# An empirical model of tropical ocean dynamics

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## Abstract

To extend the linear stochastically forced paradigm of tropical sea surface temperature (SST) variability to the subsurface ocean, a linear inverse model (LIM) is constructed from the simultaneous and 3-month lag covariances of observed 3-month running mean anomalies of SST, thermocline depth, and zonal wind stress. This LIM is then used to identify the empirically-determined linear dynamics with physical processes to gauge their relative importance to ENSO evolution. Optimal growth of SST anomalies over several months is triggered by both an initial SST anomaly and a central equatorial Pacific thermocline anomaly that propagates slowly eastward while leading the amplifying SST anomaly. The initial SST and thermocline anomalies each produce roughly half the SST amplification. If interactions between the sea surface and the thermocline are removed in the linear dynamical operator, the SST anomaly undergoes less optimal growth but is also more persistent, and its location shifts from the eastern to central Pacific. Optimal growth is also found to be essentially the result of two stable eigenmodes with similar structure but differing 2- and 4-year periods evolving from initial destructive to constructive interference. Variations among ENSO events could then be a consequence not of changing stability characteristics but of random excitation of these two eigenmodes, which represent different balances between surface and subsurface coupled dynamics. As found in previous studies, the impact of the additional variables on LIM SST forecasts is relatively small for short time scales. Over time intervals greater than about 9 months, however, the additional variables both significantly enhance forecast skill and predict lag covariances and associated power spectra whose closer agreement with observations enhances the validation of the linear model. Moreover, a secondary type of optimal growth exists that is not present in a LIM constructed from SST alone, in which initial SST anomalies in the southwest tropical Pacific and Indian ocean play a larger role than on shorter time scales, apparently driving sustained off-equatorial wind stress anomalies in the eastern Pacific that result in a more persistent equatorial thermocline anomaly and a more protracted (and predictable) ENSO event.

## Keywords

Sea-surface temperatures ENSO Climate variability Ocean-atmosphere interaction Coupled models## Notes

### Acknowledgments

The authors thank Antonietta Capotondi, Cécile Penland, Amy Solomon, David Battisti and two anonymous reviewers for helpful comments. This work was partially supported by a grant from NOAA CLIVAR-Pacific.

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