Sadly, the main governing equations of weather (eg Navier–Stokes equation for fluid dynamics) are still very much non-linear. Non-linear does not mean unpredict

Sadly, the main governing equations of weather (eg Navier–Stokes equation for fluid dynamics) are still very much non-linear. Non-linear does not mean unpredictable, it just means that it is very hard to solve (currently no analytical solution for the Navier–Stokes equation) and that, well, the system is not linear. (And it applies to gas, btw.) For weather, other important effects are phase change of water at given pressure/temperatures (which can store large amounts of energy), radiative transport (again, non-linear equation, not solved) and heat transfer (non-linear equation, solved (easy)). For forecasts, you also cannot measure the full state of the system at any point in time. This makes it a very hard problem - otherwise weather forecasts would have been perfect ages ago. With the advent of cluster computing and measurement satellites, it is now possible to improve the forecasts vastly, but it's still hard.