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How much does a cloud weigh?

In our blog the other day we looked at one of the weather-related documentaries that the BBC is currently showing on our screens, that is Operation CloudLab: Secrets of the Skies. Its first episode appeared on Wednesday 16th of July and a team of scientists take to the skies in one of the world's largest airships for a unique exploration of the Earth's atmosphere and to discover the many ways it shapes our world. We took a look at what the first episode covered in a recent blog post which you can read here.

One of the interesting questions they asked (and answered!) is "How much does a cloud weigh?"

For many of us, when we look up at the skies, even on dull rainy days, those bubbling clouds look lighter than air (they are floating up there after all!) and we think to ourselves that they surely couldn't weigh all that much! Even when they are laden with rain and those raindrops are pelting off our lovely umbrellas, we rarely think too much about where those raindrops came from and why they are now suddenly falling.

Well, one of the first tasks that the team in Operation CloudLab, led by Meteorologist and explorer Felicity Aston, explore is just how much water is contained in a cloud. They fly the airship up to a single cumulus cloud and by using onboard laser (LIDAR) measurements, they work out the rough dimensions of a single cumulus cloud. As they progress through the cloud they measure the size and density of the water droplets contained in that cloud, and with these measurements, a simple calculation allows them to work out its overall weight!

Here comes the science bit...

Step 1 - Calculate the dimensions of the cloud

In the documentary they assume that the singular cumulus cloud is an ellipsoid in shape. This is a realistic assumption, as the cloud they choose is elongated in one direction, and of similar width/height in the other two dimensions. Sure, cumulus clouds are irregular in shape, but the ellipsoid will provide a good approximation of the overall shape, and make the calculation easier to undertake.

  • The length of the cloud they take to be: 960 metres
  • The width of the cloud is around: 200 metres
  • The height of the cloud, is: 200 metres

Now we have our dimensions, we can calculate its overall volume.

Step 2 - Calculate the volume of the cloud

Now, this bit will take us back to high-school maths, but the Volume of an Ellipsoid is calculated by taking each of the measurements above and multiplying them by pi/6 (where pi = 3.14159...) So basically, the formula for the volume is:

So this works out as: Volume = pi/6 x (960 x 200 x 200)

Which gives us an overall volume of 20,106,192 cubic metres! Yes, you read right, that's 20 million cubic metres in a single cumulus cloud! But how much does it weight?

Step 3: Calculating the weight of a cloud

In order to calculate the weight of a cloud (i.e. its mass) we need to know one more thing, just how much 'stuff' is compacted in there. That is, we need to know its density. In the programme they measure the density by flying through the cloud and measuring the overall size of the water droplets and number of them. Giving an overally water density of around 0.2 g/cubic metre.

So from here the weight calculation is simple:

Giving us Weight = 20,106,192 x 0.2 = 4,021,238 g

Yes, that's right, a small cumulus cloud weighs 4 million grams, or 4000 kg, or if you prefer 4 tonnes!

So next time you look up at the sky, even on a dry day, those small 'light' clouds are anything but! They are carrying vast amounts of water that will eventually fall as rain.

Created On  20 Jul 2014 20:57  -  Permalink


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