Another look at climate sensitivity
1Department of Mathematics and Statistics, University of Nevada, Reno, USA
2Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), Ecole Normale Supérieure, Paris, France
3Department of Atmospheric & Oceanic Sciences and Institute of Geophysics & Planetary Physics, University of California, Los Angeles, USA
Abstract. We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such a response would imply irreducible uncertainty in climate change predictions and thus have notable implications for climate science and climate-related policy making. We show that equilibrium climate sensitivity in all generality does not support such an intrinsic indeterminacy; the latter appears only in essentially linear systems. The main flaw in the analysis that led to this claim is inappropriate linearization of an intrinsically nonlinear model; there is no room for physical interpretations or policy conclusions based on this mathematical error. Sensitive dependence nonetheless does exist in the climate system, as well as in climate models – albeit in a very different sense from the one claimed in the linear work under scrutiny – and we illustrate it using a classical energy balance model (EBM) with nonlinear feedbacks. EBMs exhibit two saddle-node bifurcations, more recently called "tipping points," which give rise to three distinct steady-state climates, two of which are stable. Such bistable behavior is, furthermore, supported by results from more realistic, nonequilibrium climate models. In a truly nonlinear setting, indeterminacy in the size of the response is observed only in the vicinity of tipping points. We show, in fact, that small disturbances cannot result in a large-amplitude response, unless the system is at or near such a point. We discuss briefly how the distance to the bifurcation may be related to the strength of Earth's ice-albedo feedback.