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.




Stepping into the twilight zone

Some days I wonder if I misread the description and accidentally applied to a biology REU. Applied math by definition is interdisciplinary- you need something to apply that math to-, but I underestimated the extent to which other disciplines come into play. While I have picked up quite a few new math skills, most of my gained knowledge has been focused in the fields of biology and computer science. For the last week or so, I've mostly been reading biology papers and coding- and I find that awesome. After all, I chose to attend a liberal arts college for a reason. Some of the most interesting classes I've taken have been rather discussion-based and somewhat student-led. I find it interesting to see and experience different perspectives. How does a biology major read Frankenstein compared to an English major? How can psychology help us realize why so many people seem to dislike math?

I was able to experience this shift in perspective from both sides this week. When I shadowed the anthropology team, I was reminded of the human factor in the equation. All of the disciplines I am studying this summer are rather data driven, some of the real-word implications are lost when a story is stripped down to the numbers.  While we're working to predict blooms, they are collecting the stories of how people are affected by the blooms.  When the Econ team visited, we got to see how those who have not been exposed to the background of the problem and the math behind it react to our work. It will help us immensely when it come times to tell our story to the community.

Exposure to the unfamiliar helps us to see what biases and perspectives we may take for granted. An interdisciplinary approach may push you into vastly unfamiliar territory. It pushes your boundaries of your knowledge and encourages you to think critically, explore new paths, and recognize when you are out of your depth and need to ask for help.

Transforming Fiction and Reality

The great majority of my free time is spent reading fiction. I love immersing myself into a fantasy world where life's stressors are immaterial, where reality is replaced by fantasy. Specifically, I love to read fanfiction, particularly stories about Harry Potter. Fanfiction involves fans of a work transforming it and making it their own. An author may write about a character hardly mentioned or may wondering how the story would change if A happened instead of B. Fanfiction explores the world beyond the scope of the work's original universe and allows readers to look at the work from different perspectives. Is Snape a hero or a villain? What if Neville Longbottom was the Boy-Who-Lived? Why did Regulus Black defect from the Death Eaters? Fanfiction encourages its' readers to think critically and imagine possibilities.

To me, research and fanfiction share a lot of similar properties. Research is generally built off of and inspired by other research- you take a concept and add your own angle or twist to what already exists. Both are reviewed by peers and critiqued, though, understandably, the processes are just a tad different. They both involve critically examining the source material in order to understand the ideas presented, to investigate claims, and to reach conclusions of your own as informed by the information found within. Different papers or stories may cause you to reexamine your views or consider new angles. Most importantly, both involve creativity, imagination, and the willingness to consider possibilities outside the currrent realm of thought.

If this sounds interesting to you, fanfiction is pretty freely available all around the Internet, concerning just about everything you could be a fan of, from sports, to books, to shows and movies. There's also been some interesting research on fanfiction and fan culture in general done by Henry Jenkins. Check it out!

Drinking Water From a Fire Hydrant

One of the first things that our mentor, Keith, told us was that the first few weeks we would feel like we are trying to drink water from a fire hydrant. Boy, was he right. As our part of the project involves a lot of differential equations, and I had taken no differential equations, the first week or two, for me, has been essentially trying to understand roughly a semester's worth of material via an intense crash course. By necessity, I will be learning a lot of new math this summer and new ways of using and understanding old math.

I will also learn in depth and detail how to go about the process of creating a mathematical model. I've done this before in small doses, but it involved about equal parts knowledge and making it up on the fly- I'm hoping by the end of the summer that ratio will be much more in favor of knowledge. For the purposes of this project, we're hoping to create a model that will help us predict blooms, which can be used by later groups to see the positive or negative effects of possible programs and solutions. Currently, we are diving into practice models, of a sort, that should give us a better understanding of models and the modeling process that we can use in creating our model.

Though it is exciting to be learning new math and programming skills, I am truly hoping that this program will ultimately help me learn a bit more about myself and my interests, so that I can make more informed decisions regarding my future plans. If I feel time is moving quickly now- I can't believe we're almost done with our second week!-, I can only imagine how quickly my final year at college will fly by.

A Familiar Stranger

To me, Menomonie and UW-S is like a familiar stranger. I grew up on a farm outside of a small town of about 6,000 in northern Iowa. People wave as you walk or drive by, even if they don't know you, though odds are they either know you or one of your immediate family members. Most of the stores are locally owned. There's a great sense of community and tradition. From what I have been exposed to, Menomonie feels a lot like my hometown, albeit with a few more trees and hills.

I get a similar feeling from UW-S. It's certainly bigger than my campus of Simpson College- we only have about 1400 undergrads and any point on the campus is easily within about ten minutes walking distance from another- but it feels familiar. The professors are wonderful; they are incredibly helpful and care about us, both academically and personally. It's for this exact reason that I wished to attend a small college and I am delighted to find it true of UW-S.

I am primarily hoping for a learning experience in regards to the LAKES REU. As I am entering my senior year of college, I grow ever closer to having to make some pretty significant career decisions. Before choosing whether or not to attend grad school, I wish to see whether I actually enjoy research and, if so, determine which areas I might be interested in further studying. The fact that I can help a great community through my soul-searching is just icing on the cake. I also get to work on a pretty nifty application of mathematics and have the opportunity to explore ways that I can combine my major of math with my minor in computer science. Judging by the last couple of days, I certainly won't be bored! I can't wait to see what this little adventure will bring.