Synopsis of 2013 AAAS Tipping Point Symposium organized by Mary Lou Zeeman and Mary Silber

The Mathematics of Tipping Points, organized by Mary Lou Zeeman (pictured below introducing the symposium), Bowdoin College, and Mary Silber, Northwestern University


Silber was the first speaker and gave the large audience insights into tipping points and bifurcation theory. She began by saying that tipping points involve

  • a threshold
  • a qualitative change in a system's behavior, and
  • hysteresis.

She then gave a detailed analysis of Earth's energy balance, especially in regard to ice albedo feedback. Ice reflects heat better than land or water does, so in simple terms less ice means more heat is trapped, which means a warmer planet, which means less ice ...

Silber showed graphs illustrating how a change in the amount of energy radiated out (right) could result in a loss of equilibrium and movement along the S-curve above. It is unknown whether the movement would be to a nearby state or to one that is far away. In the image above, the planet is in a "hothouse" state. (Images above by Mary Lou Zeeman and Mary Silber.)

The second speaker at this symposium, Sebastian Wieczorek (University of Exeter, UK), examined tipping points that he thinks are caused by changes in rates of quantities in a system, rather than by bifurcations. His primary example was peat lands, which relate on a smaller scale to compost piles. The latter can spontaneously combust, so does this means that if the planet warms, then peat could spontaneously combust as well? Wieczorek said that instability results when the soil temperature (which is related to soil carbon content and the atmospheric temperature) rises too fast, which in this case was linked to an atmospheric temperature rise of 8°C/100 years. He concluded by asking whether mathematics could suggest new techniques to predict tipping points.

That conclusion was a good segue to the next speaker, Marten Scheffer (Wageningen University, Netherlands) whose talk was titled, "Anticipating Critical Transitions." We may not be able to understand completely the systems, because they are so complex, but there may be a way to see a tipping point coming. Scheffer showed temperature data and pointed out that historically a slowing down of temperature fluctuations and an increased autocorrelation presaged eight abrupt climate changes.

He also talked about three different habitats: forest, savannah, and deserts. Regions tend to settle in to one or the other, but nothing in between. In regions with lots of rain, for example, there is one equilibrium: a forest. In regions with a medium amount of rain, there are two equilibria: forests and savannah. People can use that information to see which forests are stable and which are fragile, and devote resources to the places where it will do the most good.

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