Abstract
The atmospheric component of E3SM relies on probability density functions (PDFs) to represent subgrid-scale variability of prognostic variables. While PDFs characterize the horizontal variability, a separate treatment is needed to account for the vertical structure of clouds and precipitation. When sub-columns are drawn from these PDFs for microphysics or radiation parameterizations, as well as for instrument simulators, appropriate vertical correlations must be enforced via PDF overlap specifications. In this presentation, we evaluate the representation of PDF overlap currently employed in the Subgrid Importance Latin Hypercube Sampler (SILHS) as part of the turbulence and cloud scheme called the Cloud Layers Unified By Binormals (CLUBB) and propose an improved treatment, which takes into account a dependence on hydrometeor properties.
In SILHS, the PDF overlap is quantified by a correlation length scale, z0, indicating how fast rank correlation of distributions at two levels diminishes with increasing level separation. We show that z0 varies widely for different properties (e.g., number and mass mixing ratios) and different hydrometeor types (cloud liquid and ice, rain, snow, and graupel) and that corresponding fall speed, Vf, is the primary factor controlling the degree of their vertical alignment, with vertical shear of the horizontal wind playing a smaller role. Linear and power-law parametric relationships between z0 and Vf are derived using cloud-resolving simulations of convection under mid-latitude continental and tropical oceanic conditions, as well as observations from vertically-pointing dual-frequency radar profilers near Darwin, Australia. Being based on a physical property (i.e., fall speed) of hydrometeors rather than artificially defined and scheme-specific hydrometeor types, the proposed parameterization of vertical PDF overlap can be applied to a wide range of microphysics treatments. It also provides a mechanism to unify currently diverse overlap treatments in microphysics, radiation, and instrument simulators in future versions of E3SM.