Applied Analysis Seminar: Dr. Jody Reimer

Title: Modeling Feedbacks and Uncertainty in Sea Ice Ecosystems
Polar sea ice is a highly heterogeneous environment where ice algae actively modify their habitat by excreting extracellular polymeric substances (EPS) that clog brine pores and limit nutrient transport. In this talk, I present a mathematical framework to investigate this biophysical feedback and the challenges of modeling its dynamics under significant environmental uncertainty. We first develop a dynamical systems model of EPS-modulated algal blooms, using fast-slow decomposition to show that explicit modeling of EPS leads to emergent oscillatory dynamics that simplified models fail to capture. We then address the limitations of using mean parameter values to represent these nonlinear processes across varying spatial scales. By employing generalized polynomial chaos (gPC) expansion, we treat growth rates as random variables to efficiently propagate local heterogeneity through the model. Our results demonstrate that accounting for this uncertainty fundamentally alters predictions of bloom timing and magnitude, highlighting the necessity of coupling mechanistic biophysical models with robust stochastic frameworks to understand polar ecosystems.