Willis Eschenbach and his carbon uptake mistake at WUWT

Willis Eschenbach is wondering about how much extra CO2 can go into the air (archived here, latest here). He's done some calculations and figured that atmospheric CO2 can't double. Even without doing any calculations it's easy to see that he's wrong. This is why.

Willis has used two models for his estimate, and two estimates of fossil fuel available to burn. He got his estimates from a diagram in the IPCC WG1 AR5 report, which put fossil fuel reserves at between around 900 GtC (gigatonnes of carbon) and 2000 GtC.  I will leave it to the experts to quibble over how much of the remaining fossil fuel reserves would be technically feasible to exploit. This article is about how and perhaps why Willis has underestimated the impact - or so it seems to me. Willis' two examples are described here as:

• Example 1: burning 900 GtC by 2100 and
• Example 2: burning an extra 2,000 GtC by 2100.

As far as I can tell, where he went wrong was in using single pulse models. That is, there's an inherent assumption in the models he used that CO2 will be released as a single pulse, followed by nothing. (Willis doesn't assume that himself, but the models he uses do, I think. That leads to a flaw in his reasoning.) Update: Willis mentions a tau of 33 years, suggesting he has factored in additional removal of CO2 from the air, over and above what the biosphere, oceans and land surface can already handle. In other words, he's erroneously double counted.

Anyway, I'm not going to bother with his models. I've looked at things from another angle. It seems to me a fairly straightforward exercise to show that Willis did something wrong. In both examples below the assumption is that 1 ppm by volume of atmosphere CO2 = 2.13 Gt C (see here)

Example 1: Every year from now 10 GtC is emitted

If 10 gigatonne of carbon were emitted from now to the end of the century, this is what it would look like. The plot is of annual emissions over time. Nothing fancy:

Data source: CDIAC for actual to 2011

If you make some simple assumptions, you can get a rough estimate of what will happen in the atmosphere. Assuming that the biosphere, oceans and land surface absorbs half of what is released each year right through to 2100, this is how it would be in the atmosphere in ppm. Atmospheric CO2 would have doubled over pre-industrial in 2084:

Data source: Scripps CO2 program for actual

Example 2: Between now and 2100, 2000 GtC is emitted

In the next example, 2000 GtC is emitted. For the sake of illustration, let's assume that each year the amount increases up until 2100. That's not realistic if you assume that if 2,000 GtC was emitted that would use up all the fossil fuel reserves available. However it will do for the purpose of illustration. By rough estimation, I've assumed 10 Gt was released in 2012, and each year after that to 2100, there was an increase of around 1.7% a year. That would be around 2,018 GtC emitted from 2014, which is close enough for the purpose. Below is what the emissions trajectory would look like. Note that the scale on the y axis has had to change from the one above:

Data source: CDIAC for actual (to 2011)

Again, making a simple assumption that the oceans, biosphere and land surface absorbed half of what is released each year right through to 2100, this is how it would be in the atmosphere in ppm. Atmospheric CO2 would have doubled over pre-industrial in 2084:

Data source: Scripps CO2 program for actual

Now even if the CO2 burning curve had a different slope, it wouldn't change the fact that there is a limit to how much CO2 can be absorbed by the biosphere, oceans and land surface each year. I think it could be argued that if emissions were released more quickly early on, then less than 50% of it would be absorbed in those years so the amount left in the air would still increase substantially, and by 2100 would probably still be close to what is shown in the chart, even if the trajectory is changed a bit. (See references below.)

Willis says this won't happen

Willis' article at WUWT had the headline: "Double The Atmospheric CO2? Fuggeddaboutit!". He thinks that it's not possible for atmospheric CO2 to double this century. He even thinks that even if all fossil fuel reserves were burnt atmospheric CO2 would be unlikely to double. He wrote:

This year, the atmospheric CO2 level is right around four hundred ppmv. So to double, it would have to go to eight hundred ppmv … and even assuming we could maintain exponential growth for the next eight decades and we burned every drop of the two thousand gigatonne high-end estimate of the fossil reserves, CO2 levels would still not be double those of today.

And in fact, even a fifty percent increase in CO2 levels by 2100 seems unlikely. That would be six hundred ppmv … possible, but doubtful given the graph above.

Short version? According to the IPCC, there is not enough fossil carbon on the planet to double the atmospheric CO2 concentration from its current value.

Best regards to all,

Despite his best regards, I don't know exactly what Willis has done. Going by the fact that he says he used the Bern model and simple exponential model, I assume that he did his calculations as if there was a pulse of CO2 and then no more emissions. That doesn't work when there are continuing emissions.

Whatever he's done, it's fairly clear from his article that he has assumed that the oceans and land surface will start absorbing more CO2 as we continue emissions. That is, a greater proportion of emissions will be absorbed, considerably more than half. It is more likely that some of the sinks will become saturated and there will be proportionately less absorbed as emissions increase. (See references below.)

The bottom line

The bottom line, if there is such a thing, is that before we can applaud ourselves for reducing atmospheric CO2, we have to get it to level out. We probably have to drop to maybe 70% or 80% of current emissions before atmospheric CO2 would stabilise. We're rapidly using up the CO2 budget, which is now around 1,100 Gt CO2 or less than 300 Gt carbon. Authors of a recent paper in Nature said:

Our results suggest that, globally, a third of oil reserves, half of gas reserves and over 80 per cent of current coal reserves should remain unused from 2010 to 2050 in order to meet the target of 2 °C. 

Feel free to quibble or point out if you think I've made an error or made flawed assumptions, bearing in mind this is just a rough estimate to demonstrate that Willis' estimates are flawed.

From the WUWT comments

I started writing this before there were any comments. Let's see if anyone has figured where Willis went off the rails. Not that I can see.

Anthony Watts was first to comment, with the denier equivalent of "I don't understand a word but it's brilliant":

March 27, 2016 at 11:04 pm
Well done, Willis.

Bill H wonders what all the fuss is about:

March 27, 2016 at 11:06 pm
Nice… Even if we burn all the hydrocarbons on the planet there is no catastrophic emergency of any sort…
1. Why then is this a hot button political issue?
2. Why are we worried about it? We obviously cant make enough CO2 to create a runaway atmospheric temperature problem.
This them is just a ruse for political gain… Where have i heard this before? Ottmar Edenhoffer’s statement now come to mind… 

charles the moderator comes up with some ideas that he thinks "alarmists" would counter with:

March 27, 2016 at 11:24 pm
“Channeling standard alarmist”:
1. But we’re already half way there!. Current levels are 50% above preindustrial.
2. As the Ocean warms it will vomit up more CO2 than we are able to emit!
3. As the Arctic warms and the permafrost collapses, the methane explosion will dwarf the effect from CO2 only.
Can’t think of anymore, but there are probably some.

Nick Stokes quotes Willis:

March 27, 2016 at 11:54 pm
“For the larger case, two thousand GtC implies a burn rate that increases every year by 1.4%. If that happens, then by the end of this century we’d have burned two thousand gigatonnes of carbon.”
“According to the IPCC, there is not enough fossil carbon on the planet to double the atmospheric CO2 concentration from its current value.”

The IPCC is citing GEA estimates of reserves. An estimate of reserves is not an upper limit of the total fossil carbon on the planet.

To put your arithmetic and assumptions the other way around, on the high estimate, increasing 1.4% would leave a possibly manageable GHG problem in 2100. But we would also be totally out of fossil fuel. Do you expect that to happen? 

Willis Eschenbach replied:

March 28, 2016 at 12:23 am
Thanks, Nick. I take no position on the likelihood of their numbers being correct. I’m saying that their estimate (according to the graphic shown in Figure 1) is that there are a total of 900-2000 gigatonnes of fossil fuel carbon in the earth. Note that this is reported in the same manner as their estimates of the various reservoir masses, as being their best estimate of the total amount of carbon in that form and location.

All I did was calculate how high the atmospheric CO2 would go if we burned all of their best estimate of the total fossil carbon. I didn’t say that their assessment was accurate, which is why I headed my conclusion “According to the IPCC” …
Regards,
w. 

References and further reading

McGlade, Christophe, and Paul Ekins. "The geographical distribution of fossil fuels unused when limiting global warming to 2 °C." Nature 517, no. 7533 (2015): 187-190. doi:10.1038/nature14016 (pdf here)

Nakano, H., M. Ishii, K. B. Rodgers, H. Tsujino, and G. Yamanaka. "Anthropogenic CO2 uptake, transport, storage, and dynamical controls in the ocean imposed by the meridional overturning circulation: A modeling study." Global Biogeochemical Cycles 29, no. 10 (2015): 1706-1724. doi:10.1002/2015GB005128.

Hauck, Judith, Christoph Völker, D. A. Wolf‐Gladrow, Charlotte Laufkötter, Meike Vogt, Olivier Aumont, Laurent Bopp et al. "On the Southern Ocean CO2 uptake and the role of the biological carbon pump in the 21st century." Global Biogeochemical Cycles 29, no. 9 (2015): 1451-1470. doi:10.1002/2015GB005140. (pdf here)

Mystakidis, Stefanos, Edouard L. Davin, Nicolas Gruber, and Sonia I. Seneviratne. "Constraining future terrestrial carbon cycle projections using observation‐based water and carbon flux estimates." Global change biology (2016). doi:10.1111/gcb.13217 (open access)

Heede, Richard, and Naomi Oreskes. "Potential emissions of CO 2 and methane from proved reserves of fossil fuels: An alternative analysis." Global Environmental Change 36 (2016): 12-20. doi:10.1016/j.gloenvcha.2015.10.005 (open access)

Enting, Ian G., T. M. L. Wigley, and Martin Heimann. Future emissions and concentrations of carbon dioxide: key ocean/atmosphere/land analyses. No. 31. Australia: CSIRO, 1994. (pdf here)


From the HotWhopper archives

• How much CO2 can the atmosphere take? - January 2014
• Christopher Monckton mixes things up @wattsupwiththat - the carbon budget - July 2015
• Is CO2 sentient? Ari Halperin and Anthony Watts claim the carbon cycle is "fraud" - March 2016