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flows and have emphasized the urgent need to incorporate, in modeling studies of
microphysics of clouds and rain, the theory of nonlinear dynamical systems as sum-
marized in the following.
Rain is a highly turbulent process yet there is a wide gap between the turbu-
lence and precipitation research. It is still common for turbulence to be invoked as
a source of homogenization, an argument used to justify the use of homogeneous
(white noise) Poisson process models of rain.
Dimensional analysis shows that the cumulative probability distribution of non-
dimensional drop mass should be a universal function dependent only on scale.
Starting in the 1980s, a growing body of the literature has demonstrated that—at
least over large enough scales involving large numbers of drops—rain has nontriv-
ial space-time scaling properties. While the traditional approach to drop modeling
is to hypothesize specific parametric forms for the DSD and then to assume spatial
homogeneity in the horizontal and smooth variations in the vertical, the nonlinear
dynamics approach on the contrary assumes extreme turbulent-induced variability
governed by the turbulent cascade processes and allows the DSD to be constrained
by the turbulent fields.
The conventional methods of modeling the evolution of raindrops give turbu-
lence at most a minor (highly “parameterized”) role: the atmosphere is considered
homogeneous and the spatial variability of the DSD arises primarily due to complex
drop interactions.
It is shown on dimensional grounds that the dimensionless cumulative DSD as
a function of the dimensionless drop mass should be a universal function of dimen-
sionless mass (Lovejoy and Schertzer
2008
). Khain et al. (
2007
) have given critical
comments to results of investigations of drop collisions in turbulent clouds and
conclude that the fact that turbulence enhances the rate of particle collisions can be
considered as being established.
3.5
Data
Four data sets, namely, two aerosol (I and II), one cloud drop size (III), and one
rain drop size (IV) were used for comparison of observed with model predicted
suspended particle size spectrum in turbulent atmospheric flows.
3.5.1
Data Set I, Aerosol Size Spectrum
TARFOX_WALLOPS_SMPS: Tropospheric Aerosol Radiative Forcing Observa-
tional eXperiment (TARFOX), Langley DAAC Project—Scanning Mobility Par-
ticle Sizer (TSI Incorporated, St. Paul, MN) data taken at Wallops ground station
(37.85° lat, − 75.48° lon) in the US Eastern seaboard. Ground-based ambient size
distribution of aerosol (10.7-749 nm diameter, fine mode) at point measurements
at 5 min time intervals was taken during the period 10th-31st July 1996. Raw data
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