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Andrew M. Moore
Javier Zavala-Garay
Youmin Tang
Richard Kleeman
Anthony T. Weaver
Jérôme Vialard
Kamran Sahami
David L. T. Anderson
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Michael Fisher


The optimal forcing patterns for El Niño–Southern Oscillation (ENSO) are examined for a hierarchy of hybrid coupled models using generalized stability theory. Specifically two cases are considered: one where the forcing is stochastic in time, and one where the forcing is time independent. The optimal forcing patterns in these two cases are described by the stochastic optimals and forcing singular vectors, respectively. The spectrum of stochastic optimals for each model was found to be dominated by a single pattern. In addition, the dominant stochastic optimal structure is remarkably similar to the forcing singular vector, and to the dominant singular vectors computed in a previous related study using a subset of the same models. This suggests that irrespective of whether the forcing is in the form of an impulse, is time invariant, or is stochastic in nature, the optimal excitation for the eigenmode that describes ENSO in each model is the same. The optimal forcing pattern, however, does vary from model to model, and depends on air–sea interaction processes.

Estimates of the stochastic component of forcing were obtained from atmospheric analyses and the projection of the dominant optimal forcing pattern from each model onto this component of the forcing was computed. It was found that each of the optimal forcing patterns identified may be present in nature and all are equally likely. The existence of a dominant optimal forcing pattern is explored in terms of the effective dimension of the coupled system using the method of balanced truncation, and was found to be O(1) for the models used here. The implications of this important result for ENSO prediction and predictability are discussed.

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