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Statistical models of cloud-turbulence interactions Jeffery, Christopher A. M.

Abstract

The application of statistical turbulence theory to the study of atmospheric clouds has a long history that traces back to the pioneering work of L. F. Richardson in the 1920s. At a phenomenological level, both atmospheric clouds and turbulence are now well understood, but analytic theories with the power to predict as well as explain are still lacking. This deficiency is notable because the prediction of statistical cloud change in response to anthropogenic forcing is a preeminent scientific challenge in atmospheric science. In this dissertation, I apply the statistical rigor of new developments in passive scalar theory to problems in cloud physics at small scales (9(10 cm), where a whitein- time or (^-correlated closure is asymptotically exact, and at large scales 0(100 km) where a statistical approach towards unresolved cloud variability is essential. Using either the 5-correlated model or a self-consistent statistical approach I investigate (i) the preferential concentration or inertial clumping of cloud droplets; (ii) the effect of velocity field intermittency on clumping; (iii) the small-scale spatial statistics of condensed liquid water density and (iv) the large-scale parameterization of unresolved low-cloud physical and optical variability. My investigations, (i) to (iv), lead to the following conclusions: Preferential Concentration: Inertial particles (droplets) preferentially concentrate at scales ranging from 6Oη at St ≈ 0.2 to 8η at St ≈ 0.6, where η is the Kolmogorov length and St is the Stokes number. Clumping becomes significant at St ≈ 0.3. Effect of Intermittency: An effective Stokes number, Stefj = St(F/3)½ where F is the longitudinal velocity-gradient flatness factor (kurtosis) explicitly incorporates velocity-gradient intermittency (i.e. non-Gaussian statistics) into the St-dependence of particle clumping. In the atmospheric boundary-layer, Steff ≈ 2.7St. Intermittency effects significantly increase the degree of preferential concentration of large cloud droplets. Cloud Spatial Scaling: Density fluctuations of an inert passive scalar are typically spatially homogeneous, whereas root-mean-square cloud liquid water (qi) fluctuations increase linearly with height above, cloud base. As a result, the qi spectral density is axisymmetric and complex. A model of low-cloud viscous-convective statistics where axisymmetric/non-homogeneous production of scalar covariance due to condensation/ evaporation is balanced by an axisymmetric rotation reproduces recent experimental measurements [Davis et al, 1999]. Low-cloud Optical Properties: The assumption of height-independence in unresolved saturation vapour density fluctuations (s) and the introduction of unresolved cloud-top height fluctuations (z't0 ) into a statistical cloud scheme couple parameterized subgrid low-cloud physical and optical variability. Analytic relationships between optical depth, cloud fraction and (s,z'top) provide a convenient framework for a G CM cloud parameterization that prognoses both the mean and variance of optical depth

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