are unreliable") We know that isnt true. The isotope ratios for fossil fuel produced CO2 is different from that produced by carbon cycle feedbacks. If you look at the isotopes in CO2 from ice core bubbles, the increased CO2 during warming is from carbon cycle. If you look at isotope ratio in current atmosphere, you see increase is due to fossil fuel. At the moment, the carbon sinks are cleaning up about half our emissions. Over longer time, this will reverse.
  16. One clearly can see in the backside of the direct corrolation between CO2 and temperature, that the CO2 is too high to match. If one seperates the GHGs and notes three basic facts about methane-ice then it can explain alot about why the simple CO2 corrolation is off. One fact is that methane is about 50 times stronger as a GHG than CO2. The second is that it turns into CO2, over time, as it is oxidized. The last fact is that it takes a long time for methane-ice to build up (persisting when the environment is colder). A guess is that it may take 20 to 50 thousand years of cool times for it to become a signicant factor again, once it is released. Noting these points one can then shift the alignent for CO2 down and add the methane-ice release effect on top of it in the initial phases of warming after cooler periods. As for the simple effect of methane released by life forms, it may be a small factor; yet I suspect it pales in comparison to the huge amounts released by the thousands of years of bacteria production in the whole of the earth soils being released over a short period of time.
  17. Where in the chart can you show me "amplification of original warming by CO2"? There is none. [accusation of dishonesty deleted]
    Response: [Dikran Marsupial] Please read the comments policy (link provided below) and adhere to it in future. In general posts that contravene the comments policy are deleted rather than edited, I have been lenient on this occasion.

    Welcome to Skeptical Science! There is an immense amount of reference material discussed here and it can be a bit difficult at first to find an answer to your questions. That's why we recommend that Newcomers, Start Here and then learn The Big Picture.

    I also recommend watching this video on why CO2 is the biggest climate control knob in Earth's history.

    Further general questions can usually be be answered by first using the Search function in the upper left of every Skeptical Science page to see if there is already a post on it (odds are, there is). If you still have questions, use the Search function located in the upper left of every page here at Skeptical Science and post your question on the most pertinent thread.

    Remember to frame your questions in compliance with the Comments Policy and lastly, to use the Preview function below the comment box to ensure that any html tags you're using work properly.

  18. jpat - I do not believe so because the carbon-cycle feedbacks are from multiple sources, act over different time scales, (including a negative feedback - enchanced vegatation growth), as well as coupling with an albedo feedback. It is not obvious to me that the feedbacks should even be symmetrical. (Some like methane release versus methane storage are clearly not).It appears to me that you are thinking about this by analogy to a forced oscillator whereas a much more complex physical model is involved. More light on this should emerge from Ar5 models. However, the corollary of your question seems to imply that you think either: 1/ GHG do not cause warming - or 2/ the CO2 increase in atmosphere is causing warming rather than other way round. Both of these can be discounted from other evidence.
  19. 323, meghaljani, I'd like to answer your question, but I can't puzzle out what you mean by it. Can you re-phrase it in a clearer, more meaningful way?
  20. Again, show me where in the chart do you see CO2 affecting temperature? Show me. You have just long lectures and "climate models". When it comes to past data, you have nothing. For sphaerica, I asked to show me the area where CO2 is causing the temperature rise on the chart given in the discussion.
  21. @meghaljani "Show me. You have just long lectures and "climate models"." What is the point of showing you if you refuse to engage all reasonable attempts to show you? But this question reminded me that I often think people do not understand why the ice core CO2 temp relationship is such a compelling proof of the effect of CO2 on climate because they don't understand know the scientific story behind those ice core records. Sometimes, constructing a historical narrative, like Specncer Weart does, clarifies what can seem counterintuitive in hindsight. In the 70s we knew that glacial periods existed in the past, and we guessed that Milankovitch forcing provided the initial cue - the corrletaion was simply to amazing to be chance. But we could not explain the large deviations in global temp during glaciation cycles as a function of Milankovitch cycle forcing. Albedo effects helped related to northern hemisphere ice and snow cover helped, but were similarly too small to account for the change - even taking account of temp-water vapor feedbacks. - without using unreasonable assumptions about the physics. (Yes, we knew this based on models -although they were relatively simple at the time). It was a quandry for a decade or so. One solution posed to this quandry was that changes in temperature could alter the global carbon cycle, thereby causing changes in CO2. That change in CO2 could then result in enough forcing to cause the glacial cycles given a small initial input. The ice core data were collected partly to test this theory, and they indeed showed that CO2 increased with temp sufficiently to cause the forcing required. So the ice core records were a test of the idea that CO2 affects climate. But it was never part of anyones thinking that CO2 would lead the temperature change, quite the opposite in fact. Asking to see such a pattern just doesn't even make sense. It's also impossible to understand why it is so compelling unless you embrace the physics behind the greenhouse effects and global climate models - and the feedbacks being discussed now by KR and jpat. To understand that, you actually do need to roll up your sleeves and read lectures/textbooks and do calculations yourself. Luckily we do pay people to do what you seem too impatient to do. Good for you!
  22. 326, meghalnai,
    ...show me the area where CO2 is causing the temperature rise on the chart given in the discussion.
    If you are not willing to look in detail at the subject, no one in the world can make it easy for you.
    You have just long lectures and "climate models".
    Um, no, actually we have a detailed understanding of the intricacies of the system. That you want this watered down to a single graph that a child could interpret is your problem, not ours. I will give you a hint, however. CO2 rises with temperature increases, and temperature rises with CO2 increases. They are interlocked. So an initial orbital forcing sparks a small temperature rise, which in turn sparks a CO2 rise, which raises temperatures further, which raises CO2 levels further. This cycle results in an ongoing upswing in temperature, up to a point where CO2 levels reach about 280 ppm. At that point things stall because the relationship between CO2 and temperature is logarithmic. Unfortunately, mankind has found a way to pump well beyond 280 ppm of CO2 into the atmosphere for the first time in millions of years. But the main point is that a small temperature increase starts a feedback cycle involving CO2 that results in a large temperature increase. Without accompanying increases in CO2 you would not see the temperature rise much beyond -8 ˚C.
  23. Meghaljani--a simple question so I know a little bit more about the physical model you work from: does atmospheric CO2 absorb and emit radiation at particular, pressure-broadened frequencies? Yes? Then your actual question should be "how do we know the CO2 concentration before direct instrumental measurement of the atmosphere?" because you accept that an atmosphere with CO2 is warmer than an atmosphere without CO2, all other things being equal. No? You need to either provide evidence that contradicts decades of high-quality research and the engineering that has relied (and still relies) on that research, or you need to do a bit more studying on the physics of CO2, CH4, H20, etc. For a simple demonstration, see this video (just about a minute in). You seem to be saying that correlation is not causation, but there's a big "unless" involved here, and that is the physical connection. If there's a physical connection between CO2 and temperature, then it's reasonable to assume that the connection didn't just spring into existence of its own will. It's been around as long as CO2 has been around.
  24. to Sphaerica and to DSL: All you got is to tell me that I am childish, may be that's the best you can do when there is no physical evidence in earth's history to support your theory. If your theory is correct, where in the history of the earth did you find co2 causing temperature rise? They are not interlocked based on the 600 million years history of earth's climate which can be measured by rock analysis. Show me any time in last 600 million years where co2 caused temperature rise. If you cannot show that, you can take your "climate models" and "deep research" and run around like chicken little and ask for carbon taxes.
    Response:

    [DB] "If you cannot show that, you can take your "climate models" and "deep research" and run around like chicken little and ask for carbon taxes."

    Now you are acting childish.  And churlish.  If you don't understand the explanation than ask for a simplified version.

  25. Uhh . . . where did I treat you like a child, Meghaljani? Show me the evidence. I asked you a simple question--simple as in basic/fundamental, not as in "simple-minded". You have yet to answer it. I'll ask it again: "does atmospheric CO2 absorb and emit radiation at particular, pressure-broadened frequencies?"

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