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The Errors of Arrhenius

The Swedish physical chemist, Svante Arrhenius, is credited with establishing the scientific basis of global warming due to carbon dioxide created by human activities. Arrhenius published his work in English in the Philosophical Magazine and Journal of Science in 1896. The scientific world considered this work for about ten years but by 1905 rejected it on the basis that the amount of carbon dioxide in the air was so small compared to the amount of water vapor that even a doubling of it would have an insignificant effect on global temperature. This was a consensus of opinion in the scientific world that lasted until about 1950. Around 1950 new, more detailed measurement of the absorption spectra of water vapor and carbon dioxide revealed that there were some wavelengths of infrared radiation that carbon dioxide absorbed that water vapor did not. This meant that theoretically carbon dioxide could have an effect on global temperatures even though its concentration is small compared to water vapor. The concentration in the overall atmosphere of water vapor is about 0.4 of 1 percent. Adding carbon dioxide at a concentration of 0.03 of 1 percent increases the greenhouse gas concentration from 0.4 of 1 percent to 0.43 of 1 percent, an increase of 7.5 percent. A further increase in the carbon dioxide content to 0.06 of 1 percent is an increase in greenhouse gas concentration of only 7 percent for the wavelengths of radiation for which the absorption spectra of water vapor and carbon dioxide overlap. But for the wavelengths which water vapor does not absorb but carbon dioxide does the increase is 100 percent. Thus carbon dioxide was not just a greenhouse gas duplicating the effect of water vapor; it was a greenhouse gas with a difference. For more on the absorption spectra of greenhouse gases see Absorption Spectra.

There were articles then published arguing that not only could anthropogenic carbon dioxide affect global temperatures but that it had already done so. One of these articles, by Gilbert N. Plass of Johns Hopkins University, is solid scientific analysis. Another was by Guy S. Callendar of London which is usually credited with establishing global warming. The Callendar article however is not science. See Early history of the role of CO2 in climate analysis. The Callendar article is basically fakery. Callendar purported to show that temperatures around the world had increased by ½°C over the period 1885 to 1950. Callendar gives the temperature record for five areas; the British Isles, Japan, Turkestan, New Zealand and Chile. Somehow the temperature records for all other areas, including the United States, Canada and Australia, were not suitable for inclusion. Of the five he showed, two, Japan and Chile, did not show a temperature increase. Turkestan showed an increase of about ½°C; whereas the British Isles and New Zealand showed a temperature increase of about 1°C. Thus Callendar's figure was an average over the five figures; (0+0+½+1+1)/5=½.

Callendar showed the temperature record for the British Isles going back to 1850. However if he had used the temperature record for central England which goes back to about 1820 it would have revealed that the temperature in 1830 was just as high as it was in 1950. Thus Callendar through selection of the countries and the time period got partial support for his thesis that temperatures around the world had increased by ½°C over a 65 year period.

After realizing the flimsiness of Callendar's publication and the weakness of the greenhouse effect on clear winter's nights I began to suspect something might be wrong with Svante Arrhenius' work. Fortunately thanks to the internet and Google's program for digitizing publications the Arrhenius article is readily available.

Arrhenius was a world-class scientist but even scientists can make conceptual and quantitative errors. An examination of Arrhenius' reveals that this was true also in his case.

Arrhenius was interested in possible mechanisms for preventing the Earth from entering another ice age. The evidence for the past ice ages had just become available in the 19th century and people of Sweden could be expected to be concerned about a re-occurrence. By hand Arrhenius computed the effects of various changes in the levels of carbon dioxide in the air, from a 33 percent decrease to a two hundred percent increase. He did this for 13 latitude bands and four seasons of the year. The case that gets attention is the one for a hundred percent increase, a doubling of the concentration of CO2. In his 1896 publication Arrhenius asserted that a doubling of the CO2 level would increase the world's average temperature by 5 to 6°C, with the high latitudes increasing more and the tropics less. Other scientists, such as the Swedish scientist Knut Angstrom, objected to the value that Arrhenius had used as the absorption coefficient for CO2. At the time Angstrom made his objection of the quantitative accuracy of the absorption coefficient (1900) Arrhenius rejected it, but by 1906 Arrhenius gave a revised estimate of the effect of a doubling of CO2 being 1.2°C directly and 2.1°C with the water vapor feedback effect included. Thus Arrhenius had acknowledged that he had overestimated the impact of a doubling of CO2 by about two hundred and fifty to three hundred percent. This overestimate had to have come largely, if not exclusively, from an overestimate of the absorption coefficient for carbon dioxide.

The Effect of Doubling the Concentration
of CO2 in the Atmosphere

The Intergovernmental Panel on Climate Change (IPCC) asserts that the doubling of the concentration of CO2 would increase the average global temperature by the year 2100 by 2 to 4.5°C. Earlier a committee of the National Academy of Sciences issued a report that gave the range being 1.5 to 4.5°C. The story of that 1.5 to 4.5°C range is amusing and instructive of the nature of climate science in the past.

In the 1970's climatologists began experimenting with computer models of the global climate that took into account the general circulation of the atmosphere. There were two people who had developed such models. One was Sukimoto Manabe of Princeton. Manabe is a well-respected meteorologist of the genius class who was noted for attempting to expand the theoretical scope of climate models. He was very meticulous in his approach to model building. The other was James Hansen of the Goddard Institute of Space Science. Hansen could be best characterized as a climatologist of the loose-canon class. His background was physics and the closest he came to climatology was analyzing the greenhouse effect on Venus. In such work there can be very little comparison between the analysis and the reality.

In 1979 a branch of the National Academy of Sciences created a committee under the chairmanship of Jules Charnes to review the state of global climate modeling. The committee met at Woods Hole, Massachusetts and had Sukimoto Manabe and James Hansen make presentations. After hearing the presentations the committee issued a report in which it stated that the effect of a doubling of CO2 would be an increase in average global temperature of 1.5 to 4.5°C. Sukimoto Manabe told how this figure was arrived at. He was working on his model at the time and said that he had had "All kinds of numbers, but it just happened to be 2[°C] at the time." He did not consider that figure a final result. James Hansen created his model and did his computational run and came up with the figure of 3.9°C. Manabe said the committee took his figure of 2.0°C and subtracted a half degree and Hansen's figure rounded to 4.0°C and added a half degree to get a range of 1.5 to 4.5°C. That range of 1.5 to 4.5°C is still around and is treated as a solid scientific figure.

Thus Arrhenius' figure for the effect of a doubling of the CO2 went from 5 to 6°C to 2.1°C as a result of revision of his estimate of the absorption coefficient of CO2. The elaboration of climate modeling around 1980 by Sukimoto Manabe gave essentially the same result. Arrhenius estimated that it would take about three thousand years for the level of CO2 to double. The level of CO2 has increased at an average rate of 0.4 of 1 percent per year since accurate measurements of CO2 levels have been available from the side of Mauna Loa in Hawaii. At this rate it would take 173 years for the CO2 to double. The current models use a rate of increase of CO2 of 1 percent per year, 2.5 times the historical average rate, because that gives a doubling in 69 years. Projections beyond the year 2100 just do not have the impact of those that will occur within the 21st century.

The computation of absorption coefficients is sufficiently complicated that it is difficult to say whether any value is right or wrong. These coefficients should be experimentally measured rather than computed.

(To be continued.)

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