On the covariability of cloud and rain water as a function of length scale

Microphysics parameterizations in large-scale models often account for subgrid variability in the calculation of process rates by integrating over assumed subgrid distributions of the input variables. The variances and covariances that define distribution width may be specified or diagnosed. The correlation rho of cloud and rain mass mixing ratio/liquid water content (LWC) is a key input for accurate prediction of the accretion rate and a constant value is typically assumed. In this study, high-frequency aircraft measurements with a spatial resolution of approximate to 22 cm are used to evaluate the scaling behavior of cloud and rain LWC (q(c) and q(r), respectively) and to demonstrate how and why covariability varies with length scale l. It is shown that power spectral densities of both q(c) and q(r) exhibit scale invariance across a wide range of scales (2.04-142 m for q(c); 33-1.45 x 10(4) m for q(r)). Because the cloud-rain cospectrum is also scale invariant, rho is therefore expected to vary with l. Direct calculation of rho shows that it generally increases with l, but there is significant variability in the rho-l relationship that primarily depends on cloud drop number concentration N and cloud cellular organization, suggesting that rho may also vary with cloud regime. A parameterization of rho as a function of l and N is developed from aircraft observations and implications for diagnosis of rho from limited-area model output are also discussed.