Cumulus Cloud Model - Rain Formation in Warm Clouds: General Systems Theory - page 32

Chapter 2
Cumulus Cloud Model

Abstract A cumulus cloud model that can explain the observed characteristics of
warm rain formation in monsoon clouds is presented. The model is based on clas-
sical statistical physical concepts and satisfies the principle of maximum entropy
production. Atmospheric flows exhibit self-similar fractal fluctuations that are ubiq-
uitous to all dynamical systems in nature and are characterized by inverse power-
law form for power (eddy energy) spectrum signifying long-range space-time
correlations. A general systems theory model for atmospheric flows is based on
the concept that the large eddy energy is the integrated mean of enclosed turbulent
(small-scale) eddies. This model gives scale-free universal governing equations for
cloud-growth processes. The model-predicted cloud parameters are in agreement
with reported observations, in particular, the cloud drop-size distribution. Rain for-
mation can occur in warm clouds within a 30-min lifetime under favourable condi-
tions of moisture supply in the environment.

Keywords General systems theory · Nonlinear dynamics and chaos · Fractals ·
Long-range space-time correlations · Inverse power-law eddy energy spectrum ·
Maximum entropy production principle

2.1 Introduction

The knowledge of the cloud dynamical, microphysical and electrical parameters
and their interactions are essential for the understanding of the formation of rain
in warm clouds and their modification. Extensive aircraft observations of cloud
dynamical, microphysical and electrical parameters have been made in more than
2000 isolated warm cumulus clouds formed during the summer monsoon seasons
(June-September) in Pune (18°32′N, 73°51′E, 559 m a.s.l), India (Selvam et al.
1980 , 1982a , 1982b , 1982c , 1982d , 1983 , 1984a , 1984b , 1984c; Murty et al. 1985;
Selvam et al. 1991a , 1991b ). The observations were made during aircraft travers-
es at about 300 m above the cloud base. These observations have provided new
evidence relating to the dynamics of monsoon clouds. A brief summary of the im-
portant results is given as follows: (i) Horizontal structure of the air flow inside
the cloud has consistent variations with successive positive and negative values of
vertical velocity representative of ascending and descending air currents inside the