First off, it is important to show numerically how the concentration of carbon dioxide has changed over the past 1000 years, as shown in the figure below [3].
As can be seen on the figure, the level of carbon dioxide emissions was relatively constant until the year 1769, the start of the Industrial Revolution and the burning of fossil fuels. The year 1769 conveniently marks the year in which carbon dioxide emissions started rising and has not looked back, with the level of emissions still growing today. Thus, it can be concluded that there is sufficient proof from scientists that the human fossil-fuel burning has in fact increased carbon dioxide emissions.
The second step in the scientific bases for AGW is proving that carbon dioxide is indeed a greenhouse gas. According to David McKay, carbon dioxide is not the strongest GHG, but nonetheless it is a greenhouse gas and acts as any other normal greenhouse gas does. “It absorbs infrared radiation (heat) heading out from the Earth and reemits it in a random direction […] the fact is not based on complex historical records of global temperatures but on the simple physical properties of carbon dioxide molecules.” [3]
Finally, the third step in proving that increases in GHGs causes increases in temperatures is by far the most uncertain. However, many scientists do agree that the two subjects are directly related. David McKay proclaims in his book that the consensus of the best climate models predicts that “doubling the CO2 concentration would have roughly the same effect as increasing the intensity of the sun by 2%, and would bump up the global mean temperature by something like 3°C.” [3]
These three steps form the basis of AWG and are widely accepted by scientists.