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Many present-day numerical weather prediction (NWP) models are run at resolutions that permit deep convection. In these models, however, the boundary layer turbulence and boundary layer cloud features are still grossly underresolved. Underresolution is also present in climate models that use a multiscale modeling framework (MMF), in which a convection-permitting model is run in each grid column of a global general circulation model. To better represent boundary layer clouds and turbulence in convection-permitting models, a parameterization was developed that models the joint probability density function (PDF) of vertical velocity, heat, and moisture. Although PDF-based parameterizations are more complex and computationally expensive than many other parameterizations, in principle PDF parameterizations have several advantages. For instance, they ensure consistency of liquid (cloud) water and cloud fraction; they avoid using separate parameterizations for different cloud types such as cumulus and stratocumulus; and they have an appropriate formulation in the ‘‘terra incognita’’ in which updrafts are marginally resolved. In this paper, an implementation of a PDF parameterization is tested to see whether it improves the simulations of a state-of-the-art convection-permitting model. The PDF parameterization used is the Cloud LayersUnifiedBy Binormals (CLUBB)parameterization.The host cloud-resolving model usedis theSystem forAtmosphericModeling(SAM).SAMisrunbothwithandwithoutCLUBBimplementedinit.Simulations of two shallowcumulus(Cu)cases andtwo shallowstratocumulus(Sc)casesarerun ina 3D configurationat 2-, 4-, and 16-km horizontal grid spacings. Including CLUBB in the simulations improves some of the simulated fields—such as vertical velocity variance, horizontal wind fields, cloud water content, and drizzle water content—especially in the two Cu cases. Implementing CLUBB in SAM improves the simulations slightly at 2-km horizontal grid spacing, significantlyat4-kmgridspacing,andgreatlyat 16-kmgridspacing.Furthermore,thesimulationsthatinclude CLUBB exhibit a reduced sensitivity to horizontal grid spacing.

PDF Parameterization of Boundary Layer Clouds in Models with Horizontal Grid Spacings from 2 to 16 km