The Melting of the Greenland IceSheet and the Rise in Global Sea-Level
Chapter 01 Project
Math 018
Joe Kudrle
1. What is the approximate volume of the ice contained in the Greenland Ice Sheet? Give your
answer in cubic kilometers. Please give your answer in scientific notation.
The volume of Greenland Ice-Sheet is approximately 3.832  106 cubic km.
Using the Greenland map, an approximate measurement on the thickness of the Ice-Sheet
covering the island was determined by using the following method.

It was first noted that each grid square on the map accounted for a 200 km by 200 km
(40,000 square kilometer) region.

The map was then broken into four regions dependent on the thickness of the ice
covering the region. The four regions had ice-thicknesses ranging from 0 km to 1 km, 1
km to 2 km, 2 km to 3 km, and 3 km to 3.1 km (which is the maximum thickness of the
ice-sheet on Greenland).

The number of grid squares within each region was counted, allowing for a quick
computation of the approximate area of the region using the formula:
Area of Region  Number of Grid Boxes in Region 
40000 km2
1 Grid Box

To compensate for the varying ice-thicknesses within each region, an average, based on
the lower and upper bound, was found.

The volume for each region was then computed using the formula:
Volume of a Region = Area of a Region × Average Thickness

The total volume resulted from a quick sum of these volumes.
Note: All information and work can be found in the table shown below.
Ice-Thickness
(km)
0–1
1–2
2–3
3 – 3.2
Average Thickness
# of Grid Boxes
(km)
(count)
0.5
4.5
1.5
13.25
2.5
25.75
3.1
3
Total Volume of Ice-Sheet
Area
(square km)
180,000
530,000
1,030,000
120,000
Volume
(cubic km)
90,000
795,000
2,575,000
372,000
3,832,000
2. Based off of your approximation from question (1), what is the volume of all land-bound
freshwater ice in the world? Give your answer in cubic kilometers. Please give your answer in
scientific notation.
The volume of all land-bound freshwater ice in the world is approximately 3.484  107 cubic km.
Using the fact that the Greenland Ice-Sheet accounts for about 11% of the world’s land-bound
freshwater ice, the following proportional equation was used to compute the answer.
Greenland 3.832  106 km3 11
:

World
World
100
World 
3.832  106 km3  100
 3.484  107 km3
11
3. Assuming that all of the land-bound freshwater ice in the world has melted, what would be the
resulting volume of water? Give your answer in cubic kilometers. Please give your answer in
scientific notation.
Once all of the ice has melted the volume will be 3.135  107 cubic km.
Using the fact that when ice melts, it contracts to 90% of its original volume, the following
equation was used to compute the answer.
Water
Water
90
:

7
3
Ice
3.135  10 km 100
Volume of Water = 0.90  3.484  107 km3  3.135  107 km3
4. How many Olympic swimming pools could be filled by the resulting melt from all land-bound
freshwater ice? Give your answer rounded to the nearest whole number. Please give your
answer in scientific notation.
It was determined that approximately 1.2541  1013 Olympic size swimming pools could be filled
with all of the ice-melt.
Using the fact that one Olympic size swimming pool holds 2.5 million liters, the following
method was used to compute the answer.
Volume of Water = 3.135  107 km3 
Number of Pools = 3.135  1019 L 
109 m3 1000 L

 3.135  1019 L
1 km3
1 m3
1 Pool
 1.2541  1013 Pools
2.5  106 L
5. Assuming that all of the land-bound freshwater ice in the world has melted, how high will the
ocean’s rise? Give your answer in meters. Round your answer to two decimal places.
The approximate rise will be 91.9435 meters.
Using the fact that the surface area of the Earth’s oceans is known to be 3.62  108 , the
following method was used to compute the answer.
Volume = Area × Height
Height =
Volume 3.135  107 km3
1000 m

 0.0919435 km 
8
2
Area
3.62  10 km
1 km
Heigth = 91.9435 m
6. If we use 2013 as a starting point, what year will it be when all of the land-bound freshwater ice
has melted? Give your answer as a year.
Based on some quick calculations, it will take about 3600 years and it will be the year 5607 when
all of the land-bound freshwater ice has melted.
Using the fact that in 2007 the rise in sea-level is about 1.7 mm per year and this rate is
accelerating by 0.013 mm per year per year, we can make an approximation on the time that it
would take for the sea-level rise to reach a level of 91.9435 m or 91,943.4 mm.
Assume that the year 2013 is time t = 0, we start by looking at time in 1000 blocks.

Rise in sea-level at time t = 0 is 1.7 mm per year and the rise in sea-level at time t = 1000
is 1.7  1000  0.013  14.7 mm per year. This averages out to 8.2 mm per year over the
1000 years. So, over the first 1000 years, sea-levels would rise by about 8,200 mm.

Rise in sea-level at time t = 1000 is 14.7 mm per year and the rise in sea-level at time t =
2000 is 1.7  2000  0.013  27.7 mm per year. This averages out to 21.2 mm per year
over the 1000 years. So, over the second 1000 years, sea-levels would rise by an
additional 21,200 mm. So, after 2000 years, total sea-level rise is about 29,400 mm.

Rise in sea-level at time t = 2000 is 27.7 mm per year and the rise in sea-level at time t =
3000 is 1.7  3000  0.013  40.7 mm per year. This averages out to 34.2 mm per year
over the 1000 years. So, over the third 1000 years, sea-levels would rise by an
additional 34,200 mm. So, after 3000 years, total sea-level rise is about 63,600 mm.

Rise in sea-level at time t = 3000 is 40.7 mm per year and the rise in sea-level at time t =
3600 is 1.7  3600  0.013  48.5 mm per year. This averages out to 44.6 mm per year
over the 600 years. So, over these 600 years, sea-levels would rise by an additional
26,760 mm. So, after 3600 years, total sea-level rise is about 90,360 mm.

This process could continue and we could make our answer slightly more accurate.
7. A rise in sea level will certainly cause flooding in coastal regions around the world. To explore
the severity of flooding, search the World Wide Web to find and compare the elevations of two
coastal cities. Of course, the elevation of any region is not constant, but varies according to
local topography.
Finding elevations of regions outside the U.S. will require some searching. Beware that some
maps give elevations in feet and some in meters, but often will not indicate which unit is being
used!
a) List the two locations that you are comparing, along with their average elevations in meters.
List the source(s) from which your data was obtained.
Open answers.
b) Using a similar process as problem (6), calculate the year in which each of your locations
would be “swallowed by the seas,” if possible.
Open answers.
c) Give one example of the type of environmental damage that would be caused by the
flooding of the coastal regions? Is this type of damage already being seen in certain coastal
regions? Be specific with your example and elaborate in a paragraph or two.
Open answers.
d) Describe two different ways that you might measure the environmental damage of flooding
in coastal regions. Be specific with how you plan to measure environmental damage and
elaborate in a paragraph or two.
Open answers.