First of all, let's explain feedback theory. Imagine
you have a system where the output signal y (for instance
is determined by the input signal x
(for instance CO2
concentration) and that there is a gain (or sensitivity) A
between the two:
y = A x
Now we add feedback, stating that part of the output signal y
is added to the input
with a factor β
y = A x'
x' = x
+ β y
The overall gain of this
system is then
y = A/(1-Aβ) x
You can see that the output y
can be arbitrarily large for a careful selection of parameters
A and β. Now you
understand how the IPCC can
simulate any temperature variation based on any CO2
variation with a careful choosing of only two parameters,
namely A and β. It is as simple as that. They can
even, should the need arise, predict 100-degrees temperature
If in 1998 it is very warm, these parameters are adjusted to
retroactively predict the temperature. Then, in their
reasoning, the temperature of 1998 is seen as proof of the
correctness of the parameters and any predicted subsequent
rise on basis of these parameters seen as unavoidable.
That while their entire idea of feedback does not make sense.
Why? Read further
Positive feedback vs.
The above is an example of positive feedback (if β>0) and
will typically result in a runaway system. Every cycle through
the loop (which can take some time in real life) will increase
the overall amplitude of the output y. Imagine I look at my bank account and add
every day the amount that is already there (Aβ=1). I start with 1
euro. Next day I will add 1 and have 2 euros. Then 4, then 8
... etc. This is a runaway system. Adding every day twice the
amount of money already there is equally a runaway system (1,
3, 9, 27, ... ).
It is only stable if Aβ<1.
In which case the system is stable, and the amplitude y can only be large for
values close to 1. The IPCC talks about "the system is
unstable and we are reaching a critical point of no return",
showing that indeed this is their way of analyzing the climate
system; their parameters are indeed close to 1 (stable, but
large amplitude) or even beyond 1 (runaway). The sheer
probability of Aβ
being close to 1 is astronomically small, never mind that that
can make them simulate a tiny fragment of the climate history.
Moreover, we would have observed quite different climate
phenomena in the past.
For negative feedback, however, Aβ<0, the system is stable. Any deviation
from a stable situation would have 'forces' bringing the
system back to the stable situation. And this must be the
case. All the time the climate system is brought off-balance
by: seasonal (summer and winter) fluctuations, daily (day and
night) fluctuations, random (weather) fluctuations, incidental
(volcanic) events. The climate always recovers.
It is impossible to have
large positive feedback (Aβ>1).
It is highly unlikely to have positive feedback at all (Aβ>0).
It is very likely there is negative feedback (Aβ<0).
This means that
the resulting amplitude, y
= A/(1-Aβ) x
, is smaller
than what can be expected without feedback, because A/(1-Aβ) <
. We can thus expect a climate sensitivity
of CO2 smaller than 0.1 degrees for doubling CO2 in the
atmosphere. The exact value can be a point of discussion.
For more information, contact me at The University of The
Prof. Peter Stallinga