Nonlinear response to anomalous tropical forcing

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 Nino 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 (20 days) was chosen such that this soluiton is marginally stable. The steady states were computed as a function of a dimensionless parameter alpha, 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 (alpha << 1) compares well with the observed seasonal mean anomaly pattern. After the fold at alpha=0.65, the agreement is smaller. A further increase in alpha 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 behaviour despite their unstable nature. The resulting time-mean patterns are very similar to the steady states. Periodic, quasi-periodic and complete chaotic behaviour are observed.
Increasing the Rayleigh friction coefficient to 10 days results in a disappearance of the fold as well as the isolated branch. As for a Rayleigh friction of 20 days, the agreement between the steady state-response and the observed pattern decreases when alpha is increased.