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nostalgebraist comments on In praise of gullibility? - Less Wrong Discussion
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Climatological models and meteorological models are very different. If they weren't, then "we can't predict whether it will rain or not ten days from now" (which is mostly true) would be a slam-dunk argument against our ability to predict temperatures ten years from now. One underlying technical issue is that floating point arithmetic is only so precise, and this gives you an upper bound on the amount of precision you can expect from your simulation given the number of steps you run the model for. Thus climatological models have larger cells, larger step times, and so on, so that you can run the model for 50 model-years and still think the result that comes out might be reasonable.
(I also don't think it's right to say that Newtonian-style diffeqs aren't much use; the underlying update rules for the cells are diffeqs like that.)
I'm not sure if I'm understanding you correctly, but the reason why climate forecasts and meterological forecasts have different temporal ranges of validity is not that the climate models are coarser, it's that they're asking different questions.
Climate is (roughly speaking) the attractor on which the weather chaotically meanders on short (e.g. weekly) timescales. On much longer (1-100+ years) this attractor itself shifts. Weather forecasts want to determine the future state of the system itself as it evolves chaotically, which is impossible in principle after ~14 days because the system is chaotic. Climate forecasts want to track the slow shifts of the attractor. To do this, they run ensembles with slightly different initial conditions and observe the statistics of the ensemble at some future date, which is taken (via an ergodic assumption) to reflect the attractor at that date. None of the ensemble members are useful as "weather predictions" for 2050 or whatever, but their overall statistics are (it is argued) reliable predictions about the attractor on which the weather will be constrained to move in 2050 (i.e. "the climate in 2050").
It's analogous to the way we can precisely characterize the attractor in the Lorenz system, even if we can't predict the future of any given trajectory in that system because it's chaotic. (For a more precise analogy, imagine a version of the Lorenz system in which the attractor slowly changes over long time scales)
A simple way to explain the difference is that you have no idea what the weather will be in any particular place on June 19, 2016, but you can be pretty sure that in the Northern Hemisphere it will be summer in June 2016. This has nothing to do with differences in numerical model properties (you aren't running a numerical model in your head), it's just a consequence of the fact that climate and weather are two different things.
Apologies if you know all this. It just wasn't clear to me if you did from your comment, and I thought I might spell it out since it might be valuable to someone reading the thread.
I did know this, but thanks for spelling it out! One of the troubles with making short comments on this is that it doesn't work, and adding detail can be problematic if you add details in the wrong order. Your description is much better at getting the order of details right than my description has been.
I will point out also that my non-expert understanding is that some suspect that the attractor dynamics are themselves chaotic, because it looks like it's determined by a huge number of positive and negative feedback loops whose strength is dependent on the state of the system in possibly non-obvious ways. My impression is that informed people are optimistic or pessimistic about climate change based on whether the feedback loops that they think about are on net positive or negative. (As extremes, consider people who reason by analogy from Venus representing the positive feedback loop view and people who think geoengineering will be sufficient to avoid disaster representing the negative feedback loop view.)