What is the Trend in the Airborne Fraction of CO2?

In the wake of the recent CO2 fertilization/greening world paper (I think this is good coverage of what it means, which is not "hallelujah"), And Then There's Physics wrote a post about the airborne fraction (AF) of CO2 -- what fraction of the CO2 we emit stays in the atmosphere? Because as we continue to emit CO2, its AF is by no means guaranteed to stay what it is now, and no one seems to really know how it will change. The concern, of course, is that it increases as nature becomes closer to saturation (the Amazon is already taking up less CO2) and as the ocean continues to warm.

ATTP gave a result by Pierre Friedlingstein that gives a result based on RCP, since 1990:

You can read his discussion.

There are surely studies around that discuss this. But I thought I might have enough spreadsheets laying around to perhaps estimate down-and-dirty the actual trend in airborne fraction.

Here are my data:

• the atmospheric CO2 fraction since 1959 (the Keeling Curve), where for each year I took the average of 12 months from the monthly Mauna Lea data, from which one can compute the mass of CO2 in the atmosphere, 1959-2015.
• World CO2 emissions from combustion, cement production and gas flaring from CDIAC, 1751-2005.
• World CO2 emissions from land use changes from CDIAC, 1850-2005.
• I assumed atmospheric CO2 for 1850 was 280 ppm.

Here are the trends I find (click to enlarge):

There's considerable annual variation (blue points), but basically the 10-year moving average for AF is flat. So is the total AF since 1850. The last 10 years look like the annual AF has less variation, but that's also where my input data is the less certain (see note below).

N.b. Someone doing this right would need good data all the way to 2015, or up to the last year that is available. One problem in my data are the last two datasets stop in 2005. As an attempt to extend them, I used these data for combustion+cement+flaring for 2006-2008. Beyond 2008 I used IEA data for fossil fuel emissions; for land use emissions I assumed 400 Mt C/yr from 2006-2015, slightly bigger than the last few numbers here up to 2005 (Chinese growth), and flaring emissions of 1.3 Mt C/yr, the value for 2008 (it's a small amount anyway). And I assumed land use emissions per year for 2007-2015 were the average of the previous 10 years, which is 1,479 Mt C/yr. I ignored methane emissions, which converts to CO2 after several years. (I said, down-and-dirty.)