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

Abstract

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? And are there precise mathematical results that can help us answer this question? We examine some efforts in the literature to answer this last question in the affirmative and find them to be unconvincing. * 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!

Filosofía de la Ciencia del Cambio Climático

“…Mientras que los filósofos de la ciencia ligados a la London School of Economics responden afirmativamente (Frigg et ál. 2014), amparándose en el carácter no lineal de estos modelos, otros lo hacen de modo negativo, indicando que no se puede generalizar y hay que ir caso por caso, estudiando modelo a modelo (Nabergall, Navas y Winsberg 2019;Winsberg 2018). 12 Para intentar controlar el caos, se utiliza la predicción por conjuntos (ensemble prediction), una técnica diseñada por Tim Palmer y Eugenia Kalnay, entre otros, que consiste en usar conjuntos de condiciones iniciales distintas o diferentes modelos climáticos a la vez.…”

Climate Models and the Irrelevance of Chaos

“…The arguments of the LSE group have spawned a series of responses (Goodwin and Winsberg 2016;Nabergall, Navas, and Winsberg 2019;Winsberg 2018;Winsberg and Goodwin 2016) from a group of philosophers and scientists associated with the University of South Florida (who I'll term the "USF group" for parallel's sake). The main contention of the USF group is that the analogy between systems that exhibit SDIC and what I above termed sensitive dependence on dynamical equations cannot be made precise for two reasons.…”

Climate modelling and structural stability

“…On the other hand, Winsberg and Goodwin (2016), Nabergall et al (2019) raise a number of issues and object to the general relevance of the hawkmoth effect for climate projections; in particular, they challenge the general scope (in view of decision-making) of the absence of (a proof of) structural stability. 3 This paper does not aim to settle all aspects of this debatesomewhat surprisingly, beyond the bold claims, it seems that both sides actually agree that structural model error can be a real worry in certain cases, one of the main points of disagreement being rather about the scope of the worry and the precise role of structural stability.…”

“… See Winsberg and Goodwin (2016),Nabergall et al (2019), as well as the paragraph 5.6 and the appendix inWinsberg (2018).20 SeeWerndl (2009) for a discussion of chaos theory in the philosophy of science literature: in intuitive terms, sensitive dependence to initial conditions "means that small errors in initial conditions lead to totally different solutions" (203), and topological mixing "means that any bundle of solutions spread out in phase space like a drop of ink in a glass of water" (204).21 Such an evaluation requires a metric, which allows to measure distances, e.g. in phase space; no metric is required to discuss structural stability.…”