Scientists describe this as "the butterfly effect", where a butterfly flapping its wings in the Amazon jungle could impact weather patterns in very dramatic ways, perhaps trigger below normal winters in South Dakota or drought in Russia.
When they teach differential equations in school, they will always include exercises, drills, and examples of how supplying correct initial conditions are mandatory for a useful solution to systems of differential equations. Like they say, "garbage in, garbage out".
When it comes to weather, only God can know the correct initial conditions, and He plays his cards close to His chest.
FYI, I repurposed some of your phraseology in a FB post. Hope that’s OK. ;-)
I would have offered attribution, but we are anonymous here.
Thanks for turning the mathematical phrases!