Since 1958 the CO2 content of the atmosphere has been measured. The volume of CO2 has clearly increased from an average of 315.97 ppm in 1959 to 404.21 in 2016.
This time series has a significant linear trend. R2 = 0.99 (p = 1.07E-57)
We are told that this increase is driven by human emissions, significantly from burning fossil fuels:
1958 8.999 Gt (http://cdiac.ornl.gov/CO2_Emission/timeseries/global)
2016 33.5084 Gt ( BP Statistical Review of World Energy June 2016)
This time series also shows a significant linear trend. R2 = 0.97 (p = 2.46E-44)
Although there is a significant linear trend in atmospheric CO2, year to year changes are not uniform.
The trend in inter-annual change shows a significant linear trend. R2 = 0.54 (p = 7.64E-11)
but the proportion due to human emissions does not, and in two years emissions do not account for the observed increase. The variability of emissions to observed increase is also of interest.
Given a fixed rate of natural fluxes human emissions have risen to a peak of 4.62% of natural fluxes in 2013.
The lack of measurement of natural global fluxes means that it is assumed that they are uniform, a weak scientific position on par with the narrative that climates pre 1950 were uniform and benign.