A spatiotemporal oscillator model for ENSO

Abstract

A spatiotemporal oscillator model for El Niño/Southern Oscillation (ENSO) is constructed based on the thermodynamics and thermocline dynamics. The model is enclosed by introducing a proportional relationship between the gradient in sea surface temperature (SST) and the oceanic zonal current and can be transformed into a standard wave equation that can be decomposed into a series of eigenmodes by cosine series expansion. Each eigenmode shows a spatial mode that oscillates with its natural frequency. The first spatial mode, that highlights SST anomaly (SSTA) contrast between the eastern and western Pacific—a fundamental characteristic of the eastern Pacific (EP) El Niño events, oscillates with a natural period of around 4.6 years, consistent with the quasi-quadrennial (QQ) mode. The second spatial mode, that emphasizes SSTA contrast between the central and the eastern, western Pacific—a basic spatial structure of the central Pacific (CP) El Niño events, oscillates with a natural period of 2.3 years that is half of the first natural period. It is also consistent with the quasi-biennial (QB) modes. The combinations of the eigenmodes with different weights can feature complex spatiotemporal variations in SSTAs. In open ocean that is far away from the coastlines, the model can predict waves propagating both eastward and westward. Besides, the net surface heating further complicates the temporal variations by exerting forced frequencies. The model unifies the temporal and spatial variations and may provide a comprehensive viewpoint for understanding the complex spatiotemporal variations of ENSO.

The El Niño Southern Oscillation Recharge Oscillator with the Stochastic Forcing of Long-Term Memory

“…The ensemble mean for the OU process converges rapidly (exponential law) to zero so that it can be neglected. However, according to Equation (6) or Equation ( 8) the ensemble mean for the FOU process converges slowly (negative power law) to zero so that it can manifest its influence during the integration time period. In reality, the ensemble mean determined by the first term on the right-hand side of Equation (6) or Equation ( 8) has an asymptotic representation f (α)t −α when t → ∞ , where f (α) is a bounded function [30].…”

“…A recharge oscillator (RO) model is constructed to emphasize the recharge-discharge of the equatorial heat content as the phase-transition mechanism [5]. Recently, a spatiotemporal oscillator model was proposed to characterize the complex temporal and spatial variations in ENSO [6]. These studies considered ENSO as a slow deterministic oscillation of the atmosphere-ocean interaction.…”