A Simple Warm-Pool Displacement ENSO Model

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Abstract
The authors derive analytical and numerical solutions to a simple model of the zonal displacement of the western equatorial Pacific warm pool. The model is based on a single variable x(t), the anomalous displacement of the eastern edge (28.5°C isotherm) of the warm pool. Although the physics differs, this model has a similar mathematical form to the delayed oscillator ENSO model. As in delayed oscillator models, although the wave-propagation time delay is crucial to the existence and period of the oscillation, the oscillation period is also critically dependent on the relative importance of the growth rate of the instability and the negative feedback. Consequently, the period of the oscillation can be several times the wave propagation time. Unlike delayed oscillator models, the wave propagation time delay is dependent on x(t) since the wave’s propagation time depends on the distance of the edge of the warm pool from the ocean boundaries. If the wave propagation delay time is approximated as a constant, explicit analytical solutions for growth rate and oscillation period can be obtained. More realistically, when the delay depends on x(t), the model time series has a structure consistent with that of observed ENSO time series, namely, the bigger the warm ENSO episode, the longer to the next cold ENSO episode. Comparison of model results with observations suggests that ocean wave reflection from the western ocean boundary is more important to the ENSO mechanism than ocean wave reflection from the eastern ocean boundary.

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