If the Terrestrial Poles Were to Melt...
Problem:
If the terrestrial poles were to melt, then estimate how much the earth's
oceans would rise.
Solution:
If the poles
melted, then
-
The
north polar ice would make essentially no contribution since it
is float ice.
-
The
south polar ice would make a considerable contribution since it
overlays the Antarctic land mass and is not float ice.
First,
let us estimate the total volume of the south polar ice. We begin by
noting that, on the Earth, 1 degree of latitude corresponds to a distance
of 69.2 mi. Now, using a well marked map, Antarctica may be estimated
as having an angular radius of 18 degrees of latitude, or a radius in
miles of rA = 69.2 mi/deg x 18 deg = 1.25 x 103
mi. Its estimated surface area is then rA2
= 4.91 x 106 mi2. If we assume the average thickness
of the Antarctic ice to be 1 mi, then the total ice volume is
VIce
= 4.91 x 106 mi3.
If
this ice melts, the resulting volume of liquid water is 4/5 of this
value or
VWater
= 3.93 x 106 mi3.
Now,
let this volume of water be spread in a uniform, thin shell over a uniform
Earth (for the moment, we will ignore the continents). The total surface
area of the Earth is AE = 4rE2
= 1.97 x 108 mi2, where rE = 3.96 x
103 mi. Since the thickness of this shell, rE,
may be assumed to be << the Earth's radius, rE , we
may write
3.93
x 106 mi3 AErE1
or,
rE
= 1.99 x 10-2 mi = 105 ft.
If
we now return the continents to their proper place, it is easy to see
that the value of rE
must become larger. Since only 2/3 of the earth's surface area is ocean,
the thickness of the water shell must be increased by a factor of about
3/2:
rE
= (3/2) x 105 ft = 158 ft. 2
Thus,
we have estimated that if the polar ice were to melt, the Earth's oceans
would rise by about 150 ft. Reference to a map showing land elevations
allows us to determine that coastal areas and major river valleys (such
as the Mississippi or the Amazon river valleys) would be flooded. The
land distribution would appear somewhat differently than it does on
the globe today. But the majority of land would still be above sea level.