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

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 variations and tend to propagate equatorward and westward in accord with findings from previous theoretical and modeling studies. Instantaneous growth rates and propagation characteristics of idealized transient disturbances are diagnosed via the linearized atmospheric potential vorticity equation and via propagation characteristics of atmospheric equatorial Rossby waves. Constraints on the poleward extent of initial conditions or imposed steady forcing that can lead to tropical meridional mode variations are identified through analysis of the steady coupled equations. Three constraints limit the poleward extent of forcing that can generate tropical meridional mode variations: (i) a dynamical constraint imposed by the damping rate of the temperature equation as well as the propagation speed of the mode along its wave characteristic; (ii) a constraint imposed by the effectiveness of zonal wind variations in generating surface latent heat flux anomalies; and (iii) the surface moisture convergence, which limits the poleward extent and strength of ocean to atmosphere coupling.