Mathematical Modeling to Forecast Chlorophyll Levels and Algae Blooms

I worked on mathematical models for forecasting chlorophyll concentration and finding a condition for blooming. Mathematical models help with understanding important processes that govern chlorophyll concentration.  These models are analyzed by considering all relevant variables on the same time and length scale to determine the relative impact of each physical process. This normalization yields non-dimensional parameters that assist in the interpretation of analytic and computational results. We analyzed data from past REU students and the DNR to use in our models.We modeled chlorophyll growth because there is a direct relationship between chlorophyll and algae counts because algae produces chlorophyll as a by-product of photosynthesis and chlorophyll is more easily measured.

The forecasting model predicts how long after a large flushing event it takes for the lake to turn green and smelly if there’s no rain. We used a logistic growth model to capture longer term algae growth and a carrying capacity was estimated by looking at how much the algae can grow if there’s no nutrients for them to consume. We ran 100 simulations varying the carrying capacity and then the growth rate. We found the most variation when the carrying capacity was varied but in all simulations we found that it takes about 3 weeks to hit the carrying capacity level, which corresponds well with data collected from past REUs and the DNR.

The bloom condition was found by solving an equation that describes chlorophyll growth over time based on its growth and movement. The bloom condition was found by solving the equation analytically and was found to rely on Secchi depth and the ratio between growth rate and turbulence. The equation was also solved numerically using computer programming and found very similar results to the analytic solution.  

 Both of these models can take proposed solutions to the algae problem and test how effective they would be at preventing blooms. Both models advocate the solution of increasing turbulence and flow in the lake and the bloom condition models also suggests lowering the algae growth by limiting phosphorus and nitrogen to help solve this problem.