The only number I have found is 280ppm CO2 for pre-industrial (in the UN IPCC materials), I cannot find a preindustrial CO2e number anywhere. A calculation would also need assumptions on N2O, which was about 270 ppb in 1800.
https://www.eea.europa.eu/data-and-maps/daviz/atmospheric-concentration-of-carbon-dioxide-3#tab-chart_5_filters=%7B%22rowFilters%22%3A%7B%7D%3B%22columnFilters%22%3A%7B%22pre_config_polutant%22%3A%5B%22N2O%20(ppb)%22%5D%7D%7D
After a bit of digging, I found the following suggested values:
CO2: 278 ppm
CH4: 722 ppb
Stratospheric Water: ??
N20: 270 ppb
Tropospheric Ozone: 270 ppb
CF4: 10
-7 ppt
C2F6: 3.47x10
-6 ppt
Using Forcing factors (W/m
2/ppb) of:
CO
2: 0.014
CH
4: 0.037
N
2O: 0.12
H
2O: 0.011
O
3: 0.02
CF
4: 0.25
C
2F
6: 0.09
This results in a total forcing of 3,956 and reverses to a CO
2(e) of 282.56 ppm, or 4.56 ppm above the CO
2 background level. Stratospheric water may change that a little. So, about 4.5 ppm above the CO
2 level.
The most commonly used methods use a logarithmic ratioing to the preindustrial levels. It is cleaner and likely better not to do it that way.
Worse though is that the reality is so much more complex than the simple methods suggest. The various gases exist in differing quantities at different altitudes, latitudes, and seasons, rather than as a homogeneous picture through the entire column. The IR reflections and refractions occur in differing frequency bands with very complex overlaps. Sun angles, latitude, seasonality, cloud decks and more all play roles. Etc... To actually model all of that would take an extremely sophisticated model and a supercomputer to evaluate. It isn't something we can easily do using computers at home.
Still, the simple models do seem to fairly accurately portray the situation as a smeared average. Do not take the number of digits in the result as significant. The result is only a likely central value, lacking any attempt at an error estimate.
Still, the calculation is instructive. Where we were at CO
2 of about 278 ppm and CO
2(e) of about 282.5 ppm. We are today at about 414 ppm (Mauna Loa today) CO
2 and circa 540 ppm CO
2(e). That represents increases since pre-industrial of about 136 ppm CO
2 and 258 ppm CO
2(e).
That is of course - assuming that I haven't blundered badly somewhere in the data or math. Please check the results before using them. Assuming that I haven't seriously erred in the calculation, that suggests a starkly different consideration of the conditions using the CO
2 versus CO
2(e) numbers. Using the CO
2(e) values, it suggests we will reach a doubling of the background in 8-9 years. Again, please check my math - especially if you have access to better models or approaches to perform the calculation.
Sam