Climate Change and Chaos Theory: Turbulence Ahead

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16th Feb 2016




Kieran Kelly is a theoretical mathematics expert working to apply theory to big data sets, including climate. His research is showing that we can't predict the ultimate impacts of climate change because the stronger human impact becomes, the more likely it will result in non-linear outcomes (things we can't predict). 

Climate Chaos: Understanding Coarse Synchronicity

When you trade financial markets you quickly learn that 10% up and 10% down are not the same thing. If we were to grow $100 in 1000 incremental steps of 0.0095315% we will arrive at $110.  And if we subsequently unwind/decline from this $110 in 1000 incremental steps of 0.0095315% we will arrive back at $100.  If however we were to grow the same $100 to $110 in one incremental step of 10%, and then decline from $110 in one incremental step of 10% we will not arrive back at $100 but at $99 instead.  

So why is this?  The reason is simple.  Smooth incremental change will synchronize up and down movements, but coarse incremental change will not.   This simple idea can explain what can happen with climate change.

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Chaos Theory

The lack of coarse behaviour in a system is the basis for something called “linear approximation” or “linearization”.  Linearization is used in every area of science; from physics to engineering, from economics to ecology.  By assuming that things change in a smooth continuous fashion we can approximate the system’s behaviour as being “linear dynamics”, which are effectively the dynamics of predictable behaviour. But the reason linear dynamics are predictable is because “linear (approximated) behaviour” is really just another way of saying that a systems behaviour is “not affected (very much) by feedback”... 

Chaos Theory is the study of the effects of positive feedback within negative feedback systems.  In the investment analogy above, desynchronization was the result of the coarse compounding effect of coarse positive feedback; because coarse positive feedback upsets the smooth synchronizing dynamics of the up and down movements.  

Damping

Most people know that good shock absorbers can damp out a bumpy ride in a car.  By dissipating excess vibrational energy, the shock absorbers can maintain the car’s ride at a smooth stable equilibrium. However, damping and stabilization does not only occur as a result of the dissipation of energy, it can also occur as a result of  the natural re-distribution of energy (or matter).

Many systems in nature are natural equilibrium seeking systems (i.e. left to themselves they will spontaneously mix).  Thermal systems naturally seek thermal equilibrium which is the name given to the settled warm mixture of hot and cold fluids.  And dynamic systems naturally seek dynamic equilibrium which is the name given to the settled end state of a self-mixing process (e.g. ink and water).  

Any system that is a spontaneous equilibrium seeking system ( like hot coffee and cold milk in a mug, or buyers and sellers in a market) can also be thought of as a self-stabilizing negative feedback system.  But just because a system is self-stabilizing does not mean it will always be able to find a completely stable thermal or dynamic equilibrium.  

Coarse Damping

In an equilibrium-seeking system, if self-stabilizing negative feedback can damp down and damp out any internal positive feedback then there will be no chaos because the system will be able to fine-tune its way to equilibrium.  If, however, the self-stabilizing negative feedback is unable to fully damp down the internal positive feedback we start to see the system behave in unpredictable ways, as the systems tries, unsuccessfully, to coarse-tune its way to equilibrium.

Chaos Theory tells us that excessive positive feedback within negative feedback systems causes coarse-negative-feedback, and this “coarse damping” to equilibrium disrupts the stabilizing pull of a pure thermal or dynamic equilibrium, causing residual behaviour to emerge in its stead... this is what one might call 'unintended consequences'.

Turbulence is a classic example of such coarse nonlinear dynamics.  In the simplest possible terms turbulence occurs when the rate of energy input or energy accumulation overwhelms the system’s natural ability to self-stabilize.  

Incompressible Feedback

We live in a universe of nonlinear dynamics, some of it compressible, most of it not.  More and more in the early part of this 21st century we are becoming aware of (or in some cases being made to realize) the creative or destructive power of incompressible feedback.

In some systems and arenas such as a multicultural society, the economy, technology, the arts, and even our daily lives, positive feedback is a source of great diversity and creativity; but in other areas such as financial markets, terror networks and the global climate it can be a source of great instability and destruction.   

An increase in global temperatures of a few degrees may not seem much and will definitely not induce global turbulence, but it will certainly make it more difficult for the global climate to find its way to its historically stable and liveable equilibrium. 

This post is adapted from Kieran Kelly.