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So, I take it that a closed form climate change model where one can plug in the current values of known parameters is not yet possible and maybe is inherently not ever possible? Is that another way of saying the climate system is chaotic? Or is it a case where orders of magnitude faster computers are needed?

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Yes, CFD experts have known from the time climate modeling was an idea in James Hansen's convoluted mind that the results would have very large numerical and subgrid model errors. In reality the results will only be skillful on those outputs used in tuning or closely related to them. Recently, a few modelers have come clean including Palmer and Stevens who are proposing massive increases in resolution.

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