PDF parameterization of boundary layer clouds and turbulence at resolutions that permit deep convection

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 cloud features are still grossly under-resolved. Under-resolution is also present in climate models that use the multi-scale modeling framework (MMF), in which a convection-permitting model is run in each grid column of a global general circulation model.

In order to better represent boundary layer clouds and turbulence in NWP and MMF models, we have developed a parameterization 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 water and cloud fraction; they avoid an artificial separation of the parameterizations of different cloud types such as Cu and Sc; they have an appropriate formulation in the ``terra incognita" in which updrafts are marginally resolved; and they allow consistent results over a range of horizontal grid spacings.

In this paper, we test whether the implementation of a PDF parameterization improves the simulations of a state-of-the-art cloud-resolving model. The PDF parameterization that we use is the Cloud Layers Unified By Binormals (CLUBB) parameterization. The host cloud-resolving model that we use is the System for Atmospheric Modeling (SAM). We run SAM both with and without CLUBB implemented in it. Simulations are run in a 3D configuration at 2-km, 4-km, and 16-km horizontal grid spacings. We simulate two shallow Cu cases and two shallow Sc cases.

The simulations that include CLUBB improve the simulated vertical velocity, liquid water content, and rain water content, especially in the two Cu cases. Implementing CLUBB in SAM improves the simulations marginally at 2-km horizontal grid spacing, significantly at 4-km grid spacing, and greatly at 16-km grid spacing. The simulations that include CLUBB exhibit a reduced sensitivity to horizontal grid spacing.