The wavelength dependence of the gross moist stability and the scale selection in the instability of column integrated moist static energy

Gross moist stability (GMS), a measure of how efficiently divergent flow exports column-integrated moist static energy (MSE), is a widely used quantity in current simplified models of the tropical mean circulation and intraseasonal variabilities such as the Madden–Julian oscillation (MJO), where it is often assumed to be constant. In this paper, it is shown, with cloud-system-resolving model experiments that incorporate feedback from the large-scale flow, that the GMS is smaller at longer wavelengths. The reason for this wavelength dependence is that temperature anomalies required to maintain a given divergent flow increase with wavelength. At long wavelengths, the required temperature anomalies become sufficiently strong to affect the shape of convective heating. As a consequence, the divergent flow is forced to be less top heavy in order to maintain the balance of momentum, heat, and moisture, as well as consistency with the behavior of cumulus convection. A simple model is constructed to illustrate this behavior. Given the ongoing theoretical efforts that view the MJO as resulting from instability in column-integrated MSE, the results presented here provide a planetaryscale selection for such instability, which is absent in current theoretical models that assume a constant GMS.