## Uncertainty Estimation Quality Assurance and Quality Control

Carbon stocks and changes should be neither overestimated nor underestimated as far as can be judged (IPCC 2000). The uncertainty is normally high in biological and land-use sectors given the large variation in factors contributing to carbon stocks and changes. Uncertainty in the estimates that make up a carbon inventory is considered as a barrier in land-use sector, particularly in forest sector, to mitigating climate change. The uncertainty in estimated carbon stock and changes in land-use sectors is often estimated to be 25-70% of the actual values, which has to be considered high. As a consequence, assessing the reliability and accuracy of the estimated carbon stocks and changes becomes a critical requirement, and the goal of any carbon inventory programme should be to minimize such uncertainty. It is always desirable that reported estimates of carbon stocks and changes are accompanied by estimates of uncertainty: most often, this is not so because of the complexities involved in estimating uncertainties; also, not all sources of uncertainty can be quantified. The uncertainties are in many cases so high that project managers or inventory compilers hesitate to estimate and report them. A broad approach to reducing uncertainty involves the following steps:

• Identify the types and sources of uncertainty, such as lack of data, measurement error, sampling error and model limitations

• Quantify, aggregate and estimate the extent of uncertainty by source

• Increase the sample size, adopt correct statistical sampling methods, improve the representativeness of samples, reduce or avoid measurement errors and improve the model

The uncertainty analysis should help prioritize the efforts to reduce uncertainty in the estimates of carbon stocks and changes in carbon mitigation projects, round-wood production and national greenhouse gas inventory programmes. All these activities involve repeated multiperiod or multiyear and long-term measurement, monitoring and estimation of carbon stocks and changes. IPCC (2003, 2006) provides approaches to and methods for identification, estimation and reduction of uncertainty in greenhouse gas (GHG) inventory programmes. These approaches and methods could be adopted in estimating uncertainty in estimates of carbon stocks and changes in land-based climate change mitigation projects and round-wood production programmes.

### 18.1 Causes of Uncertainty

Estimates of carbon stocks and changes made using field methods, laboratory techniques and models are likely to differ from the true values on the ground because of several factors. Some causes of uncertainty, such as sampling error, may generate well-defined and quantified estimates of the range of potential uncertainty; other causes such as bias in locating a sample plot or in choosing a biomass estimation equation may be much more difficult to identify and quantify (Rypdal and Winiwarter 2001). Uncertainty could arise from various parameters required for estimating carbon stocks and changes including

• Above-ground and below-ground biomass stocks and growth rates, litter, dead-wood stocks and soil carbon density

• Biomass expansion factors for converting commercial biomass to total tree biomass

• Model or equation coefficients

Attempts must be made to account for and estimate all the causes of uncertainty, both quantifiable and others. Some of the causes of uncertainty are listed below (IPCC 2006):

(i) Lack of completeness Incomplete observations or recording is common wherever field measurements are involved. Some of the observations, such as diameter at breast height (DBH) and height, may be missing, incomplete, not recorded or not entered in the database. Data on some carbon pools, such as litter or below-ground biomass, may be missing or may not be recorded.

(ii) Lack of data Data on some of the parameters required may not be available. For example, data on height of trees may not be collected because of the difficulty in measuring the height of tall trees in a mature forest or plantation although a suitable biomass estimation equation may require DBH and height values. Similarly, litter data may not be available and further, no default values may be available for the vegetation types selected. Absence of such data may lead to incomplete estimation of carbon stocks or changes.

(iii) Lack of representativeness Lack of representativeness as a source of uncertainty is associated with the lack of complete correspondence between conditions associated with the collected data and those with vegetation on the ground. Further, the sample plots selected for a given forest or grassland type may not fully represent the variation in the field due to

° Differences in the age of the forest stands

° Variation in tree density

° Changes in species mix

° Variation in soil type and topography

° Management practices

(iv) Statistical sampling error Sampling error as a source of uncertainty is associated with data obtained from a sample of finite size determined not by the variance of the population - as it should be - but by factors such as limitations of resource and time. Errors may also be due to the location of the sampling unit.

(v) Measurement error Errors in measuring may be random or systematic and result from defective instruments or techniques of measurement or may creep in during recording and transmission of information.

(vi) Laboratory estimation error Errors in laboratory estimations could occur because of impurities in reagents and poor calibration of instruments.

### 18.2 Estimation of Uncertainty

Estimated carbon stock changes or CO2 emissions and removals from land-use activities have uncertainties associated with area or other activity data, biomass growth rates, expansion factors and other coefficients. This section describes how to estimate and combine these uncertainties at the carbon pool or land-use category level and also how to estimate uncertainty in the inventory as a whole. It assumes that estimates of uncertainties in input data are available as default values, based on expert judgement or sound statistical sampling.

Uncertainties should be reported as a confidence interval giving the range within which the underlying value of an uncertain quantity is thought to lie with a specified probability. The IPCC Guidelines (2003) suggest the use of a 95% confidence interval, which is the interval that has a 95% probability of containing the unknown true value. This may also be expressed as a percentage uncertainty, defined as half the confidence interval width divided by the estimated value of the quantity. Percentage uncertainty is applicable when either the underlying probability density function is known or when a sampling scheme or expert judgement is used. Probability density function (PDF) is a function that represents the probability distribution in terms of integrals and is represented by a curve such that the area under the curve between two numbers is the probability that the random variable will be between those two numbers. The most common PDF is the normal distribution. Uncertainty is estimated for parameters such as biomass and soil carbon, wood density and carbon fraction of dry matter, which can be assessed from the standard deviation of measured sample values, and is estimated using the following equation

m where:

Us = percentage uncertainty in the estimate of mean parameter value m = sample mean value of the parameter

IPCC Good Practice Guidance (IPCC 2003) suggests two methods for estimating and aggregating uncertainty. Uncertainty is also often estimated based on expert judgement.

(i) Simple error propagation

(ii) Monte Carlo simulations

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