Universal Spectrum for Atmospheric Suspended Particulates: Comparison with Observations: Data Set III - Rain Formation in Warm Clouds: General Systems Theory - page 81

5.2 Data

Daily mean volume particle size distribution d V ( r )/dln r (μm 3 /μm 2 ) retrieved in 22
logarithmically equidistant bins in the range of sizes 0.05 μm ≤ r ≤ 15 μm for Davos
(Switzerland) and Mauna Loa (Hawaii) for the year 2010 and Izana (Spain) for the
year 2009 were obtained from AERONET aerosol robotic network (http://aeronet.
gsfc.nasa.gov/new_web/data.html). For Izana (Spain), the complete data set for the
12-month period of 2009 was available and hence it was used. Daily average data
are calculated from all points for each day when three (3) or more points are avail-
able. Data sets for a total of 54, 180, and 133 days, respectively, were available
for the three stations Davos, Mauna Loa, and Izana. The formulas for calculating
standard parameters of the particle size distribution (http://aeronet.gsfc.nasa.gov/
new_web/Documents/Inversion_products_V2.pdf) are given below.
AERONET retrieves the aerosol size distribution of the particle volume d V ( r )/
dln r . It relates to the distribution of particle number as follows:

dr Vr dN r

dV r ()

ln()

()
ln()

= 4
3

dN r
dr

()
ln() .

3

= ()

dr r

π

Volume concentration (μm 3 /μm 2 ):

dV r
dr

()
ln() .

r

= ∫

max

C

v

r

min

The details of computations in the present study are as follows:

1. The mid-point (center of size bin) radius r was used to calculate the distribution
of particle number d N ( r )/dln( r ) from the volume concentration d V ( r )/dln( r ) for
fine (f) and course (c) aerosol modes.
2. The radius range for fine (f) mode is 0.05 < r ≤ 0.6 µm and the radius range for
the coarse (c) mode is 0.6 < r ≤ 15 µm.

∑ ( ) for fine (f) and coarse (c) modes
were calculated from d N ( r )/dln( r ) since dln( r ) is a constant equal to d( r )/ r for the
retrieved size spectrum with logarithmically equidistant bins. The constant dln( r )
computed as equal to ( r 2 − r 1 )/ r 1 from the known values of mid-point (center of size
bin) radii r is equal to 0.31207.

The total number concentrations N N ()

5.3 Analysis and Results

The atmospheric suspended particulate size spectrum is closely related to the verti-
cal velocity spectrum (Sect. 1.6). The mean volume radius of suspended aerosol
particulates increases with height (or reference level z ) in association with decrease
in number concentration. At any height (or reference level) z , the fractal fluctuations