WUWT has an excellent post on Chaos Theory, no math or technical expertise required. If you want a good discussion on how this stuff works, then check it out.
This is not intended to be a scientific paper, but a discussion of the disruptive light Chaos Theory can cast on climate change, for non-specialist readers. This will have a focus on the critical assumptions that global warming supporters have made that involve chaos, and their shortcomings. While much of the global warming case in temperature records and other areas has been chipped away, they can and do, still point to their computer models as proof of their assertions. This has been hard to fight, as the warmists can choose their own ground, and move it as they see fit. This discussion looks at the constraints on those models, and shows that from first principles in both chaos theory and the theory of modelling they cannot place reliance on these models.
First of all, what is Chaos? I use the term here in its mathematical sense. Just as in recent years Scientists have discovered extra states of matter (not just solid, liquid, gas, but also plasma) so also science has discovered new states that systems can have.
Systems of forces, equations, photons, or financial trading, can exist effectively in two states: one that is amenable to mathematics, where the future states of the systems can be easily predicted, and another where seemingly random behaviour occurs.
This second state is what we will call chaos. It can happen occasionally in many systems.
For instance, if you are unfortunate enough to suffer a heart attack, the normally predictable firing of heart muscles goes into a chaotic state where the muscles fire seemingly randomly, from which only a shock will bring them back. If you’ve ever braked hard on a motorbike on an icy road you may have experienced a “tank slapper” a chaotic motion of the handlebars that almost always results in you falling off. There are circumstances at sea where wave patterns behave chaotically, resulting in unexplained huge waves.
IPCC on modeling:
In sum, a strategy must recognise what is possible. In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible. The most we can expect to achieve is the prediction of the probability distribution of the system’s future possible states by the generation of ensembles of model solutions. This reduces climate change to the discernment of significant differences in the statistics of such ensembles. The generation of such model ensembles will require the dedication of greatly increased computer resources and the application of new methods of model diagnosis. Addressing adequately the statistical nature of climate is computationally intensive, but such statistical information is essential.