Vertical overlap of probability density functions of cloud and precipitation hydrometeors

Abstract

Coarse‐resolution climate models increasingly rely 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 subcolumns are drawn from these PDFs for microphysics or radiation parameterizations, appropriate vertical correlations must be enforced via PDF overlap specifications. This study evaluates the representation of PDF overlap in the Subgrid Importance Latin Hypercube Sampler (SILHS) employed in the assumed PDF turbulence and cloud scheme called the Cloud Layers Unified by Binormals (CLUBB). PDF overlap in CLUBB‐SILHS simulations of continental and tropical oceanic deep convection is compared with overlap of PDF of various microphysics variables in cloud‐resolving model (CRM) simulations of the same cases that explicitly predict the 3‐D structure of cloud and precipitation fields. CRM results show that PDF overlap varies significantly between different hydrometeor types, as well as between PDFs of mass and number mixing ratios for each species—a distinction that the current SILHS implementation does not make. In CRM simulations that explicitly resolve cloud and precipitation structures, faster falling species, such as rain and graupel, exhibit significantly higher coherence in their vertical distributions than slow falling cloud liquid and ice. These results suggest that to improve the overlap treatment in the subcolumn generator, the PDF correlations need to depend on hydrometeor properties, such as fall speeds, in addition to the currently implemented dependency on the turbulent convective length scale.

Dependence of Vertical Alignment of Cloud and Precipitation Properties on Their Effective Fall Speeds

“…Results presented above and earlier in Ovchinnikov et al () point to the fall speed as one of the primary factors controlling the PDF overlap, as measured by the correlation length scale z 0 . Here, we seek to quantify the z 0 —fall speed relationship in a way that can be used in a parameterization of PDF correlation in large‐scale models.…”

“…The dependence of the rank correlation on the layer separation is mitigated by computing a correlation length scale, defined as a distance over which the rank correlation drops by a factor of e −1 , assuming exponential decay of correlation with increasing distance between the layers. This study builds on the work by Ovchinnikov et al (), who found that the vertical overlap for PDFs of different properties (i.e., number and mass mixing ratios) and different hydrometeor types (i.e., cloud liquid and ice, rain, snow, and graupel) varies widely and suggested that corresponding fall speed might be the primary factor controlling the degree of their vertical alignment. Here, we quantify the relationship between the length scale z 0 for the correlation between PDFs of a cloud or precipitation property at two levels and the mean fall speed V f for that property using cloud‐resolving model (CRM) simulations and radar profiler observations.…”

“…That study used SAM model with a one‐moment microphysics, in which cloud water diagnosed from the prognostic total water variable is partitioned into liquid and ice using a simple temperature‐dependent formulation. Using the same model (SAM) with a more elaborate two‐moment microphysics, we find qualitatively similar z 0 profiles for cloud liquid and ice water, but significantly different profiles for rain and other precipitating species (see also Ovchinnikov et al, ). Thus, additional studies are needed to find a more general way to represent variation of z 0 with altitude.…”

“…Figure 9 shows z 0 for ranked correlation coefficients computed for PDFs of model-predicted hydrometeor mass mixing ratios at two adjacent levels. Unlike Ovchinnikov et al (2016), who analyzed the behavior of z 0 profiles over selected 24-hr periods, here z 0 evolution is presented for the entire simulations, although the main features of the mean profiles remain the same. These include larger z 0 (i.e., stronger PDF correlations) for rain and graupel compared to snow, which is especially evident in the SGP simulation, and a significantly different PDF correlation for rain mixing ratio above and below the melting level.…”

“…Previous studies have examined vertical alignment of various cloud properties, including radar-retrieved cirrus ice water content (Hogan & Illingworth, 2003), model-generated total (vapor + cloud liquid and ice) water content (Pincus et al, 2005), and cloud (liquid + ice) water content (Raisanen et al, 2004;Wang, 2017). Ovchinnikov et al (2016) used a cloud-resolving model to examine the vertical PDF overlap of 10 microphysical variables. that is, number and mass mixing ratios for five hydrometeor types: cloud liquid, rain, cloud ice, snow, and graupel.…”