If you aren't familiar with the distinction between correlation and causation in scientific research and statistics I really would recommend you look into it.
Modelling studies can never prove likely causation, at best they prove likely correlation. Meaning, two things seem highly likely to happen together but we can't say one caused the other.
Carbon emissions and carbon in the atmosphere has been shown highly correlated with the increase in average global temperatures, weather pattern changes, etc. That doesn't directly say carbon emissions caused those though, they could both be side effects of a more fundamental root cause.
Said differently, we know carbon emissions and average temperatures after the year 1850 both went up at similar rates. We also know, though, that many other things changed over that time. We can't run a controlled study of the entire environment is impossible, we can't isolate variables and compare outcomes when only one facto changes (in this case carbon).