Evaluation of the Bulk Mass Flux Formulation Using Large-Eddy Simulations

Abstract

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 interobject variability due to differences between the average properties of different cloud objects, and the intraobject variability due to perturbations within each cloud object. Using a simple cloud–environment decomposition, the interobject and intraobject 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 cannot be parameterized with a rescaling method. A downgradient assumption is also not appropriate to parameterize the neglected flux contributions because a nonnegligible part is associated with nonlocal 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, composed 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.

Pressure Drag for Shallow Cumulus Clouds: From Thermals to the Cloud Ensemble

“…It must therefore be parameterized with a different approach. Our findings support a treatment for pressure drag that should take as its starting point for multiple drafts with different strengths, as in the “core‐cloak” conceptual model of Gu et al (2016a) for example. A recent theoretical study (Yano, 2020) also suggests that the inhomogeneity of vertical velocity must be introduced in the plume model; otherwise, the buoyancy and entrainment effect will perfectly cancel out with the counterbalancing force from the pressure, leaving a pure drag force to prevent a steady state solution.…”

“…The Smagorinsky‐Lilly scheme (Lilly, 1962; Smagorinsky, 1963) is used for the parameterization of subgrid turbulence. Further details of the model configuration can be found in Gu et al (2020). Our analyses cover a period of equilibrium from Hour 5 to Hour 6 of the simulation, with 1 min output frequency.…”

“…The first step is to label cloudy points for which we use the criteria that cloud liquid water q l > 10 −5 kg kg −1 . Contiguous labeled points are combined to form an individual cloud object by checking the neighboring grid points in six directions, corresponding to the six faces of the grid cell around the cloudy points, until no more cloudy points are found (Gu et al, 2020).…”

“…Meanwhile, for parameterization purposes, it is the mean vertical velocity of a cloud that is often needed, rather than the velocity at updraft center. Furthermore, a recent study (Gu et al, 2020) found that a partitioning into the mean velocities of the “core” and “cloak,” namely, the strong and weak parts of the updrafts respectively, can significantly improve the representation of vertical transport in a simple bulk transport equation. This indicates the importance of predicting vertical velocities in different parts of clouds and thus the need for a better understanding of pressure drag, not only in the cloud center but also off the central axis.…”

Pressure drag for shallow cumulus clouds: from thermals to the cloud ensemble

“…Meanwhile, for parameterization purposes, it is the mean vertical velocity of a cloud that is often needed, rather than the velocity at updraft center. Furthermore, a recent study (Gu et al, 2020) found that a partitioning into the mean velocities of the "core" and "cloak," namely, the strong and weak parts of the updrafts respectively, can significantly improve the representation of vertical transport in a simple bulk transport equation. This indicates the importance of predicting vertical velocities in different parts of clouds and thus the need for a better understanding of pressure drag, not only in the cloud center but also off the central axis.…”