General Systems Theory Concepts in Atmospheric Flows - Rain Formation in Warm Clouds: General Systems Theory - page 4

of research, it is still very difficult to define the analytical functions from which
to compute their statistics and have an intuition for how these systems behave
(Parmeggiani 2012 ). Realistic mathematical modeling for simulation and predic-
tion of atmospheric flows requires alternative theoretical concepts and analytical or
error-free numerical computational techniques and therefore comes under the field
of “General Systems research” as explained in the following.
Space-time power law scaling and nonlocal connections exhibited by atmo-
spheric flows have also been documented in other nonequilibrium dynamical sys-
tems, e.g., financial markets, neural network of brain, genetic networks, Internet,
road traffic, flocking behavior of some animals and birds. Such universal behavior
has been subject of intensive study in recent years as “complex systems” under the
subject headings SOC, nonlinear dynamics and chaos, network theory, pattern for-
mation, information theory, cybernetics (communication, control and adaptation).
Complex system is a system composed of many interacting parts, such that the
collective behavior or “emergent” behaviors of those parts together is more than
the sum of their individual behaviors (Newman 2011 ). Weather and climate are
emergent properties of the complex adaptive system of atmospheric flows. Com-
plex systems in different fields of study exhibit similar characteristics and therefore
belong to the field of “General Systems.” The terms “general systems” and “general
systems research (or general systems theory)” are due to Ludwig von Bertalanffy.
According to Bertalanffy, general systems research is a discipline whose subject
matter is ‟the formulation and derivation of those principles which are valid for
‛systems' in general” (von Bertalanffy 1972 ; Klir 2001 ).
Skyttner ( 2005 ) quotes basic ideas of general systems theory formulated by
Fredrich Hegel (1770-1831) as follows:

1. The whole is more than the sum of the parts
2. The whole defines the nature of the parts
3. The parts cannot be understood by studying the whole
4. The parts are dynamically interrelated or interdependent

In cybernetics, a system is maintained in dynamic equilibrium by means of com-
munication and control between the constituent parts and also between the system
and its environment (Skyttner 2005 ).

1.3 General Systems Theory for Fractal Space-Time

Fluctuations in Atmospheric Flows

General systems theory for atmospheric flows is based on classical statistical physi-
cal concept where ensemble average represents the steady-state values of param-
eters such as pressure, temperature, etc., of molecular systems (gases) independent
of details of individual molecule. The ideas of statistical mechanics (SM) have
been successfully extended to various disciplines to study complex systems (Haken
1977 ; Liu and Daum 2001 ). Liu and his group (Liu 1992 , 1995 ; Liu et al. 1995 ; Liu