Linear Response Functions of a Cumulus Ensemble to Temperature and Moisture Perturbations and Implications for the Dynamics of Convectively Coupled Waves

An approach is presented for the construction of linear response functions of a cumulus ensemble to large-scale temperature and moisture perturbations using a cloud system resolving model (CSRM). A set of time-invariant, horizontally homogeneous, anomalous temperature and moisture tendencies is added, one at a time, to the forcing of the CSRM. By recording the departure of the equilibrium domain-averaged temperature and moisture profiles from those of a control experiment and through a matrix inversion, a sufficiently complete and accurate set of linear response functions is constructed for use as a parameterization of the cumulus ensemble around the reference mean state represented by the control experiment. This approach is applied to two different mean state conditions in which the CSRM, when coupled with 2D gravity waves, exhibits interestingly different behaviors. With a more strongly convecting mean state forced by the large-scale vertical velocity profile taken from the Tropical Ocean and Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA COARE), spontaneous development of convectively coupled waves requires moisture variations above the boundary layer, whereas with a mean state of radiative-convective equilibrium (RCE) not forced by large-scale vertical advection, the development of convectively coupled waves is stronger and persists even when moisture variations above the boundary layer are removed. The linear response functions were able to reproduce these behaviors of the full CSRM with some quantitative accuracy. The linear response functions show that both temperature and moisture perturbations at a range of heights can regulate convective heating. The ability for convection to remove temperature anomalies, thus maintaining convective neutrality, decreases considerably from the lower troposphere to the middle and upper troposphere. It is also found that the response of convective heating to a lower tropospheric temperature anomaly is more top-heavy in the RCE case than in the TOGA COARE case. Comparing the linear response functions with the treatment of convection in an earlier simple model by the present author indicates general consistency, lending confidence that the instability mechanisms identified in that model provide the correct explanation to the instability seen in the CSRM simulations and the instability's dependence on the mean state.