The Moisture Mode in the Quasi-Equilibrium Tropical Circulation Model. Part II: Nonlinear Behavior on an Equatorial beta Plane

Numerical calculations of a simplified quasi-equilibrium tropical circulation model (QTCM) on the equatorial beta plane have been performed to explore the nonlinear regime of the moisture mode. Sensitivity tests have examined the effects of nonlinear advection and nonlinear wind-induced surface heat exchange (WISHE). Starting from a spatially homogeneous radiative-convective equilibrium with some background gustiness, the model develops quasi-stationary moisture modes, as expected from linear analysis. Upon nonlinear saturation due to thermodynamic limiting processes, a different regime emerges. A classical Gill model augmented with a prognostic humidity variable is found to be able to capture the nonlinear dynamics of the moisture mode; the time evolution solely resides in the humidity variable, and it is possible to understand its dynamics by examining the humidity budget. A scaling analysis shows that the approximation with a Gill model is valid for disturbances whose time scale is much longer than the damping time scale of equatorial waves. When nonlinear WISHE is included, a large-scale disturbance of wavenumber 1 grows and moves westward because evaporation is enhanced to the west of increased convection. Turning on nonlinear advection leads to disturbances of wavenumber 10 that translate eastward via advection of dry air by Rossby gyres. Combining nonlinear WISHE and nonlinear advection leads to gross moist instability and prohibits long-term numerical integration, which suggests that QTCM must be refined to fully describe the nonlinear dynamics of the moisture mode.