Simple systems can be famously unpredictable [1]. Our bodies manage entropy; that should make them complex but predictable. The weather, on the other hand, has no governors or raison d'être.
Arbitrary precision, not arbitrary length. Even "from [a] mathematical viewpoint, given an exact initial condition, we can gain mathematically reliable trajectories of chaotic dynamic systems" to only a "finite...interval" [1]. (This is due to "numerical noises, i.e. truncation and round-off error, where truncation error is determined by numerical algorithms and round-off error is due to the limited precision of numerical data, respectively.")
For a physical system like the weather, uncertainty "mainly comes from limited precision of measurement," though there is also the "inherently uncertain/random property of nature, caused by such as thermal fluctuation, wave-particle duality of de Broglie’s wave, and so on."
[1] https://www.sciencedirect.com/science/article/abs/pii/S10075...
For example, I can calculate the Fibonacci sequence to an arbitrary length but not infinite.
Skim the paper. Numerical noise means you cannot calculate the 3-body problem to an arbitrary length. There is a finite, mathematical limit even with perfect knowledge of initial conditions.
There isn’t any claim that mathematically exact starting values can’t be propagated with arbitrary precision to arbitrary length, and I would claim that this is possible (but not practical due to compute being limited, of course).
But there’s no hard limit of precision and length where a simulation can’t be made if the starting conditions are exact. The point of the paper is that starting conditions are never exact which limits the length you can propagate.
It talks about that. Which is relevant when we're talking about the weather. But it opens by discussing the hard mathematical limits to numerical methods.
> there’s no hard limit of precision and length where a simulation can’t be made if the starting conditions are exact
Wrong.
Read. The. Paper. Numerical methods for chaotic systems are inherently, mathematically uncertain.
Beyond a certain number of steps, adding precision doesn't yield a more precise answer, it just produces a different one. At a certain point, the difference between the different answers you get with more precision covers the entire solution space.
Even with perfect knowledge of initial conditions, numerical noise limits the forecast interval.
Is this a chaos theory prediction? Why 14 days?
Why not? What's so special about 7-14 days? I can see plenty of reasons one might want to predict accurately the weather even a year out, just one example: will the weather support an outdoor bbq event this late in fall next year?
Sure, but there could be a disease outbreak, or a pork meat recall that prevents it anyways. The weather, as a factor, is generally insignificant with respect to loss of life events. To the extent they are we can see those events far enough in advance at 7 to 14 days to compensate correctly.
A better example would be "can we launch a space craft from this launch site next year." Even then, we never pick a launch day, we establish a launch window, because we already know, the weather changes fast enough that it's unlikely to remain identical for several days in a row. So conditions on a single day are effectively meaningless.
The Space Shuttle program got even better with this by feeding in wind data from high atmosphere probes back into the launch vehicle software so it could plan it's maneuvers ahead of the wind so it could reduce vehicle stresses to within tolerable parameters. They went from a 20% launch probability to an 80% launch probability with this system.
I mean.. enjoy your BBQ either way just bring some popup tents.