Eutrophication: Advanced Exercises

Three exercises are provided for the student with advanced interest in limnology. They challenge you to build, verify and improve upon Anderson's original model.

1. Simulate Oxygen as a Stock Variable

Expand the model in Figure 1 to simulate the oxygen in the hypolimnion as a stock variable. The stock of oxygen will be consumed by the decay of detritus and the respiration of the biomass based on the assumption that one gram of carbon is stoichiometrically equivalent to 2.67 grams of oxygen. The stock of oxygen in the hypolimnion will be replenished from the epilimnion by seasonal turnover. Follow Anderson's approach and simulate your model to verify that your simulations match his results. For example, set the flow of nutrient into the lake to the value used to create the "cultural eutrophication" results shown on page 133 of Toward Global Equilibrium. When you simulate the model for 150 years, you should see a large accumulation of biomass and deutritus in the lake. And you should see a reduction in the oxygen in the hypoliminon.

2. Can We Avoid the Spurious Oscillations After the 150th Year on Page 133?

If you build a Stella model to match the approach by Jay Martin Anderson, you will see oscillations in the oxygen, biomass and detritus after the 150th year. But there is NO EXPLANATION of these oscillations in Anderson's article. Since he does not explain them, I suspect these are spurious oscillations. In other words, they do not represent oscillations that would appear in a real lake. Rather, they are an artifact of the particular combination of stocks and flows that Anderson's used to represent the depletion of Oxygen in the the lower layer of the lake. I believe it is possible to represent the depletion of oxygen in the lower layer without the spurious oscillations, as explained in a short note which you may download here.

3. Adapt to a Different Nutrient

Anderson (1973, p. 124) acknowledges that nitrogen and phosphorous are more commonly associated with artificial eutrophication. Build a new model based on Anderson's approach to simulate eutrophication with either phosphorous or nitrogen as the "limiting factor."

4. Multiple Nutrients

Anderson assumes that carbon is the limiting nutrient throughout the simulation. But he is aware that "an obvious extension of the model would examine the possibility that, as one nutrient is increased, some other nutrient becomes the growth-limiting factor" (Anderson 1973, 124). Expand the model from the previous exercise to simulate two nutrients. Design a simulation that will allow growth in the biomass to be limited by one nutrient early in the simulation and limited by the second nutrient later in the simulation.