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.