BOE: Gaussian PDF for Cumulative Fossil Fuel CO2 Emissions
In the previous post, I used two estimates of emissions from the burning of coal, oil, and natural gas reserves – proven and ‘optimistic’ – to estimate total fossil fuel CO2 emissions at
2200 2700 gigatonnes and 5200 7800 gigatonnes respectively via conversion factors lifted from BP Statistical Review 2011. The estimate excluded methane/methyl hydrate emissions as either a forcing (fuel consumption) or a feedback (triggered by arctic warming).
The basis for the ‘optimistic’ reserve estimate is unclear. The claim is not well cited. The given reference, Oil & Gas Journal is not freely available for review. I cannot find a well referenced version of the claim (eg one that includes OGJ vol and date). I continue to research the source of the claim.
Proven reserves are those that can be extracted profitably under current economic conditions and current technology. Proven reserves have been continually growing even as reserves are exploited faster than new discoveries are made. This is because higher prices and improvements in extraction techniques make a greater percentage of the discovered resources available for production. Because of this continued reserve growth, it is very likely that the amount fossil fuels ultimately extracted will exceed the amount of fossil fuels currently considered as proven, just based on price and technology growth. In addition, new discoveries will continue to add incrementally to the both the ‘discovered resources’ and ‘proven reserve’ counts.’
I have chosen to fit these two scenarios to a Guassian curve to create a probability distribution for CO2 emissions from fossil fuel consumption. That the probable range of fossil fuel consumption fits a normal distribution is my first assumption. To complete the fit, I need to make two additional assumptions. The first is that it is 95% likely that we will consume all the proven reserves. The other is that it is only 16% likely that we will consume as much fossil fuels as in the ‘most optimistic’ reserve estimate. These two fits are graphed as points (a) and (b) on the chart above. It should also be apparent that the two points, as determined by my above assumptions, are three sigma apart, making it trivial to define the peak of the gaussian PDF (point (c)) and giving us a third scenario to play with … the ‘most likely’ scenario with cumulative emissions at
4200 6100 gigatonnes of CO2.
Setting the ‘optimistic’ scenario at +1 sigma allows for consumption of non-conventional fossil fuel sources such as oil sands and oil shales and are assumed to be included in this PDF.
While fossil fuels emit CO2, only about 50% of it remains in the atmosphere. This 50% is known as the airborn fraction. The other 50% or so is absorbed into the oceans or into land-based carbon stores (mostly the biosphere). The IPCC estimates the airborn fraction variously as 60% and 55%. Knorr’s 2009 finds a near constant airborn fraction of 43%. (h/t sks) For this purpose, I am using a constant 50%.
We can estimate the amount of CO2 emitted up to now by working the concentration calculation in reverse. Currently, CO2 concentration is about 100 ppm above preindustrial levels. It is estimated that about 65% of this is from fossil fuel sources and 35% from land use changes and a bit from cement production. Given a 50% airborn fraction and a conversion factor of 7.81 GtCO2 per PPMV, we can estimate that we emitted just over 1000 gigatonnes of CO2 from fossil fuel sources prior to the present. (CDIAC FAQ).
The chart below shows the cumulative CO2 concentration PDF due to fossil fuel production assuming a constant airborne fraction of 0.5 and 1000 GtCO2 of emissions prior to the present. You can roughly estimate future CO2 concentration by adding 280 ppm CO2 for the preindustrial concentration and another 35 for the land use changes and cement production prior to the present.