Delayed Oscillator Model
The wave theory describe above is used in a dynamical
nonlinear model called the delayed oscillator model. This model helps to
understand the dynamics behind ENSO. This model relies on :
-a strong positive feedback
in the coupled ocean-atmosphere system
-non-linear mechanisms to limit the growth of unstable perturbations.
The amplitude of the
observed El Niņo variability at low frequencies requires some strong positive
feedback mechanism to balance the restoring effects of the surface heat
exchanges on SST anomalies. Like in the linear model, the feedback arises from
the coupling of the tropical ocean and atmosphere : ocean temperature
perturbations produced by advective processes, result in atmospheric heating and
wind responses that drive the ocean currents so as to enhance the original
perturbations. The Central Pacific shows the strongest coupled feeback because
it is the area of largest SST and wind anomalies in the Tropical Pacific.
The nonlinear effects are introduced to limit the growth from the equilibrium state of the system. Nonlinear mechanisms are could be either the advective processes in the ocean or the moist processes in the atmosphere. The westerly wind stress anomalies (see figure below) (in the model the wind stress is applied during a fixed period) induced by SST perturbations in the Central Pacific (coupled region) lead to the generation of an eastward downwelling Kelvin wave and an upwelling Rossby wave (see figure below).
The Kelvin wave travels rapidly to the east where it is able to deepen the thermocline, lessen the upwelling-induced cooling, and thereby warm the SST. Meanwhile, the Rossby wave elevates the thermocline in the western Pacific. When the Rossby wave reaches the western boundary it is reflected as an eastward propagating equatorial upwelling Kelvin wave. During its westward propagation, the Rossby wave is hidden from the coupled problem, but as the reflected upwelling Kevin wave crosses the coupled region, it reenters the coupled problem after a time delay equal to their transit time. The coupled perturbation equation is therefore given by :
where is the wave transit time, T is the amplitude of the growing disturbance, and measures the influence of the returning signal relative to that of the local feedback.
The Kelvin wave elevates the thermocline and thus acts to reverse the earlier warming. Consequently a reduction of the in the intensity of the interactions between the ocean and atmosphere occurs. During El Niņo, the persistence of the westerly wind anomalies in the Central Pacific implies continued excitation of Rossby and Kelvin waves that further erode the development of El Niņo conditions in the Central Pacific until the westerly wind anomalies start to decay and La Niņa starts to develop (see figure above). As before, the easterly wind anomalies in the Central Pacific now sow the seeds for the destruction of la Niņa in the form of westward-traveling Rossby waves that deepen the thermocline. These waves reflect off the western coast and in due course El Niņo replaces La Niņa.