Implications of Convective Quasi-Equilibrium for the Large-Scale Flow

Abstract

Convective parameterizations attempt to approximate the Reynolds-averaged effects of a convective ensemble on the large-scale flow as a function of the large-scale parameters. The interaction of convective ensemble effects with the large-scale circulation can produce phenomena not found in a non-convecting atmosphere, and the theoretical understanding of this interaction has long been a goal of tropical meteorology. Since convective closures are often complicated to work with in a theoretical model, most such work has been done with very simplified representations of convection. Most commonly, these fix the vertical structure of convective heating, with its magnitude taken proportional to low-level convergence or moisture convergence. These are referred to here as convergence-feedback parameterizations. They are sometimes referred to as “CISK” parameterizations, since they may produce instabilities in the large-scale model flow known as CISK (conditional instability of the second kind). The view of the tropical circulation resulting from such models has had a strong influence upon the field, both for tropical internal variability (Charney and Eliassen 1964; Ooyama 1964; Yamasaki 1969; Hayashi 1970, 1971a,b,c; Lindzen 1974a,b; Chang and Piwowar 1974; Stevens and Lindzen 1978; Davies 1979; Crum and Stevens 1983; Lau and Peng 1987; Hendon 1988; Wang 1988; Sui and Lau 1989; Bladé and Hartmann 1993, Wang and Li 1994) and the response of the tropical atmosphere to sea surface temperature (SST) boundary conditions. In the latter case, most work has been done with very few vertical layers, usually with no moisture equation, and often with semi-empirical linkages of convective heating to SST. Nonetheless these models give useful simulations of anomalous tropical low-level winds (Gill 1980; Webster 1981; Zebiak 1986; Weare 1986; Lindzen and Nigam 1987; Neelin and Held 1987; Kleeman 1991; Wang and Li 1993), and it is of interest to seek justification for why they work, using a model with a more detailed representation of deep convection.