Once again, don't confuse predictability with ability to understand a system. We actually have a fairly good understanding of weather dynamics and turbulence - and I can give you the formula for both of these - the Navier-Stokes equation! Not the simplest equation, but something understandable (yes, I know there's a Millenium Prize problem to see if we always get a smooth solution). We do understand how turbulence arises from this. And we understand the weather very well.

However, we can't predict the weather, nor can we predict the earthquakes. And as you correctly point out, the reason for this is chaos. The reason is not that we don't understand the underlying processes that govern these dynamics. Rather, the uncertainties in our initial conditions increase exponentially with time (due to chaos) and make long-term predictions unreliable.