I don't know much about the topic of climate change to be honest. However, I've been attending a number of talks recently on the topic. As someone who studies mathematical models and uncertainty quantification, one thing that I do know is that weather models are extremely complicated and very sensitive to time. The error in weather model accumulated very fast, which makes long term behaviors fuzzy or uncertain. My knowledge is not related to the study on climate much, so that is about all I know.
I read up a bit on the climate issue and understand that the data suggests that climate change is real. I look at the data (from Nasa website) and agree that it supports that claim. So my question is not about whether climate change is real or not. My question is how some scientists make claims like "in 50 years..." My guess is that they observe the trends in history and use that as the basis for their prediction. I hope this question is clear. If you have an understanding on the topic, please point me to the right source.