Nonlinear Response to Anomalous Tropical Forcing

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Abstract
We have investigated the nonlinear steady-state response of a barotropic model to an estimate of the observed anomalous tropical divergence forcing for the El Niño winter of 1982/83. The 400 mb climatological flow was made a forced solution of the model by adding a relaxation forcing. The Rayleigh friction coefficient (ϵ−1 = 20 days) was chosen such that this solution is marginally stable. The steady states were computed as a function of a dimensionless parameter α, that governs the strength of the anomalous forcing. The computed steady-state curve deviates markedly from a straight line, displaying a fold and an isolated branch. The linear steady state (α ≪ 1) compares well with the observed seasonal mean anomaly pattern. After the fold at α = 0.65, the agreement is smaller. A further increase in α after the fold results in saturation of the response. The streamfunction patterns of the isolated branch display unrealistically large amplitudes. Time integrations show that the steady states govern the time-dependent behavior despite their unstable nature. The resulting time-mean patterns are very similar to the steady states. Periodic, quasi-periodic, and complete chaotic behavior are observed. Increasing the Rayleigh friction coefficient to ϵ−1 = 10 days results in a disappearance of the fold as well as the isolated branch. As for ϵ−1 = 20 days, the agreement between the steady-state response and the observed pattern decreases when α is increased.

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