The Moisture Mode in the Quasi-Equilibrium Tropical Circulation Model. Part I: Analysis Based on the Weak Temperature Gradient Approximation

Abstract

Abstract The moisture mode in a simplified version of the quasi-equilibrium tropical circulation model (QTCM) of Neelin and Zeng is analyzed. Perturbation expansion based on the ratio of temperature tendency to adiabatic cooling simplifies the system and dispersion relationship. The weak temperature gradient (WTG) approximation of Sobel, Nilsson, and Polvani naturally emerges as the dynamical balance of the moisture mode. The condition of the expansion can be phrased in terms of the nondimensional wavenumber and is satisfied in the tropics even for the planetary scale. The WTG growth rate equation demonstrates that the moisture mode is unstable when moist static energy sources such as cloud radiative forcing and gustiness-enhanced evaporation exceed its export. Wind-induced surface heat exchange does not affect the growth rate at the leading order, although it propagates the mode eastward in the mean easterly wind. For typical values of parameters, the time scale of moisture mode instability is several days. Nonlinear WTG calculations show that the moisture mode nonlinearly saturates by a thermodynamic limiting process. In the standard parameter regime, a phase diagram reveals two stable fixed points in addition to the unstable solution of radiative–convective equilibrium.