Photo credit: J.D. Kinnon
A recurring problem in many bodies of water is algal bloom. An algal bloom is a rapid rise in the population of some form of algae. The algae grows to such an extent that in some cases it depletes the water of oxygen and nutrients. This can kill all of the other species in the water and itself as well.
Photo credit: J.D. Kinnon
Some of the algae release toxins that can make the water undrinkable, kill fish, and even larger animals like whales and manatees.
Dr. Dan Baden and Florida Department of Environmental
Conservation
Algal blooms also are a problem recreational reasons. Algae can become so dense that the water becomes murky and unsafe to swim in. It is a continual problem in swimming pools and one of the reasons that chlorine is added to the water. This is the impetus for this project.
During a visit to an unspecified hotel in Illinois, I was looking forward to some swimming. I was going to be there for a week and was not going to have much opportunity for recreation. When we arrived, the pool was closed. Why? Algae. Algae had built up in the pool enough that the pool had turned a nice murky bluish green color. The primary algae to blame in most swimming pool algal blooms is some form of cyanobacteria, or "blue-green algae". I was a bit annoyed that the pool was closed, but since my stay at the hotel was for a computational science workshop, I decided to model the pool and turn it into a projecct.
For information about harmful algal blooms in general, the following websites may be useful for answering some of the project questions.
http://www.whoi.edu/redtide - Woods
Hole Oceanographic Institute
http://www.csc.noaa.gov/crs/habf
- National Oceanic and Atmospheric Administration
Our goal in this lab is to understand algal blooms in the context of the model of the swimming pool somewhere in Illinois (I withhold the name of the hotel, although this is hardly an uncommon or necessarily recurring problem).
Some of the parameters were not immediately available for the model, so I was forced to estimate reasonable values, but some were available using a simple web search. In the model, I have provided a skeleton of the model with some of the estimated parameter values already included. Those values that are not included, you will need to either find on the web or estimate based on other information.
One of the features of algal blooms that we want our model to exhibit is hysteresis. Hysteresis is the phenomenon that when a parameter is changed in one direction, the model behavior (not blooming to blooming) changes at one particular value, while changing in the other direction (blooming to not blooming) changes at a different value (usually a very abrupt change).
This simple model has three quantities which we will be tracking: algae, nutrients, and chlorine. We will assume that the algae is a single generic type of cyanobacteria, that all nutrients are the same, and that we are not going to use any algaecides (like copper sulfate, etc.).
The density of algae will increase by eating nutrients and decrease by natural death and by interaction with chlorine.
The amount of chlorine will be initially set to a constant.
The density of nutrients will increase by natural accumulation with a carrying capacity and decrease by consumption by algae. The accumulation is affected by chlorine.
We can depict these relationship by the following cartoon,
With Berkeley Madonna, we can construct the model two ways, using differential equation laws and typing in the equations, or by using the flowchart editor. For this lab, I have constructed the basic model using the flowchart, but have left out several of the key parameters.
Basic Model (Berkeley Madonna File Format)
Question 1: Using any resources you can find, fill in the missing parameter values in the model. These parameters are the ones with the question mark in the circle. You may not be able to find all of them, but you may find information that helps to guide your estimates of the remaining parameters.
Question 2: One of the causes of algal blooms in swimming pools is a change in the pH of the water. As the pH rises, chlorine loses its effectiveness in destroying the algae. Changing the pH from 7 to 7.4 can reduce the effectiveness by as much as 20%. By changing the initial density of algae, describe the change in the chemical death rate needed to initiate an algal bloom.
Question 3: Change the initial algae density to that of the algal bloom in Question 2. By changing the chlorine pulse size, find the value needed to eradicate the algae (bring down to healthy levels).
Question 4. Explain hysteresis in the context of your answers to Question 1 and 2.
Question 5. Describe a strategy for preventing algal blooms in swimming pools.
Question 6. Could these same strategies be put in place in natural settings (lakes, rivers, etc)? Why or why not? If so, how? If not, what might be done in those settings?
A full report should be able to be read without knowing the project. That is, the report should provide an introduction to the main problem, a background to the biology, the methods of solution, graphs and accompanying captions, conclusions, and references.
Extension 1. So far we have assumed that the concentration of chlorine is constant. Change the chlorine to a more realistic and see what kinds of differences this makes. Try a periodic bolus of chlorine which then decays as it reacts with the nutrients and algae.
Extension 2. What can be done to this model to make it more realistic? In addition to the fact that some of the rate constants are fit the behavior we wanted, there are other aspects of the phenomena of algal blooms that are significant. Draw a diagram of an improved model and suggest how the interactions might be changed to make the model more realistic.