The theory reveals that the mobility of droplets, which the scientists define as their ability to move with surrounding air, is inversely related to their "effective terminal velocity" (ETV). This is defined as the average of all droplet terminal velocities – their maximum speed when falling – weighted by their mass. Since droplet mobility is a key factor in cloud behaviour, and since aerosols have an impact on ETV, the theory should provide a new way of linking cloud behaviour to aerosol conditions.

"Droplet mobility is a key property of the cloud that will determine much of the way by which water will be distributed, how tall a cloud can be, rain formation and many [other] key properties," said Ilan Koren of the Weizmann Institute of Science, Israel,. "The beauty of ETV is that it can be easily calculated."

The basic mechanism of convective cloud formation requires rising humid air. As the air's altitude increases it cools, pushing its humidity to saturation. At full saturation droplets begin to condense and form a cloud – as long as there are aerosol particles for them to condense around.

When there is a low concentration of aerosols the cloud droplets are large but few, but for a high concentration of aerosols the droplets are small and numerous. The movement of these droplets is important because it affects the distribution of water.

"All cloud properties – reflectance, extent, lifetime, onset of rain and rain duration – depend on the way in which condensed water is distributed in a cloud," said Koren.

Droplets with a greater ETV fall relatively fast and are less inclined to move with the air motion, according to the researchers. Greater ETV is found in larger droplets, which are generally produced alongside low aerosol concentrations; lower ETVs are found in smaller droplets amid plentiful aerosols and pollution. "We have seen that the ETV or mobility effect is very strong, and can explain a great part of the difference between clean and polluted cloud evolution," said Koren.

In addition, Koren and colleagues have shown that the dispersion of ETV – a measure of the standard deviation of the ETV distribution relative to its mean – can characterize the point at which droplets begin to collide and coalesce with each other. "Rain formation depends strongly on the collision–coalescence process," Koren explained. "Without it droplets cannot grow from tens of microns to the millimetre scale in a realistic timescale."

The team reported their results in Environmental Research Letters (ERL).

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