**Document ID**: 02_10_97_1

**Date Received**: 1997-02-10 **Date Revised**: 05/17/99 **Date
Accepted**: 05/09/97

**Curriculum Topic Benchmarks**: S1.3.2, M1.3.2, S2.4.1, M1.4.2

**Grade Level**: \[6-8\] Middle School

**Subject Keywords**: Ice sheets; sea level rise

**Rating**: Moderate

**Ice Sheets and Sea Level Rise**

**By**: Claire L. Parkinson, Oceans and Ice Branch, Code 971, NASA
Goddard Space Flight Center, Greenbelt MD 20771 e-mail:
clairep@neptune.gsfc.nasa.gov

**From**: The PUMAS Collection http://pumas.jpl.nasa.gov

©1997, California Institute of Technology. ALL RIGHTS RESERVED. Based on
U.S. Gov\'t sponsored research.

**Audience**: Geography or Earth Sciences students in middle school and
high school. No math is required beyond basic arithmetic.

**Background**: The ice sheets of Greenland and Antarctica contain
massive amounts of frozen water (i.e., ice) that, if broken off or
melted, for instance from extended global warming or from outward ice
flow, would go largely into the oceans. In view of the vast size of the
oceans, covering over 70% of the Earth's surface area, many people might
at first think that the addition of ice or melted ice from the ice
sheets would have little impact on global sea level. The numbers prove
otherwise, however, and doing the calculations helps to instill this
fact as well as recognition of the vast size of the Earth's two major
ice sheets. The Antarctic ice sheet, for instance, has an area far
exceeding the area of the United States, and over sizable regions its
ice extends to a depth of greater than 2 miles (3.2 kilometers).

**Exercise**: Determine the amount that sea level would rise, averaged
around the globe, in response to the complete melting of (a) the
Greenland ice sheet, (b) the Antarctic ice sheet, and (c) both the
Greenland and Antarctic ice sheets.

**Needed information**: The calculations require the area of the Earth's
oceans and major seas (either as a total or as individual areas to be
added), the volume of the ice sheets overlying land, the densities of
ice and water, and knowledge that glacier ice is fresh-water ice rather
than sea-water ice. This information can be obtained by the students
from a world atlas or various other sources, or it can be handed to them
in the form of tabulated information, as in Tables 1-3.

**Table 1. Water Areas of the Earth.**

**[Ocean or Sea]{.underline}** **[Area (in square
kilometers)]{.underline}**

Pacific Ocean 166,241,700

Atlantic Ocean 82,522,600

Indian Ocean 73,426,500

Arctic Ocean 14,056,000

Caribbean Sea 2,512,300

Mediterranean Sea 2,509,700

Bering Sea 2,266,250

Gulf of Mexico 1,554,000

Sea of Okhotsk 1,528,100

East China Sea 1,248,400

Sea of Japan 1,007,500

Hudson Bay 822,300

North Sea 575,000

Black Sea 479,150

Red Sea 437,700

Baltic Sea 422,170

Remaining surface water area 9,522,630

Source: *Hammond Citation World Atlas*, Hammond, Maplewood, New Jersey,
1992, p.352.

**Table 2. Ice Sheet Areas and Thicknesses.**

**[Ice Sheet]{.underline}** **[Area (in square
kilometers)]{.underline}** **[Average Thickness (in
kilometers)]{.underline}**

Greenland 1,736,095 1.50

Antarctica 11,965,700 2.45

Source for the Greenland data: Williams, R. S., Jr., and J. G. Ferrigno,
editors, Preface, *Satellite Image Atlas of Glaciers of the World:
Greenland*, USGS Professional Paper 1386-C, United States Geological
Survey, Washington, DC, 1995, p.v.

Source for the Antarctic data: Swithinbank, C., Antarctica, *Satellite
Image Atlas of Glaciers of the World: Antarctica* (Richard S. Williams,
Jr., and Jane Ferrigno, editors), USGS Professional Paper 1386-B, United
States Geological Survey, Washington, DC, 1988, p.B12.

**Table 3. Densities.**

**[Substance]{.underline}** **[Density (in kilograms per cubic
meter)]{.underline}**

Fresh water Approximately 1000

Glacier ice Approximately 900 (generally between 830 and 917)

**Solution**: (1) Add the areas of the oceans, major seas, and other
surface water areas (lesser seas, bays, etc.) from Table 1, obtaining
361,132,000 square kilometers. This is the area over which the added
water must be averaged to obtain the resultant sea level rise.

\(2\) Calculate the volume of each ice sheet, by multiplying the
ice-sheet areas by their average thicknesses, all provided in Table 2,
obtaining ice sheet volumes of 2,604,142 cubic kilometers and 29,315,965
cubic kilometers for Greenland and Antarctica, respectively.

\(3\) Convert the Greenland and Antarctic ice sheet volumes to the
approximate volumes of water that would result if the ice sheets were to
melt. To do this, first calculate the ice mass, by multiplying the ice
volume obtained in #2 by the ice density provided in Table 3. Then,
recognizing from the principle of conservation of mass that the mass
remains the same when the ice melts, divide by the density of water to
obtain the corresponding water volume. The net calculation is simply a
multiplication of the ice volumes by 0.9, obtaining water volumes of
2,343,728 cubic kilometers and 26,384,368 cubic kilometers for Greenland
and Antarctica, respectively.

Note: Ice that calves into the ocean, becoming a floating iceberg, has
the same effect on sea level as ice that melts and flows as liquid water
into the ocean. This is because, by Archimedes' principle, the iceberg
displaces the same volume of water as the volume of water that its
melting would produce. Teachers and students can instructively
demonstrate this using a see-through bowl (or beaker), water, and one or
more ice cubes. First fill the bowl part way with water, leaving
sufficient space at the top to allow the ice cubes to be added without
overflowing, but being careful also to have the water deep enough so
that the ice cubes will float. Mark the level of the water surface on
the bowl. Then add the ice cubes and mark the new, higher level of the
water, representing sea level rise. Finally, allow the ice cubes to melt
and notice that the level of the water is the same after the melting as
it was when the ice cubes were floating.

\(4\) Calculate the sea-level-rise answers by dividing the water volumes
determined in #3 by the global surface-water area determined in #1,
thereby spreading the effect of the ice sheet's water throughout the
expanse of the Earth's surface-water area. The answers are: (a)
(2,343,728 cubic kilometers)/(361,132,000 square kilometers) = 0.0065
kilometers = 6.5 meters for the Greenland ice sheet; (b) (26,384,368
cubic kilometers)/(361,132,000 square kilometers) = 0.0731 kilometers =
73.1 meters for the Antarctic ice sheet; (c) 6.5 meters + 73.1 meters =
79.6 meters for Greenland and Antarctica together.

**Further suggestions**: Have students look on a map with contour lines
of heights above sea level to see the geographic effects that the
calculated sea level rises would have. For instance, in the event of a
complete melting of both Greenland and Antarctica, Florida would be
almost completely underwater, although the peaks of some Florida hills
would remain above sea level, as islands off the reduced North American
continent. Students should consider whether or not the current location
of their community would be underwater.

**Qualifiers**: (a) There are approximations and uncertainties in
several of the numbers used in the calculations, and hence the answers
should be considered as only roughly correct. (b) Strictly speaking, the
calculations assume that the oceans and seas have vertical sides, with
the area covered by water remaining constant throughout the process of
sea level rise. Instead, as sea levels rise, the area covered by water
would increase, which would reduce the magnitude of the rise. Still, in
spite of the cautions of (a) and (b), the calculations outlined above
provide a reasonable first-order estimate of the sea-level-rise
response. (c) No knowledgeable person expects the Greenland and
Antarctic ice sheets to disappear completely within the lifetime of
anyone alive today, or within the lifetime of any of their children or
grandchildren. Hence, the threat of a 79.6-meter sea level rise should
not be seen as an immediate concern.

Much smaller rises in sea level, however, might well occur and in fact
sea level appears to have risen approximately 0.2 meters over the past
century. The twentieth-century sea level rise has resulted partly from
thermal expansion of the water due to warming and partly from melting of
mountain glaciers. It is not certain how much if any of the
twentieth-century rise has resulted from changes in the Greenland and
Antarctic ice sheets, due to a lack of adequate data. These two ice
sheets, however, are the largest potential contributors to sea level
rise, and concern has been raised in particular over the possibility
that the portion of the Antarctic ice sheet termed the West Antarctic
ice sheet, lying largely in the western hemisphere, might be unstable
and might decay relatively rapidly, perhaps even causing sea level rises
of several meters within 100 years. Although such a decay is not highly
probable, it is possible, and if it were to occur, the resulting
several-meter sea level rise would cause serious economic and personal
consequences to all highly populated low-lying coastal regions.