You can't plot the weather here on Earth more than 3 days from now accurately, but you expect us to believe you can plot the sun's weather 2 years from now?
I call BS.
We know arbitrarily far in advance that winter is colder on average than summer. Similarly, we can forecast the timing of solar-cycle peaks pretty well out into the future. I.e, this forecast based on climatology, not an initial value problem (weather; chaotic).
Basically, Earth's size, rotation rate, and stratification only support 1-2 jet streams, and there is a lot of variability. This variability, and the strong wave-radiative potential near the jet streams does not allow large-scale coherent structure to persist for "long" periods of time. Jupiter supports many jets having nearly fixed positions, which allows coherent material eddies to persist without disruption in the mixing layers between the jets.
Earth has similar eddies, on shorter timescales, in both the atmosphere and ocean. Examples include warm and cold rings in the ocean, and "cut-off" cyclones in the atmosphere. There are also less well-known vortices over the arctic that are apparent in analyses of the tropopause. Examples can be found here (try the loop feature to see the motion of vortices over the arctic):
Somebody ought to cross ball point pens with coat hangers so that the pens will multiply instead of disappear.