A number of recent papers analyzing the nature of climate models have yielded a stunning result little known outside of mathematical circles—climate models like the ones relied on by the IPCC contain “irreducible imprecision.” According to one researcher, all interesting solutions for atmospheric and oceanic simulation (AOS) models are chaotic, hence almost certainly structurally unstable. Further more, this instability is an intrinsic mathematical property of the models which can not be eliminated. Analysis suggests that models should only be used to study processes and phenomena, not for precise comparisons with nature.
The ability to predict the future state of the Earth climate system, given its present state and the forcings acting upon it, is the holly grail of climate science. What is not fully appreciated by most is that,in the prediction of the evolution of that system, we are severely limited by the fact that we do not know with arbitrary accuracy the evolution equations and the initial conditions of the system. By necessity climate models work with a finite number of equations, from initial data determined with finite resolution from a finite set of observations. These limitations are further exacerbated by the addition of structural instability due to finite mesh discretization errors (the real world isn't divided into boxes 10s or 100s of kilometers on a side; the impact of changing mesh size has been well documented in a number of recent studies
In a 2007 paper
, James C. McWilliams, of the Department of Atmospheric & Oceanic Sciences at UCLA, has termed the impact of the errors in AOS models from the change in the probability density functions (PDFs) in the climate equilibrium compared with the true PDFs from nature as “irreducible imprecision.” The main hypothesis advocated by McWilliams is that structural instability is the primary source of irreducible imprecision for climate change science. In other words, small changes in AOS model parameters or formulation result in significant differences in the longtime PDFs or the phase-space attractor and these can effect climate change projections. Virtually all physical systems have structural instability, according to a paper
in PNAS by Andrew J. Majda, Rafail Abramov, and Boris Gershgorin:
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