Parameterization of Momentum Fluxes in a PBL Mass-Flux Model

In 2001, we presented a “higher-order mass-flux model” called ADHOC, which represents the PBL’s large eddies in terms of an assumed joint distribution of the vertical velocity and scalars such as potential temperature or water vapor mixing ratio. ADHOC uses the equations of higher-order closure to predict selected moments of the assumed distribution, and diagnoses the parameters of the distribution from the predicted moments. Once the parameters of the distribution are known, all moments of interest can be computed. This version of ADHOC was incomplete, in that the horizontal velocity components and the “pressure terms” involving covariances between pressure and other variables were not incorporated into the “assumed distribution” framework. Instead, the vertical flux of horizontal momentum and the pressure terms were parameterized using standard methods. This talk will describe an updated version of ADHOC that includes consistent representations of the momentum fluxes and pressure terms. The assumed joint probability distribution is replaced by an assumed joint spatial distribution modeled on idealized coherent structures, such as plumes or rolls. The horizontal velocity and the perturbation pressure can then be determined using the continuity and momentum equations. The statistics needed to close the model can then be diagnosed. Tests of the new parameterization show encouraging agreement with statistics computed from large-eddy simulations.