** Next:** The Great Lakes

Envision It! Workshop

July 8, 1996

## Great Lakes Pollution

##### (Difference Equation Version)

Steve McKelvey, St. Olaf College
This problem is an example of the kind of modeling which can be done
with Stella and MATLAB in the secondary school setting. While the
Great Lakes version of this problem has been thoroughly studied and is
quite well known, the basic ideas behind this model can be used in any
chain of lakes situation. One area of interesting study might be the
Minneapolis chain of lakes.

Depending on the pollutant of interest and the geography and hydrology
of the area being studied, a project involving a local chain of lakes
could involve field work, library research and mathematical reasoning
crossing over the boundaries of biology (effects of pollutants on
biological activity), chemistry (identifying pollutants and the
byproducts of their decay), physics (dynamics of mixing) and
mathematics (derivation and solution of difference or differential
equations).

Another interesting exercise is discussing the effects of various
simplifying assumptions in this model. For example, the difference
equations we will derive are based on the assumption that any
pollutant introduced into a lake is immediately and perfectly mixed
within the waters of the lake. For example, raw sewage dumped into
Lake Michigan by Milwaukee is assumed to be immediately mixed evenly
throughout the lake, affecting beaches in northern Michigan as severely
as those in Milwaukee. Clearly this is not realistic. Questions for
a science class might then be: Is this model totally useless if it's
not correct in every detail? If not, what are some reasonable uses of
the model? Can we determine whether the model consistently over or
under estimates the pollution in a given lake? How could we change
the model to more accurately reflect the actual dynamics of the lake?

These discussions of the uses and limitations of mathematical models
is a crucial step in understanding the appropriate use of models.

** Next:** The Great Lakes

*Steve McKelvey *

Fri Jul 5 08:01:19 CDT 1996