**Document ID**: 01_07_99_1

**Date Received**: 1999-01-07 **Date Revised**: 1999-03-22 **Date
Accepted**: 1999-04-08

**Curriculum Topic Benchmarks**: S1.4.2,S1.3.2,M1.3.3,S10.3.7

**Grade Level**: : \[9-12\] High School

**Subject Keywords**: sea level rise, floating, swimming, oceans,
flooding

**Rating**: Moderate

**Could a World of Swimmers Raise Sea Level?**

**By**: Gregory B Pasternack, 211 Veihmeyer Hall, Department of Land,
Air, and Water Resources, University of California, Davis, CA 95616
e-mail: gpast@ucdavis.edu

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

©1999, California Institute of Technology. ALL RIGHTS RESERVED. Based on
U.S. Gov\'t sponsored research.

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

**Issue**: In the state of Maryland, a local politician claimed that sea
level is rising because there are too many people putting boats on the
open ocean! This is a true story! Is this or similar claims possible?
Imagine if all of the people in the world agreed to go float on the
ocean at the same time! Could that result in a significant sea level
rise, perhaps even destroy low-lying nations such as Bangladesh?

![](media/image1.png){width="4.972222222222222in"
height="3.0694444444444446in"}

**Background**: Observations of mean sea level have been recorded over
the last 100 years using tide gages. Longer term estimates of mean sea
level have been deduced by geologists studying glaciers and the
coastline. From all of the evidence gathered, we know that the level of
the ocean rises and falls through time.

Sea level is rising. More than 2000 of the world's top scientists have
built a consensus that the present natural rise in sea level is being
enhanced by the melting of glaciers, which is likely caused by
human-enhanced global warming.

![](media/image2.emf){width="5.763888888888889in" height="3.69375in"}

(Adapted from Gornitz, V., Lebedeff, S., and Hansen, J. 1982. Global Sea
Level Trend in the Past Century. Science 215:1611-1614.)

**Preparatory Exercise for Students**: The night before the exercise,
have students use their bathtub at home to determine how much water they
displace. To do this, follow this procedure:

1\) Fill the tub up to 4 inches below the rim

2\) Mark the water elevation with an eyebrow pencil, a lip liner, or a
piece of tape

3\) Get in and lie on your back with as much of you submerged as
possible

4\) Mark the new water elevation yourself or have a family member do it
for you

5\) Get out of the tub and dry off

6\) Fill the tub back up to the lower water line

7\) Fill the tub to the upper water line using a 2-liter soda bottle

8\) Record how many liters of water it took to do step 7. That is the
volume you displaced in units of liters.

Remember that if an object is denser than water, it sinks to the bottom,
displacing a volume of fluid equal to its own. If it is less dense than
water (as most people are), it floats, and displaces only an amount of
water equal to its weight. But if the less-dense object is forced to
submerge, it does displace its volume; the extra displaced water creates
buoyancy that forces the object back toward the surface. Think about
which of these three conditions you create in your tub. \[For further
discussion about buoyancy and water displacement, look up "Archimedes
Principle" or "Hydrostatics" in any good encyclopedia or relevant
science textbook.\]

**Data**: The calculations require estimates of human vital statistics
(Table 1 or 2) and ocean characteristics (Table 3). For higher accuracy
in the answer, advanced students may want to stratify the world's
population into different weight classes based on age and sex (Table 2)
rather than using the average value for all people (Table 1).

> Table 1: Simplified Data on Human Vital Statistics
>
> **[Variable]{.underline}** **[Estimated Value]{.underline}**
>
> World Population 6 billion people
>
> Average Human Weight 542.7 N (122 lbs)
>
> Average Human Mass 55.3 kg (3.8 slugs)

![](media/image2.emf){width="5.513888888888889in"
height="5.083333333333333in"}

> Table 3: Earth Constants
>
> **[Variable]{.underline}** **[Estimated Value]{.underline}**
>
> Density of Sea Water 1030 kg/m^3^
>
> Surface Area of Oceans 361 x 10^6^ km^2^
>
> Source: Gross, M. G. [Oceanography: a view of the earth, 5th
> Edition]{.underline}. Prentice Hall, Englewood Cliffs, NJ.

**Solution**:

\(1\) The first step is to determine the volume of water displaced by a
person when he/she is floating on the ocean. One might suppose that a
person's volume is displaced, but that is not correct for a floating
object, so the volume of a human being is irrelevant to this problem.
Instead, the volume of water displaced by a person is the volume
containing a mass of seawater equal to the mass of the person. To
calculate this, divide the mass of a person by the density of seawater:

55.3/1030 = 0.0537 m^3^/person

Advanced students should use the data in Table 2, by converting the
weight in pounds (lbs) to mass in kilograms (kg) for each age/sex class.
This can be conveniently done by setting up the data in a Microsoft
Excel spreadsheet. Note that 1 lb \~ 0.453 kg.

\(2\) If one person displaces 0.0537 m3, then everybody together
displaces that amount times the world's population:

6,000,000,000 \* 0.0537 = 3.222 x 108 m^3^ = 0.3222 km^3^

\(3\) To convert the volume displaced by floating people to a sea level
rise, divide the volume by the surface area of the world's oceans:

(0.3222) / (361 x 10^6^) = 8.93 x 10^-10^ km = 0.0009 mm

Clearly, all of the world's people swimming in unison would not have a
measurable impact on sea level!!!

**Further suggestions**: Collect information on the world's population
of boats and do the same calculation to verify for yourself that the
politicians are wrong.

**Qualifiers**: Students are encouraged to consider issues about the
assumed characteristics of ocean basins raised in a related PUMAS
Example (Document ID 02_10_97_1) entitled "Ice Sheets and Sea Level
Rise," by C. Parkinson. For the present example, the small quantity of
displacement makes these issues insignificant relative to the potential
error in world population and weight estimates, but they are good points
to discuss.