## Abstract

The optimal perturbations (singular vectors) of a dynamical coupled model, a hybrid coupled model, and a linear inverse model of ENSO are compared. The hybrid coupled model consists of a dynamical ocean model and a statistical atmospheric model. The dynamical ocean model is identical to that used in the dynamical coupled model, and the atmospheric model is a statistical model derived from long time series of the dynamical coupled model. The linear inverse model was also derived from long time series from the dynamical coupled model. Thus all three coupled models are very closely related and all produce similar ENSO oscillations. The dynamical model and hybrid model also possess similar levels of hindcast skill. However, the optimal perturbations of the tangent linear versions of each model are not the same. The hybrid and linear inverse models are unable to recover the SST structure of the optimal perturbations of the dynamical model. The SST structure of the dynamical coupled model is a result of nonnormality introduced by latent heating of the atmosphere by deep convection over the west Pacific warm pool. It is demonstrated that standard statistical techniques remove the effects of the latent heating on the nonnormality of the hybrid and linear inverse models essentially rendering them more normal than their dynamical model counterpart. When the statistical components of the hybrid coupled model and the linear inverse models were recomputed using SST anomalies that are appropriately scaled by the standard deviation of SST variability, nonnormality was reintroduced into these models and they recovered the optimal perturbation structure of the dynamical model. Even though the hybrid and linear inverse model with scaled SSTs can recover the large-scale features of the correct optimal structure, state space truncation means that the dynamics of the resulting optimal perturbations is not the same as that governing optimal perturbation growth in the dynamical model. The consequences of these results for observed estimates of optimal perturbations for ENSO are discussed.

*Corresponding author address:* Dr. Andrew Moore, University of Colorado, Campus Box 311, Boulder, CO 80309-0311.

Email: andy@australis.colorado.edu