The most convincing evidence for CO2 increase

Today global warming and climate change are widely discussed. Many people refer to "scientific evidence" that proves that climate change is caused by humans, by burning fossil fuel in particular. However, I rarely hear on public media discussion of the actual data and interpretations that serve as the scientific evidence for human-induced climate change. May be there would be more productive conversation between different members of our society on climate change if the public media discussions included some background on the scientific evidence. 

Human-induced climate change has expressed itself in elevated concentrations of CO₂ in the atmosphere. Elevated CO₂ is a consequence of releasing carbon in the atmosphere through burning fossil fuel like coal and petrol. Among multiple evidences for such change, glacial ice cores represent the most convincing indication of human-induced elevated CO₂ levels. As glacial ice forms every year it trap atmospheric air in the form of bubbles. Extracted from drill holes, glacial ice cores can be accurately dated to the recent time line (back to several thousand years). Extracted air bubbles are analyzed for concentration of gases and isotopic composition of the gases. This graph below copied from "Stable Isotope Geochemistry" by Hoefs represents the most convincing evidence for human-induced climate change.

 

Clear increase in CO₂ concentration (plot a) starting at about 1850 marks the bloom of the industrial era. Plot B shows the carbon isotopic composition (δ¹³C, ‰; delta carbon thirteen) of CO₂ from the atmosphere. Starting from industrial era, it becomes more negative, meaning CO₂ molecules in the atmosphere are increasingly depleted in the heavier isotope of carbon - ¹³C - with respect to the lighter carbon, ¹²C. Organic matter, like coal, is extremely "light" carbon, means it is depleted in heavy carbon ¹³C. Burning such "light" source of carbon makes CO₂ in the atmosphere "light" as well. Just for clarification, I include here a diagram from the same book on isotopic composition of all carbon sources known to Earth. It shows  that organic matter (such as fossil fuel) is the source of isotopically "light" carbon.

 

EDIT:

It was pointed out that the isotopic composition of CO₂ from volcanoes should be shown too since volcanic emanations contribute to the level of atmospheric CO₂. Valid point. The δ¹³C from volcanoes is almost identical to the δ¹³C of the air. See attached diagram. 

The image is taken from a Pennsylvania State University website