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. (shrink)

In a series of recent papers, two of which appeared in this journal, a group of philosophers, physicists, and climate scientists have argued that something they call the `hawkmoth effect' poses insurmountable difficulties for those who would use non-linear models, including climate simulation models, to make quantitative predictions or to produce `decision-relevant probabilites.' Such a claim, if it were true, would undermine much of climate science, among other things. Here, we examine the two lines of argument the group has used (...) to support their claims. The first comes from a set of results in dynamical systems theory associated with the concept of `structural stability.' The second relies on a mathematical demonstration of their own, using the logistic equation, that they present using a hypothetical scenario involving two apprentices of Laplace's omniscient demon. We prove two theorems that are relevant to their claims, and conclude that both of these lines of argument fail. There is nothing out there that comes close to matching the charac. (shrink)