What is the approximate mass of a cumulonimbus cloud 100 km^2 X 20 km high?

Just curious. Cumulonimbus clouds can precipitate prodigious quantities of rain and hail. Before precipitation begins what is the mass of the cloud? What percentage of its mass typically precipitates?



Another, related, question: what is the mass of a fair weather cumulus cloud 5 x 5 x 1 km?What is the approximate mass of a cumulonimbus cloud 100 km^2 X 20 km high?
Your answer is difficult to answer. First, to weight a cloud, you must remove it from the atmosphere. This is the only way you can "weight" the air. We can get an approximation by doing this: As the atmospheric pressure is roughly one kilo per square centimeter, you multiply that by the surface of your cloud and remove the part of the air that you don't need. That can't be done without a table because the pressure decrease with altitude but if you use ten kilometer, it would be a good average.

Ten kilometer is, actually about the top of the troposphere at the poles.



Once you get that, you may think: ah, but I have to add the weight of the water, right? Wrong. The specific gravity of a molecule of water is less than that of oxygen or nitrogen. But yes, there is a percentage of water in the air and that depends on the temperature. A cloud at 15 C will contain 13 grams of water per cubic meter. But at 0 C, it is down to 5 grams per cubic meter.



Now, cumulonimbus or fair weather cumulus; it's the same content in water. The only difference is that the former may result in precipitation due to its size. But how does it occur?



For precipitation to happen, the cloud must be further cooled down so that more condensation occurs and that is when the cloud is lifted either by warmer air or by orographic (a mountain) effect and it cools down by the adiabatic effect of a lesser pressure aloft. So, a cloud that produces precipitation, rain or snow, is a cloud that rises! It is only when the droplets or snowflakes get big enough that they overcome the rising by gravitation.



So, how much of the mass is lost by precipitation? That is easy to calculate once you know how much the cloud is rising. You can find the saturation absolute humidity (volume of water per volume of air) at a certain temperature. You also know that the average adiabatic lapse rate is 0.65 C per 100 meters and you can then calculate, e.g:



The cloud that rises 2,300 meters cools down by 23 * 0.65 = 15 degrees. The water content is then 5 / 13 * 100 = 38 percent of what it was. It doesn't mean that the cloud is "lighter" though! It means that it has lost some of its water content but the pressure is equalized by other molecules of air.