An antidote for hawkmoths: on the prevalence of structural chaos in non-linear modeling

  • Lukas Nabergall
  • Alejandro Navas
  • Eric WinsbergEmail author
Paper in Philosophy of the Natural Sciences


This paper deals with the question of whether uncertainty regarding model structure, especially in climate modeling, exhibits a kind of “chaos.” Do small changes in model structure, in other words, lead to large variations in ensemble predictions? More specifically, does model error destroy forecast skill faster than the ordinary or “classical” chaos inherent in the real-world attractor? In some cases, the answer to this question seems to be “yes.” But how common is this state of affairs? Are there precise mathematical results that can help us answer this question? And is dependence on model structure “sensitive” in that arbitrarily small errors can destroy forecast skill? We examine some efforts in the literature to answer this last question in the affirmative and find them to be unconvincing.


Climate science Chaos Modeling Structural stability Hawkmoth effect 



We would like to thank Mathias Frisch, Blaine Lawson, Seung-Yeop Lee, Connor Mayo-Wilson, Jessica Williams, the audience members at talks in London, Ontario and Chicago, and our anonymous reviewers for helpful comments on earlier drafts as well as many useful discussions of mathematical questions. Responsibility for any remaining errors is of course our own!


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Lukas Nabergall
    • 1
  • Alejandro Navas
    • 2
  • Eric Winsberg
    • 3
    Email author
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.School of Geography and the EnvironmentUniversity of OxfordOxfordUK
  3. 3.Department of PhilosophyThe University of South FloridaTampaUSA

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