By correlation I was thinking in comparison to something like CO2. One can get CO2 concentrations from atmospheric readings, i.e. @MaunaLoa. These are correlated to estimates derived from fossil fuel emissions -- i.e. every barrel of oil combusted will add X amount of CO2 to the air (given some fraction will diffusionally sequester). Since we have adequate estimates of total fossil fuel consumption, this correlation turns out to be very effective year-over-year.
Now, for methane, this correlation may be problematic. Estimates of methane production from livestock is probably a guess. Same with estimates from organic decomposition. That fraction due to incomplete combustion of fossil fuels and leakage/loss is probably better estimated. However, this mix of sources of methane makes it harder to get as good a correlation for methane as with CO2.
This is an ongoing issue in estimating climate sensitivity of GHGs. The "skeptics" of AGW beat climate scientists over the head on not being able to estimate contributions of various GHGs and of the poorly characterized aerosols and particulates.