Rudolf Clausius : the scientist who helped us understand the climate

In August 2021, the Inter­go­vern­men­tal Panel on Cli­mate Change (IPCC) publi­shed the first part of its Sixth Assess­ment Report¹, which focuses on the phy­si­cal sciences that under­pin our unders­tan­ding of cli­mate change. The pur­pose of the IPCC reports is to assess recent scien­ti­fic publi­ca­tions, extract a scien­ti­fic consen­sus and pro­duce a text for poli­cy makers. In this report, the name of Rudolf Clau­sius (1822–1888), whose bicen­te­na­ry is being cele­bra­ted this year, is men­tio­ned seve­ral times.

To unders­tand how such a sophis­ti­ca­ted science as cli­ma­to­lo­gy ori­gi­na­ted and deve­lo­ped, we need to go back a few centuries.

The his­to­ry of the stu­dy of cli­mate runs paral­lel to the stu­dy of the oceans, which play a cen­tral role in cli­mate regu­la­tion. The geo­gra­phy of the sea, as ocea­no­gra­phy was once cal­led, is a very old dis­ci­pline that grew out of the eco­no­mic inter­est in bodies of water for trade, fishing, wha­ling and explo­ra­tion. Until the 16^th Cen­tu­ry, howe­ver, know­ledge was acqui­red through anec­do­tal infor­ma­tion based on fisher­men’s tales and maps, some­times accom­pa­nied by eso­te­ric or magi­cal explanations.

To unders­tand how a sophis­ti­ca­ted science like cli­ma­to­lo­gy came into being, we have to go back a few centuries.

Cri­ti­cal to the unders­tan­ding of atmos­phe­ric and marine condi­tions were the inven­tions of the ther­mo­me­ter and baro­me­ter, which took place bet­ween the 16^th and 17^th Cen­tu­ries in Ita­ly (thanks in par­ti­cu­lar to the work of Gali­leo and then Evan­ge­lis­ta Torricelli).

Know­ledge of the oceans, and in par­ti­cu­lar the map­ping of cur­rents, was ham­pe­red until the mid-18^th Cen­tu­ry by an inabi­li­ty to deter­mine lon­gi­tude at sea. The deve­lop­ment of marine chro­no­me­ters enabled cur­rent map­ping to begin, ini­tia­ted in par­ti­cu­lar by Ben­ja­min Franklin.

Ocea­no­gra­phy, as a scien­ti­fic dis­ci­pline, was born bet­ween 1855, the year of publi­ca­tion of the Phy­si­cal Geo­gra­phy of the Sea by the Ame­ri­can Mat­thew Fon­taine Mau­ry, and 1872, the date of the start of the first ocea­no­gra­phic cam­pai­gn, the Chal­len­ger expe­di­tion by the Scot Charles Wyville Thomson.

In France, in 1774, Abbé Louis Cotte – who wor­ked for the Royal Socie­ties of Medi­cine and Agri­cul­ture – publi­shed the Trai­té de météo­ro­lo­gie², which is now consi­de­red one of the first texts on modern climatology.

But it was at the begin­ning of the 19^th Cen­tu­ry that the stu­dy of the atmos­phere and the gases that it is made up of became more com­plex. The concept of the green­house effect first appea­red in 1824, in a publi­ca­tion by Jean-Bap­tiste Joseph Fou­rier, who was stu­dying the mathe­ma­tics of heat flows³. This great phy­si­cist and mathe­ma­ti­cian from Franche-Com­té hypo­the­si­sed that the atmos­phere acts as an insu­la­tor, without which the Earth would be com­ple­te­ly frozen.

More infor­ma­tion was nee­ded on the role of the atmos­phe­ric gases behind the green­house effect. In 1861, in the mid­st of the hea­ted debate about the ori­gin of the ice ages, the Irish phy­si­cist John Tyn­dall – Michael Fara­day’s suc­ces­sor at the Royal Ins­ti­tu­tion and a keen gla­cio­lo­gist – dis­co­ve­red that the pri­ma­ry gas invol­ved was water vapour, fol­lo­wed by car­bon dioxide (CO₂)⁴. These gases absorb some infra­red radia­tion, and small changes in their concen­tra­tion cause cli­mate change. Simi­lar, though less suc­cess­ful, results had been obtai­ned five years ear­lier by the Ame­ri­can inven­tor and women’s rights acti­vist Eunice Foote, but there was no dis­se­mi­na­tion beyond the ocean and these ear­ly results were sub­se­quent­ly for­got­ten⁵.

Then the direct link bet­ween the car­bon cycle and the Ear­th’s tem­pe­ra­ture was demons­tra­ted by Nobel Prize win­ner Svante Arrhe­nius. The Swe­dish che­mist demons­tra­ted that an increase in CO₂ in the atmos­phere results in a signi­fi­cant tem­pe­ra­ture increase⁶. He cal­cu­la­ted that if the concen­tra­tion of atmos­phe­ric CO₂ were to double, the ave­rage tem­pe­ra­ture would have risen by 4°C to 6°C, which is not far from cur­rent esti­mates. It is a pity that the scien­ti­fic com­mu­ni­ty only accep­ted the influence of CO₂ on the atmos­phere in the 1950s. Arrhe­nius was more far-sigh­ted : he also rea­li­sed that the increase in CO₂, which was alrea­dy taking place in his time, was to be attri­bu­ted to the indus­trial use of coal and other fos­sil fuels. Only, as far as he was concer­ned, this was good news : human beings in the future would not suf­fer because of a new ice age !

Final­ly, let’s turn to the Clau­sius-Cla­pey­ron for­mu­la, which is cited 36 times in the Sixth Assess­ment Report (IPCC). Emile Cla­pey­ron (1799–1864), a student at École Poly­tech­nique from 1816 to 1818 before joi­ning École des Mines, was a Pari­sian engi­neer and phy­si­cist who, in the ear­ly part of his career, made signi­fi­cant advances in bridge engi­nee­ring. It was his deep inter­est in the nascent rail­way indus­try that led him to work on steam engines and to super­vise their construc­tion, but he was most inter­es­ted in impro­ving the effi­cien­cy of loco­mo­tives⁷.

He became aware of the work of Sadi Car­not, now consi­de­red the foun­der of ther­mo­dy­na­mics but lit­tle known at the time (he had just died, aged only 36). Cla­pey­ron divul­ged his work on the mecha­nics of heat, made it more rea­di­ly unders­tan­dable and made an enor­mous contri­bu­tion. He was one of the first to for­mu­late the second law of ther­mo­dy­na­mics, the for­mu­la­tion of the law of per­fect gases (PV=nRT) and the gra­phi­cal repre­sen­ta­tion of the evo­lu­tion of the pres­sure of change of state of a body as a func­tion of tem­pe­ra­ture (Cla­pey­ron formula).

Clau­sius took Cla­pey­ron’s for­mu­la and applied it to the spe­cial case of a liquid-vapour equilibrium.

A few years later, ano­ther foun­ding father of ther­mo­dy­na­mics, the Prus­sian phy­si­cist and mathe­ma­ti­cian Rudolf Clau­sius (1822–1888), refor­mu­la­ted the second law of ther­mo­dy­na­mics in its present form : “Heat is always trans­fer­red from a hot­ter body to a col­der one”. He also intro­du­ced the concept of entro­py. In addi­tion to his tea­ching acti­vi­ties at the Zurich Poly­tech­nic and the uni­ver­si­ties of Ber­lin, Würz­burg and Bonn, Clau­sius contri­bu­ted to the great dis­co­ve­ries in phy­sics of the 19th cen­tu­ry and was ins­pi­red by his contem­po­ra­ries Car­not, Joule, Kel­vin and Cla­pey­ron. Indeed, Clau­sius took Cla­pey­ron’s for­mu­la and applied it to the par­ti­cu­lar case of a liquid-vapour equi­li­brium⁸.

Final­ly, we arrive at the famous for­mu­la that is so use­ful for stu­dying cli­mate change. Accor­ding to the Clau­sius-Cla­pey­ron for­mu­la, a tem­pe­ra­ture increase of 1°C cor­res­ponds to an increase in atmos­phe­ric humi­di­ty of about 7%, i.e. about 1–3% more pre­ci­pi­ta­tion on a glo­bal scale. In simple words, this equa­tion helps to unders­tand the for­ma­tion of clouds, rain, snow and is very consistent with the pre­dic­tion of extreme wea­ther events such as increases in the fre­quen­cy of pre­ci­pi­ta­tion and its annual maxi­mum amount, wind speed, river floo­ding. Moreo­ver, the increase in humi­di­ty cor­res­ponds to an increase in the mass of water vapour and thus in the green­house effect, thus lea­ding to a posi­tive feed­back loop.

The Clau­sius-Cla­pey­ron for­mu­la is the­re­fore a very good phy­si­cal basis for future fore­casts, at least on a glo­bal scale. Indeed, impor­tant varia­tions on a regio­nal scale can occur depen­ding on local condi­tions, as Alexan­der von Hum­boldt (1769–1859) alrea­dy unders­tood when he stu­died the dif­ferent cli­ma­tic condi­tions of the South Ame­ri­can landscape.