Sunday, August 7, 2016

Analyzing Tainter Lake

Analyzing Tainter Lake
How previous data informs mathematical models
The goal of the mathematics team was to create a mathematical model (a method where math is used to simulate real-world situations) that can be used to determine the amount of blue-green algae in the lake. In order to do so, we had to use data gathered by last year's REU and the DNR to determine the realistic conditions of Tainter Lake; these conditions were then applied to the model we developed based on previous studies conducted on bloom-plagued waters.

The most significant difference between Tainter Lake and previously studied lakes is the lack of temperature stratification. Those lakes generally have a thermocline- a layer in which the temperature changes rapidly and is sandwiched by a warmer layer on top and a colder layer on the bottom. Tainter Lake is effectively the same temperature throughout, as it is much shallower than the studied lakes, so we had to account for this in our model.

We chose to model the blue-green algae population via the chlorophyll concentration of the lake. We were able to do this because there is a positive linear relationship between the population and the concentration- as one increases, so does the other. We decided to model chlorophyll because it is both easier to measure and visualize.

I found that as flow increases, chlorophyll decreases. Greater flow both flushes out the algae and makes it harder for them to grow as they are displaced by turbulence. The particular species of blue-green algae found in Tainter Lake, Microcystis aeruginosa, has the ability to float or sink to an optimal depth by inflating or deflating its gas vacuoles. It can float to the top to receive more sunlight or sink to the bottom to take in nutrients. If the water is more turbulent, it is more difficult to maintain its optimal depth, which slows its growth.

The neatest thing I found was a delay in bloom after a flushing event. Our model estimated that it would take about three weeks after a flushing event to reach the chlorophyll saturation level. In early July of 2015, a significant flushing event occurred. Sure enough, three weeks later the chlorophyll had reached saturation level- the highest reading of the summer! While the rain flushed out the algae, it also would have brought in massive amounts of phosphorous via runoff, which served as a replenished food source for the later bloom.

By using data specific to Tainter Lake to inform our model, the model can more accurately reflect the conditions of the lake and account for any differences that established models may otherwise miss. This makes the model a more valuable tool in assessing the extent of the effectiveness of a proposed solution.

1 comment:

  1. Did you know that you can enjoy paddleboarding on lakes because they are so calm? SUP Red Deer