Tianlang Luo | Applied Math, University of Waterloo
Conceptual Stochastic ENSO Models
El Niño–Southern Oscillation (ENSO) is a phenomenon occurring every 3-7 years in the tropical Pacific. The coupled atmosphere-ocean mechanism behind is first proposed by Bjerknes. An anomalous sea surface temperature in the eastern Pacific induces diabatic heating or cooling of the atmosphere, which alters atmospheric circulation and hence the wind stress at the ocean surface. The wind stress variations in turn modify the ocean thermal structure, giving rise to a series of positive feedbacks that sustain and reinforce the initial SST anomaly. The patterns shift back and forth between the warm phase and cold phase with irregularity in amplitude, duration, temporal evolution, and spatial structure. ENSO posts significant impact on global climate and human activities, and thus has been an active research subject over the past few decades. Recently, a simple ENSO framework was 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. In this seminar, I derive from Majda’s ENSO model a conceptual delayed-oscillator ENSO model under the localized wind assumption as a form of delay differential equation. The stability of the conceptual model is investigated by deterministic analysis including reduction to center manifold and computation of normal form. The stochastic analysis of stability is also briefly introduced.