Climate and Ecosystem Dynamics
While climate change has been the subject of a raging debate for decades, what's certain is that any changes in the climate and the ecosystems we depend on will have significant impacts on society.
I am interested in understanding the climate and at-risk ecosystems from a mathematical perspective, with the goal of understanding the consequences and developing systems which interact directly with the evironment.
Peat bogs are swampy, damp soil characterized by a high degree of decaying vegetation on the top layers of the soil. As more vegetation piles up, the old soil is separated from the atmosphere, and all of the carbon inside the soil is stored. Peat deposits are estimated to hold roughly 1/3 of the worlds' CO2. Unfortunately, peat deposits can spontaneously ignite. One concern among scientists is that if too much carbon is released into the atmosphere it will trigger a domino effect.
In the summer of 2013 I performed uncertainty quantification on the peat temperature-carbon system using Monte Carlo Generalized Polynomial Chaos methods. I found that too much incoming vegetation created possible ignition conditions. This led me to think about methods for monitoring and controlling a peat deposit or some other potentially unstable ecosystem characterized by non-linear dynamics, and jump started my interest in control theory.
This research was supported by the URSP program at George Mason University under the mentorship of Tim Sauer.
Tree Rings, CO2, and Temperatures:
One of the most studied areas in climate science is approximating historical data and predicting future conditions. In 1998 Mann published a paper using tree ring growth to predict historical temperatures. This resulted in the now ubiquitous "hockey stick" model of past global temperatures.
From the summer of 2012 to the summer of 2013, I worked with Tim Sauer, Tyrus Berry, and John Ensley in the URCM program at the George Mason Mathematics Department to improve on Mann's work. We established error boundaries for his approximation, added a term representing CO2 to his model, and performed cross validation on both sets of data.
This project is what drew my interest to climate related research, and served as an introduction to computational math and math modeling.