Penland and Sardeshmukh [1995] have built a similar autoregressive model from the observed SST. In contrast to Blumenthal, they report that error growth is not a function of season and hypothesize that ENSO results from white noise forcing of a globally stable linearized system. At first glance, these results seem at odds with the results of Blumenthal using model output. Unfortunately, the results of these two studies cannot be directly compared because Penland and Sardeshmukh used only SST data in their model, while Blumenthal included in his Markov model SST, thermocline, and wind. Of concern, however, is that the Penland and Sardeshmukh [1995] Markov model requires that the ocean dynamics be equilibrated on timescales that are rapid compared with the SST changes. The analyses of the observations by Clarke and Li [1994] and of the ocean hindcasts reported by Mantua and Battisti [1994a] indicate this assumption is not valid for the majority of the ENSO cycle: starting from a few months prior to the peak of an ENSO and extending through the event peak, the event demise and into the cold phase of the ENSO cycle, the observations are consistent with the delayed oscillator physics for ENSO. Thus, it is not surprising that Penland and Sardeshmukh found that the Markov model could not predict with skill the termination of ENSO events.
The studies of Blumenthal [1991] and Penland and Sardeshmukh [1995] come to somewhat disparate conclusions concerning the predictability and stability of the coupled atmosphere/ocean system. Nonetheless, both studies suggest that the traditional approach to assessing the variability in the atmosphere/ocean system---identification of the fastest growing normal modes ---may not be the most instructive for understanding the predictability of the system. If one writes in matrix form the evolution equations for the linearized coupled atmosphere/ocean system X:
it becomes immediately obvious that the normal modes of the
system (the eigenvectors of 
) can not be orthogonal (i.e., 
is
not Hermitian) because of the coupling.
Thus, the fastest growing normal mode will not, in general, determine
the maximum error
growth in the coupled models; forecast skill is better explained by a study
of the projection of the initial conditions on the optimal perturbations.
More on the theory of the non-self-adjoint modes
and the theory of predictability can be found in Farrell [1990].