…or perhaps Sharp Greenhouse Gas Accounting with Fuzzy Measurements

I am deep into greenhouse gas (GHG) accounting and reporting requirements just now, including ISO 14064, 14065 and training at the Greenhouse Gas Institute. This a partial explanation for the period of silence on this blog. Some readers might question whether GHG accounting topics fit on Crustybytes.com.  It turns out our perceptions of GHG are information-based, and despite the fact that each of us are responsible for producing tons of GHG each year, we generally don’t see or sense them.  As I write this post, the U.S. House of Representatives has just passed the American Clean Energy and Security Act which includes Cap & Trade for carbon/CO2 equivalents (CO2e) which will have considerable impacts on business.  Finally, each of us has to decide our position on climate change and what we are willing to do about it.  All of which is to say the subject fits the Tech, Biz and Open Source Brains meme for Crustybytes.

I am particularly interested in calculating CO2e for stationary combustion sources for numerous reasons:  they are one of the largest man-made contributors to atmospheric carbon, they are relatively well-instrumented for good measurements and therefore insight, and they are well understood.  So when a training exercise presented a chance to compute CO2e emissions for a fictitious company, I got the chance to do what I enjoy — take the apparatus apart in order to understand it better.

My challenge is to understand the confidence we can expect for calculated CO2e emissions.  These results are or soon will be the basis for complying with regulations, and may become the basis for observing caps (limits) and the buying and selling of offsets and credits.

For my purposes, I narrowed my inquiry of the exercise to stationary emission sources that burn natural gas.  I will not try to go into the detail of the calculations here, but characterize them as relatively straightforward and modestly rigorous.  Understanding accuracy or confidence is a matter of understanding the variability (the ‘fuzziness’ in the subtitle) that can arise from all the bits that make up the answer — calculated CO2e emissions.  The ‘bits’ as I call them, fall into three categories: field measurements or records; constants and conversion factors; and Global Warming Potentials (GWP).

I frame this discussion to be about uncertainty, rather than the other side of the coin, accuracy. I quantify uncertainty as the amount added or subtracted from a stated value that defines a range where 95% of the time a result can be expected to fall within that range.  For statistically normal distributions of samples, this is approximately 2 standard deviations.

Sources of Uncertainty

The constants and conversion factors involved generally are derived from first principles,  can be accepted as fixed and not subject to uncertainty (without redefining our understanding of chemistry). Fuel gas measurement, fuel gas composition and percent combustion are subject to uncertainty, and factors are assigned consistent with typical measurement technologies, fuel system variabilities and equipment performance, respectively.  Uncertainty is always present in these numbers, though we are adept at ignoring it.  We are particularly prone to accepting numbers verbatim from instruments we do not understand and computers.

GWP values are highly uncertain, reported to be as high as 35%. However, by convention GHG organizations have agreed to use the same values globally — so keep them fixed.  No need for outrage, there are precedents.  We do it all the time with the electric meter or the gas pump — we ignore uncertainty and use the measurement as the basis for a business transaction.


Here’s the approach:

  • randomly assign a value to each of the uncertain variables (fuel gas measurement, composition, combustion fraction) within the range elected (+/- 2 standard deviations)
  • record the result
  • repeat the above — a 1000 times or so, 10,000 or maybe a million, shown below
  • analyze the set of results, such as mean, standard deviation and for me, a graph works best.

Histogram of CO2e Emissions Calculations with Uncertainty


Take a single sample at any given hour in a year (8760 hours in a year), and expect the result to fall somewhere on the curve.  Understanding the curve and the probability of landing on a specific location on it, gives quantitative confidence to regulatory reporting numbers or to sizing the margin under a cap that might be sold to others.  We do not yet have a price for a ton of CO2e in the U.S., but this week’s European price is approximately $18.84 U.S. making 1 standard deviation on the graph above worth ~$14,526 U.S. per year. So sharp greenhouse gas accounting may pay.     db