Global Warming and Antarctic Ice Melting
If the Antarctic ice sheet melted, how much sea level rise would occur? Would we have
oceanfront property in Raleigh?
The Hard Way: We'll spread the ice in Antarctica over about 3/4 of the earth's surface,
but pretend we can't look up any information. All we know off hand is that the earth has a
radius of 6000 km and that the Antarctic ice sheet is about 2 km thick.
First calculate the total surface area of the global ocean (covers 3/4 of the earth).
Ocean area = 3/4 x 4 x pi x (6000 km)2
Now use the approximation that 3 x pi ~ 10
= 10 x 36 x 106 km2
= 360 million km2
But we have no way to estimate the area of Antarctica, so we looked that up>
Antarctic area = 15 million km2 => volume = 30 million km3
Divide the volume by the area to get the thickness
30 million km3 / 360 million km2 = 1/12 km = 83 m
The Easy Way: Look up the surface area of the ocean and the volume of the Antarctic ice
sheet.
 ocean surface area = 360 million km2
(source: http://en.wikipedia.org/wiki/Ocean)
 volume Antarctic ice sheet = 30 million km3
(source: http://hypertextbook.com/facts/2000/HannaBerenblit.shtml)
Divide the volume by the area to get the thickness
30 million km3 / 360 million km2 = 1/12 km = 83 m
The Easier Way: About 2% of the earth's water is contained in glacial ice; most of that is
in Antarctica. If all that ice melted and ran into the ocean, the ocean would get about 2%
deeper, or sea level would rise by 2% x 4000 m = 80 m.
YAAAY we got the same answer three different ways (victory dance)
So, sea level will rise by about 80 m when the land ice melts. Raleigh's elevation is about
150 m, so we won't have oceanfront property. Interstate 95 may become a coastal
highway in North Carolina. BOOO we've got to change our lifestyle to avoid drowning
half the state.
Energy Calculations Involving Very Large Numbers
Useful Facts
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One m3 of ice weighs 1000,000 g; one km3 of ice weighs 1015 g.
1015 = 1 followed by 15 zeros = 1,000,000,000,000,000 = 1 quadrillion
When you're multiplying large numbers together in scientific notation, you just
add up the exponents.
Latent heat of melting ice = 80 cal/g, heat capacity of water = 1 cal/g/degree.
The United States uses about 100 Quadrillion BTU's of energy each year, and one
BTU = 252 calories.
Questions:
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What is the mass of the Arctic ice cap in grams?
What is the mass of the Antarctic ice cap in grams?
Multiply the area of the global ocean by 0.001 km to calculate the volume of the
top layer of the ocean.
What is the mass of the top layer of the ocean in grams?
How much energy will it take to melt the Arctic ice cap?
How much energy will it take to melt the Antarctic ice cap?
How much energy will it take to raise the temperature of the ocean by 1 degree?
In what order will these changes occur?
How much energy does the US use in 100 years?
Is that greater or less than the amount of energy you calculated above?
1) Mass of Arctic Ice, in grams = 20,000 km3 x 1015 g / km3 = 20 x 1018 g
2) Mass of Antarctic Ice, in grams = 30,000,000 km3 x 1015 g / km3 = 30 x 1021 g
3) Volume of Ocean Surface Layer = 360,000,000 km2 x 0.001 km = 360,000 km3
4) Mass of Ocean Surface Layer, in grams = 360,000 km3 x 1015 g / km3 = 360 x 1018 g
5) Energy to melt Arctic Ice = 20 x 1018 g x 80 cal/g = 1600 x 1018 cal
= 1.6 x 1021 cal
6) Energy to melt Antarctic ice = 30 x 1021 g x 80 cal/g = 2400 x 1021 cal = 2.4 x 1024 cal
7) Energy to warm the surface ocean = 360 x 1018 g x 1 cal/g/oC x 1 oC
= 360 x 1018 cal
8) Order of events: Ocean warming, then Arctic melting, then Antarctic melting
9) US energy use = 100 year x 100 x 1015 BTU/year x 252 cal/BTU = 2.5 x 1021 cal
10) US energy use is similar to energy needed to melt the Arctic ice sheet