The Approach 2 Monte Carlo method can be used to estimate uncertainties in the trend as well as in the absolute emission value in a given year. The procedure is a simple extension of that described in the previous section.

The trend is defined here as the percentage difference13 between the base year and the year of interest (year t). Therefore, the Monte Carlo analysis needs to be set up to estimate both years simultaneously. The following steps show the procedure.

Step 1: Specify source/sink category uncertainties. Determine the probability density functions for emission factors, activity data and other estimation parameters. This is the same process as described above except that it needs to be done for both the base year and the current year, and relationships between the data need to be considered. For many categories, the same emission factor will be used for each year (i.e., the emission factors for both years are 100 percent correlated). In these cases, one distribution is described and the value selected from it is used for each year in step 3. Changes in the technologies or practices will alter the emission factor over time. In this case, two emission factors should be used, that have a lower or zero correlation. If the emission factors contain a random element or vary unpredictably from year to year, then separate emission factors should also be used (e.g., with fossil fuel carbon content that can change according to the market supply of the fuel and also contains its own uncertainty). Generally, uncertainty in activity data are assumed to be uncorrelated between years, and so two distributions should be input, even if their parameters are the same, so that two different random selections from these distributions will be generated in step 3. The computer package used may well enable other correlations to be set up and these capabilities could be used if sufficient information is available. However, this will probably be necessary in only a few cases.

step 2: select random variables. The computer program will proceed as previously described, taking into account of any correlation between probability density functions (PDF). Figure 3.7, below, shows the calculation scheme for trend analysis.

step 3: Estimate Emissions. As in the previous description, the variables selected in Step 2 will be used to estimate the total emissions.

Step 4: Results. The emissions total calculated in Step 3 is stored in a data file. The process then repeats from Step 2 until there is adequate convergence of the results. Considerations for this are the same as described above. A range of results is estimated at the same time including total and sectoral emissions/removals for the base year, total and sectoral emissions/removals for year t, and the percentage differences (trends) between these for the total and any sectors of interest.

13 percentage difference = (value in year t - value in base year) / value in base year

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