# Can anyone explain the reason why CO$_2$ increases global temperatures (not the simplistic greenhouse analogy provided for public consumption)?

The greenhouse effect analogy of global warming is that atmospheric carbon dioxide CO$$_2$$ absorbs some of the infrared radiation emitted by the Earth, and redirects a portion of that radiation back down to the Earth's surface, thereby heating the surface more than it would have done if that radiation had been able to escape into space.

Global warming is then simplistically explained to the general public by the idea that as atmospheric CO$$_2$$ concentrations rise, more infrared radiation is absorbed by CO$$_2$$ and re-emitted back down to Earth, causing increased heating of the Earth.

However, this explanation is not technically correct, because at present atmospheric CO$$_2$$ concentrations, just one kilometer of atmosphere is sufficient to fully absorb all the infrared radiation emitted by the Earth, at the wavelengths at which CO$$_2$$ absorbs.

Carbon dioxide absorbs infrared at the wavelengths of 2.7, 4.3 and 15 µm, and the CO$$_2$$ in the first kilometer of atmosphere alone is able to completely absorb all infrared at these wavelengths.

So the infrared absorption process is already fully saturated, and thus further increases in atmospheric CO$$_2$$ will not lead to any additional absorption. This is why the simplistic explanation provided for the general public does not seem to be technically correct, even though it roughly outlines the idea.

I found one blog article by Clive Best that tries to explain the actual process behind CO$$_2$$'s ability to cause global warming. Judging from that article, the actual process is more complex than the simple explanation provided for public consumption. However, I don't fully understand the explanation given in the article (and from what I did manage to understand, I am not sure if it is fully correct).

So I wonder if anyone here can provide an easy to understand explanation of the actual mechanism by which increased atmospheric CO$$_2$$ leads to global warming. Or perhaps if you know any good articles that explain it, please can you post the links.

I tried to find some info on the actual mechanism of global warming via Google, by using search terms such as "mechanism of greenhouse effect in global warming", but was surprised to find very little information available.

I also asked this question on physics.stackexchange.com here.

• The explanation, while it may be simplified, is not "simplistic". (You might consider entertaining the idea that you've made a mistake in your math.) For a basic explanation, start here: history.aip.org/climate/index.htm If you want to go deeper, consider a text on climate physics such as Ray Pierrehumbert's "Principles of Planetary Climate". Jan 16, 2020 at 19:21
• @jamesqf, the explanation provided to the general public is simplistic: it's a reduced complexity explanation. Whereas there is nothing wrong with giving a simplified explanation: that's always desirable. Jan 16, 2020 at 20:11
• @ebv, surely you must realize that when complex physics is involved, that excludes most of the population from properly understanding it. I have degree in physics, so I am hoping to be able to understand the mechanism of global warming. But don't expect your average person in the street to understand. Jan 17, 2020 at 13:20
• There is an excellent blog article by Spencer Weart realclimate.org/index.php/archives/2007/06/… that explains why the saturation at the surface argument is incorrect. It is energy balance at the top of the atmosphere that determines whether the planet warms or cools, the absorption at the surface is largely irrelevant. Jan 17, 2020 at 15:04
• BTW I would be wary of Clive Bests blog. He is a very bright chap, but tends to be resistant to correction/criticism. Being clever is not a substitute for experience and research, you'll just make the same mistakes that climatologists made 30 years ago all over again. They were clever people as well! ;o) Jan 17, 2020 at 15:15

Borrowing an explanation from one of my other answers, the basic mechanism of the greenhouse effect is roughly as follows (note this is also a simplified model)

Thus it is irrelevant that most IR emitted by the surface is absorbed by the atmosphere, it is the height from which IR is not absorbed that matters. If it is colder than the surface, it will emit less IR than the surface is emitting and hence less energy is radiated into space.

For a more detailed explanation of why absorption at the surface is of little relevance, see this RealClimate article by Spencer Weart.

Just to add a historical note, this explanation goes back at least as far as Ekholm's paper of 1901 "On The Variations Of The Climate Of The Geological And Historical Past And Their Causes":

The atmosphere plays a very important part of a double character as to the temperature at the earth’s surface, of which the one was first pointed out by Fourier, the other by Tyndall. Firstly, the atmosphere may act like the glass of a green-house, letting through the light rays of the sun relatively easily, and absorbing a great part of the dark rays emitted from the ground, and it thereby may raise the mean temperature of the earth’s surface. Secondly, the atmosphere acts as a heat store placed between the relatively warm ground and the cold space, and thereby lessens in a high degree the annual, diurnal, and local variations of the temperature.

There are two qualities of the atmosphere that produce these effects. The one is that the temperature of the atmosphere generally decreases with the height above the ground or the sea-level, owing partly to the dynamical heating of descending air currents and the dynamical cooling of ascending ones, as is explained in the mechanical theory of heat. The other is that the atmosphere, absorbing but little of the insolation and the most of the radiation from the ground, receives a considerable part of its heat store from the ground by means of radiation, contact, convection, and conduction, whereas the earth’s surface is heated principally by direct radiation from the sun through the transparent air.

It follows from this that the radiation from the earth into space does not go on directly from the ground, but on the average from a layer of the atmosphere having a considerable height above sea-level. The height of that layer depends on the thermal quality of the atmosphere, and will vary with that quality. The greater is the absorbing power of the air for heat rays emitted from the ground, the higher will that layer be, But the higher the layer, the lower is its temperature relatively to that of the ground ; and as the radiation from the layer into space is the less the lower its temperature is, it follows that the ground will be hotter the higher the radiating layer is.”

[Ekholm, 1901, p19-20]

(h/t Steve Easterbrook's blog article)

• This is very interesting, thank you! If I may ask, could you please clarify the statement "the more CO2 we put into the atmosphere, the higher this emitting layer becomes"? Why does an increased concentration of CO2 move the upper boundary of the layer higher up? And is the change in concentration of CO2 quantitatively consistent with a significant change in this layer's thickness? I'm asking because I was talking about this at work with some colleagues today, and one of them argued that there is no evidence that reducing CO2 emissions will improve anything, which baffled me a lot. Jan 17, 2020 at 17:56
• Thank you very much for your answer, @Dikran Marsupial. I am starting to get the picture, but I am still struggling to intuitively understand your statement: "If it is colder than the surface, it will emit less IR than the surface is emitting and hence less energy is radiated into space." Because if the heat is being transported up to a higher layer in the atmosphere before departing as radiation into space, wouldn't the heat just increase the temperature of that higher layer, until such time as its radiant output to space is in equilibrium with the heat energy input to that higher layer? Jan 17, 2020 at 18:05
• @user6376297 CO2 is "well mixed" in the atmosphere, so if we add more CO2 to the atmosphere, there will be more CO2 above the old effective radiating layer and it will absorb some of the IR emitted from that layer. This means that on average, more of the IR that escapes will be from slightly higher in the atmosphere than before. There isn't really an identifiable layer, in reality there is a distribution of heights from which IR escapes to space, but adding CO2 shifts the distribution a bit higher. Jan 17, 2020 at 18:19
• The atmosphere isn't any taller, it is just the height at which IR radiation can escape into space without being absorbed by greenhouse gasses rises. AIUI most of the heat transfer within the atmosphere is by convection rather than conduction or radiation, and it is that that sets up the lapse rate (the decrease in temperature with increasing height). Because there is a lapse rate, if you want the upper atmosphere to warm, you need the surface to warm as well. Jan 18, 2020 at 15:06
• FYI, here is a post from SE\physics that seems related to what is being discussed here. I confess that I scrolled to the bottom, skipping all the equations... and unfortunately I couldn't understand the conclusion :( Jan 18, 2020 at 18:23

I would like to address what appears to be an over-generalization of your premise. You seem to be simplifying the radiative heat from the Earth. Yes, if you take an average temperature and an average atmosphere, the present amount of CO2 is almost completely maxing out the sides of the absorption bands and an increase in CO2 gets you almost no additional absorption. However, that is an average. Keep in mind that the majority of warming that is currently happening is at high latitudes and high altitudes, where infrared from the Earth is far below average. The increase in global CO2 has a larger affect in these colder regions because there is greater sensitivity to the increase in CO2, affecting those fringes of the absorption bands.

CO2 is dark in the long wave infrared wavelength so the higher the concentration the darker the atmosphere will be in this wavelength, and as you probably know darker colours absorb more heat.

CO2 is not a very powerful greenhouse gas but the amount of it in our atmosphere make this effect the dominating source for the heating we can see today.

Lots of other gases have a larger heating potential than CO2 but their concentration is low at the moment. The more complex a gas is the more heating potential it will have, this is due to the size of the individual gas molecules (CO2 has 3 atoms and methane has 5, so it will look darker in the long wave infrared band and therefore have a stronger heating potential).

• I don't think this answers the question. Jan 19, 2020 at 21:25

A complimentary article to the one written by Spencer Weart and recommended by Dikran Marsupial is this other article from September 2019 written by Jason West, Professor of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill.

Climate explained: why carbon dioxide has such outsized influence on Earth’s climate

It underpins what has been said here that what matters most is the height that the carbon dioxide layer can reach at the upper atmosphere.

In the article is said that carbon dioxide is important for climate despite the fact that water vapor absorbs more infrared radiation and the two gases absorb at several of the same wavelengths.

The reason is that Earth’s upper atmosphere controls the radiation that escapes to space. The upper atmosphere is much less dense and contains much less water vapor than near the ground, which means that adding more carbon dioxide significantly influences how much infrared radiation escapes to space.

The article also re-states information given by by Spencer Weart about the role of carbon dioxide in climate change:

The scientists who first identified carbon dioxide’s importance for climate in the 1850s were also surprised by its influence. Working separately, John Tyndall in England and Eunice Foote in the United States found that carbon dioxide, water vapor and methane all absorbed heat, while more abundant gases did not.

Tyndall and Foote showed that nitrogen and oxygen, which together account for 99% of the atmosphere, had essentially no influence on Earth’s temperature because they did not absorb heat. Rather, they found that gases present in much smaller concentrations were entirely responsible for maintaining temperatures that made the Earth habitable, by trapping heat to create a natural greenhouse effect.

The reason why carbon dioxide has a much more importance in warming the planet while much more abundant gases like nitrogen and oxygen do not play an important role is related to its molecular structure:

Carbon dioxide and other heat-trapping gases have molecular structures that enable them to absorb infrared radiation. Carbon dioxide and other heat-trapping gases have three or more atoms and frequencies that correspond to infrared radiation emitted by Earth. Oxygen and nitrogen, with just two atoms in their molecules, do not absorb infrared radiation.

The article provides important pre-historic information about the concentration of carbon dioxide in the atmosphere and its correlation with the concentration of water vapor in the atmosphere and the consequences for the climate.

The influence of carbon dioxide can be seen in past changes in climate. Ice cores from over the past million years have shown that carbon dioxide concentrations were high during warm periods – about 0.028%. During ice ages, when the Earth was roughly 7 to 13 F (4-7 C) cooler than in the 20th century, carbon dioxide made up only about 0.018% of the atmosphere.

Even though water vapor is more important for the natural greenhouse effect, changes in carbon dioxide have driven past temperature changes. In contrast, water vapor levels in the atmosphere respond to temperature. As Earth becomes warmer, its atmosphere can hold more water vapor, which amplifies the initial warming in a process called the “water vapor feedback.” Variations in carbon dioxide have therefore been the controlling influence on past climate changes.

It finishes explaining why it is foolhardy not to diminish the carbon dioxide emissions to prevent big effect on Earths climate:

Today the level of carbon dioxide is higher than at any time in human history. Scientists widely agree that Earth’s average surface temperature has already increased by about 2 F (1 C) since the 1880s, and that human-caused increases in carbon dioxide and other heat-trapping gases are extremely likely to be responsible.

Without action to control emissions, carbon dioxide might reach 0.1% of the atmosphere by 2100, more than triple the level before the Industrial Revolution. This would be a faster change than transitions in Earth’s past that had huge consequences. Without action, this little sliver of the atmosphere will cause big problems.

The atmosphere has heated about .5 C since 1979. It takes 3 Zeta Joules of energy to accomplish that. That would be .075 ZJ per year if purely cumulative. Residual heat from human energy consumption amounts to .5 ZJ per year or about 20 ZJ since 1979. That is 7 times what would be needed to heat the atmosphere by .5 C. (We note that the oceans are accumulating thermal energy too). In addition to direct transfer of black body radiation to space, molecular collision induced IR generation in the upper atmosphere is where cooling of the global energy reservoir establishes equilibrium. Waste heat energy added to the climate system (with an overprint of natural fluctuation) is the primary cause of the slight increase in temperature of the atmosphere since 1979. But sceptics and alarmists alike tend to ignore waste heat as a serious contributor to climate change.

• This answer would benefit from some sources. Oct 10 at 11:01
• Refering to this your numbers are way off. earthscience.stackexchange.com/questions/3041/… Oct 10 at 12:09
• Haven't looked at your calculation... but I'm guessing it suggests it would take 3 ZJ of energy in the Earth NOW to be .5 C warmer... in other words retaining 3 ZJ over that period. Whereas energy leaves the system continually. And warmer temperature means more energy is emitted. Only by having a method to retain extra energy are you going to heat the Earth longterm. Oct 10 at 22:09
• Indeed your numbers show you're saying the Earth would have to continually retain 6 entire years worth of waste energy. Yet the temperature drop each winter shows just how well Earth sheds heat continually (including our added waste heat). The greenhouse effect, the topic of the question, is the way the Earth can retain some of its heat, including waste heat... but not 6 years worth! Instead, though, a tiny increase in greenhouse effect would wind up adding more heat, as the scale of total energy (i.e. solar insolation) is so giant compared to waste heat. Oct 11 at 3:27
• Using the exponential series sum equation $\sum_{n=0}^N r^n = \frac{r^{N+1} - 1}{r-1}$, it looks like since 1979 Earth would have to be retaining 5/6 of the waste energy annually (or a bit more since it's really a continual rather than annual decay) for it to now have 3 ZJ worth at this point? Or did I make a mistake somewhere??? (Always possible?) But if correct... it clearly doesn't retain anywhere near that amount of solar energy, or we'd have big problems, so waste heat doesn't seem the feasible culprit to me at least... Oct 11 at 3:29