Convectively coupled Kelvin waves and moisture modes in 3-D simulations

Raymond and Fuchs, 2007 (RF07) developed a simple two dimensional linearized non-rotating model, in which the rain rate is a function of the saturation fraction and convective inhibition (CIN). The model produces two unstable modes: a convectively coupled gravity mode (which maps onto an equatorial Kelvin wave in a rotating atmosphere) and a moisture mode. The model shows that the gravity mode is driven by CIN anomalies and the moisture mode is driven by saturation fraction anomalies.

Here a numerical model has been used to simulate these two unstable modes (and perhaps other modes) in three dimensions and in a rotating atmosphere. Furthermore, different heating and moisture profiles have been applied in order to explore the mechanisms that are driving and destabilizing different modes.

The model is written by Raymond in sigma isentropic coordinates (the vertical coordinate is σ=(θ-θ_b)/(θ_t-θ_b), where θ is the potential temperature and the subscripts b and t stand for bottom and top respectively). It is a channel model on an equatorial beta plane and uses the RF07 thermodynamic parametrization. Instead of radiative boundary conditions on the top of the domain there is a sponge layer that absorbs upward moving waves, in order to prevent their reflection off the top of the domain.

The top heavy heating profiles favor the Kelvin wave. The higher the maximum heating the larger their growth rate. Kelvin waves develop for bottom heavy heating profiles as well, but their phase speeds and growth rates are very small. On the other hand, the bottom heavy heating profiles which exhibit small or negative values of gross moist stability (GMS) favor the moisture mode. More negative GMS produces higher growth rates for the moisture mode. Weak moisture modes develop for top heavy heating profiles, but their growth rate is small.