Vertical Alignment of Cloud and Precipitation Properties: Controlling Factors and a Parameterization for Large-scale Models

Coarse-resolution models must characterize unresolved horizontal and vertical structure of cloud and precipitation to properly treat processes, such as radiation and sedimentation, that depend on their spatial distributions in a column. This is commonly accomplished by drawing a number of profiles, or sub-columns, which collectively represent predicted subgrid horizontal variability at each model level, while at the same time ensure the desired correlation of sampled variables in the vertical. The approach represents an extension of a traditional cloud overlap assumption used to describe the probability of presence or absence of a cloud at two levels to a situation where a given property also varies horizontally inside the cloud. When the binary representation (cloud or no-cloud) of horizontal variability is replaced by a probability density function (PDF) of cloud variables, cloud occurrence overlap is replaced by a PDF overlap. The PDF overlap can be quantified by a correlation length scale, z₀, indicating how fast rank correlation of distributions at two levels diminishes with increasing level separation. In this presentation, we demonstrate 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 is the primary factor controlling the degree of their vertical alignment. A parametric relationship between z₀ and hydrometeor fall speed is 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. The functional form of z₀ – fall speed relationship is further examined using a simple conceptual model that links variability in horizontal and vertical directions and provides insights into the role of wind shear. Being based on a physical property (fall speed) of hydrometeors rather than artificially defined and model-specific hydrometeor types, the proposed parameterization of vertical PDF overlap is applicable to a wide range of microphysics treatments in regional and global models.