The Mechanics of Rain Formation

When water evaporates from the earth’s surface, it is carried into the atmosphere as invisible vapour. Mainly because the vapour-laden air cools as it rises, a point is reached when the air is no longer able to hold water in the form of vapour. The altitude at which this happens is known to meteorologists as the Lifting Condensation Level. Further cooling by ascent above this level leads to condensation of water vapour in the form of visible clouds. Condensation inevitably takes place on minute nuclei. Eventually when the cloud droplets become large enough they fall as drizzle or rain.

Let us now consider the stage between the first condensation of vapour and the subsequent formation of rain. We refer to the myriads of floating droplets that we recognize as clouds. There are good theoretical reasons to explain why condensation at temperatures below the freezing point should be in the form of ice crystals. The saturation vapour pressure needed to maintain an ice crystal in equilibrium is considerably smaller than the corresponding value for a water droplet.

Imagine, then, that in the upper reaches of a cloud we have a mixed population of water droplets and ice crystals. We cannot entirely rule out the possibility of finding water droplets at sub-freezing temperatures because, we can see, water may exist in a super-cooled state. But because water vapour condenses more readily on an ice crystal at these low temperatures, it follows that the number of water drops will gradually dwindle. Eventually, in the course of time, the entire population should become one of ice crystals. Calculations show that the transformation of a super cooled cloud could be indeed accomplished in a matter of minutes. Moreover, it would not be unreasonable to assume that some of the ice crystals would eventually acquire large dimensions at the expense of the smaller ones. In the course of time, these larger crystals would fall more rapidly into the warmer lower atmosphere. In these warmer regions we may expect them to melt into raindrops. In the last stage of the cycle, we should see them as raindrops falling from a cloud.

This was the basis of an important theory on rain formation put forward by a Swedish meteorologist Bergeron in 1933. It was strongly supported by Findeisen in 1938. In substance, this theory asserts that all rainfall was, in effect, melted ice or snowflakes.

The theory had a few attractive, features that were well supported by observations. First observations tell us that rain bearing clouds are of large vertical growth. They are thick enough to reach the higher levels with sub-freezing temperatures, where the ice phase is almost invariably present. Such clouds have been known to exhibit a sudden transformation when rain begins to fall. The upper ‘anvil’ in a rain bearing cloud suddenly puts on a fibrous appearance, probably because of the presence of a large number of ice crystals. The freezing process does appear to play an important role in the rainfall observed from such clouds.

But the difficulty with Bergeron-Findeisen theory lay in the fact that rain was also observed from clouds that did not extend up to the freezing level. In India, during the southwest monsoon months, quite a few observations have been made of rain from low clouds, whose tops were far below the freezing levels.

In the last decade or so it was increasingly realised that although the ice phase was important, it was not essential for rain formation. In ‘warm’ clouds, that is, in clouds that did not reach the level of the freezing point, the formation was brought about by coalescence between falling water drops.

Consider a ‘warm’ cloud in which we have a population of cloud droplets and the ice phase is entirely absent. If we leave out of consideration the random irregular motion of drops by turbulent fluctuations of winds, it follows that all the drops will gradually begin to settle down under the force of gravity. Eventually, each liquid drop acquires a steady speed of fall that is known as its terminal velocity.

It is of some interest to note that the resistance offered by air follows an interesting law. For a large and heavy body, such as a brick or a stone air resistance is clearly of little consequence. But, for extremely light bodies, such as, a feather or a falling raindrop air drag is important because it determines the speed of fall. For smaller water drops of radius less than 25 microns, the terminal velocity is directly proportional to the square of the radius. This important result was predicted by Sir George Stokes more than a century ago.

Accordingly, a droplet of radius 25 microns would take about 4 hours to fall through a cloud that is 1000 metres thick. Stokes Law is not valid for the larger water drops of drizzle or rain. There is as yet no uniform law by which one can relate the terminal velocity of a spherical body with its size.

Reverting back to the population of floating drops, we can now see that the larger drops would fall at a faster rate because of their greater fall speed. On their downward path, they would encounter several smaller ones that owing to their smaller fall speed, do not have time to get out of the way. Would these smaller drops, then, be captured by the larger ones?

A part of the smaller drops would be captured and in all probability, would combine with the large drop, but there are other mechanisms that are difficult to estimate. In the first place, it is not obvious that two water drops coming together would coalescence. It is difficult to find out, by laboratory experiments alone, what happens when two small water drops meet. The little experimental evidence that there is at present suggests the possibility of a bounce-off following collision. When two drops collide, their respective spherical shapes are distorted. Collision would then be followed by coalescence. But, on the other hand, if the colliding drops are of almost equal size, there is no certainty that collision would lead to coalescence.

A considerable volume of theoretical work has been directed to ascertain the rate of rain formation by coalescence. Most theoreticians base their computations on the assumption that each collision between two drops leads to coalescence. The indications provided by these theoretical studies are that, in the initial stage, the growth of a droplet by progressive condensation of water vapour proceeds more rapidly than the coalescence mechanism, until the drop acquires a radius of 15 microns. Thereafter, the rate of growth by coalescence begins to predominate. It is likely that in clouds of large vertical extent, growth by condensation of water vapour on ice crystals initiate the precipitation mechanism. The subsequent development of rain must be the result of a combination between coalescence and progressive condensation.


Excerpt from “The Monsoon” by Dr.P.K. Das, former Director General of the National Meteorological Service of the Government of India. Published by the Director, National Book Trust, India. Price Rs.75.00