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An important question to consider when thinking about global warming is, "If the ice sheets near the poles melt, how much will the sea level rise?" This seems like a difficult question, given the odd shapes of both the ice sheets and the oceans. But there are some accurate approximations that allow the answer to be estimated fairly accurately with reasonably simple calculations.

The critical idea is
that both the thickness of the ice sheets and the amounts of the sea-level
rise are extremely small compared to the radius of the earth. The radius
of the earth is about 2/π x 10^{7} m -- more
than 6000 kilometers. The ice sheet thicknesses we will be concerned
with are single digit miles and the sea level rises will be in dozens
of feet. As a result, in thinking about them, we can essentially ignore
the curvature of the earth. We can imagine peeling the map of the earth
off a globe and flattening it out (by making cuts, not by stretching
it, so that we preserve the area). Then, both the ice and the sea level
rise can be treated as right (not tilted) cylinders (though with funny
shaped bases and tops). Since we know that the volume of a right cylinder
is the area of the base times the height, we can easily estimate all
the volumes we need. A schematic picture of this approximation (with
the height of the ice mass greatly exaggerated -- you couldn't see
it if I didn't) is shown below. The error in these approximations is
on the order of the height of the cylinder considered divided by the
radius of the earth; a very small number.

a.
Assume that (after flattening the surface of the earth in our
imaginations) the ice sheet to be considered covers an area, Generate
an equation that will allow you to calculate b. As shown in the combined satellite photo on the right (from Google Earth), Greenland is covered by a sheet of ice. This ice has been measured to have a mean thickness of about 2 km. Recent observations indicate that this ice sheet is beginning to retreat -- that it is melting at an accelerating rate. Using the depth
of the ice sheet and the scale given on the picture, estimate
how much sea level rise would be produced by the melting of the
entire ice sheet lying on Greenland. ( c. Find a website that allows you to see what the coast of Florida would look like if the sea level rose the amount you calculated. Include a printout of this picture as part of your solution and give a brief reason why you trust this site. |

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Page last modified February 3, 2010: G27