Can Eddy Forcing be Responsible for the Spatial Structure of the Northern Hemisphere Annular Mode?

In order to study the origin of the spatial structure of the Northern Hemisphere Annular Mode (NAM), a linear stochastic model is constructed empirically from the output of a GCM run. Optimal stochastic forcing in terms of the maximum variance contribution, which may be potentially related to the maintenance of the NAM, is investigated. Theoretical analysis on the dominant non-modal response to the stochastic forcing shows that this dominance is jointly decided by the properties of forcing and the non-modal growth (decay). The results of computation demonstrate that the eddy forcing corresponding to the instantaneous rapid growth of the NAM, which is indicated by the instantaneous stochastic optimum, has a roughly similar but significantly different annular structure like that of the NAM. On the other hand, the eddy forcing corresponding to the stationary variance of the NAM,which is indicated by the asymptotic stochastic optimum, has a totally different structure from that of the NAM. These results, together with our general discussion on the relationship between the spatial structure of forcing and response,suggest that one should be careful when explaining the spatial structure of the NAM by that of the eddy forcing.