The Slow Sea Surface Temperature Mode and the Fast-Wave Limit: Analytic Theory for Tropical Interannual Oscillations and Experiments in a Hybrid Coupled Model

Abstract

A modified shallow water model with simplified mixed layer dynamics and a sea surface temperature (SST) equation is employed to gain a theoretical understanding of the modes and mechanisms of coupled air-sea interaction in the tropics. Approximations suggested by a scaling analysis are used to obtain analytic results for the eigenmodes of the system. A slow time scale, unstable eigenmode associated with the time derivative of the SST equation is suggested to be important in giving rise to interannual oscillations. This slow SST mode is not necessarily linked to conventional equatorial oceanic wave modes. A useful limit of this mode is explored in which the wave speed of uncoupled oceanic wave modes is fast compared to the time scales that arise from the coupling. This is referred to as the fast-wave limit. The dispersion relationship in this limit is used to present a number of coupled feedback mechanisms, which contribute simultaneously to the instability of the SST mode. It is suggested that interannual oscillations observed in a hybrid coupled general circulation model (HGCM) are related to the slow SST mode. A method of testing applicability of the fast-wave limit in any coupled model through distorted physics experiments is presented. Such experiments with the HGCM are employed to demonstrate that the fast-wave limit is quite a good approximation for interannual oscillations at moderate coupling. It is shown that the time delay associated with oceanic wave propagation across the basin is not essential to the existence of interannual coupled oscillations. Asymptotic expressions are also derived for the eigenvalues of coupled Rossby and Kelvin wave modes in the simple model. The manner in which various coupling mechanisms affect the stability of these modes is discussed and the results are used to explain the behavior of a secondary bifurcation found in the HGCM in terms of coupled Kelvin wave instability. For coupled Rossby and Kelvin modes, various coupling mechanisms oppose one another, suggesting that instability of these modes will be less robust to changes of model parameters and basic state than that of the SST mode, in which all coupling mechanisms tend to give growth.