Volume of Water in the World.
The total volume of water is 1.4 × 109 km3 (1.4 billion cubic kilometres). What would
that look like as a very large “drop” of water? We can easily calculate the diameter of
such a spherical drop.
The volume of a sphere is given by: 4.π. r3 where r is the radius of the sphere.
3
Therefore:
4
. .r 3  1.4  10 9 km3
3
3  1.4  10 9
3
r 
4.
4.2  10 9
r3 
12.566
3
r  0.3342  10 9
r  3 0.3342 109
r  0.6939  10 3
r  693.9 km.
The large water drop would have a diameter of 1,387.8 km, i.e. it would be about one
ninth of the diameter of the Earth.
Volume of Fresh Water in the World.
However, only 3% of the water on the Earth is fresh water, all the rest is saline. We
rely on this 3% to meet our needs. If all the fresh water existed as a single large drop,
how big would that be?
3% of 1.4 × 109 km3 is 42 × 106 km3. We do the simple calculation the same way as
before.
Therefore:
4.  .r 3  42  10 6 km3
3
3  42  10 6
r3 
4.
126  10 6
r3 
12.566
r  3 10.02  10 6
r  2.156  10 2
r  215.6 km.
This large drop of fresh water would have a diameter of 431.2 km.
Even this is not the complete story, as at least 50% of the fresh water is locked up in
ice-caps and glaciers.
Volume of Liquid Fresh Water in the World.
The total volume of fresh water is 42 × 106 km3. Half of this is 21 × 106 km3. What
would be the size of the large drop of liquid fresh water?
We do the calculation as before.
Therefore
4  .r 3  21  10 6 km3
3
3  21  10 6
r3 
4.
63  10 6
3
r 
12.566
3
r  5.013  10 6
r  3 5.013  10 6
r  1.711  10 2
r  171.1 km
The liquid fresh water drop would have a diameter of 342.2 km.
A Summary of these relative diameters is shown in Table 1 below
Table 1. Diameter of the Earth compared with those of various
purities of water.
Body
Earth
All Water
All Fresh Water
All Liquid Fresh Water
Diameter (km)
12,742
1,387.8
431.2
342.2
Potential Sea Level Rise due to Melting of the Ice.
If all the ice around the world was to melt, what would be the resulting rise in sea
level? The total area of the Earth’s sphere is 510.064 × 106 km2. Of this area 71% is
covered with water.
Therefore, the total area of the world’s seas and oceans is 362.145 × 106 km2. If we
take the volume of the ice as 21 × 106 km3, and divide this volume by the area, we
shall obtain the potential sea level rise that would be brought about by melting.
21  10 6
Therefore: Depth 
362.145  10 6
Depth  0.058 km.
Depth  58 m.
How accurate is this figure? The volume of ice is larger than that used in the
calculation, as the volume of water in the ice caps is possibly over 60% of the fresh
water on Earth. However, the ice on the Arctic ocean is floating ice, and if it were to
melt it would have no effect on sea level. The Greenland and Antarctic icecaps being
on land would raise the sea level if they melted. So we have two factors, one which
would increase our estimate, and one which would reduce it. There is also the
consideration around most of the world’s coastlines, the land slopes gently upwards as
it moves inland. This means that the depth of inundation will tend to be less than the
estimate, and that a sea-level rise of between 50 and 60 metres is therefore a good
estimate in all probability.
If the ice did melt and sea level rose by 60 metres, then the coastline would follow the
60m contour line on all maps. As a result many of the world’s largest cities would be
inundated and would disappear. The list of cities that would be lost includes London,
New York, Calcutta, Sydney, St. Petersburg, Hamburg, Copenhagen, Stockholm,
Riga, Amsterdam, Tokyo, Hong Kong, and so on. Several hundred million people
would be displaced, and millions of hectares of arable land would disappear, a
scenario that would be catastrophic. There would be two main consequences; the
same population would be accommodated on a smaller are of land, giving a higher
population density, and the needs of the population would have to be met from a
reduced land area. If arable land was lost by inundation, for example, then there
would be less land to produce the food required. The loss of the infrastructure of the
flooded cities, would pose huge problems in meeting the needs of the displaced
populations. The Earth is already under tremendous population pressure, and this
scenario would make matters very much more difficult.
Conclusions.
These calculations help to illustrate how critical the support of the world’s peoples is
becoming, in terms of water supplies. Fresh water is a finite resource, and is being
accessed by a rapidly growing population. Significant global warming, such as seems
to be occurring, will result in a reduction of the amount of available fresh water,
because the melt waters will all go into the seas and become saline.
John L. Sturges
July 2009.