As a global warming noob, I wonder how a controlled environment is simulated to link climate change directly to human activity. Also, how can these claims be te

As a global warming noob, I wonder how a controlled environment is simulated to link climate change directly to human activity. Also, how can these claims be tested given that man-induced global warming cannot be repeatedly tested? Is there a formula to calculate the relation of carbon levels to temperature that can be retroactively tested for accuracy? If not, how do we know the degree to which carbon must be curved?