Entropy production and multiple equilibria: the case of the ice-albedo feedback

TL;DR

This paper explores the relationship between entropy production and multiple climate equilibria caused by ice-albedo feedback, using a dynamical systems approach and the Maximum Entropy Production principle to analyze stability and heat flux.

Contribution

It introduces an analogy between dynamical systems and the MEP principle in climate modeling, addressing stability of entropy production maxima and comparing heat flux calculations.

Findings

Entropy production maxima can be stable or unstable depending on system parameters.

The MEP principle can be reconciled with the time evolution of climate variables.

Surface heat flux estimates from MEP align with traditional bulk-aerodynamic formulas.

Abstract

Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive feedback which gives birth to multiple equilibria for some values of the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate unstable solution. In this study, we show an analogy between a classical dynamical system approach to this problem and a Maximum Entropy Production (MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the time evolution of a variable. It enables us in particular to resolve the question of the stability of the entropy production maxima. We also compare the surface heat flux obtained with MEP and with the bulk-aerodynamic formula.