Houghton Lecture Series – Ray Pierrehumbert (University of Oxford)

Bifurcations Large and Small

Here, I return to issues largely motivated by Earth’s past and future climate, though a number
of the phenomena discussed apply to planetary climate in general. Tipping points seem to
be all the rage these days. For the most part, a “tipping point” is a more colloquial term for a
“bifurcation,” though the term has a tendency to be used in a less well-defined way than the
more mathematical term. In this lecture I will review the basic mathematics underpinning
standard linearised analyses of climate sensitivity, pointing out that generically, a high linearised
climate sensitivity means the system is close to a bifurcation. The bifurcation could lead either to
a “small” change of state, or a massive change (such as Snowball Earth or runaway greenhouse),
with everything in between. I will discuss some novel mathematical concepts regarding systems
which can have “little bifurcations everywhere,” leading to non-differentiable climate responses
as a function of a smoothly varying control parameter.

About this Series:
Supported by the Houghton Fund, Houghton Lecturers are distinguished visitors from outside MIT invited by the EAPS Program in Atmospheres, Oceans and Climate to spend a period of time, ranging from a week to several months, as scientists-in-residence within our Program. For more information and Zoom password please contact Kayla Bauer: kbauer@mit.edu