The Brilliance Of Svante Arrhenius
Climate Science circa 1896
You may have heard of the Swedish scientist Svante Arrhenius (1859-1927) through his rate equation1 in high school Chemistry. But even if you said goodbye to Chemistry lessons ASAP, some of the concepts he developed should ring a bell: activation energy, electrolysis, acid-base reactions, salts dissolving into ions…
Arrhenius helped set up the Nobel Prize Foundation in 1900 and then received the Third Nobel Prize in Chemistry in 1903—suspicious! but in fact, his works deserved the accolade many times over. Today, I’ll introduce him to you as the writer of a foundational paper2, “On the influence of carbonic acid in the air upon the temperature of the ground”, published in English in 1896.
Arrhenius calculated the sensitivity of global temperatures to the atmospheric concentration of `carbonic acid’ (CO2 when in the air) to explain the ice ages. Over a year, he carried out more than ten thousand calculations by hand3 to estimate the warming in a 4-by-10 season-by-latitude grid on doubling the concentration of CO2 in the atmosphere. How did he do it?
Every model needs empirical data
Two decades earlier, the astronomer Samuel Langley had laid the technological and empirical groundwork with his invention of the bolometer, which offered startlingly sensitive measurements of radiant heat. Radiant heat is the same type of radiation seen through a thermal camera — infrared. Of two thinly rolled metal sheets in the elegant bolometer circuit, one is exposed to the radiant heat and draws less electrical current on heating up than the protected sheet, with the measured difference proportional to the intensity of the absorbed rays.
Langley worked with painstaking care at the Allegheny Observatory in Pittsburgh, often alone and in the dark of night, to measure the moon’s temperature by its radiant heat transmitted through Earth’s atmosphere. He focused the moonlight with a 13-inch refracting telescope, then, using a rock-salt prism, split the radiant heat into its constituent wavelengths (rednesses) onto the bolometer. Langley’s measurements across a range of moon elevations and seasons, altogether called lunations, allowed Arrhenius to calculate how the variation in the transmission of moonlight required a particular strength of radiant heat absorption by CO2, along with a host of other factors.
Watch out for a future post on The inventions that unlocked the characterisation of Earth's climate for more details on the bolometer. In a charming twist of history, it also connects the rivals of “the current war”: the bolometer was used both in Nikola Tesla’s first demonstration of wireless power transmission and in Langley’s race with Thomas Edison to measure the temperature of the solar corona.
The foundational physics
In his analysis that variation in CO2 concentrations could explain glacial periods, Arrhenius effectively founded the scientific field of climate change. He built on Joseph Fourier’s conception of planetary temperature to state:
“The atmosphere must, therefore, radiate as much heat to space as it gains partly through the absorption of the sun's rays, partly through the radiation from the hotter surface of the earth and by means of ascending currents of air heated by contact with the ground.”
which already holds the principle underpinning Suki Manabe’s Nobel Prize-winning radiative-convective equilibrium model to be developed in 1967.
He used the foremost equation of climate, the Stefan-Boltzmann Law of Blackbody Radiation, to predict
“Thus if the quantity of carbonic acid increases in geometric inogression, the augmentation of the temperature will increase nearly in arithmetic progression.”
To my knowledge, this is the first statement of what is now called the equilibrium climate sensitivity4. To translate, you might remember the rules for arithmetic and geometric series from high school. If we increase carbon dioxide by a constant multiplicative factor, i.e., in a geometric series, the global mean temperature will rise by a constant additive difference in corresponding terms, an arithmetic series.
Let’s insert modern numbers to sample this principle: If emissions do not peak before 2050, humanity could be locked into doubling preindustrial CO2 levels from 280 ppm to 560 ppm, leading to an estimated 3°C of long-term warming5. Carbon dioxide already makes up 420 parts per million of the atmosphere today. For worst-case emission rates continuing past 2100, another doubling of the CO2 concentration above preindustrial levels to 1120 ppm could occur, adding another 3°C to make a total of 6°C long-term human-induced warming compared to pre-industrial times.6
To simplify the modelling, Arrhenius took the atmosphere as a single layer above ground of a different temperature while correctly including estimates of humidity effects (water-vapour feedback), changes in reflectivity with ice coverage (ice-albedo feedback), and the impact of average cloud cover. His intuition of the underlying physical principles was astonishingly strong, and the opportunity to use Langley’s observations of the transmission of moonlight through the atmosphere was providential. But there were inevitably errors in the groundbreaking data and analysis, and two fortuitously cancelled out7 — we will come back to these in another post. Even accounting for these errors, the paper is still a monumental triumph.
Did Arrhenius comment on anthropogenic global warming?
Yes, but not with the negative connotations and context it is understood today: first in a public lecture given in Swedish in 1895 at the Högskola, but also in a 1000-page textbook called Lehrbuch der kosmischen Physik published in German in 1903 and in a popular book called Worlds in the making: The Evolution of the Universe in 1908.
A trove of USA newspapers from 1899 to 1903 also reference Arrhenius’s idea, with charming headlines including "Nothing But Summer” (Saint Paul Globe), “Hint to Coal Consumers" (Selma Morning Times), and “Earth’s Atmosphere Becoming Warmer, Declares Prof. Arrhenius” (Chetopa Advance). The earliest example8 I found is from the Buffalo Tribune below, which provides helpful historical context, being on the longer side.
A translation from Chat-GPT seems to manage the gist (to be updated with a proper translation):
“Carbon Dioxide and Earth's Heat. Is the Earth heading towards a warmer or colder era? This question might seem quite superfluous and quickly answered to some; because one might think, and it has been said countless times, that the Earth continues to cool with increasing age and that, therefore, the temperature on its surface must continue to drop until eventually, the famous "last humans" crowd around the equator and end their existence in an icy scene. A young Swedish naturalist, Svante Arrhenius, a staunch believer in the most accurate scientific and well-founded claim that the Earth is actually warming and that moist carbon dioxide gas plays a significant role in influencing the Earth's climate.
The very difficult to explain fact that large parts of the Earth went through a real "ice age" so many hundred thousand years ago and that it has become noticeably warmer on Earth since then, Arrhenius deciphers by assuming that the atmosphere back then had too little carbon dioxide. According to his investigations, carbon dioxide has the property of allowing the heat rays of the sun to pass through from above, but retaining the heat reflected back from the Earth, thus contributing to the increase in temperature on the Earth's surface. The Swedish scholar goes even further, believing he can assert that in our atmosphere, due to industrial activity, steam mills, and heating systems, the sun's heat is increasingly trapped.”
The newspaper article presents Arrhenius as putting forward a mechanism to solve the contemporary paradox between the Earth cooling down from a hot birth on geological timescales and the opposing fact of escaping from a previous ice age more than a hundred thousand years ago. Arrhenius correctly hypothesises that there was less CO2 around to act as an atmospheric blanket during the last Ice Age. He further commented on how industrial activity will increase carbon dioxide concentrations and warm the world.
Burning coal into the atmosphere
Having established that CO2 helps the atmosphere to be a warming blanket, what maintains and influences the CO2 concentration must be reasoned out. A colleague, Arvid Högbom, pioneered the concepts of a geological carbon cycle a few years earlier. Arrhenius translated a passage from Högbom to English for his 1896 paper:
“The world's present production of coal reaches in round numbers 500 millions of tons per annum, or 1 ton per km2 of the earth's surface. Transformed into carbonic acid, this quantity would correspond to about a thousandth part of the carbonic acid in the atmosphere.”
Arrhenius and Högbom did not foresee the exponential boom in population nor the use of oil and gas. The annual burning of fossil fuels is now 40 billion tonnes, an eightyfold increase9. In a public lecture in Sweden in 1895, Arrhenius states 10
“For example, if all other processes which produce or absorb carbonic acid were in equilibrium, and it was only necessary to take account of the carbonic acid production due to the burning of coal, then as a result of the absorbing effect of the world's oceans 3000 years would need to pass before the carbonic acid content of the air had increased by 50% instead of 500 years if the oceans did not exist. During the period the temperature would rise by 3.4 degrees centigrade.”
Arrhenius also overestimated the oceans' CO2 uptake. However, he had the right intuition that the ocean would not simply absorb the excess emissions — a passive assumption of much of the scientific community until Bert Bolin's more rigorous analysis in 195811. Bolin, who also chaired the first IPCC report, is another of the figures we will meet later.
Take-home statement
Arrhenius’s most explicit written statement of warming in the paper of 1896 finds
“A simple calculation shows that the temperature in the arctic regions would rise about 8° to 9º C., if the carbonic acid increased to 2.5 or 3 times its present value.”
It highlights how Arrhenius leapt ahead by starting with a regional calculation, anticipating the Arctic amplification of global warming: the poles do indeed warm faster than the equator.12
So, Arrhenius's corresponding estimates of globally averaged warming on doubling atmospheric carbon dioxide (interpolated from a table in 1896 and revised in his later articles) fall in the range of 4 to 6°C. These values fall remarkably close to current Intergovernmental Panel on Climate Change estimates of 2 to 4.5°C. This closeness is partly a coincidence, but even when correcting for the unavoidable errors, which we leave to future discussion, the figure still falls in the right ballpark because Arrhenius had the correct physics.
From 1896 to today
The news headlines generated by Jim Hansen’s testimony to Congress a century later mark a turning point in public understanding and awareness of what Arrhenius partially predicted. The modern update was the rate of climate change, definitive attribution and an understanding of the dangers.
We started with Arrhenius’ work as it is climate science’s end of the 19th-century milestone. He skillfully tied together threads of work from Arvid Högbom, John Tyndall, Eunice Foote (likely unbeknownst), Joseph Fourier, and Samuel Langley, to name just a few. Unfortunately, a severely flawed refutation of Arrhenius’s work by Knut Ångström, among other factors, held back the progress of climate science by a few decades. As a leading public scientist, Arrhenius took positions on issues of his time, including eugenics, which was widely accepted at the time but is now seen as deeply problematic.13
In one of our next articles, we will revisit the theme of discovery by moonlight. Ninety years after Arrhenius unlocked carbon dioxide’s role in climate, Susan Solomon stood on the roof of an Arctic station collecting moonlight to demonstrate the accelerated breakdown of ozone by CFCs in Polar Stratospheric clouds. This work quickly led to the successful Montreal Protocol on substances that deplete the ozone layer. Solomon has since contributed key papers on the millennial persistence of carbon dioxide emissions. The impact of her science and advocacy on policy is an inspiring example of what can be achieved.
Have a great week!
-Richard and the Climate Physics Team
P.S. Something that never ceases to astonish me is how bracingly the modern age of physics arrived. Arrhenius theorised that salts dissolve into ions. His student, Oskar Klein, developed a quantum interpretation (the same quantum as in `Schrödinger’s Cat’) of relativistic equations (think Einstein’s work) involving an extra curled-up dimension. This idea was later revived for the weird and wonderful String Theory (see Kaluza-Klein theory).
Updated on Thursday 18th July with headers and footnotes.
The key Arrhenius paper on which this article is based
Elisabeth Crawford: Arrhenius' 1896 model of the greenhouse effect in context, 1997; Ambio 26,6-11.
The Warming Papers: The Scientific Foundation for the Climate Change Forecast, David Archer and Ray Pierrehumbert, John Wiley & Sons, 2011.
If you know of the earliest Swedish newspaper article, please contact us.
Discussion of artic amplification of global warming, also referring to Arrhenius
Scarce details are readily available on this. Elisabeth Crawford’s fantastic biography (Arrhenius: From Ionic Theory to the Greenhouse Effect) does not appear to mention the association with eugenics.