Zhu, P. (2015). On the Mass-Flux Representation of Vertical Transport in Moist Convection. *J. Atmos. Sci.*, *72*(12), 4445–4468.

This study investigates to what extent the convective fluxes formulated within the mass-flux framework can represent the total vertical transport of heat and moisture in the cloud layer and whether the same approach can be extended to represent the vertical momentum transport using large-eddy simulations (LESs) of six well-documented cloud cases, including both deep and shallow convection. Two methods are used to decompose the LES-resolved vertical fluxes: decompositions based on the coherent convective features using the mass-flux top-hat profile and by two-dimensional fast Fourier transform (2D-FFT) in terms of wavenumbers. The analyses show that the convective fluxes computed using the mass-flux formula can account for most of the total fluxes of conservative thermodynamic variables in the cloud layer of both deep and shallow convection for an appropriately defined convective updraft fraction, a result consistent with the mass-flux dynamic view of moist convection and previous studies. However, the mass-flux approach fails to represent the vertical momentum transport in the cloud layer of both deep and shallow convection. The 2D-FFT and other analyses suggest that such a failure results from a number of reasons: 1) the complicated momentum distribution in the cloud layer cannot be well described by the simple top-hat profile; 2) shear-driven small-scale eddies are more efficient momentum carriers than coherent convective plumes; 3) the phase relationship between vertical velocity and horizontal momentum components is substantially different from that between vertical velocity and conservative thermodynamic variables; and 4) the structure of horizontal momentum can change substantially from case to case even in the same climate regime.