Guest Post by Willis Eschenbach
On another thread here at WUWT we were discussing the Bern carbon dioxide model used by the IPCC. The Bern Model calculates how fast a pulse of emitted CO2 decays back towards the pre-pulse state. See below for Bern model details. We were comparing the Bern model with a simple single-time-constant exponential model. Someone linked to a graphic from the IPCC AR5 report, Working Group 1, Chapter 6:
ORIGINAL CAPTION (click image to enlarge): Figure 6.1 | Simplified schematic of the global carbon cycle. Numbers represent reservoir mass, also called ‘carbon stocks’ in PgC (1 PgC = 10^15 gC) and annual carbon exchange fluxes (in PgC yr–1). Black numbers and arrows indicate reservoir mass and exchange fluxes estimated for the time prior to the Industrial Era, about 1750 (see Section 220.127.116.11 for references). Fossil fuel reserves are from GEA (2006) and are consistent with numbers used by IPCC WGIII for future scenarios. The sediment storage is a sum of 150 PgC of the organic carbon in the mixed layer (Emerson and Hedges, 1988) and 1600 PgC of the deep-sea CaCO3 sediments available to neutralize fossil fuel CO2 (Archer et al., 1998).
Red arrows and numbers indicate annual ‘anthropogenic’ fluxes averaged over the 2000–2009 time period. These fluxes are a perturbation of the carbon cycle during Industrial Era post 1750. These fluxes (red arrows) are: Fossil fuel and cement emissions of CO2 (Section 6.3.1), Net land use change (Section 6.3.2), and the Average atmospheric increase of CO2 in the atmosphere, also called ‘CO2 growth rate’ (Section 6.3). The uptake of anthropogenic CO2 by the ocean and by terrestrial ecosystems, often called ‘carbon sinks’ are the red arrows part of Net land flux and Net ocean flux. Red numbers in the reservoirs denote cumulative changes of anthropogenic carbon over the Industrial Period 1750–2011 (column 2 in Table 6.1). By convention, a positive cumulative change means that a reservoir has gained carbon since 1750. …
Now, there are many things of interest in this graphic, but what particularly interested me in this were their estimates of total fossil fuel reserves. Including gas, oil and coal, they estimate a total fossil fuel reserve of about 640 to 1580 gigatonnes of carbon (GtC). I decided to apply those numbers to both the Bern Model and the simple exponential decay model.
Now, the Bern model and the simple exponential model are both exponential decay models. The the difference is that the simple exponential decay model uses one value for the half-life of the CO2 emissions. On the other hand, the Bern model uses three different half-lifes applied to three different fractions of the CO2 emissions, plus 15% of the emitted CO2 is said to only decay over thousands of years.
My interest was in finding out what would happen, according to the two CO2 models, if we burned all of the fossil fuels by 2100. For the smaller case, burning 640 GtC by the year 2100 implies a burn rate below current emissions, that is to say about 7.5 GtC per year for the next eighty-five years.
For the larger case, 1,580 GtC implies a burn rate that increases every year by 1.1%. If that happens, then by the end of this century we’d have burned 1,580 gigatonnes of carbon.
So, given the assumptions of the two models, how would this play out in terms of the atmospheric concentration of CO2? Figure 2 shows those results:
Figure 2. CO2 projections using the Bern Model (red and blue) and a single exponential decay model (purple and light green). Single exponential decay model uses a time constant tau of 33 years. Note that this graph has been replaced, the original graph showed incorrect values.
Now, there are several things of interest here. First, you can see that unfortunately, we still don’t have enough information to distinguish whether the Bern Model or the single exponential decay model is more accurate.
Next, the two upper values seem unlikely, in that they assume a continuing exponential growth over eighty-five years. This kind of long-term exponential growth is rare in real life.
Finally, here’s the reason I wrote this post. 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 are not enough fossil fuel reserves (oil, gas, and coal) on the planet to double the atmospheric CO2 concentration from its current value.
Best regards to all,
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