Runaway tipping points of no return

I wonder if any else has noticed that we appear to have crossed a threshold in the usage of the phrase ‘tipping point’ in discussions of climate? We went from a time when it was never used, to a point (of no return?) where it is used in almost 100% of articles on the subject. Someone should come up with a name for this phenomenon….

Regardless of the recent linguistic trends, the concept has been around for a long time. The idea is that in many non-linear systems (of which the climate is certainly one), a small push away from one state only has small effects at first but at some ‘tipping point’ the system can flip and go rapidly into another state. This is fundamentally tied to the existence of positive feedbacks and is sometimes related to the concept of multiple ‘attractors’ (i.e. at any time two different ‘states’ could be possible and near a transition the system can flip very quickly from one to another). Another ‘tipping point’ in non-linear systems occurs when as some parameter varies, the current attractor changes character or disappears. However it is currently being used interchangeably a number of potentially confusing ways and so I thought I’d try and make it a little clearer.

Positive feedback

A positive feedback occurs when a change in one component of the climate occurs, leading to other changes that eventually “feeds back” on the original change to amplify it. The classic ones in climate are the ice-albedo feedback (melting ice reduces the reflectivity of the surface, leading to more solar absorption, more warming and hence more melting) and the water vapour feedback (as air temperatures rise, water vapour amounts increase, and due to the greenhouse effect of the vapour, this leads to more warming), but there are lots of other examples. Of course, there are plenty of negative feedbacks as well (the increase in long wave radiation as temperatures rise or the reduction in atmospheric poleward heat flux as the equator-to-pole gradient decreases) and these (in the end) are dominant (having kept Earth’s climate somewhere between boiling and freezing for about 4.5 billion years and counting). But it is the postive feedbacks that make weather chaotic and climate interesting.

People often conclude that the existence of positive feedbacks must imply ‘runaway’ effects i.e. the system spiralling out of control. However, while positive feedbacks are obviously necessary for such an effect, they do not by any means force that to happen. Even in simple systems, small positive feedbacks can lead to stable situations as long as the ‘gain’ factor is less than one (i.e. for every initial change in the quantity, the feedback change is less than the original one). A simple example leads to a geometric series for instance; i.e. if an initial change to a parameter is D, and the feedback results in an additional rD then the final change will be the sum of D+rD+r2D…etc. ). This series converges if |r|<1, and diverges (‘runs away’) otherwise. You can think of the Earth’s climate (unlike Venus’) as having an ‘r‘ less than one, i.e. no ‘runaway’ effects, but plenty of positive feedbacks.

Tipping points

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