| description abstract | The core of the mass flux formulation, on which the majority of the current cumulus parameterizations are based, is to transport physical variables by the so-called mass flux for individual physical components, such as convective updrafts, downdrafts, and environment. These parameterizations use horizontal means over the subdomains occupied by these physical components to define the mass fluxes and transported variables. However, evaluations of the mass flux formulation against high-resolution spatial data obtained from explicit numerical models reveal that it substantially underestimates vertical transport of heat, moisture, and momentum by deep convection. The present paper proposes an alternative approach, in which the effective values weighted toward extreme values are used both for the mass flux and the transported variable to obtain an accurate estimate of vertical transport. Statistically, the distribution of convective variables is so widely distributed within individual subdomains that the vertical transports are controlled by extreme values, rather than by simple means. Evaluation for these effective values are facilitated by considering four categories depending on the sign of both the vertical velocity and the transported variable, instead of the conventional convective-type classifications. A best estimate of the effective value is obtained empirically by weighting the variable by a power of one-quarter during the averaging. A major consequence of this alternative approach is that the mass fluxes must be defined differently for the individual variables. Thus, chemical species would not be transported by the same mass flux as that for temperature or moisture. With this extra elaboration, the proposed formulation provides more robust estimation of the subgrid- scale convective transports. | |
