Clausius-Clapeyron law: How extreme weather in the Mediterranean can be explained by formula

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Floods in Spain: hunger for steam in the air

Photo: Europa Press / ABACA/ IMAGO

There is a recipe for catastrophes: for the fires in Canada, the floods in Greece, the droughts in Spain or heat records in Italy. Most people are probably already familiar with it: warm air can absorb more water vapour, around seven percent more per degree of warming. This has been explained by climate researchers for many years, again and again in the weather report.

The underlying law of physics was recognized in 1834 by the French physicist Émile Clapeyron, and the German physicist and "father of thermodynamics" Rudolf Clausius derived it from the basic laws of thermodynamics in 1850.

This CC law – as experts abbreviate it – shows how much water vapor fits into one cubic meter. The maximum amount of water vapor increases exponentially with temperature (see graph). This has astonishing and sometimes even devastating consequences, of which we have seen more this summer than we would like. Not only for extreme precipitation, but also for droughts, forest fires and even for the full extent of global warming.

Extreme rain

In general, it rains when moist air masses rise. This is because the air cools down considerably when ascending, with every kilometre more altitude, the air becomes around six degrees colder and, according to the CC formula, can hold less and less water – it falls to the ground. In addition, if it is one degree warmer, then according to the formula, there is around seven percent more water vapor in an air mass saturated with humidity (i.e. 100 percent relative humidity) and rains down.

Measurement data for heavy rainfall broadly confirm this theoretical expectation. A study by ETH Zurich has shown this specifically for weather stations in Germany, the Netherlands, Austria and Switzerland. Extreme precipitation has increased significantly here – by an average of just 7.3 percent per degree of warming in the northern hemisphere. Data from weather stations also show an increase in extreme rainfall worldwide. The frequency of new records in the daily sum of precipitation has been statistically significantly increased since the nineties and continues to rise.

Particularly favourable conditions for extreme rainfall prevail in the vicinity of relatively warm water surfaces, which provide a supply of moisture-saturated air masses, as is currently the case in the eastern Mediterranean.

For thunderstorms, studies suggest that they increase particularly strongly – even more than expected according to the Clausius-Clapeyron law. Possibly because the updraft in the thunderstorm cell becomes stronger, driven by the latent heat of the water vapor released, so that more moist air from the environment is sucked into the thunderstorm cell. Here, the CC law has a double effect: on the water content and on the intensity and size of the thunderstorm cell.

More on the subject

• Heat, drought and fire 2023: The year of climate anomaliesBy Marco Evers

• Water reservoirs, fog catchers, artichokes: Europe is drying up – this is how countries want to protect themselves

• Rising temperatures:This is how dry Europe isBy Susanne Götze

Drought

This summer, you could see the "climate skeptics" lamenting again on social media: "Just a moment ago, climate change was supposed to be to blame for the drought, and now all of a sudden it's heavy rain?!" Admittedly, that sounds contradictory at first. Nevertheless, both are true: they are two sides of the same coin, more precisely the CC law. Because warm air can absorb more water vapor, the so-called steam hunger of the atmosphere also increases exponentially, as the graph shows. Water evaporates faster when the air eagerly absorbs the water vapor and transports it away. The warmer air sucks the water out of soils and vegetation.

It is also important to know that with global warming, the relative humidity almost does not change on average, because the fuller the atmosphere is with water vapour, the more it rains down again. And what "full" means is determined by the relative humidity: It indicates how close you are to the upper limit according to the CC law, i.e. at 100 percent relative humidity.

And that explains the hunger for steam. An air mass with (for example) 60 percent relative humidity can absorb more water vapor the warmer it is (red arrows in the graphic). The evaporation of water from soil or plants is faster the more water vapor the air absorbs.

Soils and forests, gardens and arable crops dry out faster the warmer it gets – because of the CC law. If there is hardly any rain for some time, drought will occur more quickly. Precipitation would have to increase significantly in order to compensate for the faster drying out due to evaporation in a warmer climate.

Forest fires

The fact that CO₂ is a greenhouse gas whose increase leads to global warming is elementary physics and has been proven since the 1850s by the work of Eunice Foote and John Tyndall. But how strong is this warming? Here, too, the CC law plays a decisive role. This is because the direct radiation effect of a doubling of CO₂ in the air has a heating effect of 3.7 watts per square meter of the earth's surface, which would only lead to one degree Celsius of warming, as can be calculated directly from the Stefan-Boltzmann law of physics, which has been established since 1884.

But there are amplifying feedbacks, and the most important is water vapor feedback. This is because water vapour, like CO₂, is a greenhouse gas. Higher temperature means more water vapor in the air, as required by the CC law and as confirmed by measurement data, and this then increases the temperature further. This doubles the warming caused by CO₂ from one to two degrees Celsius. Through further feedback, this is amplified by a further 50 percent, to a total of around three degrees Celsius after a doubling of CO₂.

These are the reasons why the CC law is a recipe for disasters: for a doubling of global warming, for extreme rains with flash floods, for droughts with crop failures, and for wildfires out of control. In order to understand the background of the increasing weather extremes, one does not need a climate model, nor do you need elaborate attribution studies – only a basic understanding of physics, which has been known since the 19th century. The measurement data confirm these correlations. The only question left is how much further we want to heat up our home planet by burning fossil fuels. With all the consequences and for thousands of years.