### Re: What is the average weight of a cloud?

Date: Thu May 21 19:46:33 1998
Posted By: John Christie, Faculty, School of Chemistry, La Trobe University, Bundoora, Victoria, Australia
Area of science: Earth Sciences
ID: 893104173.Es
Message:
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The problem with this question is that it is difficult to define things
precisely. If we are talking about woolly clouds (cumulus) it is fairly
clear how big "a cloud" is, although we should remember that sometimes
there are little broken off bits. If we were to count them as separate
clouds, it would make the average smaller! But what about storm clouds
(nimbus) that might cover the whole of the sky for an area 100 kilometres
in any direction? Or the high up wispy clouds, or mares' tails, or mottled
clouds, or thin hazy cloud (cirrus, stratus, cirrostratus) -- do we count
the separate strands or lumps as parts of a single cloud, or as separate
clouds?

Surprisingly, there is also a problem with the idea of an average when
there is a large range of sizes involved. Let me give an example: What is
the average size of the particles in concrete mix? You might think that
that is fairly easy. You make up concrete by taking one part (by weight) of
Portland cement, two parts of sand, and three parts of screenings. The
particle size in the Portland cement is 0.01 mm, in the sand it is 1 mm,
and in the screenings it is 10 mm. so the average is

(0.01 x 1 + 1 x 2 + 10 x 3)/6, which comes to 5.3 mm.

But if you were to take a sample, and actually count the particles, you
would find, typically, that there were 1 billion cement particles for each
2 thousand sand particles for each 3 lumps of screenings. The average would
be

(0.01 x 1 000 000 000 + 1 X 2 000 + 10 x 3)/ 1 000 002 003

which comes to 0.01 mm ! Which is the 'true' average?

Scientists actually talk about the 'number average' and the 'mass average'
in these sorts of circumstances. Their values can be quite different. The
number average mass of clouds would be quite different to the mass average.

Finally, what do we mean by "the weight of a cloud". Are we referring to
just the weight of the ice crystals in the cloud, or do we also include the
weight of the air contained in the cloud? There is about 100 times as much
air as ice in a typical cloud!

So let us get back to clouds. I am going to talk about the "typical weight"
of a cloud, rather than the average weight. I am going to talk just about
the ice, not the air that is also present. And I am going to talk about a
cumulus or cumulonimbus cloud -- the sort of woolly cloud that forms at a
reasonably low height when humid air rises, and that might later turn
darker coloured and lead to a thunderstorm type shower of rain.

There are two ways that I can think of of estimating the weight of the
cloud. The first and easiest is by thinking about the rainfall it might
produce. An estimate of 5 mm of rain in an area 8 x 5 km seems not
unreasonable for a single bank of showery cloud. (Translating for those who
do not use international units, that means 20 points of rain over a 5 x 3
mile area). That amounts to a volume of 200 000 cubic metres of water,
which would weigh 200 000 tonnes (I am much more comfortable with metric
units. I will not stretch my translation skills any further, except to say
that tonnes and tons are near enough to the same thing).

The other way of estimating the weight of the cloud is a bit harder. You
think about the water content of the parcel of air it comes from. Suppose
that the air started off down at sea level at 25 deg C and 70% humidity.
Then when that air rises it gets to a colder temperature, and soon it can
no longer hold its water vapour content, and ice crystals start to form. We
can calculate that the humid air contains about 16 g of water vapour per
cubic metre, and somewhere between half and all of this will finish up as
ice crystals in the cloud. If we work on this basis, then the ice in a lump
of cloud that comes from an air parcel about 1 km long by 1 km wide by 200
m thick turns out to weigh 1 600 to 3 200 tonnes.

If you have ever looked at satellite photographs of cloud, you will have
seen tropical cyclones (hurricanes), where a bank of unbroken cloud
stretches for perhaps 300 to 500 km in all directions from the centre of
the storm. And you will have seen cloud banks associated with cold fronts,
stretching perhaps 1000 km long and 50 km wide. If you regard these as
single clouds, then they are huge. Wispy, high altitude clouds, on the
other hand, can be really very thin and light.

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