PhD Comprehensive Exam | Tianlang Luo, Stochastic Dynamics of and ENSO Model

M3 3103

Candidate

Tianlang Luo | Applied Mathematics, University of Waterloo

Title

Stochastic Dynamics of and ENSO Model

Abstract

El Niño–Southern Oscillation (ENSO) is a climate phenomenon occurring every 3-7 years in the tropical Pacific. It is a pattern shifting between anomalous warm and cold events within equatorial Pacific, with irregularity in amplitude, duration, temporal evolution, and spatial structure. This research focuses on a specific ENSO model developed by Majda and coworkers, where state-dependent stochastic wind bursts and nonlinear advection of sea surface temperature are coupled to a simple ocean–atmosphere model that is otherwise deterministic, linear, and stable.

We aim to build on Majda’s stochastic PDE model to improve ENSO predictability. The first goal of this investigation is one of modelling - understanding the specific form of the relevant ENSO equations and the proper formulation of the time-dependent perturbations. Next, we derive a conceptual delay differential equation from the SPDEs, as well as to verify it by learning methods. A major part of this research deals with stochastic analysis of nonlinear SPDEs, where we apply stochastic bifurcation theory to study the full infinite dimensional models. Finally, we will also develop novel numerical algorithms based on proper orthogonal decomposition (POD) to build reduced-order models. Two-dimensional POD basis functions will be constructed from a collection of solution snapshots computed from Majda’s SPDEs numerically. Through the combination of both analytical and numerical approaches, we will carefully examine the asymptotic long-term behavior of ENSO. This work will contribute to more accurate and comprehensive understanding of the underlying mechanisms as well as the prediction of ENSO.