The Navier Stokes equations describe atmospheric flow as affected by heat, mass and density. They are non-linear, which means that future states can not be predicted long term. That is why weather predictions fail miserably at 7 to 10 days, and often sooner.
Predict multiple days correctly tens of years in advance? That is not possible.
The sun is another consideration, again, the flow is affected by heat, mass and density, and described by non-linear differential equations. The sun can not be predicted long term.
Climate study as a historical exercise can be performed, so long as you know that “average temperature” is an artifact of the way you collect your data, and has no ability to predict the future (past a few days). Since Hershel, it has been known that the number of sun spots affect plant growth, as he found correlation between sun spots and warm weather (with his surrogate being grain prices).
Yeah! I know!
I was on to this game YEARS ago.