Transient Growth of Thermodynamically Coupled Variations in the Tropics under an Equatorially Symmetric Mean State*

Abstract

The dynamics of thermodynamically coupled disturbances in the tropics that bear a strong resemblance to observed meridional mode variations are investigated using two simple linear coupled models. Both models involve an ocean equation coupled to the atmosphere via the linearized effect of zonal wind variations on the surface bulk latent heat flux. The two models differ in their atmospheric components, which consist of (i) a Gill–Matsuno style model of the free troposphere in which atmospheric heating is parameterized to be linearly proportional to sea surface temperature and (ii) a reduced-gravity model of the tropical boundary layer in which SST anomalies are associated with hydrostatic pressure perturbations throughout the boundary layer. Both atmospheric models follow the standard shallow-water equations on an equatorial beta plane. Growth rates and propagation of coupled disturbances are calculated and diagnosed via eigenanalysis of the linear models and singular value decomposition of the Green’s function for each model. It is found that the eigenvectors of either model are all damped, not orthogonal, and not particularly meaningful in understanding observed tropical coupled variability. The nonnormality of the system, however, leads to transient growth over a time period of about 100 days (based on the choice of parameters in this study). The idealized initial and final conditions that experience this transient growth resemble observed tropical meridional mode variation…