addressing uncertainty in oil and natural gas industry greenhouse

to characterize the probability distributions. Without such information, the potential error introduced
from incorrectly specifying the distributions for a Monte Carlo simulation could outweigh the potential
error that might be associated with applying an uncertainty propagation technique for sources with large
uncertainties. Therefore, this document suggests that the first assumption can be relaxed for emission
estimates with a small overall contribution to the GHG inventory. Through the propagation of uncertainty
for all emissions in the inventory, the impact of small emission sources with large uncertainties can be
evaluated relative to the entire inventory. This evaluation can be used to identify and prioritize emission
sources that require more data to reduce the overall uncertainty of the inventory.
The second assumption is based on the normality of the distribution of the underlying source data (i.e.,
symmetrical around the mean). According to the Central Limit Theorem, for a large enough sample size
(n>30), we can relax the normality assumption but still assume that the sampling distribution of the
sample means is normally distributed (Casella and Berger, 1990). Hence, if the calculated uncertainty is
based on statistical sampling of the population, one would need to obtain more samples to approach
normality. Alternatively, we might consider data transformation, i.e., mathematically transforming the
data to a different scale and using that transformed ‘normal’ distribution to derive the 95% confidence
interval. For example, in the case where the data distribution is skewed and the uncertainty is > 100% of
the mean (i.e., where the lower limit would be less than zero), the data could be transformed to a
lognormal distribution. This approach, however, requires the confidence interval to be transformed back
to the original scale to express the uncertainty in the original units, which can introduce error. As a result,
there is a trend away from using transformational approaches due to issues in transforming the data back
to their original scale.
The third assumption states that there is no significant covariance between the uncertainties that are to be
combined, which is equivalent to saying that the errors or uncertainties are independent or that there is no
correlation between the uncertainty terms. The uncertainties in two quantities would be considered
independent if they were estimated by entirely separate processes and there was no common source of
uncertainty. The uncertainties in two quantities would be dependent if they had a common source of
uncertainty (Williamson, 1996). Covariance between two uncertainty terms can be addressed through an
additional term in the uncertainty propagation equations (discussed further in Section 4.2.2). However,
the IPCC Good Practices document suggests avoiding the need for the covariance term in the equation by
“…stratifying the data or combining the categories where the covariance occurs” (IPCC, 2001).
Pilot Version, September 2009 4-5