Treatment of Uncertainties for National Estimates of Greenhouse Gas Emissions



  1. Analysis of Uncertainties
In the discussion below, it may be assumed that the approach adopted in 2010 is same as for 1990. Where different assumptions were adopted, or different data sources employed, these are highlighted in the respective sections.

 3.1 Carbon Dioxide

3.1.1 Uncertainties in the Baseline (1990) Estimates

Prior to performing the data analysis, the source categories of the carbon dioxide emissions were mapped from those appropriate for the UK National Atmospheric Emissions Inventory (NAEI) onto the standard IPCC categories (see Tables A1 to A7 in Appendix 1 of Reference 1). In most cases, there is a clear one-to-one correspondence, but where necessary descriptions of categories in the IPCC Guidelines were used to map individual NAEI categories onto their IPCC equivalents.

Table 1 summarises the degrees of uncertainty in the emission factors and activity rates for current carbon dioxide emissions in the UK. As discussed above, where emissions cannot be represented as products of these, more direct estimates of uncertainties have been made. The data specific to land use change are given in Table 2, and summarised in Table 1.

The emission factors used for sources of carbon dioxide were obtained from Appendix 1 of Reference 1. The magnitudes of the numerical uncertainties in the emission factors were taken from this recent work. In many cases they had been derived largely on the basis of expert judgement. Prior to their adoption in the current study, the reasoning behind the quantification of the uncertainty in each parameter was reviewed.

The uncertainties in the emission factors for coal were derived by comparing those used in the NAEI with some recent measurements, whereas information from British Gas [7] allowed an estimate of the uncertainty in the carbon content of natural gas to be made. Time series data of gross calorific value of a range of other fuels used in the UK [8] were used to give some indication of the relative variabilities in the carbon contents. The corresponding uncertainties in fuel emission factors for these other fuels (notably petroleum and derivatives) were therefore based on judgements as to whether they were likely to be more similar in this regard to either coal or natural gas.

In the case of non-fuel sources, the uncertainty depends on the purity of limestone or the lime content of clinker, so the uncertainties estimated must be regarded as more speculative.

The uncertainties in the fuel activity data were estimated from the statistical differences data published by DTI [8]. These are effectively the residuals when a mass balance is performed on the production, imports, exports and consumption of fuels. For solid and liquid fuels both positive and negative results were obtained, indicating that these are uncertainties rather than losses. For gaseous fuels these figures include losses and tended to be negative. For natural gas, a correction was made to take account of leakage from the gas transmission system [1] but for other gaseous fuels this was not possible. The other uncertainties for minor fuels (colliery methane, orimulsion, solid smokeless fuel (SSF), petroleum coke) and non-fuels (limestone, dolomite and clinker) were estimated on the basis of judgements of their relative uncertainty compared with the known fuels. The high uncertainty in the aviation fuel consumption reflects the lack of specific information on the actual split between domestic and international aviation fuel consumption.

In the case of fossil fuel combustion, the emission factors (closely related to the carbon content) of gas and oil are assumed to be correlated within the analysis, as the data relate to national statistics. This means that in each of the individual calculations of the product of emission factor and activity rate that are ultimately summed within the overall probabilistic analysis, the same values of emission factor of (for example) diesel oil are used in parallel for all the combustion sources derived from this fuel, as would the same values of emission factor for jet gasoline. In the case of coal, no such relationship is imposed, and hence in the analysis the emission factors for distinct uses of coal are sampled independently from the appropriate distributions.3

Where the available information did not allow the uncertainties in the component emission factors and activity rates to be estimated meaningfully, uncertainties in emissions were estimated directly. Uncertainties in emissions from flaring were estimated by comparing the current estimate with that of a recent study by the UK Offshore Operators Association [9]. In the context of land use change, there is no corresponding category in the NAEI, although the estimates are reported under the IPCC categories 5A to 5D. The estimates of emissions and associated uncertainties have therefore been based on work undertaken at the Institute of Terrestrial Ecology (ITE) [10, 11] including research undertaken for the DETR [12]. These were estimated directly by ITE experts on the basis of past research. The uncertainties in forest biomass and timber products change, forest and grassland conversion (soil carbon release) and abandonment were inferred from variation in model parameters, and used to formulate truncated normal distributions. Uncertainties in forest and grassland conversion (above ground biomass decay), upland peat drainage, lowland wetland drainage and peat extraction were specified using expert judgement, and to reflect the lower confidence in this assignment, the emissions were represented in the main as uniform distributions.4

In accordance with IPCC reporting instructions [6], removals of carbon dioxide which result from activities such as land use change are not subtracted from the gross emissions, but are analysed and reported separately as sinks.

 3.1.2 Uncertainties in Estimates for 2010


The emission factors utilised for 2010, together with their uncertainty estimates, were assumed to be unchanged from 1990.

With the exception of the Other Industry sector (see below), the combustion source data for all sectors excluding the electricity supply industry were generated as follows. The activity rates for the 2010 scenario were calculated using data given in Energy Paper 65 [13]. They were derived by multiplying the 1990 activity values by the ratio of the values of final energy demand by fuel for 1990 and the mean of the Central High and Central Low scenarios for 2010 (Tables A1 to A12 in above reference). This ratio effectively accounts for predicted changes in usage between 1990 and 2010.

The activity rates for 2010 for all fuels for the Other Industry sector and all fuels apart from natural gas for the electricity supply industry were evaluated by applying a second factor, derived from Tables E2 to E6 of Energy Paper 65 [13]. This factor was applied to the 1990 emission values to generate those for 2010, and ensured consistency with the predicted emissions of carbon dioxide by end user.

As the natural gas usage for the electricity supply industry for 1990 quoted in Energy Paper 65 [13] was zero, a valid ratio for the increase between 1990 and 2010 could not be generated. The emission 5 was calculated directly from the mean of the predicted values of natural gas usage for the Central High and Central Low scenarios given in Table C3 of Reference 13.

Data for the land use change (Table 2) were supplied by ITE [10, 11] and processed as those for 1990. The errors do not include those in the land areas involved for 2010. The error range is greater for 2010, however, because uncertainty in the models relating changes in area to changes in carbon stored (e.g. tree growth) give poorer predictions over longer time periods.

3.2 Methane

3.2.1 Uncertainties in the Baseline (1990) Estimates


For many sources of methane, it was not possible to estimate uncertainties in emissions by analysing the impacts of uncertainties in emission factors and activity rates. This follows directly from the lower quality of the underlying data. More direct estimates were therefore made of the uncertainties from the affected individual sources, either on the basis of published information, or if not, from expert judgement. In general, the uncertainties are much greater than for carbon dioxide. With the exception of landfills, for which a detailed study of uncertainties has already been undertaken [15], the uncertainties in the sources of methane were represented as normal distributions. Table 3 contains a list of the sources of methane, the assessed source uncertainties, and the references on which these estimates of uncertainties are based, together with the classes of the distributions.

Some sources were found to have uncertainty distributions with large variances. As this would imply a small probability of (non-physical) negative emissions from some sources, the affected distributions were truncated so that the lower limit represented what was judged to be a credible lower limit.

In the UK methane inventory, no data could be found to justify a referenceable estimate of the uncertainty in emissions from fuel combustion. The uncertainty is known to be relatively large owing to the considerable variation in efficiency of combustion of fuels within the large range of facilities and transport vehicles. As combustion comprises a minor source of emissions, the approach adopted here has been to assign upper bound estimates to these uncertainties. For the reason given above, the uncertainty in the emission of methane per unit combustion will in any case be much greater than those in the activity rates. A cautious estimate of uncertainty of 50% was assumed for the combustion sources as a whole.

The other uncertainties given in Table 3 were derived from the source documents for the estimates [1] or from the Watt Committee Report [16]. The uncertainty in offshore emissions is based on a comparison of the source data [19] with those of another study on offshore emissions [20].

Aitchison et al. [15] estimated the uncertainty distribution for landfill emissions using Monte Carlo analysis and found it to be skewed. This skewness is produced by the average decay time, the oxidation efficiency at type II sites and the average methane potential used in the model. The distribution histogram presented in Reference 15 for the year 1994 was used in conjunction with details of methane emissions for 1990 [] to generate an empirical distribution of emissions. The values and magnitude of the increment in the source histogram were normalised to reproduce the total emission for 1990 6.


 3.2.2 Uncertainties in Estimates for 2010


Although the numerical values of the predicted emissions of methane in each category in 2010 [21] are different to those for 1990, in the absence of information to the contrary it was assumed that the fractional uncertainties for each category (i.e. 2s¸mean emission) were unchanged. The percentage uncertainties for 2010 were therefore, the same as those for 1990 as presented in Table 3. The uncertainty distribution for landfill emission of methane was generated in the same manner [15] as that for the 1990 scenario using the predicted emission from landfill sites for 2010 [21].

 3.3 Nitrous Oxide

3.3.1 Uncertainties in the Baseline (1990) Estimates


The major sources of nitrous oxide emissions in the inventory [1] are as follows:


Information from DETR on present and projected greenhouse gas inventories [21] does not contain data on the release of nitrous oxide from other fuel combustion. This is because this source is relatively insignificant, and hence does not affect the final uncertainty significantly 7.

For the above list of sources, normal, or truncated normal (as appropriate) distributions were constructed for the emission factors and activity rates from available information and judgement. Those relating to releases from agricultural soils had a much greater range (see below), and were therefore assigned log-normal distributions. The estimates of the uncertainties used in the simulations were derived as discussed below and are summarised in Table 4.

Agricultural Soils

The largest source of nitrous oxide, which is also the most uncertain, is from agricultural soil. Current research [] indicates that emission factors (kg per hectare per year) are likely to range over two orders of magnitude. This will be determined by a complex combination of variability (i.e. as influenced by climate, agricultural practice and soil type) and uncertainty (reflecting the difficulty in quantifying the release for any single set of conditions). As the quality of the activity information (e.g. numbers of animals, fertiliser consumption, crop areas) is generally very high compared to that which is used to quantify the emission factors, uncertainties in the activity data were ignored in the analysis, and the uncertainties in emissions ascribed solely to those in emission factors. The distribution in emissions from agricultural soil in the UK was represented using a log-normal distribution, with the 95th percentile set to be 100 times larger than the corresponding 5th percentile. The mean emission for 1990 was set to be consistent with data obtained from MAFF [23]. For the purpose of the simulation, the much smaller source manure management was included in the agricultural soil total. This was because no separate information on the uncertainty of the former was available.

Adipic Acid

The emission factor for adipic acid production was based on historic data (from 1990) on emissions of nitrous oxide, together with the production of adipic acid which gives rise to it []. Uncertainty in the emission factor was estimated on the basis of the variation of the historic value of this parameter between years, and was assumed to be normally distributed. The details of the production of acid are known fairly accurately, so on the basis of judgement a nominal uncertainty of 0.5% was assumed.

Nitric Acid

Uncertainty in the emission factor from nitric acid production was estimated from a range of values in the available literature [25]. On the basis of the quality of the data, the uncertainty in production for 1990 was judged to be about 20% of the best estimate.

Road Traffic

Emissions of N2O were taken from the NAEI road traffic model [1]. The revised IPCC Guidelines document [25] was used to give a range of emission factors for nitrous oxide. As it was not possible to perform the uncertainty analysis within the overall calculational methodology using @RISK directly, a simplified simulation was undertaken. In this, the uncertainties in the emission factors were estimated from literature data [6] and on the basis of judgement, a 10% uncertainty adopted for the activity data 8.

Power Generation

Uncertainties in fuel consumption data (i.e. the activity rates) were based on Salway [1]. Percentage uncertainties in the emission factors were estimated based on the available literature data [6, 25, 26, 27].

Other Fuel Combustion

Uncertainties in the activities were taken from Salway [1]. Uncertainties in emission factors were estimated based on information available in the literature [25, 27]. Within the sampling regime of the probabilistic uncertainty calculations, the emission factors of similar fuels burnt in different sectors were assumed to independent.

 3.2.2 Uncertainties in Estimates for 2010

The approaches adopted for projected emissions were designed to be as similar to those for 1990 as information allowed. As a general default, emission factors and their distributions were assumed to be unchanged, so that most of the observed changes in emissions were due to changes in the activity rates.

Agricultural Soils

The mean emission of nitrous oxide for 2010 was set to be consistent with current projections. The uncertainties in emissions were taken from those used for 1990. Both sets of information were obtained from MAFF [23].

Adipic Acid

By 2010, using abatement technology, emissions of nitrous oxide are assumed to be reduced to 5% of their 1990 values [24]. This reduction was applied to the 2010 emission factors.

Nitric Acid

Available data [25] seem to suggest that the uncertainty in the production of nitric acid in 2010 would be lower than those in 1990 (viz. 20%). In this study it was assigned a value of 10%.

Road Traffic

The projections in UK road traffic used for 2010 were based on the 1989 National Road Traffic Forecast [].


Power Generation

Projections in UK power generation to 2010 were based on DTI estimates [13]. The percentage uncertainties in this, and in the emission factors, were as used for 1990.

Other Fuel Combustion

As discussed above, uncertainties in this source (which are projected to be relatively insignificant in any case) were only evaluated for 1990.

 3.4 Halocarbons and Sulphur Hexafluoride

Some emissions of these gases are caused by leaks from equipment using these materials (e.g. as a refrigerant or insulator). The amount that is lost over any time is dependent on the stock of gas that has been accumulated over the preceding years. It follows that emissions in any year will not be solely dependent on the consumption in that year.

The evaluation of uncertainties in emissions of many of these gases necessitates a significantly different approach to those outlined above; the product of an (uncertain) emission factor and an (uncertain) activity rate. As a result, it is easier to discuss the estimation of uncertainties in historic and projected emissions for these gases together.

Emissions of hydrofluorocarbons (HFCs), perfluorocarbons (PFCs) and sulphur hexafluoride were based on the March Consulting Group (MCG) model [29]. Uncertainties in the emissions of HFC, PFC and SF6 in 1990 and in projected emissions in 2010 were calculated on the basis of this core dataset.

Emissions arise from a large number of sources:


The typical data inputs used to model emissions comprise the following:


The methodology used by MCG to estimate emissions of halocarbons, together with the emission factors, are detailed in Reference 29. The spreadsheet based on MCG data [30] evaluates and tabulates these emissions. The MCG methodology utilises a series of annual mass balance calculations to quantify the inventory of fluids which would be contained within the range of products (refrigerators, air conditioning systems, foams, etc.) as a function of time (the 'bank'). This in turn will be dependent on information and judgements about the consumption of the fluids, losses in production, leakage from the products, and their eventual disposal. The amount of fluid that will be disposed of in the future is an estimate made by MCG. Annual leakages from products are therefore estimated as the product of an empirical factor and the quantity of the fluid held in the bank in that year.

Using this approach, it is clear that emissions of halocarbons in any one year would be partly dependent on consumption in previous years. In order to estimate uncertainties in 2010 it is therefore necessary to take into account the uncertainties for all years between 1990 and 2010. From 1996 onwards the projected emissions given by MCG were produced in the form of two scenarios. These were modelled separately in the current study, and the 2010 emission was taken as the mean of the two bounding estimates.

The estimation of uncertainties involved interfacing the MCG spreadsheet with the @RISK tool. Owing to the relatively large uncertainties uncovered for these emissions, it was necessary in most cases to use truncated normal parameter distributions.

Uncertainties in emission factors (i.e. leakage and loss rates) were evaluated based on ranges suggested in IPCC guidelines [6, 25, 26] in conjunction with judgement. Uncertainties ranged from 20% to 50%, with uncertainties toward the upper end of this range tending to be allocated to the lower numerical loss rates and lower uncertainties to the higher numerical loss rates. In the probabilistic calculations the parameters representing leakage and loss rates for different years were all linked (i.e. correlated).

Uncertainties in activity data were implied from the accuracy of the tabulated data (i.e. the number of significant figures), and for the consumption data, for example, ranged from 10% to 50%. The projected values of consumption were assumed to be accompanied by the same fractional uncertainties as were the historic data, and the uncertainties in disposals were assumed to be no lower than those in fluid consumption. In some cases, it was found that the quantity of fluid disposed of was equal to the fluid bank for that year. In these cases the disposal rate was not an independent variable and in effect was an intermediate in the calculation.

For some sources a bank of fluid already existed for 1990. In these cases, the percentage uncertainty in the volume of the pre-existing bank was taken cautiously to be the same as that for fluid consumption.

In the calculations, it was assumed that the parameters representing consumption and disposal for all years 1990-2010 were not related in any way, so that no correlation of their values within the probabilistic simulation would have been appropriate.

The values of the key parameters used in the calculation of uncertainties in emissions of halocarbons and sulphur hexafluoride are given in Table 5. These were derived as outlined above on the basis of the data generated by MCG [30].

 3.5 Total Emissions: Application of Global Warming Potentials

In order to provide some overall measure of the uncertainty in impact of UK inventories of greenhouse gases in 1990 and 2010, the respective global warming potentials (GWPs) of the considered gases (per unit emission) were incorporated into the analysis. Aggregate emissions were evaluated, along with uncertainties in these. The GWPs used to weight the individual emissions are tabulated in Table 6. These quantify the relative impacts of specific emissions in terms of global warming potential over a 100 year horizon.

The sums of the weighted emissions were evaluated by combining all of the separate calculations outlined in Sections 3.1-3.4 above.

 3.6 Changes in emissions between 1990 and 2010

In parallel with the need to quantify the uncertainties in emissions for the specified years 1990 and 2010, uncertainties in emission trends are also of great importance in that they will inform the confidence with which the UK will achieve its international obligations in limiting future emissions of greenhouse gases. Accordingly, probabilistic calculations were also undertaken to quantify the differences between the (uncertain) emissions in the year 2010 and those in 1990.

The difference between two distributions gives rise to two numerical quantities, the expected change between them (as a percentage of the value in 1990), and the distribution of possible differences. The appropriate method of calculating these quantities will depend crucially on the degree to which the two distributions are related (specifically whether the respective inputs are independent or not) 9.

Where emissions of gases are estimated from products of emission factors and activity rates, it is assumed that all possible changes in activity between 1990 and 2010 (which are sampled from the two distributions) would be included in the probabilistic set (e.g. values toward the upper end of the distribution in 1990 and the lower end in 2010 and vice versa). In contrast, within this modelling framework, the emission factor is a time-independent concept. Hence, in evaluating the distribution of possible emission changes between these two years, only one (sampled) value of emission factor was used in each individual calculation of the difference in emission within the probabilistic set 10.

3.7 Sources of Uncertainties

Notwithstanding the large volume of data involved, inspection of the information on which the calculations of uncertainties are based together with the results of the analysis discussed above in theory can allow the identification of the most important sources of uncertainties. To facilitate this objective, a formal statistical technique was applied to identify the input parameters which most directly influence the magnitude of the uncertainties in the emissions themselves. These calculations identify the dominant contributors to uncertainties in emissions in 1990 and 2010, and to uncertainties in the predicted changes in emissions between these times.

A robust measure of numerical model parameter sensitivity was employed, namely the rank order correlation coefficient. This measure, which arises from a multi-variate regression analysis, is widely recognised [2, 32] as being able to provide useful information on how the uncertainties in individual input parameter values influence uncertainties in the output. The correlation coefficients are evaluated in a stepwise fashion, with the most significant parameter in the analysis 'fitted' to the regression model first, followed by the progressively less significant parameters. In this way, the potentially complicating influence of other parameters on the singular relationship between each model parameter and the output is minimised.

The analyses were conducted on the ranks of the original data, rather than on the values themselves in order to maximise the linearity of the information on which the regression is conducted. If such a transformation were not carried out, the analysis would not be adequate if strongly non-linear relationships exist between input parameters and the output, or if there are outliers in the input.

The rank order correlation coefficient can range from -1 (signifying a strong negative relationship), through 0 (signifying no discernible relationship), to +1 (signifying a strong positive relationship). In order to keep the results table to a manageable size, only coefficients with magnitudes below -0.3, or above +0.3 are given.

The model on which the analysis of parameter sensitivity is based also makes possible an assessment of the adequacy of the individual (i.e. input parameter-dependent) regression models. As part of the overall calculations the coefficient of determination, R2, is evaluated [33]. This provides a measure of the percentage of the variation in the emission which can be explained by the rank regression model constructed on the basis of the individual input parameters. A low value of R2 would indicate that the results of the regression analysis which produced the rank order correlation coefficients would be unreliable.

It should be noted that for the analyses of how parameter uncertainties affect the emissions in 1990 and 2010, only positive rank correlations occur, reflecting the fact that an increase in the value of a parameter such as an emission factor, or a leakage rate (in the case of halocarbons) will increase the total emission. For changes in emissions between 1990 and 2010, variations in parameters can act in either sense, so that in some circumstances (e.g. declining parameter significance over time) a decrease in a parameter value may lead to an increase in the output (in this case the difference), giving rise to a negative rank correlation coefficient.



3 This is justified as coal is more variable in carbon content, and the analyses on which the data used in this study rely were conducted in small scale analytical laboratories, not on the level of a national fuel stock.
4 Total range of distribution = 2 X error estimate
5 Expressed as million tonnes of oil equivalent using 1 tonne oil equivalent = 397 therms [13], emission factor for carbon dioxide from natural gas = 1.501 ktC/Mtherm [14].
6 The various incomplete sources of data that were available in fact supported a distribution of emissions similar in shape to that generated by Aitchison et al.
7 This conclusion was confirmed by evaluating the uncertainties in these emissions for 1990 using other information.
8 I.e.: Emission = Activity X Factor, where Activity = 1 with an uncertainty (2s) of ±10% Factor = the numerical value of the emission of N2O with an uncertainty equal to that of the petrol emission factor
9 If the distributions have been derived using parameters which are related, the variance of the distribution of differences will be lower than otherwise . As discussed in the next paragraph, it should be noted that high values of some parameters (notably emission factors) in 1990 will be linked with correspondingly high values in 2010.
10 In other words, these parameters are correlated in the probabilistic analysis.