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Flash floods resulting from extreme rainfall pose a major risk to people and infrastructure, especially in urban areas. Higher temperatures due to global climate change affect continuous rainfall and short rain showers in somewhat equal measure.

However, if both types of precipitation occur at the same time, as is typical for thunderstorm cloud clusters, the amount of precipitation increases more strongly with increasing temperature, as shown in a study by two scientists from the University of Potsdam and the Leibniz Centre for Tropical Marine Research (ZMT) in Bremen. The study has just been in the journal Nature Geoscience.

Extreme rainfall can cause rapid flooding, so-called "flash flooding." How does such extreme rainfall change with temperature? This question has been studied for decades using appropriate recordings of rainfall and temperature, measured at short intervals of one hour or less.

Rainfall and clouds form when the water vapor in the air saturates, thus forming small droplets that eventually lump together to form raindrops. According to the Clausius-Clapeyron relation, saturation requires roughly 7% more vapor when temperatures rise by one degree Celsius. This relation might, as an oversimplified image, be motivated by a sponge that can capture more water as temperatures increase. An extreme rainfall event in this image corresponds to squeezing the sponge to release most of its water.

This hypothesis was challenged in 2008 by analysis of a long time series of rainfall data in the Netherlands. The authors of that study, Lenderink and van Meijgaard, concluded from their statistical approach that the Clausius-Clapeyron relation was insufficient to describe the increase in extreme rainfall, in particular that of thunderstorms which could increase at 14% per degree Celsius—thus twice the rate of Clausius-Clapeyron.

In the past 17 years, the work by Lenderink and van Meijgaard, now cited more than 1000 times, has led to numerous investigations into the phenomenon, without being able to unambiguously confirm or reject the groundwork laid out by the Netherlands study. In particular, it was difficult to determine how far the blend of different rainfall types could give rise to statistical superpositions.

The current work takes a detailed look at two precipitation types: stratiform rainfall that is continuous and uniform in intensity compared to short rain showers typical for thunderstorms.

"We make use of a large and high-frequency dataset from Germany which is combined with a novel lightning detection dataset. Since lightning indicates thunderstorm activity, stratiform rainfall can be separated in this way," explains Nicolas Da Silva from the University of Potsdam.

"The result is rather striking: when carefully selecting only clear thunderstorm rainfall and studying the extremes at each temperature, the increase is almost perfectly along the Clausius-Clapeyron theory," adds Jan O. Härter from the University of Potsdam, who is also affiliated with the Leibniz Centre for Tropical Marine Research (ZMT).

Equally, when selecting only for stratiform rainfall alone, the data fit the Clausius-Clapeyron relation very well. Only when combining the statistics of both types of rainfall, much higher temperature increase rates emerge, as proposed in the study of Lenderink and van Meijgaard. The authors Da Silva and Härter state that this "super-Clausius-Clapeyron" increase is thus of purely statistical origin, such that a long-standing controversy may now finally be settled.

However, the current study points out that the statistical super-Clausius-Clapeyron increase in rainfall extremes does apply to clusters containing both thunderstorms and stratiform clouds. Such cloud clusters are responsible for most of the extreme flash flood inducing rainfall.

"Assuming the temperature changes projected for the coming decades under climate warming, extreme rainfall may indeed reach unprecedented risk levels for humans and infrastructure, especially in urban areas," the authors stress.