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.