| Summary: | 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 === Science, Faculty of === Earth, Ocean and Atmospheric Sciences, Department of === Graduate
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