15 Feb 2023
 | 15 Feb 2023
Status: this preprint is open for discussion.

Review Article: Dynamical Systems, Algebraic Topology, and the Climate Sciences

Michael Ghil and Denisse Sciamarella

Abstract. The definition of climate itself cannot be given without a proper understanding of the key ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it is not surprising that concepts and methods of this theory have percolated into the climate sciences as early as the 1960s. The major increase in public awareness of the socio-economic threats and opportunities of climate change has led more recently to two major developments in the climate sciences: (i) the Intergovernmental Panel on Climate Change's successive Assessment Reports; and (ii) an increasing understanding of the interplay between natural climate variability and anthropogenically driven climate change. Both of these developments have benefitted from remarkable technological advances in computing resources, in throughput as well as storage, and in observational capabilities, regarding both platforms and instruments.

Starting with the early contributions of nonlinear dynamics to the climate sciences, we review here the more recent contributions of (a) the theory of nonautonomous and random dynamical systems to an understanding of the interplay between natural variability and anthropogenic climate change; and (b) the role of algebraic topology in shedding additional light on this interplay. The review is thus a trip leading from the applications of classical bifurcation theory to multiple possible climates to the tipping points associated with transitions from one type of climatic behavior to another in the presence of time-dependent forcing.

Michael Ghil and Denisse Sciamarella

Status: open (until 12 Apr 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • CC1: 'Complimentary comment on egusphere-2023-216', Paul PUKITE, 24 Feb 2023 reply
    • CC2: 'Reply on CC1', Paul PUKITE, 24 Feb 2023 reply
      • AC1: 'Reply to “Complimentary comment on egusphere-2023-216” CC1 & CC2', Denisse Sciamarella, 26 Feb 2023 reply

Michael Ghil and Denisse Sciamarella

Michael Ghil and Denisse Sciamarella


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Short summary
The problem of climate change is that of a chaotic system subject to time-dependent forcing, such as anthropogenic greenhouse gases and natural volcanism. To solve this problem, we describe the mathematics of dynamical systems with explicit time dependence and that of studying their behavior through topological methods. Here, we show how they are being applied to climate change and its predictability.