Home > BOE, Energy > BOE: Gaussian PDF for Cumulative Fossil Fuel CO2 Emissions

BOE: Gaussian PDF for Cumulative Fossil Fuel CO2 Emissions

2012 May 24

UPDATE 20120524: Reworked the estimates for coal, oil, and natural gas under both the proven and ‘optimistic’ scenarios. The original two charts can be found here and here.

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.

  1. Nick Stokes
    2012 May 24 at 3:11 am

    Looking at your previous post, the figures seem low. Taking coal alone, you seem to just extrapolate current daily production for 148 years? But your Wiki ref gives the commonly quoted proven reserves of 900 Gtons. If that were pure C, proven coal alone would give 3,300 Gtons CO2. Now there may be a carbon content fraction, but still…

    There are quoted proven reserves in Gton – I can’t see why you’ve done this daily rate calc.

  2. 2012 May 24 at 8:52 am

    The daily calc was to move the ‘optimistic’ reserve numbers in the wiki from ‘years’ to gigatonnes.

    Prompted by your concern, I ran through the numbers with more rigor using BP Statistical Review 2011 for everything possible – and indeed I have revised numbers, but not as high as you may think. One of the key conversions is from ‘tonnes of coal’ and ‘billion cubic meters of ng’ to ‘tonnes of oil equivalent.’ That conversion is required to use the ‘tonnes of fuel to tonnes of CO2’ factors that BP provides (2.35 for NG, 3.07 for oil, 3.96 for coal).

    The corrected estimate is: 2700 GtCO2 for ‘proven’, 7800 GtCO2 for ‘optimistic’, with a ‘most likely’ of 6100 GtCO2 and a sigma of 1700 GtCO2. I will update this tonight and link the code for your review.

    I appreciate the poke.

  3. 2012 May 24 at 9:11 am

    The corrected range for CO2 emissions is: mu = 454ppm, sigma = 108 ppm (for fossil fuel contribution)

  4. Nick Stokes
    2012 May 24 at 2:43 pm

    This World Energy Report is handy, not just for the numbers, but for the conversion table at the end.

    RB: the numbers are here (pdf)

  5. 2012 May 24 at 3:10 pm

    heh! just went through it a few hours ago looking at in-ground coal, proven-prob-possible nat gas, and oil sands and oil shale potential.

  6. Nick Stokes
    2012 May 24 at 4:50 pm

    FWIW, the WGIII, has coal estimates in EJ. The WEC report says 1 tce=29.3 GJ. WG3 give
    22000EJ = 750 GTon coal proved
    11000EJ = 375 Gt probable
    100000EJ = 3410 Gt estimated possible
    Total 133000EJ = 4915 Gt (Gt using 29.3)

    The going rate seems to be coal = 80% C, so all categories gives 3932 Gt C, or 14400 Gt CO2

    That’s just coal.

  7. Nick Stokes
    2012 May 24 at 5:01 pm

    More directly, the WG3 says 92 g CO2/MJ. That makes 12200 Gt CO2. I guess 80% was high.

    There’s a handy table 4.2 in WG3, with those conversion factors. I add up 20,240 GTon CO2 from coal, oil and gas, including unconventional,

  8. 2012 May 24 at 6:52 pm

    Thanks for continuing to look at these. I am busy reconciling your numbers to the BP Statistical Review. For instance –

    obviously in the ballpark
    the 750 Gt coal proved WGIII < 861 BP Gt coal Stat Rev 2011
    the 3410 Gt coal possible WGIII ~= 3032 in the ‘optimistic’ estimate for coal

    The WGIII coal ratio of possible / proven ~ 4.5
    The WEC coal ratio of inplace / proven for the sum of countries with both data ~ 7.8

    WGIII Table 4.2 is using “available resource” which is probably the same as “in place” and “in place” is much greater than actual recoverable – proven, probable, or possible,


  1. 2012 May 26 at 6:18 am
  2. 2012 May 28 at 1:23 pm
  3. 2012 June 8 at 7:24 pm
Comments are closed.