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.