Evaluation of the bulk mass flux formulation using large eddy simulations

In this study, bulk mass flux formulations for turbulent fluxes are evaluated for shallow and deep convection using large-eddy simulation data. The bulk mass flux approximation neglects two sources of variability: the inter-object variability due to differences between the average properties of different cloud objects, and the intra-object variability due to perturbations within each cloud object. Using a simple cloud-environment decomposition, the inter-object and intra-object contributions to the heat flux are comparable in magnitude with that from the bulk mass flux approximation, but do not share a similar vertical distribution, and so can not be parameterized with a rescaling method. A down-gradient assumption is also not appropriate to parameterize the neglected flux contributions because a non-negligible part is associated with non-local buoyant structures. A spectral analysis further suggests the presence of fine structures within the clouds. These points motivate investigations in which the vertical transports are decomposed based on the distribution of vertical velocity. As a result, a ``core-cloak" conceptual model is proposed to improve the representation of total vertical fluxes, comprised of a strong and a weak draft for both the updrafts and downdrafts. It is shown that the ``core-cloak" representation can well capture the magnitude and vertical distribution of heat and moisture fluxes for both shallow and deep convection