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Y. Wakata
and
E. S. Sarachik

Abstract

The effect of nonlinearities on a previously investigated coupled atmosphere–ocean basin mode is examined. The nonlinearity in the thermodynamic equation for sea surface temperature arises mainly from the dependence of subsurface temperature on the thermocline depth anomaly in the parameterization of entrainment into the mixed layer. This nonlinearity ultimately suppresses the linear growth of the unstable mode and equilibrates it at a finite amplitude. Because this nonlinearity acts differently for warm and cold states, the warm states are enhanced at finite amplitude. It is found that multiple equilibrium states appear as the coupling coefficient increases and as the reflection coefficient of the oceanic Rossby mode at the western boundary decreases. The finite-amplitude warm equilibrium state turns out to be stable, but the finite-amplitude cold state is unstable. The explicit inclusion of the dependence of the coupling strength on the warm and cold sea surface temperature anomalies modulates the sinusoidal-like oscillation and increases the period, but aperiodic solutions could not be obtained.

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Y. Wakata
and
E. S. Sarachik

Abstract

The fundamental modes of oscillation of a coupled atmosphere–ocean basin system in the presence of a spatially varying oceanic basic state are investigated by formulating and solving an eigenvalue problem, thereby extending the work of Hirst. The model reduces essentially to the linearized Zebiak and Cane model as discussed by Battisti and Hirst. With conventionally chosen basic states, the unstable eigenmode closely resembles the El Niño–Southern Oscillation (ENSO) cycle in these models.

It is shown that the unstable low-frequency eigenfunction consists primarily of a Kelvin mode and a gravest equatorial Rossby mode, and the oscillation can be understood in particularly simple term essentially those proposed by Suarez and Schopf and others. The oscillatory nature of the ENSO cycle can be explained by a transition mechanism resulting from the interaction of these two equatorial (but not necessarily propagating) modes. A growing unstable positive wind anomaly in the central Pacific produces a growing eastward-propagating downwelling Kelvin mode and a growing westward-propagating upwelling equatorial Rossby mode. The down-welling Kelvin mode propagates eastward and enhances the growing warm phase of the ENSO. On the other hand, the upwelling Rossby mode propagates westward and produces an upwelling Kelvin mode via rejection at the western boundary. This growing Kelvin mode propagates to the central and eastern Pacific where it then grows without propagation, cools the warm anomaly, eventually changes the phase of the warm event to cold, and therefore switches the sign of the air–sea coupled instability in the eastern Pacific. The regular ENSO cycle is the repeated application of this mechanism.

The nature of the propagation of the ENSO anomalies is shown to be sensitive to the meridional profile of the upwelling velocity near the equator. The sea surface temperature (SST) anomaly changes synchronously (i.e., without propagation) in the eastern Pacific only if the entrainment velocity is tightly confined meridionally to the equator, while it begins to propagate eastward if the entrainment velocity expands in the meridional direction, all other parameters held constant.

In examining the parameter dependence of the unstable modes, it was found that two nonoscillatory solutions appear as a transition from the oscillatory solution as the air–sea coupling parameter and the Rayleigh friction parameter of the ocean are increased.

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