Universal Spectrum for Atmospheric Suspended Particulates: Comparison with Observations: Data Set I - Rain Formation in Warm Clouds: General Systems Theory - page 67

normalized radius less than 1, the model predicted and the total average spectrum
(right-hand side of Fig. 3.3a ) are within two standard deviations from the mean, a
standard statistical criterion for “goodness of fit.”

3.6.4 Analysis Results Data IV: TWP-ICE, Joss-Waldvogel

Disdrometer Rain DSDs

The Joss-Waldvogel disdrometer ( http://cires.colorado.edu/blogs/twc-ice/2009/09
/19/4-0-joss-waldvogel-disdrometer) was operational from 3 November 2005
through 10 February 2006. The original JWD data were collected at the full 127
diameter channels and with a 10 s dwell time. These high-resolution data were re-
duced to the standard 20 diameter channels and to a 1-min resolution. A dead-time
correction (Sheppard and Joe 1994 ; Sauvageot and Lacaux 1995 ) was applied to
the raindrop counts. The data products are provided using the dead-time corrected
raindrop counts and 60 s dwell time.
The ASCII data files are day files with 1-min resolution and contain 1440 rows.
Bad or missing data values are indicated with a value of − 99.9. The ASCII data
files can be found on the ftp site: ftp://ftp.etl.noaa.gov/user/cwilliams/Darwin/dis-
drometer/dat/
The values of d(lnr an ) for the rain drop size spectrum was calculated from the
number of raindrops in each raindrop diameter size in a total of 20 standard di-
ameter channels ranging from 0.34 to 5.37 mm and corresponding channel width
(mm). A total of 99 data sets (days) are available for the study. The average (daily)
rain drop size spectra for each of the 99 data sets are plotted on the left-hand side
and the total average (daily) spectrum for the 99 data sets is plotted on the right-
hand side in Fig. 3.4a along with the model predicted scale independent aerosol size
spectrum. The corresponding standard deviations for the average spectra are shown
as error bars in Fig. 3.4a . The average values of (i) mean volume diameter mm, (ii)
rain drop total number, (iii) number of observations in each of the 20 channels, and
(iv) channel diameter and channel width (mm) for the 20 drop size channels are
given in Fig. 3.4b .
The total average raindrop size spectrum (right-hand side of Fig. 3.4a ) shows a
reasonably good fit (within two standard deviations from the mean) even though
the individual average raindrop size spectra (left-hand side of Fig. 3.4a ) show large
error bars which may be attributed to the large variability in total number of drops
sampled corresponding to each mean volume radius (Fig. 3.4b ).

Conclusions

A general systems theory for fractal space-time fluctuations in turbulent atmospher-
ic flows predicts a universal scale-independent mass or radius size distribution for