An Application of the Exact Response Theory to Climate System Perturbations

The anthropogenic contribution to the evolution of climate is currently a central topic in scientific studies. The Intergovernmental Panel on Climate Change (IPCC) assessment reports are based on the best science at hand, and summarize the progress in observing, modeling, understanding and predicting the evolution of the climate system. The climate system is forced, dissipative, nonlinear, chaotic, and out of thermodynamic equilibrium. Along with the difficulties that these characteristics come with, the climate system presents some particularities such as, the presence of well-defined subsystems, the continuous variation of the forcings, lack of scale separation, etc., which add more obstacles to the task. In this context, several theories and models are developed to predict the response of the system to perturbations. In particular, Valerio Lucarini's approach is reviewed. He makes use of Ruelle’s linear response theory, which was found to be too restricted since it is limited to linear perturbations applied to Axiom A systems. The Exact Response Theory proposed here, would overcome these limitations. It was developed within the field of Nonequilibrium Molecular Dynamics, and it is expected to predict the response of a system with many degrees of freedom even in the presence of arbitrarily large perturbations and modifications of states, allowing the study of the relaxation of particle systems to equilibrium or non-equilibrium steady states. The theory introduces the Dissipation Function, Ω, as its basis. The Dissipation Function determines non-equilibrium properties the same way the thermodynamic potentials determine equilibrium state properties. In order to apply the theory, it was studied the dynamical model describing the Pleistocene ice ages developed by Saltzman. That approach to the climate system reproduces the evolution of global ice mass, atmospheric concentration of carbon dioxide and North Atlantic deep water amount. There were found three fixed points and an attractor, the later responsible of the oscillations that the evolution exhibits along the time. The evolution of an observable when the system is perturbed, was computed by means of the presented theory.