Nonnormal Multidecadal Response of the Thermohaline Circulation Induced by Optimal Surface Salinity Perturbations

Abstract

Abstract Optimal perturbations of sea surface salinity are obtained for an idealized North Atlantic basin using a 3D planetary geostrophic model—optimality is defined with respect to the intensity of the meridional overturning circulation. Both optimal initial and stochastic perturbations are computed in two experiments corresponding to two different formulations of the surface boundary conditions: the first experiment uses mixed boundary conditions (i.e., restoring surface temperature and prescribed freshwater flux), whereas the second experiment uses flux boundary conditions for both temperature and salinity. The latter reveals greater responses to both initial and stochastic perturbations that are related to the existence of a weakly damped oscillatory eigenmode of the Jacobian matrix, the optimal perturbations being closely related to its biorthogonal. The optimal initial perturbation induces a transient modification of the circulation after 24 yr. The spectral response to the optimal stochastic perturbation reveals a strong peak at 35 yr, corresponding to the period of this oscillatory eigenmode. This study provides an upper bound of the meridional overturning response at multidecadal time scales to freshwater flux perturbation: for typical amplitudes of Great Salinity Anomalies, initial perturbations can alter the circulation by +2.25 Sv (1 Sv ≡ 106 m3 s−1; i.e., 12.5% of the mean circulation) at most; stochastic perturbations with amplitudes typical of the interannual variability of the freshwater flux in midlatitudes induce a circulation variability with a standard deviation of 1 Sv (i.e., 5.5% of the mean circulation) at most.