An antidote for hawkmoths: on the prevalence of structural chaos in non-linear modeling
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.
KeywordsClimate 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!
- Allen, M., Kettleborough, J., Stainforth, D. (2002). Model error in weather and climate forecasting. In T. Palmer., & R. Hagedorn (Eds.) Predicatability of weather and climate (pp. 391–427). Cambridge: Cambridge University Press.Google Scholar
- Bradley, S., Frigg, R., Du, H., Smith, L.A. (2014). Model error and ensemble forecasting: a cautionary tale. In Scientific explanation and methodology of science: selected papers from the international conference on SEMS 2012, World Scientific, pp. 58–66.Google Scholar
- Thompson, E. (2013). Modelling North Atlantic storms in a changing climate. PhD diss., Imperial College, London.Google Scholar
- Werndl, C. (2019). Initial conditions dependence and initial conditions uncertainty in climate science. The British Journal for the Philosophy of Science (forthcoming).Google Scholar