addressing uncertainty in oil and natural gas industry greenhouse

s
± t ×
(Equation 4-1)
n
where
s = standard deviation;
n = sample size; and
t = t-value for “n-1” degrees of freedom.
and
n
1
2
s = ∑ ( xi
−x)
(Equation 4-2)
−
n 1 i=
1
where
x i = the ith observation in the data set and
x = the mean of the data set.
x
n
∑
n
x
i
i=
= 1 (Equation 4-3)
Tables for the Student’s t-distribution can be found in most basic statistics references. Most spreadsheet
software programs have a function that will calculate the necessary t-value. This is the preferred method
since the software generally retains more significant digits for the t-value than a look-up table would
display.
4.2 Overview of Uncertainty Propagation
Uncertainty propagation involves mathematically combining individual sources of uncertainty to establish
an estimate of the overall uncertainty. Specific uncertainty propagation techniques are discussed in
Section 4.2.1.
The following three assumptions are important when applying the uncertainty propagation technique for
overall uncertainty assessment (IPCC, Section A1.4.3.1, 2001):
1. The uncertainties are relatively small, which is defined as the standard deviation divided by the
mean value being less than 0.3;
2. The uncertainties have Gaussian (normal) distributions; and
3. The uncertainty values (i.e., the errors or uncertainties associated with the measured data or
reported values) are mutually independent.
In many cases, the first assumption may be difficult to meet. For example CH 4 and N 2 O emissions often
have very sparse data and large associated uncertainties. Conducting a Monte Carlo simulation
(discussed further in Section 4.6.1) is an option if the standard deviation divided by the mean is greater
than 0.3. However, Monte Carlo simulations require a significant level of detail for the description data
Pilot Version, September 2009 4-4