A Stability Analysis of Tropical Ocean–Atmosphere Interactions: Bridging Measurements and Theory for El Niño

TLDR

Tropical ocean–atmosphere interactions generate natural oscillation modes whose period, intensity, spatial structure, and propagation direction depend on the mean state, characterized by trade‑wind intensity, thermocline depth, and temperature difference across the thermocline. A coupled ocean–atmosphere model reveals two unstable mode families—a long‑period delayed oscillator requiring a deep thermocline and a short‑period, westward‑propagating mode needing a shallow thermocline—both requiring strong zonal winds, while larger ΔT and thermocline depth stabilize them; intermediate depths produce hybrid modes, matching the current Southern Oscillation, whereas paleorecords indicate a past pure delayed oscillator with decade‑scale periods.

Abstract

Interactions between the tropical oceans and atmosphere permit a spectrum of natural modes of oscillation whose properties—period, intensity, spatial structure, and direction of propagation—depend on the background climatic state (i.e., the mean state). This mean state can be described by parameters that include the following: the time-averaged intensity τ of the Pacific trade winds, the mean depth (H) of the thermocline, and the temperature difference across the thermocline (ΔT). A stability analysis by means of a simple coupled ocean–atmosphere model indicates two distinct families of unstable modes. One has long periods of several years, involves sea surface temperature variations determined by vertical movements of the thermocline that are part of the adjustment of the ocean basin to the fluctuating winds, requires a relatively deep thermocline, and corresponds to the delayed oscillator. The other family requires a shallow thermocline, has short periods of a year or two, has sea surface temperature variations determined by advection and by entrainment across the thermocline, and is associated with westward phase propagation. For the modes to be unstable, both families require that the background zonal wind exceed a certain intensity. An increase in ΔT, and in H beyond a certain value, are stabilizing. For intermediate values of H, between large values that favor the one mode and small values that favor the other, the modes are of a hybrid type with some properties of each family. The observed Southern Oscillation has been of this type for the past few decades, but some paleorecords suggest that, in the distant past, the oscillation was strictly of the delayed oscillator type and had a very long period on the order of a decade.