When will CO2 ... Part IV - The AGGI with an improved fit to monthly data

In our previous posts, we have examined NOAA's AGGI data for the major non-condensing greenhouse gases and their cumulative radiative forcings. 

In this post, we first reduce monthly variations by using a twelve month moving average, and second, use the moving average to extrapolate those forcings to the point where twice the pre-industrial era ceiling is crossed.

The following figure compares the monthly data with that of the moving average over twelve months.

Note that the time series for the twelve-month moving average is shorter than that for the original data by half an year at each end,

It is clear that the twelve-month moving average is nearly linear, and is well-approximated by a quadratic fit.

The error in the quadratic fit to the twelve-month moving average AGGI ranges from -0.0045711 to 0.00380524 with an rms error 0.00203621. 

The following figure shows the original monthly AGGI data for total radiative forcings computed from mole fractions of CO₂, CH₄, and N₂O plus the quadratic estimate for forcings from the other species in the atmosphere, its moving average over twelve months, and the quadratic fit to the twelve-month moving average AGGI. There is not much difference between the latter pair.

So the question remains: When will the AGGI reach the equivalent of 2x pre-industrial levels?

Note: All calculations were performed within Mathematica Home Edition 13.2.1.0. on a MacBook Pro with macOS Sonoma 14.5. A PDF of the original Mathematica output is available upon request to Jim Diamond, jimd at Linfield dot edu.