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Vaniver comments on In praise of gullibility? - Less Wrong Discussion
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Even single-precision floating point gives you around 7 decimal digits of accuracy. If (as is the case for both weather and climate modelling) the inputs are not known with anything like that amount of precision, surely input uncertainty will overwhelm calculation noise? Calculation noise enters at every step, of course, but even so, there must be diminishing returns from increased precision.
See the second half of this cousin comment. But a short summary (with a bit of additional info):
First, I see a philosophical difference between input uncertainty and calculation noise; the mathematical tools you need to attack each problem are different. The first can be solved through sampling (or a number of other different ways); the second can be solved with increased precision (or a number of other different ways). Importantly, sampling does not seem to me to be a promising approach to solving the calculation noise problem, because the errors may be systematic instead of random. In chaotic systems, this problem seems especially important.
Second, it seems common for both weather models and climate models to use simulation time steps of about 10 minutes. If you want to predict 6 days ahead, that's 864 time steps. If you want to predict 60 years ahead, that's over 3 million time steps.