Does the butterfly effect apply to models intended to be long-term? We know that complex models, especially for the atmosphere, are likely to be subject to the butterfly effect, meaning that small variations in initial conditions may result in very different states in the long term evolution of the model.
How, then, should we treat models that are intended to be long term, but still exhibit non-linear and possibly chaotic behaviors? For example, what about climate models that aim at predicting for 50 years down the road? Or ocean and ice sheet models that look for the year 2100? Why would they be reliable?
My guess is that the reliability of the long-term models stems from the fact that the time step over which they are computed is much bigger, maybe in the range of months, compared to short term weather forecast, in which the time step is of minutes. This would imply that the chaotic behavior is there even in long-term models, and that it only takes longer for it to become evident. But I am not sure this is what is going on.
 A: As long as large-scale global circulation is stable, the weather patterns do not change too much and it is possible to calculate averages. For example of the total heat balance. Many models exclude potentially important feedback mechanisms, like the effect of melting Arctic sea ice on albedo. And it is of course impossible to model feedback mechanisms that we do not know enough about (permafrost emissions, ice-sheet collapse). That means that  there is not much of a hysteresis effect according to manageable, stable models. But such models are incomplete, and that means that one should not place too much confidence in them.
The predictability over medium-time periods is already difficult. It is difficult to know to know how weather patterns in the Northern hemisphere will be affected as a consequence of an ice-free Arctic. 
And long-term predictability is really difficult. There is probably a bifurcation somewhere to a hothouse earth state (and another one to a snowball earth). Ocean currents may change, atmospheric cells may collapse. Geology seems to indicate that transitions can be fast.
A: Chaotic dynamics typically occurs on an attractor state. At large times where on the attractor the system ends up is unpredictable - but it is highly predictable that it will be on the attractor. So short term unpredictability is not a problem for long term predictability.
A: One thing climate models take into account is ranges. They don't just model something once they alter the numbers and models. This is why many reports include phrases like "worst-case scenario" or "best-case scenario" They are accounting for things being at the extreme ranges. While this isn't an exact accounting for chaos-theory it does account for variations and unexpected occurrences. Sadly, as pointed out by Pieter, there is a lot we don't know and sometimes that can throw off models drastically. 
