Penland, C., and P. D. Sardeshmukh, 1995: The optimal growth of tropical sea surface temperature anomalies. J. Climate, 8, 1999-2024.
It is argued from SST observations for the period 1950-90 that the tropical Indo-Pacific ocean-atmosphere system may be described as a stable linear dynamical system driven by spatially coherent Gaussian white noise. Evidence is presented that the predictable component of SST anomaly growth is associated with the constructive interference of several damped normal modes after an optimal initial structure is set up by the white noise forcing. In particular, El Niño-Southern Oscillation (ENSO) growth is associated with an interplay of at least three damped normal modes, with periods longer than two years and decay times of 4 to 8 months, rather than the manifestation of a single unstable mode whose growth is arrested by nonlinearities. Interestingly, the relevant modes are not the three least damped modes of the system. Rather, mode selection, and the establishment of the optimal initial structure from which growth occurs, are controlled by the stochastic forcing. Experiments conducted with an empirical stochastic-dynamical model show that stochastic forcing not only adds energy to the system, but also plays a role in setting up the optimal structure.
It is shown that growth from modal interference can occur for as long as 18 months, which within the confines of this model defines a predictability limit for growth events. Growth associated with the stochastic forcing is also possible, but is unpredictable. The timescale on which the predictable and unpredictable components of SST growth become comparable to each other gives a more conservative predictability limit of 15 months.
The above scenario is based on empirical evidence obtained from SST anomalies alone. From the results of several tests based on statistical properties of linear and nonlinear dynamical systems, one may conclude that much of the ENSO cycle in nature is dominated by stable, forced dynamics.