Question

So I was looking out the sky one day and I wondered how I would go about calculating how much water was contained in a cloud. I figured the following simple outline

1) We need to roughly know how big it is. We'll also be figuring out how high the cloud is. Use some sort of geometric method? Triangles?

2) We need to relate its color to its density. (Darker clouds more dense) (White fluffy clouds less dense)

3) Correction factors due to lighting conditions during different parts of the day.

Can some body help me figure out the relevant calculations needed? Or how much water does a cloud contain based on its category?

Answer 1

If you are just standing on the ground and looking up, you will be able to see the base of the cloud. I suggest that your estimate for a cloud more or less directly overhead (and closer) will be more accurate than for distant clouds visible on the horizon. The altitude to the base of the clouds is called the ceiling, and can be measured using a instrument such as a Ceiling Projector. If you observe some horizontal limit to the extent of your cloud, and have measured the altitude of its base, you can use an instrument such as an alidade and then trigonometry to calculate lateral dimensions. From the ground, you won't be able to see the top of the cloud very easily (being obscured by the intervening cloud,) so you will need to estimate the maximum height of the cloud based on an informed guess. A practical way to guess the maximum height of the cloud is to make observations of its appearance and then classify the cloud by qualitative type. Much has been learned and documented about the physical characteristics of the qualitative cloud classes through observational meterology.

Before cloud-physics, there was the natural-science of clouds. I recommend the book: The Invention of Clouds: How an Amateur Meteorologist Forged the Language of the Skies if you are interested in "every-day life physics."

Once you have the extrinsic size of the cloud in mind, you need to know how much liquid water and how much water vapor each cubic meter contains. (Because a cloud is only visible because it contains liquid droplets or ice crystals) You can find some characteristic data for this as well. For example for the liquid water content (LWC):

Cloud Type LWC (g/m3)

cirrus .03

fog .05

stratus.25-.30

cumulus .25-.30

stratocumulus .45

cumulonimbus 1.0-3.0

The content of water vapor (i.e. 100% humidity) depends on temperature and pressure. And the temperature and pressure gradients within the cloud won't be too much different than an adiabatic gradient.

All this can be used to calculate the "total water content" of your cloud. Very roughly. Without proper instruments, and measurements, and possibly a platform such as an aircraft or space satellite - an accurate calculation of how much water is in an actual cloud is going to be very difficult . . .