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Abstract
The Lagrangian motions of floating matter on the sea surface were simulated by using the surface current data based on shipdrift data produced by Meehl. The validity of the simulation was confirmed by comparing the results of the model with the trajectories of satellite tracked drift in the eastern North Pacific observed by Kirwan et al. Some cases which originated in the western North Pacific Ocean were investigated. It was found that drifters set in the ocean during spring quickly migrated to North America on the strong eastward North Pacific currents of the summer season. Trajectories started during autumn showed a loop in the western North Pacific and took more time to arrive in the eastern area of the North Pacific Ocean. Each trajectory that arrived in the eastern area of the North Pacific Ocean, showing a large loop, traveled over a one year interval owing to the large surface current vortex. This vortical sea surface current was driven by the clockwise winds around the atmospheric subtropical high pressure region located in the North Pacific.
Numerous calculations with initial positions randomly scattered in space and time were performed, and the accumulated matter density was obtained. High density areas where the debris concentrated were found at several places (i.e., near Berinuda, west of Australia, the center of the South Atlantic, and north of the Hawaiian Wands). In focussing on the North Pacific, it was found that three identifiable high density areas circulate with three year periods. It is emphasized that the instantaneous strong convergence areas do not always agree with the high accumulation density areas owning to the hysteresis or memory of the floating debris.
Abstract
The Lagrangian motions of floating matter on the sea surface were simulated by using the surface current data based on shipdrift data produced by Meehl. The validity of the simulation was confirmed by comparing the results of the model with the trajectories of satellite tracked drift in the eastern North Pacific observed by Kirwan et al. Some cases which originated in the western North Pacific Ocean were investigated. It was found that drifters set in the ocean during spring quickly migrated to North America on the strong eastward North Pacific currents of the summer season. Trajectories started during autumn showed a loop in the western North Pacific and took more time to arrive in the eastern area of the North Pacific Ocean. Each trajectory that arrived in the eastern area of the North Pacific Ocean, showing a large loop, traveled over a one year interval owing to the large surface current vortex. This vortical sea surface current was driven by the clockwise winds around the atmospheric subtropical high pressure region located in the North Pacific.
Numerous calculations with initial positions randomly scattered in space and time were performed, and the accumulated matter density was obtained. High density areas where the debris concentrated were found at several places (i.e., near Berinuda, west of Australia, the center of the South Atlantic, and north of the Hawaiian Wands). In focussing on the North Pacific, it was found that three identifiable high density areas circulate with three year periods. It is emphasized that the instantaneous strong convergence areas do not always agree with the high accumulation density areas owning to the hysteresis or memory of the floating debris.
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.
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.
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.
Abstract
In order to test certain aspects of the ENSO mechanism proposed by Suarez and Schopf and by Battisti and Hirst, we force a shallow water ocean with 28 years of observed (FSU) winds and decompose both the atmospheric forcing and ocean response into equatorial modes.
The proposed mechanism was verified in the following sense. For each warm phase of the cycle, a downwelling Kelvin mode directly forced by the weakening of the trade winds in the central Pacific was found. The same wind anomaly forces an upwelling gravest Rossby mode which propagates freely westward and reflects as a freely propagating Kelvin mode at the western boundary. This Kelvin mode returns to the scene of the original warming and acts as a retarded forcing (of opposite sign) eventually switching the phase of the oscillation from warm to cold. The cold phase then proceeds by the same mechanism but with modes of opposite signs, to eventually switch to the warm phase.
The contribution of the higher Rossby modes to this process is estimated. It is found that almost all the Kelvin response in the western Pacific results from the reflection of the gravest symmetric equatorial Rossby mode so that the ENSO cycle is defined by the interaction of only two ocean modes, the Kelvin and lowest Rossby mode. These modes are sometimes forced directly by the wind as part of an intrinsic coupled atmosphere–ocean mode and sometimes propagate freely where the wind forcing is negligible. The distinction between these two manifestations of the ocean modes is of the greatest importance and is stressed throughout the paper.
The case of the warm event of 1976 is an interesting example of the failure of the switching mechanism, and is discussed in the conclusion.
Abstract
In order to test certain aspects of the ENSO mechanism proposed by Suarez and Schopf and by Battisti and Hirst, we force a shallow water ocean with 28 years of observed (FSU) winds and decompose both the atmospheric forcing and ocean response into equatorial modes.
The proposed mechanism was verified in the following sense. For each warm phase of the cycle, a downwelling Kelvin mode directly forced by the weakening of the trade winds in the central Pacific was found. The same wind anomaly forces an upwelling gravest Rossby mode which propagates freely westward and reflects as a freely propagating Kelvin mode at the western boundary. This Kelvin mode returns to the scene of the original warming and acts as a retarded forcing (of opposite sign) eventually switching the phase of the oscillation from warm to cold. The cold phase then proceeds by the same mechanism but with modes of opposite signs, to eventually switch to the warm phase.
The contribution of the higher Rossby modes to this process is estimated. It is found that almost all the Kelvin response in the western Pacific results from the reflection of the gravest symmetric equatorial Rossby mode so that the ENSO cycle is defined by the interaction of only two ocean modes, the Kelvin and lowest Rossby mode. These modes are sometimes forced directly by the wind as part of an intrinsic coupled atmosphere–ocean mode and sometimes propagate freely where the wind forcing is negligible. The distinction between these two manifestations of the ocean modes is of the greatest importance and is stressed throughout the paper.
The case of the warm event of 1976 is an interesting example of the failure of the switching mechanism, and is discussed in the conclusion.
