addressing uncertainty in oil and natural gas industry greenhouse

Are the data based on a single
point measurement or multiple
measurements?
Multiple points
Do the measurements
represent a sampling of the
measured parameter?
Yes
Apply Equations 4-1 through 4-3 to calculate the mean and
standard deviation, respectively.
Apply Equation 4-8 to estimate the uncertainty based on the
measured data, OR apply Equation 4-9 to estimate uncertainty for a
single observed estimate where other data is used for to quantify
the uncertainty.
The sample standard deviation “includes contributions to the precision both from the measurement system
and from the material composition variation from sample to sample” (Coleman and Steele, 1989). In other
words, if the measured data for an emission source are derived from a statistical sample, the use of the
standard deviation as a measure of the spread of the data accounts for uncertainty of the measurement
instrument and the differences among the samples. For example, if three samples are taken every month
and the data for the 36 samples are used to calculate a yearly mean, the uncertainty calculated from these
samples accounts for both the uncertainty in the measurement instrument and the variability among
observations. Thus, this uncertainty will be larger than the uncertainty due to measurement error alone. As
the sample size increases, the uncertainty that combines the instrument error and context-specific factors
will decrease.
Next, we would calculate the standard deviation of the sample using Equation 4-1. The IPCC Good
Practices document and others recommend applying the Equation 4-8 to quantify the uncertainty of the
data set (IPCC, 2001), which is also referred to as the relative expanded uncertainty and can be thought of
as half the bandwidth of a 95% confidence interval (ISO, 2005).
t×
s( x)/
n
U( rel)( x) = × 100%
(Equation 4-8)
x
where
U(Rel)(x) = the relative expanded uncertainty in the data set (%);
t = a value based on Student’s t-distribution with n-1 degrees of freedom which gives a 95%
confidence interval;
x = is the mean for the set of data calculated in Equation 4-3;
s( x ) = the standard deviation of the data set calculated in Equation 4-2; and
n = the sample size for the set of data.
If one uses a single observation as an estimate and uses other data to calculate the uncertainty,
Section A1.2.3 of the IPCC Good Practices document explains that Equation 4-9 should be used instead of
Equation 4-8 (IPCC, 2006). IPCC’s example application of this approach is for the use of single emission
estimate for a particular year that has been calculated on more than one occasion. The recalculations have
Pilot Version, September 2009 4-22