Interannual Variability in a Tropical Atmosphere–Ocean Model: Influence of the Basic State, Ocean Geometry and Nonlinearity

Abstract

The behavior of a tropical coupled atmosphere/ocean model is analyzed for a range of different background states and ocean geometries. The model is essentially that of Cane and Zebiak for the tropical Pacific, except only temporally constant background states are considered here. For realistic background states and ocean geometry, the model solutions feature oscillations of period of 3–5 yr. By comparing the full model solution with a linearized version of the model, it is shown that the basic mechanism of the oscillation is contained within linear theory. A simple linear analog model is derived that describes the nature of the interannual variability in the coupled tropical atmosphere–ocean system. The analog model highlights the properties that produce coupled atmosphere–ocean instability in the eastern ocean basin, and the equatorial wave dynamics in the western ocean basin that are responsible for a delayed, negative feedback into this instability growth. The growth rate of the local instability c together with the magnitude b and lag of the wave-induced processes determine the nature of the interannual variability displayed in the coupled model. Specifically, these processes determine the growth rate of the coupled system and, when the solutions are oscillatory, the period of the oscillation. The terms b, c, and are set by the background state of the atmosphere and ocean, and the geometry of the ocean basin. The simple analog model is used to design and interpret a set of experiments using the full linear and nonlinear numerical models of the coupled atmosphere ocean system in the Pacific. In these experiments, we examine the effects of the assumed basic state and ocean geometry on the interannual variability of the coupled system. The simple model is shown to be a remarkably good proxy of the full linear and nonlinear numerical models. The limiting nonlinearity in the full numerical model is shown to be the dependence of the temperature of the upward water on the thermocline depth. However, we find the essential processes that describe the local instability growth rate and period of the interannual oscillations in the coupled system are linear. Nonlinearities primarily act as a bound on the amplitude of the final state oscillations, and decrease the period of the firm state oscillations by about 10 percent from that obtained in the small amplitude regime of the full coupled model and the linear analog model. The nonlinear analog model for the full numerical model is derived, and compared with that proposed by Suarez and Schopf. The numerical and analog models help to explain why organized, large amplitude, interannual variability is prominent in the tropical Pacific basin, and not in Atlantic and Indian basins.