Treatment of Uncertainties for National Estimates of Greenhouse Gas Emissions

  1. Methodology Used to Estimate Emission Uncertainties
2.1 Overview
The general approach may be summarised as follows:

  1. 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).
  2. 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.
  3. Using the software tool @RISK™, each input pdf was sampled 10,000 times, and the emission calculations performed to formulate a converged output distribution.
  4. 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.

2.2 Description of Methodology
It is recognised that the current level of knowledge on uncertainties in the UK emission data base varies significantly with individual gases and sectors. Notwithstanding this, the study team felt that significant benefit would be obtained if one method could be used for the entire analysis of uncertainties. Such an approach would clearly have considerable presentational advantages in that the results for individual sources and sectors could be compared directly. In addition, to facilitate comparison of uncertainties over a number of sectors, numerical measures are obviously to be preferred.

In the light of the available information on greenhouse gas inventories (discussed in Section 3), the direct simulation techniques reviewed in Appendix A satisfy the required technical criteria, and were therefore applied to this analysis. These techniques are accepted generally as constituting the most satisfactory methods of both representing the uncertainties in the input data and subsequently of transmitting these through to the final uncertainties in the sector and total emission estimates for each gas. In virtually all cases, it was possible to produce numerical or 'near-numerical' (1) estimates of the uncertainties in the individual source category emissions, or in the parameters used in the calculation of these emissions themselves. These estimates of uncertainty were based on previous work (which included the recorded judgement of experts), or on that of judgements made by the study team during the course of the current work.

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 products of the emission factors and the activity rates was undertaken by conducting a probabilistic analysis using Latin Hypercube samples (LHS) of the inputs (Appendix A). This statistical procedure is based closely on the simpler Monte Carlo sampling (MC), but has the advantage of possessing a greater sampling efficiency, and produces lower variances for the estimator. The software tool @RISK™ [2] was used to calculate the uncertainties in the emissions estimates and the emission total from the uncertainties in the individual emission factors and activity rates. Where it was not possible to represent the emission inventories as functions of emission factors and activities, other, more direct means were adopted to estimate emission uncertainties.

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 ±2
s [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 correlation between the input parameters of the uncertainty model. If parameter values are somehow related (such as the quantity of carbon dioxide emitted per unit mass of a fuel burned both for domestic and industrial purposes), individual values in the probabilistic calculations (usually emission factors) may need to be correlated 2. The default adopted was that emission factors for distinct sources of greenhouse gases are uncorrelated. Activity rates are unrelated, and therefore were always uncorrelated with each other.

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.

1 That is, uncertainties expressed as ‘a few tens of percent’, rather than as a single value. In practice the objective difference between these general categories is often small as most uncertainty estimates are derived from a wide range of information and the interpretation of experts’ views.

2 This ensures that in the main, in the contruction of the probabilistic ‘set’, the sampled values of one parameter may be, or may not be, selected from their pdfs with any reference to those values selected for another parameter from its pdf. An example of related parameters would be the carbon contents of UK natural gas (and of other fuels, such as oil) as used for a range of sectors, e.g. gas-oil used in one sector is correlated with gas-oil used in another. The information to which the uncertainties relate are relevant to national averages and other statistics.