Definitions
and examples:
system: a set or arrangement
of things so related or 'coupled' as to
form a unity or organic whole.
state of a system:
a description of a system at a fixed point in
time. Usually involves a set
of numerical values of a prescribed set
of indices. For example, the
present state of the U.S. economy can
be described in terms of indices
like rate of expansion, unemployment
rate, inflation rate, national debt,
trade surplus or deficit.. In a
similar manner, the current state
of the earth system can be
described in terms of indices like
global mean temperature and sea
level, the concentration of carbon
dioxide in the atmosphere, total
global biomass, mass of ice stored
in glaciers and continental ice
sheets... The descriptions
of the state of complex systems like the
earth system are only partial descriptions
at best.
couplings: one way
linkages in which one component of a system
affects another component.
In positive coupling between components A
and B, denoted by A ---> B in the
text, a change in A causes a change
of the same sign in B. In negative
coupling, denoted by A ----o B, a
change in A causes a change of the
opposing sign in B.
Examples of couplings:
As the temperature of the atmosphere
increases, the air becomes
capable of holding more water vapor.
This coupling, which is
positive, can be represented
schematically by
temperature ---------> water vapor
Like carbon dioxide, water vapor
is a greenhouse (heat trapping) gas.
Other things being equal, the more
water vapor in the atmosphere, the
warmer the temperature of the earth's
surface
water vapor ----------> temperature
If the earth were to become warmer,
the polar ice caps would tend to
melt back and shrink in area
temperature ----------o ice cover
The larger the fraction of the earth
that is covered by ice, the
whiter the planet and the larger
the fraction of incoming solar
radiation that is reflected back
to space without warming the surface
of the planet
ice cover ----------o temperature
The warmer the earth the more infrared
radiation it emits to space
temperature ----------> emitted radiation
If the incoming solar energy remained
constant, an increase in
emitted radiation would tend to
cool the earth
emitted radiation ----------o temperature
Definition:
feedback loop:
two or more couplings acting in sequence to form a
closed loop. In a positive
feedback loop a positive or negative
change in one of the components
of the system is amplified by the
sequence of couplings whereas in
a negative feedback loop the change
is reduced in amplitude.
Examples of feedback loops:
temperature-water vapor:
If the temperature warmed for any reason,
atmospheric water vapor would increase,
which would increase the
greenhouse effect and thereby further
raise the temperature. In a
similar manner, if the earth cooled,
atmospheric water vapor would
decrease, causing further cooling.
This is a positive feedback loop.
In symbolic form:
------------->
temperature
water vapor
<-------------
temperature-ice extent: If
the earth were to warm, the ice caps would
melt back, making the planet less
reflective so that it would warm
further. In a similar manner,
if the earth cooled, the ice caps
would expand, causing further cooling.
This is also a positive
feedback loop.
-------------o
temperature
ice extent
o-------------
temperature - emitted radiation:
If the earth were to warm, it would
emit more radiation, causing it
to cool and lose heat, and vice
versa. This is a negative
feedback loop:
------------->
temperature
emitted radiation
o-------------
Rule for inferring whether a feedback
is positive or negative
Add the number of negative couplings
(indicated by (o) in the
diagrams). If it's even (0,
2, 4..) the feedback is positive: if
it's odd (1, 3..) the feedback is
negative.
Definitions:
equilibrium state:
a state of balance between opposing effects. Once
in an equilibrium state a system
will remain there so long as it is
undisturbed.
stable equilibrium:
a small disturbance will provoke a reaction that
brings the system back to equilibrium.
unstable equilibrium:
a small disturbance will provoke a reaction
that pushes the system farther away
from equilibrium.
neutral equilibrium:
a small disturbance will not provoke a response.
Examples:
A cone resting on its base is in
a stable equilibrium. If displaced
slightly and released, it will return
to its equilibrium position.
An inverted cone is in an unstable
equilibrium: if displaced slightly
and released, it will fall over.
A cone resting on its side is in
neutral equilbrium: if displaced
slightly and released it will remain
where it is.
A marble placed in a bowl with a
round bottom is in a stable
equilibrium. A marble
placed on top of the same bowl, inverted, is
in an unstable equilibrium.
These situations are illustrated
by Fig. 2-3 in the text. A marble
placed on a flat surface is in neutral
equilibrium.
A small water balloon placed at mid-depth
of a large tank of water in
which the temperature increases
with height is in a stable
equilibrium. If the balloon
is raised slightly and then released, it
will find itself surrounded by warmer,
less dense water. The water
in the balloon will be denser (and
therefore heavier) than the water
that it displaces so the balloon
will tend to sink back toward its
original level in the tank.
In a similar manner, if the balloon is
lowered and then released, it will
find itself surrounded by colder,
denser water and it will be lighter
than the water it displaces and
therefore rise toward its original
level.
The same balloon, placed in a tank
of water in which the temperature
decreases with height would be in
an unstable equilibrium. (I say
'would be' because such a situation
is could not be maintained: the
water in such a tank would overturn
almost instantly, making the
temperature uniform)
If the balloon is raised slightly and then
released, it would find itself surrounded
by colder, denser water.
The water in the balloon will be
lighter than the water that it
displaces so the balloon will tend
to rise farther. In a similar
manner, if the balloon is lowered
and then released, it would find
itself surrounded by lighter, less
dense water and will sink.