The graph shows the ever-increasing concentration of CO₂ in the atmosphere (green) since 1900 and the remarkably parallel graph of estimates of the emissions of carbon into the atmosphere from the burning of fossil fuels (black). The correlation is clearly very strong and the value of the correlation coefficient between the two sets of data is 0.98, near to perfection. As ever, correlation does not prove causation and other evidence is required other than straightforward statistics.

The evidence for a dominating human role in the CO₂ increase is extremely strong. The 36% increase (in 2006) in atmospheric CO₂ observed since pre-industrial times cannot be explained in terms of natural changes. CO₂ concentrations have varied naturally throughout Earth's history. 

Furthermore, the observed progressive depletion in carbon-13 (see below) shows that the source of the CO₂ is either fossil fuels or deforestation because they produce CO₂ depleted in carbon-13. The atmospheric CO₂ increase cannot have come from the oceans because that would not have caused any depletion of carbon-13.  In fact, carbon in the oceans has itself become gradually depleted, with the greatest depletion at the surface. That implies that the signal is imposed from the atmosphere. The next piece of evidence is that we also observe a depletion of radioactive carbon-14 in the atmosphere and oceans, with the strongest signal in the atmosphere suggesting it is the place where the depletion originates.  Fossil fuels contain no carbon-14, and their combustion produces CO₂ without carbon-14.  Deforestation does not cause a change in atmospheric carbon-14.  The observed carbon-14 depletion in the atmosphere, oceans and land ecosystems is in fact quantitatively consistent with the amount of fossil fuels burned until now.  Finally, annual mean CO₂ concentrations in the northern hemisphere are higher than in the southern hemisphere, and more so in recent years compared to the early years of atmospheric CO₂ measurements. This suggests a growing source of CO₂ in the northern hemisphere, which is in fact where most of the fossil fuel burning takes place. 

Natural carbon contains two stable [i.e., non-radioactive] isotopes. Mass 12 carbon represents 98.9% of the element and the remainder is mass 13 carbon. The ratio of the abundances of the two isotopes in standard limestone, ¹³C/¹²C is 0.01122. Reduction in the ratio caused by fossil fuel burning has produced a value of about 0.01113, 0.8% lower than the standard value. Carbon-14 is present in the atmosphere to a very small extent and is produced when cosmic rays react with the nuclei of atoms in the upper atmosphere to produce neutrons. These interact with nitrogen atoms to give carbon-14 which has a half-life of 5715 years and is useful in dating carbon-based materials.

The science does not care whether recent CO₂ increases are 100% anthropogenic or 100% natural.  So, why is there so much reluctance to address the clear evidence that some of it could, in fact, be natural? In the 20th century, for the increase in the CO₂ concentration to be entirely due to an increase in temperature that should have been around 5^oC. That has not occurred and leads to the inevitable conclusion that the recent increases in CO₂ concentrations are because of the burning of fossil fuels. The answer comes from a study of the temperature dependence of the Henry's law coefficient for the solubility of CO₂ in seawater. This has been very carefully quantified by the Brookhaven National Lab and can be relied upon. That the 20th century saw an increase of temperature of 0.6 +/- 0.2 C implies that an increase in CO₂ atmospheric concentration should have resulted of around 10 +/- 3 ppmv. That much more than this increase occurred seems to lead to the conclusion that there is another source. All the evidence we have in the literature points towards the burning of fossil fuels. So, about 10 ppmv from a slight temperature increase and the rest is down to us.