Southern Hemisphere Annular Mode Variability and the Role of Optimal Nonmodal Growth

Abstract

The southern annular mode is the leading mode of Southern Hemisphere circulation variability, the temporal evolution of which is characterized by large amplitudes and significant persistence. Previous investigators have suggested a positive feedback mechanism that explains some of this low-frequency variance. Here, a mechanism is proposed, involving transient nonmodal growths of the anomalies, that is at least as effective as the positive feedback mechanism in increasing the low-frequency variance of the southern annular mode. Using the vector autoregressive modeling technique, a number of linear inverse models of southern annular mode variability from National Centers for Environmental Prediction?Department of Energy (NCEP?DOE) Reanalysis 2 is derived. These models are then analyzed applying the ideas of the generalized stability theory. It is found that, as a consequence of the nonnormality of the system matrices, a significant increase in the low-frequency variance of the southern annular mode occurs through optimal nonmodal growth of the zonal wind anomalies. The nonnormality arises mainly from the relative dominance of the eddy forcing, while the nonmodal growth is caused by the interference of the nonorthogonal eigenvectors of the nonnormal system matrix. These results are demonstrated first in a simple model that retains only the two leading modes of the zonally averaged zonal wind and eddy-forcing variability, and then in a more general model that includes all the important modes. Using the more general model the authors have determined, among other things, the optimal initial perturbation and the time scale over which it experiences the maximum nonmodal growth to evolve into the pattern associated with the southern annular mode.