Using Idealized Coherent Structures to Parameterize Momentum Fluxes in a PBL Mass-Flux Model

Abstract

In 2001, the authors presented a higher-order mass-flux model called assumed distributions with higher-order closure (ADHOC), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars such as potential temperature or water vapor mixing ratio. ADHOC is intended for application as a PBL parameterization. It 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. The first version of ADHOC was incomplete in that the horizontal momentum equations, the vertical fluxes of horizontal momentum, the contributions to the turbulence kinetic energy from the horizontal wind, and the various pressure terms involving covariances between pressure and other variables were not incorporated into the assumed distribution framework. Instead, these were parameterized using standard methods. This paper describes an updated version of ADHOC. The new version includes representations of the horizontal winds and momentum fluxes that are consistent with the mass-flux framework of the model. The assumed joint probability distribution is replaced by an assumed joint spatial distribution based on an idealized coherent structure, such as a plume or roll. The horizontal velocity can then be determined using the continuity equation, and the momentum fluxes and variances are computed directly by spatial integration. These expressions contain unknowns that involve the parameters of the assumed coherent structures. Methods are presented to determine these parameters, which include the radius of convective updrafts and downdrafts and the wavelength, tilt, and orientation angle of the convective rolls. The parameterization is tested by comparison with statistics computed from large-eddy simulations. In a companion paper, the results of this paper are built on to determine the perturbation pressure terms needed by the model.