Climate Sensitivity, Feedback and Bifurcation: From Snowball Earths to the Runaway Greenhouse

The concept of climate sensitivity lays at the heart of assessment of the magnitude of the imprint of human activities on the Earth's climate. Most commonly, the "climate" is represented by a simple projection such as a global mean temperature, and we wish to know how this changes in response to changes in a single control parameter -- usually atmospheric CO2 concentration.  This problem is an instance of a broad class of related problems in parameter dependence of dynamical systems. I will discuss the shortcomings of the traditional linear approach to this problem, particularly in light of the spurious "runaway" states produced when feedback becomes large. The extension to include nonlinear effects relates in a straightforward way to bifurcation theory.  I will discuss explicit examples arising from ice-albedo, water vapor, and cloud feedbacks.  Finally, drawing on the logistic map as an example, I will discuss the problem of defining climate sensitivity for problems exhibiting structural instability.

Raymond Pierrehumbert, University of Chicago, USA

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