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addressing uncertainty in oil and natural gas industry greenhouse

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number of observations, the st<strong>and</strong>ard deviation of the mean decreases as the number of observations<br />

<strong>in</strong>creases.<br />

Estimat<strong>in</strong>g uncerta<strong>in</strong>ties <strong>in</strong> emission <strong>in</strong>ventories is based on the characteristics of the variable(s) of<br />

<strong>in</strong>terest (<strong>in</strong>put quantities) as estimated from the correspond<strong>in</strong>g data set. The statistical computations<br />

could entail the determ<strong>in</strong>ation of:<br />

−<br />

−<br />

−<br />

−<br />

−<br />

The arithmetic mean (mean) of the data set;<br />

The st<strong>and</strong>ard deviation of the data set (the st<strong>and</strong>ard error, the square root of the variance);<br />

The st<strong>and</strong>ard deviation of the mean (the st<strong>and</strong>ard error of the mean);<br />

The probability distribution of the data; <strong>and</strong><br />

Covariances of the <strong>in</strong>put quantity with other <strong>in</strong>put quantities used <strong>in</strong> the <strong>in</strong>ventory calculations.<br />

The limits of the confidence <strong>in</strong>terval associated with GHG emissions from a source are directly dependent<br />

on the probability distribution, or the probability function, used to represent that data set. For some<br />

probability distributions, there are analytical relationships that relate the st<strong>and</strong>ard deviation to the required<br />

confidence <strong>in</strong>tervals. For example, when a normal distribution is assumed for the variable under<br />

consideration, the confidence limits would be symmetric about the mean, <strong>and</strong> for a 95% confidence<br />

<strong>in</strong>terval the confidence limits are approximately 2 st<strong>and</strong>ard deviations above <strong>and</strong> below the mean.<br />

Hence, the quantification of <strong>uncerta<strong>in</strong>ty</strong> <strong>in</strong>tervals for calculated GHG emissions will depend both on the<br />

accuracy <strong>and</strong> representativeness of measurement data used <strong>and</strong> the assumed distributions of other key<br />

parameters used <strong>in</strong> the computations. The uncerta<strong>in</strong>ties associated with both emission factors <strong>and</strong> activity<br />

data could be best described by probability density functions that are constructed from available data.<br />

The applicable shapes of these probability density functions could be either determ<strong>in</strong>ed empirically or by<br />

expert judgment, follow<strong>in</strong>g procedures described <strong>in</strong> many guidel<strong>in</strong>e documents <strong>and</strong> st<strong>and</strong>ards (ISO, 2005;<br />

IPCC, 2000).<br />

This section has <strong>in</strong>troduced the basic concepts that are germane to estimat<strong>in</strong>g the <strong>uncerta<strong>in</strong>ty</strong> range of<br />

GHG emissions. The applicable statistical calculation procedures are presented <strong>in</strong> greater detail <strong>in</strong><br />

Section 4.0.<br />

Pilot Version, September 2009 1-4

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