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scales since the eddy of length scale
z
encloses smaller scale eddies and at the
same time forms part of internal circulations of eddies larger than length scale
z
(Sect. 1.4). The observed atmospheric suspended particulate size spectrum also ex-
hibits a decrease in number concentration with increase in particulate radius. At any
reference level
z
of measurement the mean volume radius
r
as
will serve to calculate
the normalized radius
r
an
for the different radius class intervals as explained below.
The general systems theory for fractal space-time fluctuations in dynamical sys-
tems predicts universal mass size spectrum for atmospheric suspended particulates
(Sect. 1.6.4). For homogeneous atmospheric suspended particulates, i.e., with the
same particulate substance density, the atmospheric suspended particulate mass and
radius size spectrum is the same and is given as the normalized aerosol number
concentration equal to
1
N
N
lnr
d
an
)
versus the normalized aerosol radius
r
an
, where
d(
r
r
a
(i)
r
an
is equal to
,
r
a
being the mean class interval radius and
r
as
the mean vol-
ume radius for the total aerosol size spectrum, (ii)
N
is the total aerosol number
concentration and d
N
is the aerosol number concentration in the aerosol radius class
interval d
r
a
, and (iii) d(ln
r
an
) is equal to
dr
r
as
a
for the aerosol radius class interval
r
a
a
to
r
a
+ d
r
a
.
The average normalized aerosol size spectra for fine (f) mode for Davos, Mauna
Loa, and Izanawith 54, 180, and 133 daily mean data sets, respectively, are shown in
Fig.
5.1
along with the model predicted universal normalized aerosol size spectrum.
The corresponding aerosol size spectra for coarse (c) mode are given in Fig.
5.2
.
The observed aerosol size spectra are in close agreement with model-predicted
universal spectrum for suspended particulates in the turbulent atmospheric flows.
The total average mean volume radius and total number concentration for the three
stations for the period of study are given in Fig.
5.3
. The mean volume radius and
total number concentration are minimum for Mauna Loa (Hawaii) for both fine and
coarse aerosol modes. Coarse mode particulate number concentration is a maxi-
mum for Izana (Spain).
Discussion and Conclusions
Atmospheric flows exhibit self-similar fractal fluctuations on all space-time scales.
Fractal fluctuations are ubiquitous to dynamical systems in nature such as fluid
flows, heart beat patterns, population growth, etc. Power spectra of fractal fluctua-
tions exhibit inverse power law form indicating long-range correlations, identified
as self-organised criticality. Identification and quantification of the exact physical
laws underlying the observed self-organised criticality will help predict the future
evolution of dynamical systems such as weather patterns. A general systems theory
which satisfies the maximum entropy principle of classical statistical physics re-
cently proposed by the author enables formulation of precise quantitative relations
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