Convective quasi-equilibrium revisited, part I: theory

A dominant assumption about the interaction of deep moist convection and its environment over the past several decades has been that the time scale for the elimination of convective available potential energy by convection is small compared to other time scales in the system, e. g., of order a few hours. However, an alternative thread challenging this assumption has developed recently. This thread focuses on the idea that convection is controlled on short time scales more by factors such as integrated tropospheric moisture and convective inhibition in the lower troposphere.

We present a theoretical analysis of temperature and moisture tendencies in the atmosphere due to deep moist convection. Convection is considered to be an agent causing the vertical mixing of two quasi-conserved variables, the moist entropy and the total cloud water mixing ratio. Non-conservative processes affecting the entropy are surface latent and sensible heat fluxes and atmospheric radiation, whereas those acting on the latter are precipitation production and evaporation as well as surface moisture fluxes.

Estimates of conservative mixing by convection in the troposphere indicate that temperature and moisture tendencies resulting from such mixing have slow time scales, i. e., of order days to weeks. Surface heat fluxes and radiation affect the atmosphere on similarly long time scales. Only precipitation production acts with sufficient rapidity to produce adjustment time scales on the order of hours. Since the majority of precipitation is produced in the lower and middle troposphere, it follows that rapid adjustment, as envisioned by the convective quasi-equilibrium hypothesis, should be confined to the lower part of the troposphere, with slow adjustment to changes in the environment occurring in the upper troposphere.

This hypothesis is tested in a toy cumulus parameterization based on the above ideas. As expected, when lower tropospheric temperatures are modified from equilibrium values in a radiative-convective equilibrium calculation, a rapid precipitation pulse occurs on the time scale of a few hours, combined with a further slow adjustment on the time scale of days. However, similar modification of upper tropospheric temperatures produces no precipitation pulse, only a slow relaxation back to equilibrium.

Part II of this presentation reports similar results obtained using a cloud-resolving numerical model.