Validity of a Linear Stochastic View of ENSO in an ACGCM
Authors: Kallummal Rameshan , Kirtman Ben P. 
Published: May 2008

Abstract
Calculations of the optimal perturbations of an anomaly coupled ocean–atmosphere general circulation model (ACGCM) have been performed using a set of linear (Markov) models best fit to 300 years of continuous simulations. This study aims (i) to verify some of the findings regarding optimals from earlier studies based on relatively less complex coupled models and (ii) to assess how well a linear stochastic model reproduces the interannual variability of the tropical Pacific in the ACGCM.
The Markov models are built in a multivariate (i.e., sea surface temperature, heat content, zonal and meridional components of wind stress, and total heat flux) empirical orthogonal function (MEOF) space with reduced dimension while retaining the important covariability. These empirical models are trained in the first 300 yr and verified in the last 50 yr of the data. The Markov model with eight retained MEOFs (MK8) shows, in terms of the anomaly correlations, the best predictive skill of interannual variability in the ACGCM for up to about a year.
The main conclusions of this study are as follows:
(i) The singular values of MK8 show a strong seasonal dependence, indicating seasonal variation in the Markov models, which in turn implies the importance of seasonality in the internal dynamics. From the perspective of a stochastic model, this may also indicate that neither the nonlinearity in the system nor the seasonality in the stochastic forcing is necessary for the phase locking of the model ENSO to the annual cycle.
(ii) In the tropical Pacific, a narrow region straddling the equator is conducive for the transient growth of perturbations, independent of the season; however, a migration of the maximum growth region from the central to the eastern Pacific from spring to summer to winter is also observed. The western warm pool region is capable of generating transient growth throughout the year. However, the amplitude of the optimal shows some modulation with the annual cycle. Another region where considerable transient growth can occur is the northern subtropics. Therefore, the optimals in this study encompass the features of a coupled model with a statistical atmosphere as well as the features of the coupled model with a dynamical atmosphere in which deep convective parameterization is included.
(iii) In general, the geographical locations of the optimals do not depend on whether EOF analysis is performed on a covariance matrix or on a correlation matrix. Nevertheless, their spatial extent is larger when the correlation matrix is used.
(iv) The spatial distribution of the ratio of local amplitudes of the residual (misfit of the linear models) to the respective local anomaly points to the fact that, in general, a narrow region between 5°S and 5°N in the Pacific Ocean is in a linear regime. However, in the off-equatorial region this linear approximation generally fails. In the equatorial western Pacific west of 160°E, a region where abundant convective activity occurs both in the model and in nature, nonlinear dynamics is important. Therefore, this analysis hints at the possibility of accommodating the two competing points of views of ENSO into a single framework, by virtue of the fact that both linear and nonlinear dynamics seems to operate in a nonoverlapping manner in both space and time.