Mathematician has proven by the Lorenz equations that you can do weather predictions up to 3 days adding more computing power on it won't help since its a chaotic system.
Did you know that the weather forecast for the next day is abort 45% accurate?
It is more-less globally true; locally it depends on the weather itself -- sometimes you can make up to few weeks and be confident about it from ensemble self-consistency (think desert in dry period), sometimes it blows up few hours into future. Also there is no way of defining single "weather prediction accuracy"; this one you cite is probably some meaningless mixture of various factors (;