## Methodology for calculation of the contribution to uncertainty

The methodology for calculation of contribution to uncertainty is based upon apportioning the variance of the inventory to the variance of each category.

If the uncertainty is symmetric, then the variance is estimated, on a category basis, as:

Equation 3.8

Contribution of category X - variance for symmetric uncertainty a? =| Dx^x.

Where:

Ux = uncertainty half-range for category x, in units of percent;

Dx = the total emissions or removals for category x, corresponding to the entries in Column D of Table 3.5.

cx2 = the variance of emissions or removals for category x.

Even if the uncertainty is asymmetric, the variance can be estimated based on the arithmetic standard deviation or the coefficient of variation. The variance is simply the square of the arithmetic deviation. The variance for the category can be estimated from the coefficient of variation, vx, as:

Equation 3.9

Contribution of category X - variance for asymmetric uncertainty

Once the variance is known for a category, the variances should be summed over all categories. The result is the approximate total variance in the inventory. However, this result is not likely to agree exactly with a Monte Carlo simulation result for the inventory for at least one and possibly more reasons: (1) because of sample fluctuations in the Monte Carlo simulation, the Monte Carlo estimate of the variance may differ somewhat from the true value; (2) the analytical calculation is based upon assumptions of normality or lognormality of the distributions for combined uncertainty for individual categories, whereas Monte Carlo simulation can accommodate a wide variety of distribution assumptions; and (3) the Monte Carlo simulation may account for nonlinearities and dependencies that are not accounted for in the analytical calculation for contribution to variance. If the emission inventory calculations are linear or approximately linear, without any substantial correlations, then the results should agree fairly well. Furthermore, methods for estimating 'contribution to variance' for Monte Carlo methods are approximate. For those methods that potentially can account for all contributions to variance (e.g., Sobol's method, Fourier Amplitude Sensitivity Test), the measures of sensitivity are more complex (e.g., Mokhtari et al., 2006). Thus, the methodology described here is a practical compromise.

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