A simple model for ocean-atmosphere interaction at midlatitudes

Effects of ocean-atmosphere feedback processes and large-scale atmospheric stochastic forcing on the interdecadal climate variability in the North Atlantic and North Pacific oceans are examined in a simple midlatitude ocean-atmosphere model. In the ocean, we consider a linearized perturbation system with quasi-geostrophic shallow-water ocean dynamics and a sea surface temperature (SST) equation for a surface mixed-layer. The atmosphere is represented as stochastic wind stress and heat flux forcing. This includes a multiplicative noise component that depends on SST, as well as an additive component that is independent of SST. The model results in both oceans indicate that large-scale additive atmospheric stochastic forcing alone (the uncoupled case) can give coherent spatial patterns in the ocean, and sometimes even a weak power spectral peak at interdecadal periods. Coupling due to the influence of SST on the probability density function of the atmospheric noise can produce a more distinct power-spectral peak relative to the uncoupled ocean. Moreover, the time and spatial scales of the interdecadal mode are insensitive to the standard deviation of multiplicative noise. Thus a deterministic feedback limit can be used to simplify the coupled model for further investigation of the physical mechanisms of the interdecadal mode.; Using a version of the coupled model with only deterministic feedbacks in the atmospheric component, an eigenvalue analysis is conducted. The interdecadal mode appears as an oscillatory, weakly decaying mode, distinct from other modes of the system. This provides confirmation that the leading EOFs and spectral peaks in the stochastically forced case are indeed associated with a well-defined large-scale interdecadal coupled mode of the system. In the uncoupled case on the other hand, the spectral peaks and EOFs are not associated with an exact mode in the sense of an eigenmode of the ocean, although they may be associated with approximate modes, namely Rossby waves that do not satisfy basin boundary conditions.; In both uncoupled and coupled cases, the period of the interdecadal oscillation is determined by the zonal length scale of atmospheric wind stress and oceanic Rossby wave dynamics. The atmosphere sets the length scale of large-scale wave motion in the ocean. This wave propagates to the west due to oceanic Rossby wave dynamics and is dissipated at the western boundary. However, in the coupled case, the SST anomalies generated by geostrophic current can feed back to the atmosphere, which, in turn, brings some information back to the east and re-excites oceanic waves there. Although the magnitude of the feedback of SST on the atmosphere is much smaller than atmospheric internal variability, its effects are significant.