When carbon dioxide didn’t affect climate

This article was originally published in Finnish in Ilmastotieto-blog.

In 1861 John Tyndall published his results on laboratory experiments where he showed that certain gases were able to absorb thermal radiation. Carbon dioxide was one of such gases. Based on that Tyndall concluded that a change in the amount of greenhouse gases in the atmosphere would necessarily cause a climate change (Tyndall, 1861). Svante Arrhenius published his theory of the effect of greenhouse gases on the climate of the Earth in 1896. His calculations suggested that addition of carbon dioxide would have a strong effect to the temperature of the Earth (Arrhenius, 1896).

From left: John Tyndall (1820-1893), Svante Arrhenius (1859-1927), Knut Ångström (1857-1910) and Charles Greeley Abbot (1872-1973). Eventhough these gentlemen ended up disagreeing on the effect of the carbon dioxide in the atmosphere, they still were all great scientists.

However, in 1900 Knut Ångström published results from laboratory experiments (Ångström, 1900) which showed that carbon dioxide wouldn’t be very significant greenhouse gas after all. It seemed that addition of carbon dioxide didn’t have much effect to the amount of radiation going through the gas, and it also seemed that the absorption band of carbon dioxide was overlapping with the absorption band of water vapour. All this wasn’t exactly new information, however. For example Rubens & Aschkinass (1898) had already observed the overlapping of the absorption bands of carbon dioxide and water vapour and they also deduced that the atmosphere is completely opaque in the wavelength region that also included carbon dioxide. After Ångström’s study, however, it was thought that there’s much more water vapour in the atmosphere and hence it’s much more significant greenhouse gas, so it seemed that the effect of water vapour masked the possible effects from the changes of carbon dioxide concentration and therefore additional carbon dioxide wouldn’t cause more warming. This became general opinion of the issue for several decades. For example, Charles Greeley Abbot noted (Abbot, 1920):

The other two absorbents are each confined in their absorbing regions to comparatively narrow ranges of spectrum, but the ozone absorption band, at about 10 microns, occurs in a region where water vapor absorbs scarcely anything while the carbon dioxide absorption band at about 14 microns occurs in a region where water vapor is also powerfully absorbing. The atmospheric proportion of carbon dioxide is sensibly constant, while water vapor and ozone are variable. Accordingly, while water vapor is certainly the most important of the three, probably ozone, although much less plentiful in the atmosphere, and certainly not more powerful as an absorber for the spectrum of a perfect radiator than carbon dioxide, is yet entitled to be regarded as second in importance on account of this peculiar posture of affairs.

So, at that time ozone seemed to be more important than carbon dioxide. Abbot also said that it might be wise to monitor the ozone in the atmosphere. Here one needs to note that at that time there wasn’t good enough measurements on the atmospheric carbon dioxide yet, which caused the carbon dioxide concentration to seem constant, eventhough by that time it already was slightly increasing (this has been observed subsequently from the ice core samples containing air bubbles, which have recorded the atmospheric greenhouse gas concentrations of past times). Simpson (1929) also discussed the matter and gave three reasons why the addition of carbon dioxide is not significant factor in the atmosphere. According to him the absorption band of carbon dioxide was too narrow for it to have much significance. Second reason was above-mentioned overlapping of the absorption bands of carbon dioxide and water vapour and as a third reason he mentioned that the current amount (back then) of atmospheric carbon dioxide already absorbs its full amount of the absorption band, and the addition of carbon dioxide wouldn’t change it significantly. This has been called the saturation of the absorption band.

So there was a general opinion that addition of carbon dioxide wouldn’t have any significant effect to the thermal radiation leaving the Earth and therefore it also wouldn’t affect Earth’s temperature. However, there were some opposing voices who thought that carbon dioxide did affect the temperature. Hulburt (1931) made some calculations relating to the matter in similar manner than Arrhenius did and Hulburt gave his support to Tyndall and Arrhenius:

Calculation shows that doubling or tripling the amount of the carbon dioxide of the atmosphere increases the average sea level temperature by about 4° and 7°K, respectively; halving or reducing to zero the carbon dioxide decreases the temperature by similar amounts. Such changes in temperature are about the same as those which occur when the earth passes from an ice age to a warm age, or vice versa. Thus the calculation indicates that the carbon dioxide theory of the ice ages, originally proposed by Tyndall, is a possible theory.

But Hulburt’s work went largely unnoticed. Also Callendar (1938) arrived to a conclusion that carbon dioxide has a heating effect. Callendar observed that the temperature of the Earth was rising, so he made a summary of old measurements of atmospheric carbon dioxide concentration and got a result that the carbon dioxide concentration of the atmosphere was rising. He also presented a calculation which suggested that carbon dioxide would have strong heating effect. Callendar’s results weren’t accepted in the scientific community. The rising carbon dioxide concentration were suspected because the measurements were inaccurate. Callendar’s calculation also had some deficiencies which was one factor in the rejection of his results. However, his work arised enough interest to cause some subsequent studies on the matter.

In the laboratories the work on the absorption properties of gases also had continued. Martin & Barker (1932) showed that the absorption bands of carbon dioxide in fact consisted of many different absorption lines, which were caused by different vibrational states of the carbon dioxide molecule. This meant that the absorption band of carbon dioxide weren’t fully saturated after all, but there were room for more absorption in between the lines.

Strong & Plass (1950) studied the effect of pressure to the thermal radiation absorption properties of the atmospheric gases. They noticed that the properties were changing with the altitude. They showed that higher in the atmosphere there is less absorption of thermal radiation than in lower parts of atmosphere. Therefore some of the radiation emitted by the lower atmosphere can escape to the space. The reason is that the absorption bands are wider in lower atmosphere than in higher atmosphere which enables the thermal radiation emitted from the edges of the absorption band by the lower atmosphere to be free to escape to the space because the narrower absorption band of the upper atmosphere doesn’t reach to the edges of the absorption band of lower atmosphere (which is also an emission band in this case). It’s like trying to block a 2 cm hole in a barrel with 1 cm plug. This is important observation for the problem discussed here. Even if the absorption band of carbon dioxide would be fully saturated in the lower parts of atmosphere, it is not saturated in higher atmosphere and the addition of carbon dioxide will cause more absorption of thermal radiation. However, Strong & Plass didn’t themselves take much stand on this issue but they concentrated more on analysing the matters relating to the stratosphere. Yet, they did say:

According to equation (18), the radiation exhausted from the atmosphere by the CO₂ increases as the square root of the concentration of CO₂. Since the atmosphere is at a lower temperature than the surface of the earth, the surface temperature rises as the CO₂ concentration increases.

Gilbert Plass was then the person who finally solved the problem. In 1956 he published results from his study (Plass, 1956) where he had used latest laboratory measurements of the absorption properties of greenhouse gases and had determined the radiation flux in the primary absorption band of carbon dioxide in the atmosphere with a theoretical model (up to the height of 75 km). Among other things, his model included the pressure and Doppler broadening of absorption lines and the overlaps of spectral lines. According to his results, doubling of carbon dioxide concentration would cause 3.6°C warming to the surface of the Earth. In addition to this result, Plass also gave answers to all arguments that were thought to show that carbon dioxide wouldn’t cause warming to the surface of the Earth. Plass (1956b) wrote a popular article on the subject and the article happens currently to be freely accessible for everyone. In this article, there are answers to above-mentioned arguments. First the overlapping of the water vapour and carbon dioxide:

The fact that water vapor absorbs to some extent in the same spectral interval as carbon dioxide is the basis for the usual objection to the carbon dioxide theory. According to this argument the water vapor absorption is so large that there would be virtually no change in the outgoing radiation if the carbon dioxide concentration should change. However, this conclusion was based on early, very approximate treatments of the very complex problem of the calculation of the infrared flux in the atmosphere. Recent and more accurate calculations that take into account the detailed structure of the spectra of these two gases show that they are relatively independent of one another in their influence on the infrared absorption. There are two main reasons for this result: (1) there is no correlation between the frequencies of the spectral lines for carbon dioxide and water vapor and so the lines do not often overlap because of nearly coincident positions for the spectral lines; (2) the fractional concentration of water vapor falls off very rapidly with height whereas carbon dioxide is nearly uniformly distributed. Because of this last fact, even if the water vapor absorption were larger than that of carbon dioxide in a certain spectral interval at the surface of the Earth, at only a short distance above the ground the carbon dioxide absorption would be considerably larger than that of the water vapor.

And then the saturation of the carbon dioxide absorption band:

One further objection has been raised to the carbon dioxide theory: the atmosphere is completely opaque at the center of the carbon dioxide band and therefore there is no change in the absorption as the carbon dioxide amount varies. This is entirely true for a spectral interval about one micron wide on either side of the center of the carbon dioxide band. However, the argument neglects the hundreds of spectral lines from carbon dioxide that are outside this interval of complete absorption. The change in absorption for a given variation in carbon dioxide amount is greatest for a spectral interval that is only partially opaque; the temperature variation at the surface of the Earth is determined by the change in absorption of such intervals.

So the change in carbon dioxide affects the temperature because with closer inspection the absorption of carbon dioxide is not overlapping with the absorption of water vapour and water vapour is absorbing more strongly only in the lower atmosphere, and the saturation of certain parts of carbon dioxide absorption bands are already taken into consideration in the calculations which still result in the warming of the Earth’s surface when more carbon dioxide is added to the atmosphere.

This problem was solved in 1956, over 50 years ago. The solution is very straightforward and easy to understand, and it shouldn’t cause any confusion. Regardless of that, these already solved arguments are still presented in public forums as if they haven’t been solved.

Thanks for good comments to Jari, Kaitsu, and AJ.

References

Abbot, C. G., 1920, “The larger opportunities for research on the relations of solar and terrestrial radiation”, PNAS, 6, 82-95, [full text]

Arrhenius, Svante, 1896, “On the Influence of Carbonic Acid in the Air Upon the Temperature of the Ground.” Philosophical Magazine 41: 237-76, [full text]

Callendar, G. S., 1938, “The artificial production of carbon dioxide and its influence on temperature”, Quarterly Journal of the Royal Meteorological Society, Volume 64 Issue 275, Pages 223 – 240, [abstract]

Fleming, James R., 2002, “The carbon dioxide theory of climate change: emergence, eclipse, and reemergence, ca. 1850–1950”, 13th Symposium on Global Change and Climate Variations, AMS, [Abstract, full text]

Hulburt, E. O., 1931, “The Temperature of the Lower Atmosphere of the Earth”, Physical Review, vol. 38, Issue 10, pp. 1876-1890, [abstract]

Martin, P. E., Barker, E. F., 1932, “The Infrared Absorption Spectrum of Carbon Dioxide”, Phys. Rev. 41, 291–303, [abstract]

Plass, G. N., 1956, “The influence of the 15u carbon-dioxide band on the atmospheric infra-red cooling rate”, Quarterly Journal of the Royal Meteorological Society, Volume 82 Issue 353, Pages 310 – 324, [abstract]

Plass, Gilbert N., 1956b, “Carbon Dioxide and the Climate” – article was re-published in 2010: American Scientist, Volume 98, Number 1, Page: 58, DOI: 10.1511/2010.82.58, [full text]

Rubens, H.; Aschkinass, E., 1898, “Observations on the Absorption and Emission of Aqueous Vapor and Carbon Dioxide in the Infra-Red Spectrum”, ApJ, 8, 176, [abstract and full text]

Simpson, 1929 – information on this is from Fleming (2002), who doesn’t give any specific reference to this.

Strong, John, Plass, Gilbert N., 1950, “The Effect of Pressure Broadening of Spectral Lines on Atmospheric Temperature”, Astrophysical Journal, vol. 112, p.365, [abstract and full text]

Tyndall, John, 1861, “The Bakerian Lecture: On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connexion of Radiation, Absorption, and Conduction”, Proc. R. Soc. Lond. 11:100-104; doi:10.1098/rspl.1860.0021, [abstract, full text]

Weart, Spencer, 2009, “The Carbon Dioxide Greenhouse Effect”, [full text]

Ångström, Knut, 1900, “Ueber die Bedeutung des Wasserdampfes und der Kohlensäure bei der Absorption der Erdatmosphäre”, Annalen der Physik, Volume 308 Issue 12, Pages 720 – 732, [abstract (in German)]