Chunzai Wang
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The first term on RHS of Eq. (4a) represents the positive feedback in the coupled system. The second term represents the negative feedback due to wave reflection at the western boundary. The third term represents the negative feedback due to the wind-forced wave contribution in the equatorial western Pacific. The last term is a cubic damping term that does not affect oscillatory behavior, but it limits anomaly growth [Battisti and Hirst, 1989; Wang, 2001]. Eq. (4b) states that the off-equatorial western Pacific thermocline anomaly is controlled by the wind stress in the equatorial central Pacific, with a damping rate of  . Eq. (4c) shows that zonal wind stress anomaly in the equatorial central Pacific is related to the eastern Pacific SST anomaly, and Eq. (4d) states that the zonal wind stress anomaly in the equatorial western Pacific is related to the off-equatorial western Pacific thermocline anomaly. The unified oscillator of Eq. (4) can oscillate on interannual timescale.
By further simplifications and assumptions, the unified oscillator can reduce to the different ENSO oscillators. The delayed oscillator model does not consider the role of the western Pacific in ENSO. It is assumed that equatorial winds in the western Pacific do not affect the SST anomalies in the eastern Pacific. If we neglect the contribution of the wind-forced wave in the western Pacific, the unified oscillator of Eqs. (4a)-(4d) will exclude the role of the western Pacific in ENSO. By setting  in Eq. (4a), the western Pacific variables  and  are decoupled from the coupled system. If we further drop the time derivative of Eq. (4c), the unified oscillator reduces to:
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