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Nonlinear Effects in Coupled Atmosphere-Ocean Basin Modes

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  • 1 School of Marine Science and Technology, Tokai University, Shimizu, Shizuoka, Japan
  • | 2 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
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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.

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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