Envision It! Workshop
July 8, 1996
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.