A simple, vertically resolved model of tropical disturbances with a humidity closure

A simple linearized model for large-scale disturbances in the tropical non-rotating atmosphere with a humidity closure is presented. The precipitation rate is assumed to be directly proportional to the precipitable water in this closure with a relaxation time chosen to be one day. The model includes cloud-radiation interactions (CRI) and wind-induced surface heat exchange (WISHE). It is vertically resolved, with the single assumption that the fixed vertical profile of heating has the structure of the first baroclinic mode. The vertical profile of vertical velocity is calculated with a radiation boundary condition.

The modeled modes are of three types; fast gravity waves that resemble adiabatic modes with fundamental baroclinic vertical structure; convectively coupled gravity modes that are damped and move with a speed of 17 m/s; and a "moisture mode" which is normally stationary, but which propagates eastward under the influence of WISHE. This mode is unstable under the influence of CRI and gross moist instability.

The phase speed of convectively coupled gravity modes is close to observed speed of tropical Kelvin waves. This is a consequence of the dynamical structure of the model in which there are no a priori assumptions except the imposed vertical heating profile.

We believe that the moisture mode is related to the Madden-Julian oscillation (MJO). Thus, for the first time we have a model that simultaneously captures the MJO and convectively coupled gravity waves, the latter of which map to Kelvin modes in the equatorial beta plane case. The damping of the convectively coupled gravity wave is the biggest flaw of the model and is perhaps due to the absence of convective available potential energy (CAPE) or convective inhibition (CIN) in our convective closure.