By Roger Andrews
An important consideration in estimating future greenhouse warming risks is how long CO2 remains in the atmosphere. Here I present the results of a simple mass balance model that provides a near-perfect fit between CO2 emissions and observed atmospheric CO2 using a CO2 residence time of 33 years. This, however, is significantly longer than 36 peer reviewed estimates that cluster between 5 and 15 years and much shorter than IPCC’s estimates of 100 years or longer, hence the question mark in the title.
Figure 1: CO2 Residence Time Estimates (data: Jennifer Marohasy )
I developed the mass balance model using the following deductions and assumptions:
1. Between 1750 and 2010 fossil fuel burning and deforestation released approximately 1.85 trillion tons of CO2 into the atmosphere. If all of it had stayed there the CO2 content of the atmosphere would have risen by ~220 ppm, but it rose by only 110 ppm. We can therefore assume, all other things being equal, that about half of the CO2 emitted between 1750 and 2010 has remained in the atmosphere and that the other half has been absorbed, either by vegetation or by the oceans.
2. The half of the CO2 that was absorbed was absorbed over time in accordance with an exponential decay curve of the form:
Fraction remaining = e^(-t/T)
Where t is the elapsed time and T is the “e-folding time”, or the time it takes for the concentration to decrease to 1/e, or 36.8%, of its initial value.
3. “Residence time” is defined as as the time it takes for the fiftieth molecule in a pulse of 100 emitted CO2 molecules to be absorbed (in other words the half-life). Mathematically it works out to 0.69 times the e-folding time.
4. The residence time remains constant. It does not change with time.
5. “Synthetic” CO2 curves can be constructed from emissions data using different residence time values. The value that gives the best fit to observed CO2 concentrations provides the best estimate of residence time.
I constructed CO2 curves using a spreadsheet algorithm that begins in 1760 and works as follows. It takes 1760 CO2 emissions, calculates how much CO2 (in ppm) they added to the atmosphere in 1760 and then reduces the ppm value in each following year in accordance with the decay curve, which will vary with the residence time. The process is then repeated for 1761 and the 1760 and 1761 results are summed, ditto for 1760, 1761 and 1762 and so on for each year through 2010. The procedure, which is analogous to estimating production and depletion rates in an oil or gas field, is summarized graphically in Figure 2, The case shown begins in 1990 (emissions from earlier year are ignored for simplicity) and uses a residence time of 10 years (for illustration purposes only):
Figure 2: Graphical example of operation of spreadsheet algorithm
The data sources used were:
* Atmospheric CO2 concentrations from Mauna Loa
* Emissions data for fossil fuel burning and cement production from CDIAC
* Land use change emission estimates based on forest cover data from forest cover data from Euan Mearns which were added to the fossil fuel emissions. (I used changes in forest cover percentage to calculate the annual tonnage of carbon emitted from deforestation, based on the current estimate of 638 billion tones of carbon contained in the world’s forests.)
The emissions data used in the analysis are shown in Figure 3:
Figure 3: Annual global carbon emissions since 1760
Now to the results. Figure 4 shows the CO2 curves generated using a) the IPCC’s residence time of 100 years and b) a residence time of 10 years, which is the approximate average of the non-IPCC estimates shown in Figure 1. The 100-year curve gives far too much CO2, implying that CO2 doesn’t stay in the atmosphere for anything like as long as the IPCC’s 100-year residence time would suggest. On the other hand the 10-year curve gives far too little CO2, implying that CO2 stays in the atmosphere much longer than a 10-year residence time would suggest:
Figure 4: CO2 model/observed matches, 10 and 100 year residence times
With a 33-year residence time, however, we get a match which I submit is about as good a model/observed fit as you are ever going to see:
Figure 5: CO2 model/observed match, 33 year residence time
The fit is also quite sensitive to small changes in residence time. With a 31 year residence time the CO2 curve is clearly off on the low side and with a 35 year residence time it’s clearly off on the high side:
Figure 6: CO2 model/observed match, 31 and 35 year residence times
In summary, here we have what appears to be a robust 33-year estimate of residence time derived from a simple mass-balance model. The problem is that the estimate matches no one else’s. I don’t have much doubt that it invalidates the IPCC’s estimates, but why is it so much higher than the numerous estimates obtained from the carbon 14 and radon 222 analyses? Is there a flaw in my logic? Or do radioactive isotopes have a higher sequestration rate than carbon 12? Open for comments.
A couple of closing observations. First, someone is going to ask why I didn’t take the carbon cycle into account, given that the amount of carbon that cycles each year between the atmosphere and land-ocean sinks overwhelms man-made carbon emissions. The simple reason is that to take the carbon cycle into account I need to know how the tonnages of emitted and sequestered CO2 have changed over time, and there are no good numbers available. However, the fact that I get an excellent model-observed fit using a constant residence time suggests that the carbon cycle hasn’t changed much, if at all, since 1959.
Second, it’s not widely recognized, but the IPCC & Co. in fact agree that the residence time of CO2 in the atmosphere is short. SkepticalScience puts it thus: “Individual carbon dioxide molecules have a short life time of around 5 years in the atmosphere.”
So where do the IPCC’s ~100 year residence time estimates come from? SkepticalScience goes on to offer this explanation: “However, when they (the CO2 molecules) leave the atmosphere, they’re simply swapping places with carbon dioxide in the ocean. The final amount of extra CO2 that remains in the atmosphere stays there on a time scale of centuries.”
I’ve been trying to make sense of this statement but haven’t been having much success. Maybe someone can make sense of it for me.