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.