On the use of PDF schemes to parameterize sub‐grid clouds

Using high resolution simulations of eight well‐documented cloud cases in different climate regimes, this study investigated the statistical distributions of dynamic and thermodynamic variables in the cloud layer and examined various assumptions used by the current statistical cloud schemes. It is found that dynamic and thermodynamic variables skew differently in the cloud layer of shallow cumulus, stratocumulus, and deep convective clouds. Vertical velocity is positively skewed, but the skewed dynamic structure cannot account for the large skewness of positively skewed total mixing ratio qt and negatively skewed liquid water potential temperature θl. It is, thus, not physically sound to assume that the sub‐grid variation of different variables follows the same skewed PDF. The simulations further show that the weighted standard deviations of qt and θl have the same order of magnitude in all types of clouds, indicating that the variations of temperature and moisture are the equally important factors for sub‐grid clouds. Thus, neglecting either one of them in a statistical cloud scheme may introduce significant bias in the parameterized clouds.