Evaluating the conservation of energy variables in simulations of deep moist convection

It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE - IB and MSE + KE, wherein IB is the path integral of buoyancy (B) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE - IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE - IB is better conserved in isolated deep convection, whereas MSE - IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE - IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE - IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE - IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats.