It can clearly be observed. just look at say 10-20 years ago. Winters were colder, there was more snow, and weather was more stable, with only the oddball abnormality. Now? There's less snow, it's less cold, and weather is as abnormal as it's ever been. More major storms, and record breaking temperatures, or other abnormal weather in places that never got that type of weather before etc. Like some places that never get snow that get pounded. The trend latetly seems to be that the south gets tons of snow now when they never did, and we get less. It's not so much "global warming" as in "climate change" but it is warmer too. Scientists have also observed drastic sea level temperature increases over the years as well. The glaciers in Antarctica and North Pole are melting at an alarming rate as well. It's only going to get worse if we don't stop polluting. But it's not like we have any control over that, it's the megacorporations and governments that do, and they have no incentive to stop (they only make us think they do), and they will continue to squeeze every little bit they can out of this planet until we all die. The attitude most people have is "I'll be dead before it's a problem" which is kind of sad for future generations. I personally don't think it will become a huge issue in my life time but at the rate we are polluting I would not give the planet more than a couple hundred years. What may possibly happen is if humans die off first whatever is left of nature might slowly fix the planet and it may regain itself over time, but what will probably happen is we'll manage to survive longer than nature because of technology, but when that technology decides to break down is when we will be doomed as a species.
What is really interesting is that when the glaciers do melt completely, what kind of ancient diseases is that going to release. The flooding is only going to be an issue for coastal regions, but the diseases will affect everyone.