Analytical Prototypes for Ocean–Atmosphere Interaction at Midlatitudes. Part I: Coupled Feedbacks as a Sea Surface Temperature Dependent Stochastic Process*

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, the authors consider a linearized perturbation system with quasigeostrophic 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 noise component that depends on SST, as well as an additive component that is independent of SST. Coupling is represented by the SST dependent stochastic process, in which SST influences the probability density function of the atmospheric noise both in shifting the mean and affecting the variance. It thus includes a multiplicative noise component. 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 SST dependent stochastic process 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 the 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. 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 atmospheric spatial pattern 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 reexcites 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.