A PDF-based parameterization of subgrid-scale hydrometeor transport in deep convection

A parameterization scheme is proposed for the subgrid-scale transport of hydrometeors in an assumed probability density function (PDF) scheme. Joint distributions of vertical velocity and hydrometeor mixing ratios are typically unknown, but marginal (1D) PDFs of these variables are available. The parameterization is developed using high-resolution simulations of continental and tropical deep convection. A 3D cloud-resolving model (CRM) providing benchmark solutions has a horizontal grid spacing of 250 m and employs the Morrison microphysics scheme, which treats prognostically mass and number mixing ratios for four types of precipitating hydrometeors (rain, graupel, snow, and ice) as well as cloud droplet number mixing ratio. The subgrid-scale hydrometeor transport scheme assumes input given in the form of marginal PDFs of vertical velocity and hydrometeor mixing ratios; in this study, these marginal distributions are provided by the cloud-resolving model. Conditional sampling and scaling are then applied to the marginal distributions to account for subplume correlations. The parameterized fluxes tested for four episodes of deep convection show good agreement with benchmark fluxes computed directly from the CRM output. The results demonstrate the potential use of the subgrid-scale hydrometeor transport scheme in an assumed PDF scheme to parameterize the covariances of vertical velocity and hydrometeor mixing ratios.