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the Soviet Union indicates that droplet size spectra in stratocumulus are distributed
in logarithmic normal (Levin
1954
) or gamma (Borovikov et al.
1963
) forms. The
droplet size spectra in stratus and stratocumulus are now commonly described by
the gamma distribution. Droplet size spectra in altostratus and altocumulus as a
function of temperature and cloud thickness are given according to Mazin and Khr-
gian (
1989
) (Hobbs
1993
).
3.4
Rain Drop Size Distribution
3.4.1
Classical Cloud Microphysical Concepts
Rain drops are large enough to have a size-dependent shape which cannot be char-
acterized by a single length. The conventional resolution is to describe rain spectra
in terms of the equivalent diameter
D
0
defined as the diameter of a sphere of the
same volume as the deformed drop. The overall shaping of the spectrum is obvi-
ously quite complicated, and determined in part by such meteorological variables as
temperature, relative humidity, and wind in the subcloud region.
Various empirical relations have been advanced to describe the size spectra of
raindrops. One often used is the size distribution proposed by Best (
1950
). Probably
the most widely used description for the raindrop spectrum is the size distribution
of Marshall and Palmer (MP) (Marshall and Palmer
1948
), which is based on the
observations of Laws and Parsons (
1943
). More detailed studies have demonstrated
that the MP distribution is not sufficiently general to describe most observed rain-
drop spectra accurately.
Numerous studies have also used the gamma distribution. Another alternative
is the log normal distribution. Detailed comparison between the raindrop spectra
actually observed and these empirical distributions show that in most cases only a
partial fit can be achieved at best.
The observed raindrop spectra also show, apart from a main mode, some second-
ary modes. It is reasonable to attribute the main mode as well as the subpeaks to col-
lisional drop breakup. Unexpectedly, these peaks are not present in all rain DSDs.
One explanation for this may be that the breakup-induced peaks become masked
due to turbulent and evaporative effects. Additional factors which complicate an in-
terpretation of observed raindrop distributions are related to instrumental problems
(Pruppacher and Klett
1997
).
3.4.2
Cloud Microphysics and Self-Similar Turbulent
Atmospheric Flows
Lovejoy and his group (Lovejoy and Schertzer
2008
,
2010
) have done pioneer-
ing studies on self-similar fractal fluctuations ubiquitous to turbulent atmospheric
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