Universal Spectrum for Atmospheric Suspended Particulates: Comparison with Observations: Data Set II - Rain Formation in Warm Clouds: General Systems Theory - page 71

Chapter 4
Universal Spectrum for Atmospheric Suspended
Particulates: Comparison with Observations:
Data Set II

Abstract Atmospheric flows exhibit self-similar fractal space-time fluctuations on
all space-time scales in association with inverse power law distribution for power
spectra of meteorological parameters such as wind, temperature, etc., and thus
implies long-range correlations, identified as self-organized criticality generic to
dynamical systems in nature. A general systems theory visualizes the fractal fluc-
tuations to result from the coexistence of eddy fluctuations in an eddy continuum,
the larger scale eddies being the integrated mean of enclosed smaller scale eddies.
The model predicts that the probability distributions of component eddy amplitudes
and the corresponding variances (power spectra) are quantified by the same univer-
sal inverse power law distribution incorporating the golden mean. Atmospheric par-
ticulates are held in suspension by the vertical velocity distribution spectrum. The
atmospheric particulate size spectrum is derived in terms of the model-predicted
universal inverse power law characterizing atmospheric eddy spectrum. Model-pre-
dicted spectrum is in agreement with PCASP-B aerosol-size spectra measurements
made during the VOCALS ((VAMOS Ocean-Cloud-Atmosphere Land Study) 2008.

Keywords Universal spectrum for atmospheric suspended particulates · Fractal
fluctuations in atmospheric flows · Chaos and nonlinear dynamics · Maximum
entropy principle · VOCALS 2008 PCASP-B aerosol size spectra

4.1 Introduction

A general systems theory for fractal space-time fluctuations (Selvam 1990 2005 ,
2007 , 2009 ) (see Sect. 1.3) is applied to derive universal (scale-independent) inverse
power law distribution incorporating the golden mean for atmospheric eddy energy
distribution. Atmospheric particulates are held in suspension by the spectrum of at-
mospheric eddy fluctuations (vertical). The suspended atmospheric particulate size
distribution is expressed in terms of the atmospheric eddy energy spectrum and is
expressed as a function of the golden mean τ(≈ 1.618), the total number concentra-
tion and the mean volume radius (or diameter) of the particulate size spectrum.
A knowledge of the mean volume radius and total number concentration is suf-
ficient to compute the total particulate size spectrum at any location. Model pre-
dicted atmospheric eddy energy spectrum is in agreement with earlier observational