Another, quite independent way that we know that fossil fuel burning and land clearing specifically are responsible for the increase in CO2 in the last 150 years is through the measurement of carbon isotopes.
Isotopes are simply different atoms with the same chemical behavior (isotope means “same type”) but with different masses. Carbon is composed of three different isotopes, 14C, 13C and 12C. 12C is the most common. 13C is about 1% of the total. 14C accounts for only about 1 in 1 trillion carbon atoms.
CO2 produced from burning fossil fuels or burning forests has quite a different isotopic composition from CO2 in the atmosphere. This is because plants have a preference for the lighter isotopes (12C vs. 13C); thus they have lower 13C/12C ratios. Since fossil fuels are ultimately derived from ancient plants, plants and fossil fuels all have roughly the same 13C/12C ratio – about 2% lower than that of the atmosphere. As CO2 from these materials is released into, and mixes with, the atmosphere, the average 13C/12C ratio of the atmosphere decreases.
Isotope geochemists have developed time series of variations in the 14C and 13C concentrations of atmospheric CO2. One of the methods used is to measure the 13C/12C in tree rings, and use this to infer those same ratios in atmospheric CO2. This works because during photosynthesis, trees take up carbon from the atmosphere and lay this carbon down as plant organic material in the form of rings, providing a snapshot of the atmospheric composition of that time. If the ratio of 13C/12C in atmospheric CO2 goes up or down, so does the 13C/12C of the tree rings. This isn’t to say that the tree rings have the same isotopic composition as the atmosphere – as noted above, plants have a preference for the lighter isotopes, but as long as that preference doesn’t change much, the tree-ring changes wiil track the atmospheric changes.
RealClimate: How do we know that recent CO2 increases are due to human activities?