Applied Math Colloquium: Scott Hottovy (US Naval Academy)

Abstract: As tropical storms go, you have probably heard of Hurricanes, Tropical Cyclones, El Niño, and La Niña. But you may have not heard of the Madden-Julian Oscillation (MJO). It is the major contributor to rainfall in tropical regions and influences the climate in the United States regularly. Unlike Hurricanes and El Niño, the MJO's mechanisms are still not well understood. In an effort to understand the mechanisms of the MJO, I will describe a model building from a dynamically stationary "background" tropical rainfall model and coupling that to a tropical wave model. These models use Stochastic Differential Equations (SDE) and Stochastic Partial Differential Equations (SPDE) as the building blocks. In the "background" model, an SDE model is used which leads to characteristics of criticality and phase transitions. For the full model with waves, we use a continuous one-dimensional SPDE. Because of the simplicity of the models, we are able to solve many statistics exactly, or run fast numerical experiments.