It has been investigated if the stochastic theory can be applied to the decadal variations (Frankignoul et al. 1997). Their result is fairly consistent with the theory such that the stochastic wind stress reddens the power spectrum of the ocean dynamic field. However, observed temperature anomalies show a distinct spectral peak around decades (e.g. Robertson 1996: Deser and Blackmon 1993), so the subject of interest here is a process that compensates this inconsistency.
Fig. 5. Power spectra of T anomalies in the p-region in (a) the North Atlantic and (b) the North Pacific. The explanation for each case such as 'TD-couple' is given in the text.
In the system considered here, the decadal oscillation is weakly unstable and gain the energy through the positive feedback between the atmosphere and the ocean. Does the decadal peak shown disappear if the atmosphere-ocean coupling does not exit ? In order to answer this question, we calculated power spectra for the additional three cases with γs = 6: the noise forcing without any coupling (denoted as 'uncoupled'), the noise forcing with dynamical coupling ('D-coupled'), and the noise forcing with thermodynamic coupling ('T-coupled'). Breaking off only the dynamic or thermodynamic coupling is unrealistic, but those cases may be useful to discuss the role of each coupling in the decadal variability.
The power spectra of temperature anomalies in p-regions for the above cases are superimposed on the spectra for the standard and TD-coupled cases (Fig. 5). Almost all the cases with noise of γs = 6 shows larger variance than the standard one. Both in the North Atlantic and in the North Pacific, uncoupled cases show the temperature spectra nearly identical to the red noise spectrum, consistent with the stochastic theory. This result indicates that the atmosphere-ocean coupling has a significant role in generating the decadal spectral peak even if the coupled component is much smaller than the stochastic forcing. A comparison between spectra of the uncoupled and D-coupled cases reveal that the power spectra of the dynamical coupling increase the decadal peaks without change of the varianceat lower frequency.
