  Environmental science almost invariably proposes problems of extreme
complexity, typically characterized by strongly nonlinear evolution dynamics.
The systems under investigation have many degrees of freedom - which makes them
complicated - and feature nonlinear interactions of several different
components taking place on a vast range of time-space scales - which makes them
complex. Such systems evolve under the action of macroscopic driving (typically
the solar heating) and modulating (e.g. the Earth's rotation and gravitation)
agents. The most comprehensive example is the entire climatic system. The
description of the macroscopic dynamics of environmental systems is based on
the systematic use of dominant balances derived on a phenomenological basis in
order to specialize the dynamical equations. Such balances are suitable classes
of approximate solutions of the evolution equations which represent a
reasonably good approximation to the actual observed fields when sufficiently
large spatial or temporal averages are considered. Actually, different balances
have to be considered depending on the time and space scales we are focusing
our interest on. Such an approach reflects the fundamentally
heuristic-inductive nature of the scientific research in environmental
sciences, where the traditional reductionistic scientific attitude is not
always effective. In order to exemplify this procedure, we consider the very
relevant case of the motion of the fluids that permit the existence of life on
the Earth, air and water: the so-called geophysical fluids.
