A linear stochastic dynamical model of ENSO. Part II: Analysis

In this study the behavior of a linear, intermediate model of ENSO is exami ned under stochastic forcing. The model was developed in a companion paper (Part I) and is derived from the Zebiak-Cane ENSO model. Four variants of t he model are used whose stabilities range from slightly damped to moderatel y damped. Each model is run as a simulation while being perturbed by noise that is uncorrelated (white) in space and time. The statistics of the model output show the moderately damped models to be more realistic than the sli ghtly damped models. The moderately damped models have power spectra that a re quantitatively quite similar to observations, and a seasonal pattern of variance that is qualitatively similar to observations. All models produce ENSOs that are phase locked to the annual cycle, and all display the "sprin g barrier'' characteristic in their autocorrelation patterns, though in the models this "barrier'' occurs during the summer and is less intense than i n the observations (inclusion of nonlinear effects is shown to partially re medy this deficiency). The more realistic models also show a decadal variab ility in the lagged autocorrelation pattern that is qualitatively similar t o observations. Analysis of the models shows that the greatest part of the variability come s from perturbations that project onto the first singular vector, which the n grow rapidly into the ENSO mode. Essentially, the model output represents many instances of the ENSO mode, with random phase and amplitude, stimulat ed by the noise through the optimal transient growth of the singular vector s. The limit of predictability for each model is calculated and it is shown th at the more realistic (moderately damped) models have worse potential predi ctability (9-15 months) than the deterministic chaotic models that have bee n studied widely in the literature. The predictability limits are strongly correlated with the stability of the models' ENSO mode-the more highly damp ed models having much shorter limits of predictability. A comparison of the two most realistic models shows that even though these models have similar statistics, they have very different predictability limits. The models hav e a strong seasonal dependence to their predictability limits. The results of this study (with the companion paper) suggest that the linea r, stable dynamical model of ENSO is indeed a plausible hypothesis for the observed ENSO. With very reasonable levels of stochastic forcing, the model produces realistic levels of variance, has a realistic spectrum, and quali tatively reproduces the observed seasonal pattern of variance, the autocorr elation pattern, and the ENSO-like decadal variability.