The Monte Carlo method is suitable for forestry and other land-based projects, particularly since it helps to overcome the limitation due to lack of independence between various uncertainty values involved in assessing uncertainty at the project level. A general description of the Monte Carlo method is given in Fishman (1995), and statistical packages are available that include Monte Carlo algorithms. Winiwarter and Rypdal (2001) and Eggleston et al. (1998) provide examples of application of Monte Carlo analysis, which is designed to select random values of estimated parameters from PDFs and then calculate the corresponding change in carbon stocks. This procedure is repeated several times to obtain a mean value and the range of uncertainty. Data used for uncertainty estimation can be derived from field study or from expert judgement and need to be synthesized in such a way as to produce PDFs.
The approach to estimating uncertainties, based on Good Practice Guidance (IPCC 2003), consists of five steps; the first two require some effort from the user but the rest are carried out automatically by the software package.
Step 1: Specify uncertainties in the input variables Specifying uncertainties in the input variables includes input parameters, their associated means and PDFs and any correlations.
Input variables To provide uncertainties for the key parameters, it is desirable to independently assess the uncertainty associated with the data used in estimating carbon stocks. Ranges of uncertainty estimates for many of the input parameters required for estimating carbon stocks and changes are given in IPCC (2003, 2006) and can also be obtained from the literature, comparison with other project locations with similar conditions and even expert judgement. Uncertainty estimates can also be obtained for models (IPCC 2003).
Probability distribution function Simulating PDF requires the analyst to specify probability distributions that reasonably represents each model input for which the uncertainty is to be quantified. The function can be obtained by a variety of means including statistical analysis of data and expert judgement (IPCC 2000a). The critical step is to develop the distribution for input variables.
Step 2: Set up software package The emission inventory calculation, the PDFs, and the correlation values should be set up in the Monte Carlo package. The software performs the subsequent steps. In some cases, the carbon inventory agency may decide to set up its own programme to run a Monte Carlo simulation, which can be done using statistical software packages.
Step 3: Select input values Normally input values are the estimates applied in the calculation. This step is the start of the iterations. For each item in the input data, a number is randomly selected from the PDF of that variable.
Step 4: Estimate carbon stocks The variables selected in Step 3 are used to estimate carbon stocks for the base year and the current year (that is the beginning and the end of the carbon inventory period, e.g. year t1 and year t10) based on input values.
Step 5: Iterate and monitor results The calculated total from Step 4 is stored, and the process repeated from Step 3. The mean of the totals stored gives an estimate of the carbon stock, and the variability represents uncertainty. Many repetitions are needed for this type of analysis. The duration over which the iterations are conducted can be determined in two ways: the iterations continue until either a stipulated number - e.g. 10,000 - of runs is completed or the mean reaches a relatively stable point.
18.3 Uncertainty Analysis
Uncertainty analysis involves the following steps, which are illustrated in IPCC (2003):
Step 1: Estimate emissions or removals related to each activity - forestland remaining forest, grassland converted to forest, cropland converted to forest and so on
Step 2: Assess uncertainties related to each activity - forest land remaining forest land, grassland converted to forest land and so on Step 3: Assess the total uncertainties from the LULUCF sector - forest land remaining forest land, grassland converted to forestland and so on Step 4: Combine LULUCF uncertainties with other source categories such as energy and agriculture sectors.
According to IPCC (2006), uncertainties should be reduced as far as practicable during the process of carbon inventory and it is particularly important to ensure that the model and the data collected are a fair representation of the reality on the ground. Efforts to reduce uncertainty should focus on input parameters and models critical for estimation or projection of carbon stocks and changes. Attempts to reduce uncertainty should be preceded by an analysis of the sources of uncertainty and the extent of uncertainty associated with key input parameters and the methods used to generate them. Some of the potential options to reduce uncertainty are as follows (IPCC 2006):
(i) Improving conceptualization It is necessary to conceptualize carbon inventory process to ensure consideration of all aspects relevant to reducing uncertainty, such as
° Stratification of land-use category. ° Sample size and location of sampling units.
° Method of measurement of parameters in the field and recording of data. ° Selection of a model for analysis. ° Input parameters for the model or steps in the calculation.
(ii) Improving the models Selection of an appropriate model for the specific project type and location, improvements in model structure and parameterization would lead to a better understanding of the model characterization and contribute to reducing the uncertainties.
(iii) Improving representativeness It is very important to ensure that the sample size and location provide a good representation of the carbon status in the field. Representativeness of the sample and the parameters required for estimating carbon stocks and changes are related to stratification, sample size, sample location and parameters selected for measurement. Increasing the sample size normally improves representativeness, though not always.
(iv) Precise methods of measurement Errors in measurement can be reduced by using more precise measurement methods and ensuring that the instruments are correctly calibrated.
(v) Complete measurement It is important to ensure that field studies are conducted for all the sampling units and that the identified parameters are measured in all the plots and for all the individuals, such as trees and shrubs.
(vi) Correct recording and transmission of data Data recorded in the field should be correctly coded and entered into a computerized database ensuring correct conversions (kilograms to tonnes, inches to centimetres or metres, etc.) and uniform units of area, weight and height.
(vii) Quality control and quality assurance Adoption of quality control and assurance procedures would reduce the uncertainty significantly.
(viii) Training of staff It is very important to train the field and laboratory staff in the measurement and recording protocols.
18.5 Quality Assurance, Quality Control and Verification
Quality control (QC), quality assurance (QA) and verification procedures are important components of the carbon inventory process, particularly in reducing the uncertainty involved in estimating carbon stocks and changes. IPCC (2003, 2006) provides the definitions and procedures for QA, QC and verification to enhance the transparency and accuracy of estimates that go into a carbon inventory.
• Quality control is a system of routine technical activities to measure and control the quality of the inventory as it is being developed, and is designed to
° Provide routine and consistent checks to ensure data integrity, correctness and completeness of data. ° Identify and address errors and omissions.
° Document and archive inventory material and record all QC activities.
• Quality assurance is a planned system of review procedures conducted by personnel not directly involved in the inventory compilation/development process.
• Verification refers to a set of activities and procedures conducted during the planning and implementation of the carbon inventory methods and models, which would help to establish the reliability of the methods and procedures adopted. Verification refers to those procedures that are external to the inventory process and apply independent data and comparison with other similar studies and estimates.
QA/QC procedures need to be developed and adopted particularly for the following activities (Pearson et al. 2005b)
• Field measurements
• Sample preparation and laboratory measurements
• Data entry and analysis
• Data storage and management
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