The Quantum Weather Butterfly (Papilio tempestae) is an undistinguished yellow colour, although the mandelbrot patterns on the wings are of considerable interest. Its outstanding feature is its ability to create weather.
This presumably began as a survival trait, since even a hungry bird would find itself inconvenienced by a nasty localized tornado… From there it possibly became a secondary sexual characteristic, like the plumage of birds or the throat sacs of certain frogs. “Look at me”, the male says, flapping his wings lazily in the canopy of the rain forest. “I may be an undistinguished yellow colour but in a fortnight’s time, a thousand miles away, Freak Gales Cause Road Chaos.”
This is the butterfly of the storms.
It flaps its wings…

–Terry Pratchett, Interesting Times 

The butterfly effect applies to weather forecasting much more than climate models. Specifically, the flap of a butterfly’s wings will rearrange thunderstorms, but not so much create or destroy them.

That must be true, if you think about it carefully.  Recall that an atmospheric perturbation (e.g. a butterfly flap) grows rapidly, doubling ~every day.  Obviously, the perturbation cannot continue growing forever! If it did, in 3 weeks the butterfly would move thunderstorms; in 4 weeks, it’d move hurricanes; in 5 weeks it would be super-tornadoes; in 6 weeks, it’d rip the oceans from their basins; in 7 weeks it would shatter the Earth. And yet, we know that butterflies have been flapping their wings for many years.

Therefore, physical mechanisms stop the growth of atmospheric perturbations at some level. That level happens to be (roughly speaking) the rearrangement of thunderstorms. So weather forecasting is hard because weather forecasters need to predict where thunderstorms will be next week. But climate prediction doesn’t suffer as much from the problem, because there are always more-or-less the same total number of thunderstorms. (That’s because the total number of thunderstorms depends mostly on the solar heat flux.)

This concept is a bit subtle. Chaos always operates within some sort of bounds, because the exponential growth of perturbations that characterizes chaos can’t continue forever.  Only small perturbations grow exponentially.