Coupling of a Linearized Deep Convection Tendencies Matrix to Global Dynamics

A matrix (linear response function) which gives anomalous convective tendencies as a function of anomalies in temperature and moisture profiles has been devised by cleverly interrogating a periodic cloud resolving model (Kuang 2010 JAS). This is essentially an linearized anomaly cumulus parameterization, when applied at every time step in the columns of a global model. As shown by Kuang initially, this matrix, despite having negative eigenvalues, makes convectively coupled waves (CCWs) when coupled with dynamical equations. Here we are able to use full spherical dynamics, and linearize about realistic basic states maintained with time-independent tendencies. Within this framework, we describe both the effects of basic state structure on CCWs, and the feedbacks of CCWs onto the mean climate state. Furthermore, the matrix can be edited (e.g. to adjust the sensitivity to midlevel humidity). How does this change the nature of the CCWs and other potentially advection-dependent variability produced by the model?