CENTRAL to discussion of climate change models is the concept of “forcing” and “feedback”. So, reference is made to global warming from radiative “forcing” from elevated concentrations of carbon dioxide in the troposphere and then “positive feedback from water vapour”, adding to global warming.
Everyone talks in these terms, and it is politically correct to do so. But there are two problems.
According to the United Nation’s Intergovernmental Panel on Climate Change (IPCC) formalism, their “forcing” can include any amount of internal state variable contribution, as well as external driving function contributions. And according to this IPCC formalism, there is only one dynamically distinct internal state variable, the climate temperature, that functionally determines the apparently distinct but really merely functionally dependent “feedbacks” of their formalism.
In physics, an external driving function qualifies unequivocally as a cause. But internal state functions must always be counted as effects that are themselves caused by external drivers interacting with internal state functions acting as internal causes.
This important cause-effect structure is erased in the “forcing” concept of the IPCC formalism. It follows that cause and effect will be muddled in work that uses the IPCC formalism for simplified models. The simplified models are made of ordinary differential equations as in the qualitative theory of dynamical systems including deterministic chaos originated by Henri Poincaré in the 1880s. Poincaré used the method of phase portraits, which make explicit the presence of several dynamically distinct internal state variables.
The IPCC limitation to only one dynamically distinct internal state variable makes the IPCC concept of “feedbacks” verge on nonsense.
Roy Spencer and Danny Braswell explained this in 2008: “We can see from the plotted dots that the satellite observations are consistent with errors in diagnosed model feedback from about -0.1 to -0.8 W m^-2 K^-1”.
They showed that the IPCC formalism gives wrong answers.
At Dr Spencer’s blog he comments:
“As those who have been following our work already know, our main conclusion is that climate sensitivity has been grossly overestimated due to a mix up between cause and effect when researchers have observed how global cloud cover varies with temperature. … Significantly, our new work provides a method for identifying which direction of causation is occurring … Well…at least I thought it was new way of analyzing graphs. It turns out that we have simply rediscovered a method used in other physical sciences: phase space analysis.”
Drs Spencer and Braswell are leading the field by using Poincaré’s method of phase portraits. The two steps forward they are making here are explicit recognition of the presence of several dynamically distinct internal state variables, and clearer recognition of how the IPCC “forcing” concept leads to muddling of cause and effect, when it tries to by-pass or over-ride the difference between orthodox external driving functions and internal state variables.
I hope that the flawed IPCC formalism is on its way out as a result of their work.
June Barrow-Green, 1997/1999, Poincaré and the three-body problem, AMS
Peixoto and Oort, Physics of Climate, AIP 1992. Pg 29
Spencer and Braswell 2008 J. Climate 21: 5624-5628
Roy Spencer’s blog, http://www.drroyspencer.com/2009/03/set-phasers-on-stun/
Phase space analysis at Wikipedia, http://en.wikipedia.org/wiki/Phase_space
Image from Wikipedia illustrating the phase space of a dynamical system with focal stability, http://en.wikipedia.org/wiki/Phase_space