We often see graphs from various places predicting how the world is going to warm up over the next 100 years. Weather prediction is a complex matter since weather is a complex system and a lot of work has been done to make these predictions. A big part of this work includes the use of super computers that simulate entire climate systems and everything affecting it, including the sea, clouds, air and sun.
Chaos Theory describes that small differences in an initial dynamic system can contribute to serious unpredictability later on. This theory came about during work on weather modeling because this is where the effects of it makes the most noticeable difference.
The above graph is scoring the UK Meteorological office's predictions from 2002-2005, a total of 115 predictions for average temperature and precipitation. A score of 1 is for a 100% perfect prediction (and 0.5 would mean a 50% accurate prediction) Tmean is temperature and Precip is precipitation
As you can see from the above diagram, temperature predictions are more accurate than precipitation. It's also clear that 5-11 day predictions are the most accurate. Most importantly, 5-11 day predictions, on average, has been 35% accurate. That could also mean that it's wrong two out of three times.
Moving on to the extreme distant future of 19-32 days ahead, temperature predictions get a score of 0.05. That means one out of 200,000 times they would have the prediction spot on to the centigrade.
Predictions for future global temperatures 50 years from now show between a 1 and 2 degree warming. I believe this really has to be taken with a pinch of salt extracted from the warming ocean. We can't even get it right one month in advance.