Cumulus Cloud Model - Rain Formation in Warm Clouds: General Systems Theory - page 50

• The probability distribution for amplitude as well as variance of fractal fluc-
tuations of meteorological parameters are given by the same universal inverse
power-law function P, namely P = τ − 4 t where the normalized standard deviation
t designates the eddy length step growth number. Such a result that the additive
amplitudes of eddies when squared represent the probability densities of the fluc-
tuations is observed in the subatomic dynamics of quantum systems. Therefore,
fractal fluctuations are signatures of quantum-like chaos in dynamical systems.
• The probability distribution P of amplitudes of fractal fluctuations is close to
the statistical normal distribution for values of normalized standard deviation t
values equal to or less than two. The probability of occurrence of extreme events,
i.e. normalized deviation t values greater than two, is close to zero as given by
the statistical normal distribution, while P distribution for fractal fluctuations
gives appreciably high values as observed in practice.
• Atmospheric eddy energy (variance) spectrum follows the universal inverse
power-law form P = τ − 4 t indicating long-range space-time correlations between
local (small-scale) and global (large-scale) perturbations.
• Atmospheric particulates are suspended in the fractal fluctuations of vertical ve-
locities with amplitudes given by the universal inverse power-law P . A universal
scale-independent mass or radius size distribution for homogeneous suspended
atmospheric particulates is expressed as a function of the golden mean τ, the
total number concentration and the mean volume radius. The general systems
theory model for aerosol size distribution is scale-free and is derived directly
from atmospheric eddy dynamical concepts. At present, empirical models such
as the log-normal distribution with arbitrary constants for the size distribution of
atmospheric suspended particulates are used for quantitative estimation of earth-
atmosphere radiation budget related to climate warming/cooling trends.
• Numerical computations of cloud parameters were performed for two different
cloud-base CCN mean volume radius, namely 2.2 and 2.5 μm and computed val-
ues are compared with the observations. Cloud-base vertical velocity production
by MFC is the main driving agent for the cloud growth processes. The cloud-
growth time is about 30 min as observed in practice (McGraw and Liu 2003 ) and
is the same for the two CCN spectra since the primary trigger for cloud growth
is the persistent turbulent energy generation by condensation at the cloud base in
primary turbulent eddy fluctuations of radius r * and perturbation speed w * . How-
ever, for the larger CCN mean volume radius, namely 2.5 μm, raindrops form
earlier at a lower level and extend up to higher levels in the cloud. Under suitable
conditions of humidity and moisture in the environment, warm rain formation
can occur at a time interval short as 30 min.
• Hygroscopic particle seeding alters the dynamics of warm clouds and enhances
rainfall up to 100 % under favourable conditions of moisture supply in the envi-
ronment.