Doubling of Carbon Dioxide Does What?

Viewing the typical conversations on the climate science blogs I was struck by the humorous logic used by the doomsayers. Since RealClimate is the ultimate source for all things blog climate science let's see what their logic implies.

Since CO2 lags warming in the Vostek ice cores, realclimate stated that about half of the warming from the glacial to interglacial periods is due to CO2 increasing in concentration. Realclimate are fans of the Arrhenius equation for global warming where the increase on CO2 has a natural log relationship with temperature. So some value times ln(c1/co) is the increase in temperature due to CO2.

The glacial periods had an average concentration of 190PPM CO2 that increased to about 280PPM at the pre-industrial part of the interglacial. ln(280/190) equals 0.39 so 0.39 times some value would be about half of the warming from glacial to interglacial due to CO2. Since the pre-industrial period, CO2 has increased to about 390PPM. ln(390/280)equals 0.31 which has caused a maximum of 0.8 degrees C of warming. Let's be generous and call that one whole degree and forget about the little ice age. So if 0.31 caused one degree, the multiplier needed for determining the impact of CO2 concentration change using Arrhenius' formula would be 1/0.31 or 3.0 allowing generous uncertainty.

So if we doubled from our present concentration to 780PPm, 3.0ln(780/390) equals warming would increase by 2.07 degrees. Obviously, CO2 would require a lot of help to generate more than 3 degrees warming from the pre-industrial conditions.

From the glacial to now, CO2 got a lot of help since realclimate says that only about half of the warming is due to CO2. From the glacial until now, 3.0ln(390/190) equals 2.15 degrees of warming. Now we have a few options:

If I used the half of the actual increase of about 0.7 degrees instead of 1 full degree for the pre-industrial to now that would make the impact of CO2 pretty small. So let's use the full observational increase for the industrial age warming of 0.7 degrees. The glacial to interglacial was about half due to CO2 so let's say that during the glacial period the Earth was twice 2.15 or 4.3 degrees cooler. Thanks to man screwing things up, now is 4.3 plus the 0.7 or 5 degrees warmer than it was during the last glacial period. So from then to now the factor would be 5 and not 3 for the Arrhenius equation. 5ln(780/190) equals 7.06 degrees warmer at 780ppm than it was at 190 during the last Glacial period including a lot of help of at least half. So with a lot of help, at 780ppm the Earth would be 2.06 degrees warmer than it is today.

So if I use the Arrhenius equation and the estimate by realclimate from the last glacial, there is only 2.06degrees more warming "in the pipeline" if CO2 peaks at 780PPM. Let's say that man is completely stupid and we increase CO2 to 1000ppm. Then 5.0ln(1000/190) equals 8.30 or 3.3 degrees more possible warming including the same help that climate received from the last glacial until now. Since climate didn't get that much help from 280 until now even, assuming that the little ice age was the average temperature, do ya think that more than 3 degrees for an increase to 560ppm might be a little bit over estimated?

That is the controversy. Not if CO2 may warm the Earth but how much.