- Methodology Used to Estimate Emission Uncertainties

The general approach may be summarised as follows:

- Uncertainty distributions (probability distribution functions, pdfs) are allocated to each emission factor (release per unit throughput or consumption) and activity rate (measure of throughput or consumption).

- A calculation was set up to estimate the emission of each of the gases, sinks of carbon dioxide, and the global warming potential totals for the years 1990 and 2010, together with the percentage change between these years. The same emission factor was used in 2010 as in 1990 each time the calculation was performed.

- Using the software tool @RISK™, each input pdf was sampled 10,000 times, and the emission calculations performed to formulate a converged output distribution.

- The output files (~50 MBytes) were analysed to provide the results for the totals and to identify the significant contributors (parameters) to the overall uncertainty in each case.

In the light of the available information on greenhouse gas inventories (discussed in Section 3), the

In most cases, the reported greenhouse gas inventories [1] are expressed as the product of an appropriate emission factor and an activity rate, each of which will be subject to uncertainty. Uncertainty and confidence limits in these input parameter values used were constructed from the available information referred to earlier. The inputs were represented as pdfs, characterised by a mean value, together with some indication of its 'width' (the variance). Possible distributions include normal, log-normal, triangular, uniform and log-uniform. In principle, the available information may imply the adoption of any of these, so that any shape and width of distribution function for the input parameters may be decided upon.

The generation of uncertainties in the

Following general practice [3, 4, 5], and unless information indicates strongly otherwise, it has been assumed in this study that uncertainties in parameter values are normally distributed. The quoted range of possible error or uncertainty is taken to be ±2s [6]. In a few cases this would imply a finite probability of parameter values below zero. To avoid this, affected parameter distributions were truncated accordingly. Lognormal distributions were used where particularly large ranges of parameter values or emissions were evident, and where a truncation of the extremes would not be in accord with the available information. Where sufficient explicit information existed on the distributions of parameters or emissions, suitable empirical distributions were employed. Where fewer data were available, the pdfs had to be constructed more straightforwardly in the form of an overall (uniform) range, with upper and lower limits.

As discussed in Appendix A, the way in which uncertainties in emission factors and activities of sources impact upon those in total emissions for a gas will also be dependent upon the assumptions made regarding the

Following on from what is discussed in Appendix A on the general sources of uncertainty, it was the intention in this study to differentiate between uncertainties expressed as the spatial or temporal variability of parameter values (that is, parameter values which are believed to be genuinely 'variable', so that no amount of research would justify a single value), and those expressed as the 'degree of belief' on the single, most appropriate value that should be selected in each case. As the study proceeded, however, it became clear that the level of information available generally precluded this distinction. In some cases, however, the study team was able to offer judgements on the general natures of the numerical uncertainties presented.