Title: Bridging the Mathematical and Natural Sciences: Balancing Insight, Accuracy, and Uncertainty
Abstract: Mathematics provides a lens for understanding complex natural systems, from the coupled dynamics of El Niño Southern Oscillation and the Madden Julian Oscillation to the propagation of uncertainty in oceanic eddy diagnostics. In this talk, I present a sequence of approaches illustrating how mathematical modeling can provide insight for complex problems in geophysics from multiple perspectives. I will first discuss stochastic idealized models that capture essential multiscale dynamics and reproduce observed statistical behaviors, highlighting how minimal yet carefully constructed equations can reveal mechanisms obscured in high-dimensional simulations. Next, I introduce a framework that systematically bridges idealized models with high-resolution operational simulations via latent-space data assimilation, enabling efficient generation of realistic synthetic datasets and improved representation of extremes. Finally, I present a tractable mathematical framework for quantifying the nonlinear propagation of uncertainty through diagnostics such as the Okubo Weiss parameter, demonstrating how theoretical analysis can reveal fundamental limitations of mean-based estimates in nonlinear systems. Together, this talk emphasizes how rigorous mathematical reasoning and modeling can extract insight from complex phenomena, bridge accuracy with practicality in simulation, and quantify uncertainty propagation through complex dynamics.