The funny thing is, astrophysicists found this out a long time ago trying to model systems that are a lot less complex than weather systems. Just trying to model the movement of bodies in the solar system, they discovered that it was impossible to accurately predict the movements of a dynamic system to a great degree of accuracy once you got beyond just a couple of moving parts.
The French mathematician/physicist Poincare (April 1854 – 17 July 1912) did work in that arena - “the 3 body problem”.
https://en.wikipedia.org/wiki/Henri_Poincaré#Three-body_problem