Applied Math Colloquium – Juan M. Restrepo (Oak Ridge National Laboratory)

Formulating Effective Models, Methods, and Conceptual Frameworks for the Geoscience

Abstract: Can waves transport significant amounts of ocean heat and tracers great distances, thus affecting Earth’s climate? This question was the basis for a project which culminated in the wave-driven circulation model and a concrete answer to how this process takes place. Moreover, the project also showed that wave-generated transport was most intense in the nearshore, leading to an examination of the impact of wave-generated transport on important nearshore processes, such as movement of ocean pollution and nutrients in coastal areas. In my talk, I will describe how the vortex-force conceptualization led to the formulation of the model and a theoretical basis for how waves and currents interact at scales larger than the wave scales. The ever-present noise in natural processes and in the instruments used to measure them motivated me to create computational methods that could combine models, such as the wave circulation model and models for climate and weather, and observations in a probabilistic framework to make better predictions. While optimal estimate methods for linear problems existed, the focus of my work was instead on developing algorithms that could handle the more common noisy nonlinear processes in the geosciences. I will detail some of the strategies I used to create methods and algorithms that assimilate observations, rational models, and machine-learned data-driven constructs to improve forecasts in time-dependent problems, arising in the geosciences and beyond. Finally, I will discuss my more recent work, which employs mathematical arguments to guide in quantifying and understanding resilience in the context of a changing climate and biological systems response via adaptation to stresses.