Chapter 3: Uncertainties

CHAPTER 3

UNCERTAINTIES2006 IPCC Guidelines for National Greenhouse Gas Inventories

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Volume 1: General Guidance and Reporting

Authors
Christopher Frey (USA), Jim Penman (UK)
Lisa Hanle(USA), Suvi Monni (Finland), and Stephen Ogle (USA)

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Chapter 3: Uncertainties

Contents
3

Uncertainties
3.1

Introduction ......................................................................................................................................... 3.6

3.1.1

Overview of uncertainty analysis ................................................................................................ 3.6

3.1.2

Overall structure of uncertainty analysis ..................................................................................... 3.6

3.1.3

Key concepts and terminology .................................................................................................... 3.7

3.1.4

Basis for uncertainty analysis ...................................................................................................... 3.8

3.1.5

Causes of uncertainty ................................................................................................................ 3.10

3.1.6

Reducing uncertainty ................................................................................................................. 3.12

3.1.7

Implications of methodological choice ...................................................................................... 3.13

3.2

Quantifying uncertainties .................................................................................................................. 3.13

3.2.1

Sources of data and information ................................................................................................ 3.14

3.2.1.1

Uncertainties associated with models .................................................................................. 3.14

3.2.1.2

Empirical data for sources and sinks and activity ................................................................ 3.14

3.2.1.3

Expert judgement as a source of information ...................................................................... 3.19

3.2.2

Techniques for quantifying uncertainties .................................................................................. 3.19

3.2.2.1

Uncertainty in models .......................................................................................................... 3.19

3.2.2.2

Statistical analysis of empirical data .................................................................................... 3.20

3.2.2.3

Methods for encoding Expert Judgements ........................................................................... 3.20

3.2.2.4

Good practice guidance for selecting probability density functions .................................... 3.22

3.2.3

Methods to combine uncertainties ............................................................................................. 3.27

3.2.3.1

Approach 1: propagation of error ........................................................................................ 3.27

3.2.3.2

Approach 2: Monte Carlo simulation ................................................................................... 3.32

3.2.3.3

Hybrid combinations of Approaches 1 and 2 ....................................................................... 3.37

3.2.3.4

Comparison between Approaches ........................................................................................ 3.38

3.2.3.5

Guidance on choice of Approach ......................................................................................... 3.39

3.3

Uncertainty and temporal autocorrelation ......................................................................................... 3.39

3.4

Use of other appropriate techniques .................................................................................................. 3.40

3.5

Reporting and Documentation ........................................................................................................... 3.40

3.6

Examples ........................................................................................................................................... 3.43

3.7

Technical background information .................................................................................................... 3.57

3.7.1

Approach 1 variables and equations .......................................................................................... 3.57

3.7.2

Approach 1 – details of the equations for trend uncertainty ...................................................... 3.58

3.7.3

Dealing with large and asymmetric uncertainties in the results of Approach 1 ......................... 3.60

3.7.4

Methodology for calculation of the contribution to uncertainty ................................................ 3.62

References ......................................................................................................................................................... 3.64

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Equations
Equation 3.1

Combining uncertainties – Approach 1 – multiplication ................................................... 3.28

Equation 3.2

Combining uncertainties – Approach 1 – addition and subtraction ................................... 3.28

Equation 3.3

Correction factor for uncertainty half-range ...................................................................... 3.60

Equation 3.4

Corrected uncertainty half-range ....................................................................................... 3.61

Equation 3.5

Asymmetric confidence intervals – geometric mean ......................................................... 3.61

Equation 3.6

Asymmetric confidence intervals – geometric standard deviation .................................... 3.61

Equation 3.7

Lower/upper uncertainty half-range from error propagation ............................................. 3.62

Equation 3.8

Contribution of category X – variance for symmetric uncertainty .................................... 3.63

Equation 3.9

Contribution of category X – variance for asymmetric uncertainty .................................. 3.63

Figures

3.4

Figure 3.1

Overall structure of a generic uncertainty analysis .............................................................. 3.7

Figure 3.2

Illustration of accuracy and precision .................................................................................. 3.8

Figure 3.3

Examples of symmetric and asymmetric uncertainties in an emission factor ...................... 3.9

Figure 3.4

Example of uncertainty in emission measurements and mean emission rate .................... 3.15

Figure 3.5

Examples of some commonly used probability density function models .......................... 3.23

Figure 3.6

Illustration of Monte Carlo method ................................................................................... 3.34

Figure 3.7

Calculation scheme for Monte Carlo analysis of the absolute emissions and the trendof a single category, estimated as emission factor times an activity rate ........................... 3.36

Figure 3.8

Example frequency plots of the results of a Monte Carlo simulation ................................ 3.37

Figure 3.9

Estimates of asymmetric ranges of uncertainty with respect to the arithmetic mean
assuming a lognormal distribution based upon uncertainty half-range calculated from a
propagation of error approach ........................................................................................... 3.62

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

TablesTable 3.1

Typical strategies for dealing with different causes of uncertainties ................................. 3.12

Table 3.2

Approach 1 uncertainty calculation ................................................................................... 3.31

Table 3.3

General reporting table for uncertainty .............................................................................. 3.42

Table 3.4

Example of an Approach 1 uncertainty analysis for Finland ............................................. 3.44

Table 3.5

Example of reporting of Approach 2 uncertainty analysis
using general reporting table for uncertainty ..................................................................... 3.51

Boxes
Box 3.1

A brief example of detailed Expert Judgement ................................................................. 3.22

Box 3.2

Example of Monte Carlo uncertainty assessment dealing with correlations ..................... 3.26

Box 3.3

Dealing with model uncertainty in a probabilistic analysis ............................................... 3.39

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3 UNCERTAINTIES
3.1

INTRODUCTION

This chapter provides guidance in estimating and reporting uncertainties associated with both annual estimates ofemissions and removals, and emission and removal trends over time. It is written from the viewpoint of theinventory compiler and provides, with examples, two approaches for combining category uncertainties into
uncertainty estimates for total national net emissions and the trend.

3.1.1

Overview of uncertainty analysis

Uncertainty estimates are an essential element of a complete inventory of greenhouse gas emissions andremovals. They should be derived for both the national level and the trend estimate, as well as for the component
parts such as emission factors, activity data and other estimation parameters for each category. This guidance
therefore develops a structured approach to estimating inventory uncertainty. It includes methods for:•

Determining uncertainties in individual variables used in the inventory (e.g., estimates of emissions from
specific categories, emission factors, activity data);•

Aggregating the component uncertainties to the total inventory;•

Determining the uncertainty in the trend; and•Identifying significant sources of uncertainty in the inventory to help prioritise data collection and efforts toimprove the inventory.

While the methods outlined below are intended to estimate uncertainties for the national inventory, it isimportant to recognize that some uncertainties that are not addressed by statistical means may exist, including
those arising from omissions or double counting, or other conceptual errors, or from incomplete understanding of
the processes that may lead to inaccuracies in estimates developed from models.
An uncertainty analysis should be seen, first and foremost, as a means to help prioritise national efforts to reduce
the uncertainty of inventories in the future, and guide decisions on methodological choice. For this reason, themethods used to attribute uncertainty values must be practical, scientifically defensible, robust enough to be
applicable to a range of categories of emissions by source and removals by sinks, methods and national
circumstances, and presented in ways comprehensible to inventory users. A reference section is provided formore detailed and more theoretical information on topics discussed in this chapter.
Quantitative uncertainty analysis is performed by estimating the 95 percent confidence interval of the emissions
and removals estimates for individual categories and for the total inventory. The definition of the 95 percent
confidence interval is given in Section 3.1.3, Key Concepts and Terminology.

3.1.2

Overall structure of uncertainty analysis

This section provides a brief overview of the overall structure of uncertainty analysis, as illustrated in Figure 3.1.
Emissions/removals estimates are based on: (1) conceptualisation; (2) models; and (3) input data andassumptions (e.g., emission factor and activity data). Each of these three can be a source of uncertainty. The
analysis begins with a conceptualisation. This is a set of assumptions regarding the structure of an inventory orof a sector. These assumptions typically include the scope of geographic area, temporal averaging time,categories, emissions or removal processes, and gases that are included. The assumptions and the methodologicalchoice determine the needs for data and information. There can be some interaction between data andassumptions and methodological choice, indicated by the two-way arrow in the figure. For example, the ability
to disaggregate categories, which may be necessary for higher tier methodologies, can depend on the availabilityof data. Data, whether empirical or based on expert judgment, should undergo appropriate data collection and
QC procedures, as detailed in Chapters 2, Approaches to Data Collection, and Chapter 6, Quality
Assurance/Quality Control and Verification, respectively.
Models can be as simple as arithmetic multiplication of activity and emission factors for each category andsubsequent summation over all categories, but they may also include complex process models specific toparticular categories. The data and information obtained from data collection become input to a more specific3.62006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

knowledge base of data and judgment for uncertainty, as shown in the figure and as discussed in detail in Section
3.2.1, Sources of Data and Information. Specific causes of uncertainty in the conceptualisation, models, and data
are discussed in Section 3.2.1 and techniques for quantifying uncertainties in input data are set out in Section
3.2.2. These necessary data include percentage uncertainty estimates and underlining probability density
functions (PDFs - discussed in Section 3.1.4) for input to an emission inventory uncertainty analysis. Methods
for combining input uncertainties to arrive at uncertainty estimates for single categories and the overall inventory
result are detailed in Section 3.2.3. Two Approaches are given for combining uncertainties. Approach 1 is arelatively simple spreadsheet-based calculation procedure based upon some assumptions to simplify thecalculations. Approach 2 is based upon Monte Carlo simulation and can be applied more generally. Either
approach provides an estimate of the overall uncertainties associated with the total greenhouse gas inventory.
Figure 3.1

Overall structure of a generic uncertainty analysis

Data Collection

Input Uncertainty
Quantification

Conceptualisation:
Background Assumptions
and Methodological Choice

QC

Emissions/Removal
Estimation

Combination of Uncertainties(Approach 1 or 2)

Emissions/Removals
Estimates

Uncertainty
Estimates
Note: Shaded Boxes are the focus of this Chapter.

3.1.3

Key concepts and terminology

Definitions associated with conducting an uncertainty analysis include uncertainty, accuracy, precision andvariability. These terms are sometimes used loosely and may be misunderstood. They have in fact clear
statistical definitions that should be used in order to be clear about what is being quantified and reported. Several
definitions are given here, in alphabetical order:
Accuracy: Agreement between the true value and the average of repeated measured observations or estimates ofa variable. An accurate measurement or prediction lacks bias or, equivalently, systematic error.
Bias: Lack of accuracy. Bias (systematic error), can occur because of failure to capture all relevant processes
involved or because the available data are not representative of all real-world situations, or because of instrument
error.
Confidence Interval: The true value of the quantity for which the interval is to be estimated is a fixed but
unknown constant, such as the annual total emissions in a given year for a given country. The confidence
interval is a range that encloses the true value of this unknown fixed quantity with a specified confidence(probability). Typically, a 95 percent confidence interval is used in greenhouse gas inventories. From a
traditional statistical perspective, the 95 percent confidence interval has a 95 percent probability of enclosing thetrue but unknown value of the quantity. An alternative interpretation is that the confidence interval is a range that
may safely be declared to be consistent with observed data or information. The 95 percent confidence interval is
enclosed by the 2.5th and 97.5th percentiles of the PDF.
Precision: Agreement among repeated measurements of the same variable. Better precision means less random
error. Precision is independent of accuracy.
Probability density function (PDF): The PDF describes the range and relative likelihood of possible values. The
PDF can be used to describe uncertainty in the estimate of a quantity that is a fixed constant whose value is notexactly known, or it can be used to describe inherent variability. The purpose of the uncertainty analysis for the2006 IPCC Guidelines for National Greenhouse Gas Inventories

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emission inventory is to quantify uncertainty in the unknown fixed value of total emissions as well as emissions
and activity pertaining to specific categories. Thus, throughout this chapter it is presumed that the PDF is used toestimate uncertainty, and not variability, unless otherwise stated.
Random errors: Random variation above or below a mean value. Random error is inversely proportional toprecision. Usually, the random error is quantified with respect to a mean value, but the mean could be biased or
unbiased. Thus, random error is a distinct concept compared to systematic error.
Systematic error: Another term for bias, which refers to lack of accuracy.
Uncertainty: Lack of knowledge of the true value of a variable that can be described as a probability density
function (PDF) characterising the range and likelihood of possible values. Uncertainty depends on the analyst’s
state of knowledge, which in turn depends on the quality and quantity of applicable data as well as knowledge ofunderlying processes and inference methods.
Variability: Heterogeneity of a variable over time, space or members of a population (Morgan and Henrion, 1990;
Cullen and Frey, 1999). Variability may arise, for example, due to differences in design from one emitter to another(inter-plant or spatial variability) and in operating conditions from one time to another at a given emitter (intra-plantvariability). Variability is an inherent property of the system or of nature, and not of the analyst.
Figure 3.2

Illustration of accuracy and precision(a) inaccurate but precise; (b) inaccurate and imprecise; (c) accurate but imprecise; and (d) precise and accurate

(a)

(b)

(c)

(d)

Inventories should be accurate in the sense that they are neither over- nor underestimated as far as can be judged,
and precise in the sense that uncertainties are reduced as far as practicable. Figure 3.2 provides a conceptual
comparison of accuracy and precision. An accurate inventory is one that is free of bias but that could be precise
or imprecise. A precise inventory may appear to have low uncertainty but if the inventory is inaccurate, then theinventory systematically over- or under-estimates the true emissions or removals. Inaccuracy, or bias, can occur
because of failure to capture all relevant emissions or removal processes or because the available data are notrepresentative of real-world situations. There is no predetermined level of precision, in part because of theinherent variability of some categories.

3.1.4

Basis for uncertainty analysis

The chapter uses two main statistical concepts – the probability density function (PDF) and confidence interval
defined in the previous section. While this chapter focuses on aspects of uncertainty that are amenable toquantification, there are typically nonquantifiable uncertainties as well. The quantitative uncertainty analysis
tends to deal primarily with random errors based on the inherent variability of a system and the finite sample sizeof available data, random components of measurement error, or inferences regarding the random component of
uncertainty obtained from expert judgement. In contrast, systematic errors that may arise because ofimperfections in conceptualisation, models, measurement techniques, or other systems for recording or making
inferences from data, can be much more difficult to quantify. As mentioned in Section 3.5, Reporting andDocumentation, it is good practice for potential sources of uncertainty that have not been quantified to be
described, particularly with respect to conceptualisation, models, and data and to make every effort to quantify
them in the future.
Good practice requires that bias in conceptualisations, models, and inputs to models be prevented wherever
possible, such as by using appropriate QA/QC procedures. Where biases cannot be prevented, it is good practice
to identify and correct them when developing a mean estimate of the inventory. In particular, the point estimatethat is used for reporting the inventory should be free of biases as much as it is practical and possible. Once

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Chapter 3: Uncertainties

biases are corrected to the extent possible, the uncertainty analysis can then focus on quantification of therandom errors with respect to the mean estimate.
Good practice requires the use of a 95 percent confidence interval for quantification of random errors. This may
also be expressed as a percentage of the central estimate. Where the PDF is symmetrical the confidence interval
can be conveniently expressed as plus or minus half the confidence interval width divided by the estimated valueof the variable (e.g., ± 10%). Where the PDF is not symmetrical upper and lower limits of the confidence
interval need to be specified separately (e.g., -30%,+50%).
If the range of uncertainty for a non-negative variable is small enough relative to the mean value, then theuncertainty often can be described as a symmetric range with respect to a mean value, as shown in Figure 3.3(a).
For example, if the mean emissions are 1.0 units, the 2.5th percentile of uncertainty is 0.7 units, and the 97.5th
percentile of uncertainty is 1.3 units, then the uncertainty range could be described as 1.0 units ±30%. However,when the relative range of uncertainty is large, and if the uncertainty is regarding a variable that must be nonnegative (such as an emission factor), then the uncertainty range becomes asymmetric with respect to the mean, as
shown in Figure 3.3(b). As an example, if the mean emissions are 1.0 units, the 2.5th percentile of uncertainty is 0.5
units, and the 97.5th percentile of uncertainty is 2.0 units, then the range of uncertainty can be described as 1.0 units-50% to +100%. In situations such as the latter, it is often more convenient to summarise uncertainties in a
multiplicative, rather than additive, manner. In this particular example, the lower end of the 95 percent probability
range is a half the mean, and the upper end is a multiplier of 2 larger than the mean. Such a range is commonlysummarised as a “factor of 2.” An uncertainty of a “factor of n” refers to a range bounded at the low end by(mean/n) and at the high end by (mean × n). Thus, a factor of 10 uncertainty would have a range of 0.1×mean to
10×mean. The factor 10 uncertainty is also often called “an order of magnitude”. Higher powers of 10 are referred
to as “orders of magnitude;” for example, a factor of 103 would be referred to as three orders-of-magnitude.
Figure 3.3

Examples of symmetric and asymmetric uncertainties in an emission factor( a ) Exa mp le o f a sy mm et r i c u n c er t a in t y o f ± 3 0 % r e l a t ive t o t h e m ea n
97.5thPercentile

Probability Density

2.5thPercentile
95%
Probability
Range-30% +30%
Mean

0

1
2
Example Emission Factor

3( b ) Exampl e o f a n a sy m m et r i c unc e rt a in t y of -50 % to +100 % relat ive to the mean, o ra fa cto r of t wo

Probability Density

2.5thPercentile

97.5thPercentile
95% Probability Range

-50%
Mean

0

+100%

1
2
Example Emission Factor

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3.1.5

Causes of uncertainty

Inventory estimates of emissions and removals differ from the true underlying value for many reasons. Somecauses of uncertainty (e.g., sampling error or limitations on instrument accuracy) may generate well-defined,easily characterised estimates of the range of potential uncertainty. Other causes of uncertainty (e.g., biases) may
be much more difficult to identify and quantify (Rypdal and Winiwarter, 2001). It is good practice to account, as
far as possible, for all causes of uncertainties in an uncertainty analysis and clearly document if some causes of
uncertainties have not been included.
The inventory developer should consider eight broad causes of uncertainty1:•

Lack of completeness: This is a case where measurement or other data are not available either because theprocess is not yet recognized or a measurement method does not yet exist. Typically, this cause can lead toincomplete conceptualisation, which results in bias, but can also contribute to random error depending on
the situation.

•

Model: Models can be as simple as a constant multiplier (e.g., an emission factor) and increase incomplexity, such as for complicated process models. The use of models to estimate greenhouse gas
emissions and removals can introduce uncertainty, including both bias and random error, for a variety ofreasons:(i)

Models are a simplification of real systems and therefore are not exact. For example, computer
programming may involve errors or approximations; model resolution may not be representative,
and spatial and temporal coverage may not be fully representative;(ii)

Interpolation is application of a model within a range of inputs for which the model is considered to
be valid. However, in some cases, a ‘hidden extrapolation’ can occur when the model is evaluatedbased on combinations of values of its inputs for which validation has not been done (Cullen andFrey, 1999).

(iii)

Extrapolation (application of the model beyond the domain for which model predictions are known
to be valid) can lead to uncertainty;(iv)

Alternative formulations of the model may result in different estimates; and(v)

Model inputs including activity data and parameters are generally approximated based on limited
information that create additional uncertainties beyond the model formulation.

•

Lack of data: In some situations, there simply may not yet be data available that would be necessary tocharacterise a particular emission or removal. In these situations, a common approach is to use proxy (orsurrogate) data for analogous or similar categories or to use interpolation or extrapolation as a basis formaking estimates.

•

Lack of representativeness of data: This source of uncertainty is associated with lack of complete
correspondence between conditions associated with the available data and the conditions associated withreal world emissions/removals or activity. For example, emissions data may be available for situations inwhich a plant is operating at full load but not for situations involving start-up or load changes. In this case,the data are only partly relevant to the desired emission estimate. Lack of representativeness typically leads
to bias.

•Statistical random sampling error: This source of uncertainty is associated with data that are a random
sample of finite size and typically depends on the variance2 of the population from which the sample isextracted and the size of the sample itself (number of data points). It can often be reduced by increasing thenumber of independent samples taken. Here, it is good practice to distinguish properly between variability
and uncertainty, as previously defined. For purposes of uncertainty analysis of inventories, one is typicallyinterested in uncertainty in the annual average at the national level, rather than the entire range of variability
that might occur over shorter periods of time or small geographic scales. Larger sample sizes will not reducethe inherent variability, but will lead to narrower confidence intervals that are a basis for estimating therandom component of uncertainty.

1

Further discussion can be found in Morgan and Henrion (1990) and Cullen and Frey (1999).

2

The variance of a whole population of values is the average of the square of the difference between individual values in the
population and the mean value. The variance of a sample drawn from a population is the sum of the squares of differences
between values in the sample and the mean of the sample, divided by the number of values in the sample less 1.

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Chapter 3: Uncertainties•

Measurement error: Measurement error, which may be random or systematic, results from errors inmeasuring, recording and transmitting information; finite instrument resolution; inexact values ofmeasurement standards and reference materials; inexact values of constants and other parameters obtained
from external sources and used in the data-reduction algorithm (e.g., default values from the IPCC
Guidelines); approximations and assumptions incorporated in the measurement method and estimation
procedure; and/or variations in repeated observations of the emission or removal or associated variable
under apparently identical conditions.

•

Misreporting or misclassification: Uncertainty here may be due to incomplete, unclear, or faulty definitionof an emission or removal. This cause of uncertainty typically leads to bias.

•

Missing data: Uncertainties may result where measurements were attempted but no value was available. An
example are measurements that are below a detection limit. This cause of uncertainty can lead to both bias
and random error. When measured values are below a detection limit, an upper bound on the uncertainty canbe estimated. There are rigorous statistical techniques for dealing with non-detected data as well as othertypes of missing data, such as data that are missing at random (Cohen and Whitten, 1998; Gelfand, 1996;
Zhao and Frey, 2004b). These techniques may involve estimation or imputation in portions of the
distribution where data are not available.

Particularly on the issue of extrapolation, uncertainty occurs when extrapolating from recent source and sink data
for the purpose of estimating an inventory for a year of interest for which data are not yet available (see also
Chapter 5, Time Series Consistency). Usually, the extrapolated estimates are reported as ‘provisional’ estimates
and then later are updated when the relevant data become available. However, until the update occurs, theprovisional inventory might be used. The additional uncertainty associated with extrapolation is a type of model
uncertainty. Errors associated with extrapolation can be systematic, random, or both. If there is a history of
extrapolations and subsequent correction, then it is possible to develop data regarding the distribution of theerrors that have been observed in the past. If there are biases in the provisional estimates, then the mean of this
distribution will not be zero and the biases can be quantified. This distribution would represent error in theability to predict actual source and sink fluxes based upon the extrapolation methods used in the past. If theextrapolation methods change, then expert judgement could be used to quantify the uncertainty.
Where a PDF for the mean can be identified, various causes of uncertainty can be quantified by statistical means.
As noted in Section 3.2, uncertainties can be quantified by statistical analysis of empirical data, by encoding(quantifying) of expert judgement in the form of PDFs, or by combinations of both. However, there can be
structural uncertainties that are not easily incorporated into a quantitative uncertainty analysis in the form of a
PDF. Examples of structural uncertainties include possible misidentification or mis-specification of the system tobe analysed, as well as possible problems associated with the models that are used, e.g., inappropriateness of themodel, or model errors. These latter types of situations are typically outside the scope of statistics (ISO 1993)3,
although probabilistic methods for dealing with model uncertainties have been proposed (e.g., Evans et al.,1994). For example, expert judgement can be used to assign weights to alternative models.
Table 3.1 suggests how different causes of uncertainties can be treated in an analysis. Some causes of
uncertainties (e.g., misreporting/misclassification) may be reduced or eliminated by implementing QA/QC
procedures and improvements in data collection and/or methodologies when identified.

3

There are some opportunities for addressing these sources of uncertainty. For example, uncertainties associated with model
error at least partly can be addressed by comparing modelled output with measured values. Depending on how modelled
outputs compare with measurements, one can identify biases associated with the model that may vary depending on thetype of system being modelled.

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TABLE 3.1
TYPICAL STRATEGIES FOR DEALING WITH DIFFERENT CAUSES OF UNCERTAINTIESStrategy
Causes of Uncertainty

Lack of completenessModel(bias and random errors)

Evaluated
Empirical
Other Comments 1
Conceptualisation
Expertandjudgement
and Model
Statistical
Formulation
Have key components of the system been
omitted? If so, what is the quantifiable or√nonquantifiable effect on systematic error?
Proper QA/QC should help avoid this.

√√Lack of data

Lack ofrepresentativeness of
data

√

√

Statistical random
sampling error√

Measurement error:
random component√

Measurement error:
systematic component(bias)√√Is the model formulation complete andaccurate? What is the uncertainty in model
predictions based on validation of the model?
What is the estimate of model accuracy andprecision based on expert judgment if
statistical validation data are not available?

√

If data are lacking, can expert judgment beused to make inferences based on analogous(surrogate, proxy) data or theoreticalconsiderations? May be related to lack ofcompleteness and model uncertainty.

√
E.g., statistical theory for estimating
confidence intervals based on variability inthe data and sample size.
√√

QA/QC and verification may provide insight.

Misreporting or
Misclassification√√

Proper QA/QC should help avoid this.

Missing data√√

Statistical or judgment-based approaches toestimating uncertainty because of nondetected measurements or other types of
missing data.

1

It is good practice to apply procedures for QA/QC and verification prior to or combining with developing uncertainty estimatesaccording to the guidance in Chapter 6. The QA/QC and verification procedures provide a useful basis for preventing mistakes and for
identifying (and preferably correcting) biases. Furthermore, QA/QC should prevent or help detect and correct misreporting andmisclassification errors, and there should be iteration between uncertainty analysis and QA/QC if application of the uncertainty methods
uncovers potential QA/QC problems.

3.1.6

Reducing uncertainty

Uncertainties should be reduced as far as is practicable during the process of compiling an inventory, and it isparticularly important to ensure that the model and the data collected are fair representations of the real world.
When focusing efforts to reduce uncertainty, priority should be given to those inputs to the inventory that havethe most impact on the overall uncertainty of the inventory, as opposed to inputs that are of minor or negligible
importance to the assessment as described in Chapter 4, Methodological Choice and Identification of Key
Categories. Tools for prioritising where uncertainties should be reduced include key category analysis (seeChapter 4) and assessment of the contribution of uncertainties in specific categories to the total uncertainty in theinventory (see Section 3.2.3). Depending on the cause of uncertainty present, uncertainties could be reduced inseven broad ways:•

Improving conceptualisation: Improving the inclusiveness of the structural assumptions chosen can reduce
uncertainties. An example is better treatment of seasonality effects that leads to more accurate annual
estimates of emissions or removals for the AFOLU Sector.

•

Improving models: Improving the model structure and parameterisation can lead to better understanding andcharacterisation of the systematic and random errors, as well as reductions in these causes of uncertainty.

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Improving representativeness: This may involve stratification or other sampling strategies, as set out in Section
3.2.1.2. This is particularly important for categories in the agriculture, forestry and land use parts of an
inventory, but also applies elsewhere, e.g., wherever different technologies are operating within a category. For
example, continuous emissions monitoring systems (CEMS) can be used to reduce uncertainty for somesources and gases as long as the representativeness is guaranteed. CEMS produces representative data at thefacilities where it is used, but in order to be representative of an entire source category, CEMS data must be
available for a random sample or an entire set of individual facilities that comprise the category. When using
CEMS both concentration and flow will vary, requiring simultaneous sampling of both attributes.

•

Using more precise measurement methods: Measurement error can be reduced by using more precise
measurement methods, avoiding simplifying assumptions, and ensuring that measurement technologies areappropriately used and calibrated. See Chapter 2, Approaches to Data Collection.

•

Collecting more measured data: Uncertainty associated with random sampling error can be reduced byincreasing the sample size. Both bias and random error can be reduced by filling in data gaps. This applies
both to measurements and surveys.

•

Eliminating known risk of bias: This is achieved by ensuring instrumentation is properly positioned andcalibrated (see Section 2.2 in Chapter 2), models or other estimation procedures are appropriate andrepresentative as indicated by the decision trees and other advice on methodological choice in sectoral
volumes, and by applying expert judgements in a systematic way.

•

Improving state of knowledge: Generally, improving the understanding of the categories and the processes
leading to emissions and removals can help to discover, and correct for, problems of incompleteness. It isgood practice to continuously improve emissions and removal estimates based on new knowledge (seeChapter 5, Time Series Consistency).

3.1.7

Implications of methodological choice

Choice of methodological tier for emissions and removals estimation can affect the uncertainty analysis in two
different ways. Firstly, moving to higher tier inventory methods should typically reduce uncertainties, provided
the higher tier methods are well implemented, because they should reduce bias and better represent thecomplexity of the system. Secondly, moving to higher tier methods may result in increased estimates of
uncertainty in some circumstances. Often, this increase in the estimated uncertainty does not actually represent a
decrease in knowledge; rather, it typically reveals a more realistic acknowledgment of the limitations of existingknowledge. This may occur where there was an incomplete accounting of the greenhouse gas emissions in thelower tier method, or where application of higher tier methods reveals additional complexity and uncertainties
that were not fully apparent in the lower tier method. This really means that the uncertainty was underestimatedpreviously and moving to the higher tier method in reality produces a more accurate estimate of uncertainty. In
some cases, an increase in uncertainty may occur for one inventory development method versus another because
each method has different data requirements. For example, sometimes aggregate estimates of emissions are moreaccurate because they are based upon or can be compared to easily measured values, whereas disaggregatedestimates may require additional assumptions for which data or the capability to verify estimates are not as
readily available. The appropriate level of disaggregation can differ within and between categories.

3.2

QUANTIFYING UNCERTAINTIES

After identifying the causes of uncertainties associated with inventory estimates, the inventory compiler shouldcollect the appropriate information to develop national, and category-specific estimates of uncertainty at the 95
percent confidence interval. Ideally, emission and removal estimates and uncertainty ranges would be derived fromcategory-specific measured data. Since it may not be practical to measure every emission source or sink category inthis way, other methods for quantifying uncertainty may be required. The pragmatic approach for producing
quantitative uncertainty estimates is to use the best available estimates, which are often a combination of measured
data, published information, model outputs, and expert judgement. The sectoral guidance in Volumes 2 to 5 of these
Guidelines provides default uncertainty estimates for use with the methods described in this chapter.
Although uncertainties determined from measured data are often perceived to be more rigorous than uncertainty
estimates based on models, and similarly, model-based estimates are often perceived as more rigorous than those
based on expert judgement, the actual hierarchy depends on the category and/or country-specific circumstances.
In particular it is good practice to ensure that uncertainties are representative for the application in the inventory
and national circumstances and includes all causes of uncertainty listed in Table 3.1.

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This section is organised into three major subsections that are interrelated. Section 3.2.1 focuses on sources of dataand information that can be used to identify and, where possible, quantify uncertainties. Section 3.2.2 focuses on
methods for attempting to prevent or correct for biases and for quantifying the random component of uncertainty inthe inputs to models. Section 3.2.3 presents two Approaches for combining uncertainties in inputs in order to arriveat uncertainty estimates for single emission and removal categories and the total emission inventory.

3.2.1

Sources of data and information

This section identifies sources of data and information for acquiring quantitative estimates of uncertainty. There
are three broad sources of data and information: information contained in models; empirical data associated withmeasurements of emissions, and activity data from surveys and censuses; and quantified estimates of
uncertainties based upon expert judgement.

3.2.1.1

U NCERTAINTIES ASSOCIATED WITH MODELS

A model is a representation of a real-world system. Modelling typically involves choices regarding what toinclude versus what to exclude, as well as choices regarding the level of detail (or aggregation) for thosephenomena that are included in the model. Thus, the model typically does not exactly mimic the real-world
system. The structure of the model is often thought of in terms of the equations used and in terms of inputs andoutputs of the model (Kirchner, 1990). More generally, a model may be thought of as a hypothesis regarding
how the real-world system behaves. Thus, there are two key considerations in model uncertainty: (1) has thecorrect, most relevant real-world system been identified, and have conceptualisations been constructed in a waythat properly serve as the basis for model development; and (2) is the model an accurate representation of thechosen system. Conceptualisation uncertainty describes the lack of proper identification of the system for whicha model should be developed and of the conceptualisation(s) of interest. Model uncertainty describes the lack ofproper model development relative to the intended system and conceptualisation(s).
Conceptualisation Uncertainty: The failure to specify properly appropriate and relevant inventory structural
assumptions is known as conceptualisation uncertainty (Cullen and Frey, 1999) and typically results in a bias inestimates. The causes of conceptualisation uncertainty typically include descriptive errors, errors in professional
judgement, and incomplete specification of the assumptions (EPA, 1997).
Model uncertainty: Uncertainty arises from imperfections in how the chosen conceptualisations are modelled.
Sometimes these imperfections occur because of limitations of available data. A model may have other sourcesof structural errors, such as failure to properly take into account the sensitivity of emissions to ambientconditions or other factors. Modelling can be a basis for estimating emissions or removals for specific categories
as well as for managing data in the entire inventory. In some cases, model uncertainty can be significant. It is
typically poorly characterised and may not be characterised at all.

3.2.1.2

E MPIRICAL DATA FOR SOURCES AND SINKS AND ACTIVITY

This section describes sources of empirical data, and their implications for uncertainty, and is relevant tomeasured emissions data, data obtained from literature, and activity data.

UNCERTAINTY ESTIMATES OBTAINED FROM MEASUREDEMISSIONS/REMOVALS DATAThis section assumes that good practices are used to obtain the data, as outlined in Chapters 2 and Chapter 6,
Quality Assurance/Quality Control and Verification. When estimating uncertainty from measured emissions data,considerations include: (a) representativeness of the data and potential for bias; (b) precision and accuracy of themeasurements; (c) sample size and inter-individual variability in measurements, and their implications for
uncertainty in mean annual emissions/removals; (d) inter-annual variability in emissions/removals and whether
estimates are based upon an average of several years or on the basis of a particular year.
Representative sampling (or sampling design) implies that measurements are made for typical systemcharacteristics, operating conditions, time periods, and/or geographic areas of interest. The precision andaccuracy of individual measurements will depend upon the equipment and protocols used to make themeasurements. The sample size will often be a trade-off between the desirability for more data and the cost of
making measurements. In some cases, such as for continuous monitoring, the sample size may be large enoughto effectively serve as a census, rather than a partial sample, of data. In general the variability in the data from

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one short-term time period (e.g., hour, day, week) to another will depend upon the characteristics of the category.
If the goal is to develop an estimate of annual average emissions or removals, then judgement may be required as
to whether measurements conducted over a short term are representative of rates over a longer time period and, if
not, whether the measurement programme can be expanded to additional time periods. For example, flux
measurements (data on emission factors) should represent the entire year. In the AFOLU Sector this is crucial,since emissions are highly dependent on climatic conditions which typically are not the same for the growing
period and winter period.
Figure 3.4

Example of uncertainty in emission measurements and mean emission rate(a) Fitted distribution for inter-unit variability in emissions;(b) Uncertainty in fitted distribution because of small sample size (n=20);(c) Uncertainty in mean emission rate.

(a) Inter-Unit Variability
Fitting a Distribution for Example Emission Rate
1.0

Cumulative Probability

0.8

0.6

Data
(n=20)

0.4

Lognormal

0.2

0.0
0.0

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2.8

4.1

5.5

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(b) Uncertainty in Distribution of Variability
Probability Band for Example Emission Rate
1.0

Cumulative Probability

0.8

0.6

0.4

0.2

0.0
0.0

2.3

4.5

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Uncertainty in the Mean for Example Emission Rate
1.0

Cumulative Probability

0.8

0.6

0.4

0.2

0.0
0.0

0.6

1.2

1.8

2.4

3.0

For a second example, suppose that one wishes to estimate the uncertainty in national annual emissions for aparticular category, such as emissions from gasoline-fuelled passenger automobiles. The rate of emission varies
from one individual vehicle to another, illustrated by the inter-unit variability shown in Figure 3.4(a). Because
the distribution for inter-vehicle variability is estimated from a small, finite sample of data that could be subject
to random sampling error, there is uncertainty regarding what the true but unknown population distribution forinter-vehicle variability might be, as suggested in Figure 3.4(b). There is also intra-unit variability in emissions
over time for any particular vehicle. However, for purposes of the national annual estimate, the focus is on the
combined contribution of all such vehicles to total emissions during a year long time frame. In this case, we are
not interested in the range of inter-vehicle variability, but rather in the range of uncertainty for the average
emission rate among all such vehicles (e.g., Figure 3.4(c)). Often, the range of uncertainty is substantially lessthan that for inter-vehicle (or, more generally, inter-unit) variability (e.g., Frey and Zheng, 2002). Therefore,
when the objective of an analysis requires that the assessment be based upon uncertainty in the mean, rather thanvariability among individual units, it is important to properly focus the analysis on the former. Failure to do socan lead to a misleading over-estimate of the range of uncertainty.
In the case of continuous monitoring of point emissions, or a periodic sampling scheme that captures typicalactivity patterns, there may be adequate and representative empirical data upon which to base an estimate ofuncertainty in mean annual emissions. For example, if there are several years of such data, then the averageannual emissions over several years can be quantified, and the distribution of annual emissions from year-to-year
can be used to assess a 95 percent confidence interval in the annual average. Provided that the annual average isbased upon data from many individual categories, it is unlikely that there will be correlation of errors between
years. This has implications for estimation of uncertainty in trends, as discussed in Section 3.3, Uncertainty andTemporal Autocorrelation. However, for diffuse categories, such as agricultural crops, there could be highautocorrelations if they are determined by climate, and this could affect the representativeness of the data for aparticular assessment purpose.
Where continuous emission measurements are not available, there may be periodic emission measurements
available from which to estimate uncertainty. If these measurements can be linked to representative activity data,
which of course is crucial, then it is possible to determine a site-specific emission factor, together with anassociated PDF to represent annual emissions. This can be a complex task. To achieve representativeness it may
be necessary to partition (or stratify) the data to reflect typical operating conditions. For example:•

Start-up and shut down can give different emission rates relative to activity data. In this case, the data shouldbe partitioned, with separate emission factors and probability density functions derived for steady state,start-up and shut down conditions.

•

Emission factors can depend on load. In this case, the total emissions estimation and uncertainty analysis
may need to be stratified to take account of load, expressed, for example, as percentage of full capacity. This
could be done by regression analysis and scatter plots of the emission rate against likely controllingvariables (e.g., emissions versus load) with load becoming part of the activity data needed.

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Measurements taken for another purpose may not be representative. For example, methane measurements
made for safety reasons at coal mines and landfills may not necessarily reflect total emissions because they
may have been made only when methane emissions were suspected of being high, as a compliance check. In
such cases, the ratio between the measured data and total emissions should be estimated for the uncertainty
analysis.

•

Systematic short-term measurements might not adequately sample episodic events (such as rainfall) that
initiate large fluxes of short duration that may nevertheless account for a major fraction of annual emissions.
If the sampling strategy misses a significant proportion of these events, then the annual average emission
estimate could be substantially biased. Nitrous oxide emissions from agricultural soils can fall into this class.

If the data sample size is large enough, standard statistical goodness-of-fit tests can be used, in combination withexpert judgement, to help in deciding which PDF to use for describing variability in the data (partitioned if
necessary) and how to parameterise it. However, in many cases, the number of measurements from which to makean inference regarding uncertainty will be small. Theoretically, as long as there are three or more data points, andthey are a random representative sample of the variable of interest, it is possible to apply statistical techniques toestimate the values of the parameters of many two-parameter distributions (e.g., normal, lognormal) that can beused to describe variability in the data set (Cullen and Frey, 1999, pp. 116-117). While it is commonly perceived
that one must have approximately 8 or 9 data points, and preferably more, as the basis for fitting a distribution todata, the more fundamental and key assumption that must be made in order to fit a distribution to data is that thedata are a random, representative sample. If this assumption is valid, then the sample size influences the width ofthe confidence intervals for any statistic estimated from the sample. As a matter of preference, many analysts may
prefer to have a minimum sample size, but this preference is not related to the key issue of representativeness. Data
do not become more representative only because of an increase in sample size.
With small sample sizes, there will be large uncertainties regarding the parameter estimates that should bereflected in the quantification of uncertainty for use in the inventory. Furthermore, it is typically not possible torely on statistical methods to differentiate goodness-of-fit of alternative parametric distributions when sample
sizes are very small (Cullen and Frey, 1999, pp. 158-159). Therefore judgement will be required in selecting anappropriate parametric distribution to fit to a very small data set. In situations where the coefficient of variation(standard deviation divided by the mean) is less than approximately 0.3 and is known with reasonable confidence,a normal distribution may be a reasonable assumption (Robinson, 1989). When the coefficient of variation islarge and the variable is non-negative, then a positively skewed distribution such as a lognormal may beappropriate. Guidance on the selection of distributions is elaborated in Sections 3.2.2.2 and 3.2.2.4 below.
In cases with large data sets, the uncertainty in the mean can often be estimated as plus or minus 1.96 (orapproximately 2) multiples of the standard error, where the standard error is the sample standard deviation
divided by the square root of the sample size. This calculation is based on an assumption of a normal distribution.
However, in cases of a small number of samples/measurements that will often be the case in determining
emission factors, the multiple of 1.96 is replaced with a “coverage factor,” referred to as k, that is obtained fromthe student’s t-distribution. For small sample sizes, k is greater than 1.96 for a 95 percent interval, but
asymptotically approaches 1.96 as the sample size increases to approximately 30 or more. However, in cases
where the uncertainty in the mean is not a symmetric distribution, then numerical methods such as bootstrap
simulation can be used instead to obtain the confidence interval for the mean.
Where an annual estimate is based on an average over several years, the uncertainty in the average represents theuncertainty in an average year and not the inter-annual variability. If the objective is to estimate uncertainty insource or sink fluxes for a specific year, then good practice is to make a best estimate of the annual total and toquantify uncertainty associated with the models and data used consistent with the one year time period. If,
instead, an averaged annual estimate is used, then the uncertainty in the estimate when applied to a specific year
would be described by the inter-annual variability (including measurement errors) relative to the mean, whereas
when applied to an average year it would be the confidence interval of the average.

UNCERTAINTY ESTIMATES FOR EMISSION FACTORS AND OTHER
PARAMETERS OBTAINED FROM PUBLISHED REFERENCES
When site-specific data are unavailable, inventories should where possible be based on emission factors derived
from published studies specific to the conditions in that country. Where sufficient country-specific information isunavailable, information may be derived from other published studies if those studies are reflective of conditionsin the country, or emission factors or other estimation parameters may be drawn from sectoral Volumes 2 to 5 ofthese Guidelines. Factors provided in the sectoral volumes have been derived for circumstances that are judged
to be typical. There are uncertainties associated with the original measurements, as well as with the use of thefactors in circumstances other than those associated with the original measurements.

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Where published emission factors or other estimation parameters are used, the associated uncertainties should be
estimated from:•

Original research including country-specific data: For measurement-based emission factors, the data from theoriginal measurement programme or experiments may enable an assessment of the uncertainty and possibly the
PDF. Well-designed measurement programmes and experiments will provide sample data that cover the rangeof types of plants and their maintenance, size and age, so that the factors and their uncertainties can be useddirectly. In other cases, expert judgement, taking into account the causes of uncertainty identified in Table 3.1,
will be needed to extrapolate from the measurements to the full population of plants in that particular category(detail on how to elicit expert judgement is elaborated in Section 3.2.1.3).

•

Default Values from Guidelines: For most emission factors and other estimation parameters, sectoral
guidelines provide default uncertainty estimates that should be used in the absence of other information.
Unless clear evidence to the contrary is available, the PDFs are assumed to be normal. However, theinventory compiler should evaluate the representativeness of the default for its own national circumstances.
If the default is judged to be not representative and the category is important to the inventory, improved
assumptions based upon expert judgement should be developed, assuming sufficient original research isunavailable to derive country-specific emission factors or other estimation parameters.

Default methods represent a compromise between the level of detail that would be needed to create the mostaccurate estimates for each country, and the input data likely to be available or readily obtainable in mostcountries. Default methods are often simplifications, and may introduce large uncertainties into a national
estimate. Within many of the default methods different optional levels of detail are provided to reflect whether
users have detailed data for their national situation or have to rely strictly on general default values. There may
be considerable variation in how well the general default values represent conditions of the actual population ofactivities in a particular country. For example, the uncertainty relating to default carbon emission factors for the
global population of fossil fuel combustion sources may be characterised as quite low (5-10 percent) in the IPCC
methodology; but national experts for a particular country may know that the characteristics of such fuels in theircountry vary from global average values. In such a country, use of default values would introduce a larger
uncertainty, and thus it is good practice to use country-specific estimates where possible. Thus the applicabilityof default uncertainty values should always be considered.
Another example is the use of default values to estimate country-specific emissions and removals of the AFOLU
Sector. Uncertainty could be high unless the suitability of the available default parameters to a country’s
circumstances is known. The application of default data in a country or region that has very different characteristics
from those of the category data can lead to large systematic (bias) errors in estimates of emissions or removals.

UNCERTAINTIES ASSOCIATED WITH ACTIVITY DATA
Activity data are often more closely linked to economic activity than are emission factors are. However, unlike
emission factor data, there is typically no statistical sample of alternative activity data estimates readily available
to fit distributions and estimate uncertainty. There are often well established price incentives and fiscal
requirements for accurate accounting of economic activity. Activity data therefore tend to have lower
uncertainties and a lower correlation between years than emission factor data. Activity data are often collected
and published regularly by national statistical agencies, which may have already assessed the uncertainties
associated with their data as part of their data collection procedures. These previously developed uncertainty
estimates can be used to construct PDFs. This information will not necessarily have been published, so it isrecommended to contact the statistical agencies directly. Since economic activity data are not usually collected
for the purpose of estimating greenhouse gas emissions and removals, it is good practice to assess theapplicability of the uncertainty estimates before using them.
There are several approaches that may be helpful in assessing the uncertainty of activity data in particular
circumstances:
Activity data based on complete samples (censuses): Census data are activity data that are based, in principle, on
counting every instance of a particular activity. Census typically includes both systematic and random errors.
Systematic errors arise through systematic undercounting or double counting. Random errors are typically thesum of a range of commonplace errors. Random errors usually can be expected to be normally distributed andserially uncorrelated. Because activity data are usually collected by the same people, using the same processes,
for each observation, systematic errors are likely to take approximately the same value each year. There areseveral approaches to identifying the potential uncertainty of activity data for complete samples. These
approaches are often an integrated part of a QA/QC plan:•

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To check for the size of random errors, look for fluctuations over time, and differential fluctuations in series
that ought to be highly correlated with the data of interest.

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Chapter 3: Uncertainties•

To check for bias errors, cross-check the data of interest with other, related information. One might, forinstance, look up and down the supply chain for fuels, comparing coal production, coal import/export, andreported consumption. Or, one might study activities for which data are collected independently but which
ought to be highly correlated with the data of interest, for instance reported fuel input vs. electricity output.
One might also look at activity data of different frequencies (e.g., monthly, annual), if they are collectedusing different approaches.

•Interpretation of statistical differences, within, for instance, national energy data are an example of crosschecking. The comparison between energy-related carbon dioxide emissions derived from the IPCC
reference approach is a formal cross-check with emissions estimates derived from other sources.

Census-based activity data are often ‘precise but inaccurate’ in the taxonomy shown in Figure 3.2, the random
errors are small, but there may be larger bias errors. Cross-checking can suggest upper and lower bounds forpossible bias errors, and sometimes will permit an actual estimate of the bias error. A possible bias error lurking
within these bounds may often be characterised as a truncated uniform distribution: cross-checking shows thatthe unobservable true value must lie within a particular range, but there may be no reason to think any point
within that range is more or less likely. However, because the bias errors in activity data are likely to be highly
correlated, the difference between the reported value and the unknown true value is likely to be about the same
every year, and this characteristic should be taken into account when estimating trend uncertainty.
Activity data based on random samples: Some kinds of activity data are derived from sample surveys, forinstance consumer surveys, land use surveys, or forest cover surveys. In these cases, the data will be subject tosampling errors, which will be normally distributed and uncorrelated over time. The agency conducting thesample will normally be able to advise on sampling error. If this information is unavailable, it may be possible toidentify or infer the sample and population sizes and calculate sampling error directly.

3.2.1.3

E XPERT JUDGEMENT AS A SOURCE OF INFORMATIONIn many situations, directly relevant empirical data are not available for sources, sinks, or activity inputs to an
inventory. In such situations, a practical solution to dealing with the absence of adequate data is to obtain wellinformed judgements from domain experts regarding best estimates and uncertainties of inputs to the inventory.
Chapter 2, Approaches to Data Collection, discusses the basis of formal expert elicitation protocols. In particular,
Section 2.2 and Annex 2A.1 provides a general treatment of expert judgment and elicitation. Annex 2A.1
provides details regarding expert elicitation protocol. In this chapter, methods for encoding uncertainties based
upon expert judgement are recommended in Section 3.2.2.3.

3.2.2

Techniques for quantifying uncertainties

This section discusses key techniques for quantifying uncertainties, building upon the sources of data andinformation described in the previous section. This section focuses on uncertainty in models, statistical analysis of
empirical data, identifying and selecting PDFs, and methods for encoding expert judgement regarding uncertainties.

3.2.2.1

U NCERTAINTY IN MODELS

Conceptualisation and model uncertainty can be more difficult to address than the uncertainties in the inputs to amodel. The most significant concern with conceptualisation and model uncertainties is that they have thepotential to produce substantial bias in emissions and removal estimates. Approaches to deal with these causes of
uncertainties should aim therefore to evaluate and correct for known or suspected biases.
It is clear that proper specification of a conceptualisation is set by the 2006 Guidelines, the interpretation ofwhich depends on input from experts and stakeholders who are familiar with the systems for which emissions or
removals are to be estimated. A conceptualisation should be complete, within the scope of these Guidelines, inenumerating all key components without producing redundancy or overlap, and it should be applicable to thegeographic scope, time period, and agreed set of greenhouse gases covered.
Model uncertainty is typically dealt with in several ways. One approach is to simply acknowledge the limitationsof models that are used and to qualitatively discuss the implications for uncertainty in estimates obtained using
the model. However, qualitative caveats are not useful in providing quantitative insight regarding the possible
magnitude of uncertainty, and by themselves are not considered good practice. There are at least three major
approaches for estimating uncertainty: (1) comparison of model results with independent data for purposes of2006 IPCC Guidelines for National Greenhouse Gas Inventories

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verification; (2) comparison of the predictions of alternative models; and (3) expert judgement regarding themagnitude of model uncertainty. These approaches can be used in combination.
Comparison of model predictions with independent data can be used to assess the precision and accuracy of themodel, and is an important aspect of verification, as discussed in Chapter 6. Such comparisons can reveal
whether the model systematically over- or under-predicts the quantities of interest. However, it can be difficult toobtain data for direct verification of a model. Nonetheless, sometimes these types of comparisons are the best or
only available ones, and might help in identifying unexplained inconsistencies that, in turn, might imply model
bias that could be corrected for by parameter choice.
In other cases, there may be alternative models that could be used to make predictions for the same quantities ofinterest. To the extent that the alternative models are based upon different data or theoretical assumptions, acomparison of model predictions may provide useful insight regarding the magnitude of disagreement. The factthat two or more models disagree is not conclusive proof that either of the models is wrong, since both or all of
the models could be wrong.
Based on the results of the comparison of the model used for inventory development with independent data
and/or alternative models, it may be desirable to revise model assumptions or parameters to reduce the bias. The
remaining uncertainty can then be quantitatively assessed by expert judgement about how uncertainties in thedata used to drive the model and the model parameters combine, or more formally by Monte Carlo analysis.

3.2.2.2

S TATISTICAL ANALYSIS OF EMPIRICAL DATA

Statistical analysis of empirical data is an approach that can be employed to quantify uncertainty in inventories,
emission factors and other estimation parameters, and it can be summarised as the following major steps (e.g.,Frey and Zheng, 2002):
Step 1: Compilation and evaluation of a database for emission factors, activity data and other estimation
parameters. Such data typically represent variability.
Step 2: Visualisation of data by developing empirical distribution functions (in which the data are plottedvertical according to their rank order and are plotted horizontally according to their numerical value –see Cullen and Frey, 1999, for details) for individual activity and emission factors.
Step 3: Fitting, evaluation, and selection of alternative PDF models for representing variability in activity dataand emission factor data.
Step 4: Characterisation of uncertainty in the mean of the distributions for variability. If the standard error of themean is small enough (as discussed in Section 3.2.1.2), a normality assumption can be made regardless ofthe sample size or skewness of the data. If the standard error of the mean is large, then either alognormality assumption can be made, or other methods can be employed (e.g., bootstrap simulation) toestimate uncertainty in the mean. Publicly available software tools could be used to assist with the latter.
Step 5: Once uncertainties have been appropriately specified, these can be used as input to a probabilistic
analysis for purposes of estimating uncertainty in total emissions.
Step 6: Sensitivity analysis is recommended to determine which of the input uncertainties to an inventory
contributes most substantially to the overall uncertainty, and to prioritise efforts to develop good estimatesof these key uncertainties (see Chapter 4, Methodological Choice and Identification of Key categories).
Step 3 typically involves; identification of candidate parametric PDFs to fit to the data, estimation of theparameters of such distributions, and evaluation of goodness-of-fit (e.g., Cullen and Frey, 1999). Rigorous
methods can be applied to data sets that contain values below the detection limit of a measurement method,
called non-detects (e.g., Zhao and Frey, 2004a). Distributions can be used in combination even when the datacontain two or more subgroups that cannot otherwise be separated (e.g., Zheng and Frey, 2004).

3.2.2.3

M ETHODS FOR ENCODING E XPERT J UDGEMENTS

When empirical data are lacking or are not considered fully representative for all causes of uncertainty (Table 3.1),
expert judgement may be necessary for estimating uncertainty. This section focuses on methods for encoding(quantifying) expert judgement regarding uncertainty in the form of PDFs. Encoding is the process of converting anexpert’s judgement regarding uncertainty into a quantitative PDF. Chapter 2 provides guidance on the definition ofan expert, considerations in choosing expert(s), sources of possible bias in expert judgement and how to avoid them,and a recommended protocol for expert elicitation. In the context of uncertainties, a key goal of expert elicitation is
to characterise the state of knowledge regarding possible values of a particular variable. Therefore, it is neither

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necessary nor desirable to attempt to force consensus among experts; rather, it is more useful to take into accountthe full range of values when obtaining judgements from two or more experts for the same variable.
The goal of the process of eliciting (obtaining) expert judgement is to develop a PDF taking into accountrelevant information such as:•

Is the category similar to others? How is the uncertainty likely to compare?

•

How well is the emission or removal process understood? Have all possible sources or sinks been identified?

•

Are there physical limits on how much the emission factor or other estimation parameter can vary? Massbalance considerations or other process data may place an upper limit on emissions or removal rates.

•

Are the emissions and removal estimates consistent with independent data that might be used to help verify
the inventory?

A key concern with expert elicitation is to overcome the typical heuristic biases of availability,
representativeness, and anchoring and adjustment (as described in Chapter 2, Annex 2A.1, Protocol for Expert
Elicitation) to avoid the potential problem of obtaining an ‘overconfident’ estimate of uncertainty.
‘Overconfidence’ refers to a situation in which the estimated range of uncertainty is too narrow. It is desirable to
avoid overconfidence so as not to underestimate the true uncertainty. It is good practice to use a formal
elicitation protocol, such as the Stanford/SRI protocol that is detailed in Chapter 2, Annex 2A.1. In particular,
these protocols include several steps prior to the actual encoding step for the purpose of familiarising the expert
with the purpose and methods of the elicitation and encouraging the expert to think about all relevant data,
models, theories, and other inference approaches. With this background, the expert is in a better position to makean unbiased estimate of uncertainty.
The method to be used for encoding should depend upon the expert’s familiarity with PDFs. Some commonlyused methods are:•Fixed Value: Estimate the probability of being higher (or lower) than an arbitrary value and repeat, typicallythree or five times. For example, what is the probability that an emission factor would be less than 100?

•

Fixed Probability: Estimate the value associated with a specified probability of being higher (or lower). For
example, what is the emission factor such that there is only a 2.5 percent probability (or 1 in 40 chance) thatthe emission factor could be lower (or higher) than that value.

•Interval Methods: This method focuses on the median and the quartiles. For example, the expert would be
asked to choose a value of the emission factor such that it is equally likely that the true emission factor
would be higher or lower than that value. This yields the median. Then the expert would divide the lower
range into two bins such that he or she felt it to be equally likely (25 percent probability) that the emission
factor could be in either bin, and this would be repeated for the other end of the distribution. Finally, either
fixed probability or fixed value methods could be used to get judgements for extreme values.

•

Graphing: The expert draws his/her own distributions. This should be used cautiously because some experts
are overconfident about their knowledge of PDFs.

An example of an expert elicitation that results in encoding (quantification) of a PDF is given in Box 3.1.
Sometimes the only available expert judgement will consist of a range, perhaps quoted together with a most
likely value. Under these circumstances the following rules are considered good practice:•

Where experts only provide an upper and a lower value, assume that the probability density function is
uniform and that the range corresponds to the 95 percent confidence interval.

•

Where experts also provide a most likely value (which is often likely to be the same as the point estimate
used in developing the inventory), assume a triangular probability density function using the most likely
values as the mode and assume that the upper and lower values each exclude 2.5 percent of the population.
The distribution needs not to be symmetrical. Other reasonable distribution choices, such as a normal or
lognormal distribution, can be made given appropriate justifications.

Some other sources of information on expert elicitation include Spetzler and von Holstein (1975), Morgan andHenrion (1990), Merkhofer (1987), Hora and Iman (1989), and NCRP (1996).
The subjective nature of expert judgement increases the need for quality assurance and quality control
procedures to improve comparability of uncertainty estimates between countries. Therefore expert judgements
should be documented as part of the national archiving process, and inventory compilers are encouraged to apply
QA/QC procedures to expert judgements, particularly for key categories (see Chapter 6).
Documentation requirements for expert judgement are discussed in Annex 2A.1 of Chapter 2.

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BOX 3.1
A BRIEF EXAMPLE OF DETAILED EXPERT JUDGEMENT

Suppose that the inventory compiler has identified an expert for emissions of CH4 from power
plants and wishes to obtain his/her judgement regarding the uncertainty in annual average
emissions for this category. As part of the motivation step, the elicitor has explained to the expert
the general purpose of the analysis and the expert elicitation protocol to be used. In the structuringstep, the elicitor works with the expert to set up the specific elicitation protocol. For example,
although all the inventory compiler may want is an annual average uncertainty estimate, the expert
may tell the elicitor that he/she prefers to provide judgements separately for start-up, part load, andfull load operation of the plant, and that these three judgements should be weighted in order tocome up with the combined uncertainty for an annual average. After structuring the problem, theelicitor then reviews the expert information relevant to the assessment, such as measurements that
may have been made on similar types of power plants or other combustion sources. In theelicitation step, the elicitor might ask the expert for an upper value such that there is only a one in
40 chance (2.5 percent probability) of obtaining a higher value. After getting the value, the elicitor
asks the expert to explain the logical basis for this estimate, such as the scenario of operation at theplant that might lead to such a high emission rate. Then the process might be repeated for the lower
end of the range, and perhaps for the median, 25th percentile, and 75th percentile. A mixture of
fixed value and fixed probability questions might be used. The elicitor should plot these on a graphso that any inconsistencies can be identified and corrected during the time available with theexpert. In the verification step, the elicitor would make sure that the expert is comfortable that theirjudgement has been well represented. The elicitor might also see how the expert would react to thepossibility of values outside of the interval for which judgements were provided, so as to ensurethat the expert is not being overconfident.

3.2.2.4

G OOD PRACTICE GUIDANCE FOR SELECTING PROBABILITYDENSITY FUNCTIONS

Prior to selecting a PDF, it is good practice to account for biases in the data to the extent possible. As noted
previously, data collection and QA/QC procedures can assist in preventing or correcting biases. For example, if
national statistics on timber harvest exist, but it is also suggested that these statistics have a bias of 5 percent,then the mean estimate can be adjusted by 5 percent prior to estimating the random component of the uncertainty.
It is good practice that adjustments for bias should be done in developing the point estimate emission inventory.
Another consideration is that the amount of bias can change over time as data measurement or collection
procedures change, or as the geographic and temporal scope of data collection changes. Thus, the bias
corrections may be different for different years.
However, to the extent that biases are believed or known to exist in data even after QA/QC procedures have been
applied, then either empirical or judgment based techniques can be applied to account for the bias. Apparent
biases can arise in probabilistic analysis for at least two reasons: (1) a fitted distribution may have a mean that isdifferent from the most likely value used in the point estimate of the inventory (e.g., a skewed triangular
distribution based on expert judgment); and (2) the mean value of a prediction from a nonlinear model that has
uncertain inputs can be different from the point estimate obtained from the same model if only point estimates ofthe mean values of the inputs are used. Thus, there are some types of biases that may be revealed only after an
uncertainty analysis has been done.

TYPES OF PROBABILITY DENSITY FUNCTIONSThere are many PDFs outlined in the statistical literature that often represent particular real situations. The
choice of a particular type of PDF depends, at least in part, on the domain of the function (e.g., can it have both
positive or negative values, or only non-negative values), the range of the function (e.g., is the range narrow ordoes it cover orders-of-magnitude), the shape (e.g., symmetry), and processes that generated the data (e.g.,
additive, multiplicative). These considerations are elaborated below in a brief discussion of many commonlyused distributions of practical importance. Examples of such functions and the situations they represent are4:

4

Further information on methods for developing distributions based upon statistical analysis of data are described andillustrated by Cullen and Frey (1999). Other useful references include Hahn and Shapiro (1967), Ang and Tang (1975)
D’Agostino and Stephens (1986), Morgan and Henrion (1990), and U.S.EPA (1996, 1997, 1999). Some examples ofprobabilistic analyses applied to emission inventories are given by Frey and Zheng (2002) and Frey and Zhao (2004).

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Chapter 3: Uncertainties•

The normal distribution is most appropriate when the range of uncertainty is small, and symmetric relative
to the mean. The normal distribution arises in situations where many individual inputs contribute to an
overall uncertainty, and in which none of the individual uncertainties dominates the total uncertainty.
Similarly, if an inventory is the sum of uncertainties of many individual categories, however, none of which
dominates the total uncertainty, then the overall uncertainty is likely to be normal. A normality assumption
is often appropriate for many categories for which the relative range of uncertainty is small, e.g., fossil fuelemission factors and activity data.

•

The lognormal distribution may be appropriate when uncertainties are large for a non-negative variable andknown to be positively skewed. The emission factor for nitrous oxide from fertiliser applied to soil provides
a typical inventory example. If many uncertain variables are multiplied, the product asymptoticallyapproaches lognormality. Because concentrations are the result of mixing processes, which are in turnmultiplicative, concentration data tend to be distributed similar to a lognormal. However, real-world data
may not be as tail-heavy as a lognormal distribution. The Weibull and Gamma distributions haveapproximately similar properties to the lognormal but are less tail-heavy and, therefore, are sometimes abetter fit to data than the lognormal.

•

Uniform distribution describes an equal likelihood of obtaining any value within a range. Sometimes theuniform distribution is useful for representing physically-bounded quantities (e.g., a fraction that must vary
between 0 and 1) or for representing expert judgement when an expert is able to specify an upper and lower
bound. The uniform distribution is a special case of the Beta distribution.

•

The triangular distribution is appropriate where upper and lower limits and a preferred value are provided
by experts but there is no other information about the PDF. The triangular distribution can be asymmetrical.

•

Fractile distribution is a type of empirical distribution in which judgements are made regarding the relative
likelihood of different ranges of values for a variable, such as illustrated in Figure 3.5. This type of
distribution is sometimes useful in representing expert judgement regarding uncertainty.

Figure 3.5

Examples of some commonly used probability density function models(e.g., based on Frey and Rubin, 1991)(b) TRIANGLE
Probability Density

Probability Density(a) UNIFORM

Value of
Variable(c) FRACTILE(d) NORMAL
Probability Density

Probability Density

Value of
Variable

Value of
Variable

Value of
Variable

Probability Density(e) LOGNORMAL

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ISSUES TO CONSIDER WHEN DEVELOPING THE PROBABILITY DENSITYFUNCTION
The following describes how inventory compilers can satisfy the principles of comparability, consistency andtransparency in emissions inventories when selecting a PDF:•

Where empirical data are available, the first consideration should be whether a normal distribution would beappropriate as a representation of uncertainty. If the variable must be non-negative, then the standard
deviation of the normal distribution should not exceed 30 percent of the mean value to avoid anunacceptably high probability of erroneously predicting negative values. Truncation of the lower tail of thenormal distribution should generally be avoided, because it changes the mean and other statistics of the
distribution. Typically, a better alternative to truncation is to find a more appropriate distribution that is abetter fit to the data. For example, for positively skewed data that must be non-negative, lognormal, Weibull,or Gamma distributions often can provide an acceptable fit; however, an empirical distribution of the data
can also be used;•

Where expert judgement is used, the distribution function adopted might typically be normal or lognormal,
supplemented by uniform, triangular, or fractile distributions as appropriate;•

Other distributions may be used where there are compelling reasons, either from empirical observations orfrom expert judgement supported by theoretical argument.

The issue of identifying which function best fits a set of data can be difficult. One approach is to use the squareof the skewness and the kurtosis to look for functional forms that can fit the data (Cullen and Frey, 1999).
Kurtosis and skewness should only be applied if there are sufficient data from which to estimate these values.
The function is then fitted to the data by least squares fit or other means. Tests are available to assess the
goodness-of-fit, including the chi-squared test and others (Cullen and Frey, 1999). In many cases, several
functions will fit the data satisfactorily within a given probability limit. These different functions can haveradically different distributions at the extremes where there are few or no data to constrain them, and the choiceof one function over another can systematically change the outcome of an uncertainty analysis. Cullen and Frey(1999) reiterate the advice of previous authors in these cases that it must be knowledge of the underlying physicalprocesses that governs the choice of a probability function. What the tests provide, in the light of this physicalknowledge, is guidance on whether this function does or does not satisfactorily fit the data.
In order to use empirical data as a basis for developing PDFs, the first critical step is to determine if the data are
a random, representative sample, in the case of a sample from a population. Some key questions to ask regarding
the data include:•

Are the data representative of the conditions pertaining to the emission or activity factors specific to national
circumstances? For example, in AFOLU, are the data representative of management practices and othernational circumstances?

•

Are the data a random sample?

•

What is the averaging time associated with the data set, and is it the same as for the assessment (which will
be for annual emissions in a given year)? For example, emissions data might be measured during a shorttime period and not for an entire year. Thus, expert judgment may be required in order to extrapolate shortterm data to a longer term basis.

If the data are a random, representative sample, then the distribution can be established directly using classicalstatistical techniques, even if the sample size is small. Ideally the available data will represent an annual average
but may be necessary to convert data using an appropriate averaging time. For normal distributions the 95
percent confidence interval would be plus or minus twice the estimated standard deviation of the population. In
other cases, the data may represent an exhaustive census of the sum of all activity (e.g., total energy use for aparticular fuel). In this case, information regarding errors in the measurements or survey instruments would forma basis for assessing uncertainty. The range of uncertainty of activity data might be bounded by using
independent methods or consistency checks. For example, fuel consumption data can be compared withestimates of production, including estimates of production via different methods.
There is a distinction between uncertainty in the mean and variability in the data for situations in which the data
represent intra-country variability within a category. Since the goal is to estimate annual average emissions at thelevel of an individual country, data that represent intra-country variability should be averaged over the entire
geographic area of the country, and uncertainty in this average should be assessed and used as the basis for theinventory. Conversely, if international data are available at an aggregate level, without supporting details as tohow such data can be disaggregated by country, there is a mismatch in scale that is more difficult to correct.
Typically, in this case, the uncertainty will tend to increase as the geographic scope decreases, i.e., if the numberof categories included decreases and if site-specific emissions data are not available. Thus uncertainty ranges

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Chapter 3: Uncertainties

that are developed for aggregated international data may have to be widened for applicability to individual
countries. In the absence of any empirical basis for estimating the relative range of uncertainty at the country
level versus the aggregated international level, expert judgement can be used.
For a sample of an underlying population, the need is to evaluate whether the data are random and representativeof the population. If so, classical statistical methods can be used to define the distribution. If not, then somecombination of data analysis and elicitation of expert judgement regarding distributions will be required. In theformer case, Cullen and Frey (1999) suggest exploration of the data set using summary statistics and graphics toevaluate essential features (e.g., central tendency, range of variation, skewness). The insights obtained byexamining the data, combined with knowledge of the processes that generated the data, should be consideredwhen selecting a mathematical or numerical representation of the distribution for input into Approaches 1 or 2.
(See Section 3.2.3.)
If a parametric distribution is selected as a candidate for fitting to the data set, techniques such as ‘maximum
likelihood estimation5’ or the ‘method of matching moments6’ can be used to estimate the parameters of the
distribution. The goodness-of-fit of the distribution can be evaluated in numerous ways, including comparison of
the fitted cumulative distribution function (CDF) with the original data set, probability plots, and goodness-of-fit
tests (e.g., Cullen and Frey, 1999). It is important that the selection of a parametric distribution to represent adata set should be based not solely upon goodness-of-fit tests, but upon similarities in processes that generated
the data versus the theoretical basis for a distribution (e.g., Hahn and Shapiro, 1967).
If the data are averaged over less than one year, it may be necessary to extrapolate the uncertainty over the year.
Consider an example in which the data set represents variability in daily average emissions measurements for aparticular category. One approach, described in detail by Frey and Rhodes (1996), is to fit a parametric
distribution to the data set for daily variability, use a numerical technique known as bootstrap simulation toestimate uncertainty in the parameters of the distribution, and use Monte Carlo simulation to simulaterandomised annual averages of the emission factor. Using bootstrap simulation, the uncertainty in the sampling
distribution for the parameters of the fitted distribution can be simulated (e.g., Efron and Tibshirani, 1993; Freyand Rhodes, 1996; Frey and Bammi, 2002).

DEPENDENCE AND CORRELATION AMONG INPUTSThis section provides a brief overview of issues pertaining to dependence and correlation among inputs. Moredetails on this topic can be found in Morgan and Henrion (1990), Cullen and Frey (1999), and Smith et al. (1992).
When setting up a probabilistic analysis it is preferable to define the model so that the inputs are as statisticallyindependent as possible. For example, rather than to try to estimate activity data for many subcategories forwhich data are derived at least in part by differences, it may be better to assign uncertainties to better known
aggregate measures of activity. For example, residential fuel use might be estimated as the difference between
total consumption and usage in the transportation, industrial, and commercial sectors. In this case, the estimate ofuncertainty in residential fuel use is negatively correlated with the uncertainties in fuel use in the othersubcategories, and may even be very large compared to the uncertainty in total consumption. Therefore, rather
than trying to estimate uncertainties separately for each subcategory, it may be more practical to estimate
uncertainty for aggregated categories, for which good estimates and cross-checks may be available.
Dependencies, if they exist, may not always be important to the assessment of uncertainties. Dependencies
among inputs will matter only if the dependencies exist between two inputs to which the uncertainty in theinventory is sensitive and if the dependencies are sufficiently strong. In contrast, weak dependencies among
inputs, or strong dependencies among inputs to which the uncertainty in the inventory is insensitive, will be ofrelatively little consequence to the analysis. Of course, some interdependencies are important and failure toaccount for those relationships can lead to misleading results. Positive correlations between inputs tend toincrease the range of uncertainty in the output, whereas negative correlations tend to decrease the range of
uncertainty in the output. However, positive correlations in uncertainties when comparing two years as part oftrend analysis will decrease uncertainty in the trend.
Techniques can be considered for incorporating dependencies into the analysis including:•stratifying or aggregating the categories to minimise the effect of the dependencies;

5

The method of maximum likelihood selects as estimates the values of the parameters that maximise the likelihood of theobserved sample (e.g., Holland and Fitz-Simons, 1982).

6

The method of moments finds estimators of unknown parameters by equating corresponding sample and population
moments. The method is easy to employ and provides consistent estimators. In many cases, the method of moments
estimators are biased (Wackerly, Mendenhall III and Scheaffer, 1996; pp. 395-397).

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modelling the dependence explicitly;•

simulating correlation using restricted pairing methods (that are included in many software packages);•use of resampling techniques in cases where multivariate datasets are available;•considering bounding or sensitivity cases (e.g., one case assuming independence and another case assuming
complete positive correlation); and•time series techniques can be used to analyse or simulate temporal autocorrelation.

As a simple example, Zhao and Frey (2004a) evaluated the implications of whether or not emission factor
uncertainty estimates for different categories obtained from the same data source should be considered as
dependent or independent among the categories, and found that it did not matter to the overall inventory
uncertainty. Of course, this result is specific to the particular case studies and should be tested in otherapplications. As a more complex example, given in Box 3.2, Ogle et al. (2003) accounted for dependencies intillage management factors, which were estimated from a common set of data in a single regression-type model,
by determining the covariance7 between factors for reduced tillage and no-till management, and then using that
information to generate tillage factor values with appropriate correlation during a Monte Carlo simulation8. One
should consider the potential for correlations among input variables and focus on those that would be likely tohave the largest dependencies (e.g., applying management factors for the same practice in different years of an
inventory, or correlations among management activities from one year to the next).
BOX 3.2
EXAMPLE OF MONTE CARLO UNCERTAINTY ASSESSMENT DEALING WITH CORRELATIONS

Ogle et al. (2003) performed a Monte Carlo analysis to assess uncertainty in a Tier 2 inventory that
addressed changes in soil C attributed to land use and management of agricultural lands in the
United States. Management factors were estimated from about 75 published studies using linear
mixed effect models. PDFs were derived for the management effect at a depth of 30 cm following
20 years after its implementation. Reference stocks were estimated using a National Soil Survey
Characterisation Database, which contained pedon data collected by United States Department ofAgriculture (USDA). PDFs were based on the mean and variance from about 3700 pedons, taking
into account the spatial autocorrelation of pedon locations due to clumped distribution patterns.
The land use and management activity data were recorded in the USDA National Resources
Inventory, which tracks agricultural land management at more than 400,000 point locations in the
United States, along with supplemental data on tillage practices provided by the Conservation
Technology and Information Center (CTIC). The Monte Carlo analysis was implemented using acommercially available software package and code developed by U.S. analysts. Their analysis
accounted for dependencies between estimation parameters that were derived from common
datasets. For example factors for set-aside lands and land use change between cultivated anduncultivated conditions were derived from a single regression analysis using an indicator variable
for set-asides, and hence were interdependent. Their analysis also accounted for dependencies in
the land use and management activity data. When simulating input values, factors were considered
completely dependent from the base and current year in the inventory because the relative
influence of management on soil C was assumed to be the same regardless of the year when apractice was implemented. As such, factors were simulated with identical random seed values. In
contrast, reference carbon stocks for the various soil types in each climate region were simulated
independently, with different random seeds, because stocks for each region were constructed fromseparate independent sets of data. U.S. analysts chose to use 50,000 iterations for their Monte
Carlo analysis. This was satisfactory because they were only reporting one digit after the decimal,and simulation results were considered relatively stable at that level of significance. Ogle et al.
(2003) estimated that mineral soils gained an average of 10.8 Tg C yr-1 between 1982 and 1997,
with a 95 percent confidence interval ranging from 6.5 to 15.3 Tg C yr-1. In contrast, managed
organic soils lost an average of 9.4 Tg C yr-1, ranging from 6.4 to 13.3 Tg C yr-1. Further, Ogle etal. (2003) found that the variability in management factors contributed 90 percent of the overall
uncertainty for the final estimates of soil carbon change.

7

The covariance between two variables (x and y) measures the mutual dependence between them. The covariance of asample consisting of n pairs of values is the total of the products of the deviation of individual x values from the mean x
value times the deviation of the corresponding individual y value from the mean of the y values, divided by (n-1).

8More discussion and examples of these types of methods are given in Cullen and Frey (1999), Morgan and Henrion (1990),
and USEPA (1996). These documents also contain reference lists with citations to relevant literature.

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Chapter 3: Uncertainties

3.2.3

Methods to combine uncertainties

Once the uncertainties in activity data, emission factor or emissions for a category have been determined, they
may be combined to provide uncertainty estimates for the entire inventory in any year and the uncertainty in theoverall inventory trend over time. Results from sampling theory, as described in Section 2.5.1, MeasurementBased Tier 3 Inventories, of Chapter 2 in Volume 4 for the AFOLU Sector, may be used in cases where
sampling is applied for direct measurement of, e.g., carbon stock changes. In these situations, sampling theory
provides an estimate of the uncertainty in emissions/removals for a given category, without need to separately
characterise an activity and emission factor.
Two approaches for the estimation of combined uncertainties are presented in the following sections: Approach
1 uses simple error propagation equations, while Approach 2 uses Monte Carlo or similar techniques. Either
Approach may be used for emission sources or sinks, subject to the assumptions and limitations of eachApproach and availability of resources. Complementary step by step explanation of the statistical calculation
methods of Approaches is given in Sections 3.7.1 and 3.7.2.
Biases should be addressed prior to applying either Approach 1 or 2, as set out in Section 3.2.2.1. For example, as
discussed in Section 3.2.2.1, an assessment of bias, and potential disagreements among modelling approaches,should be conducted, and any action identified to improve the inventory estimate should be taken. Approaches 1
and 2 focus on quantifying the random component of the uncertainty of the inventory results where known sourcesof bias have been removed. The inventory estimates may still include unknown bias and in the analysis all errors
are assumed behaving as random (Winiwarter and Rypdal, 2001).

3.2.3.1

A PPROACH 1: PROPAGATION OF ERROR

Approach 1 is based upon error propagation and is used to estimate uncertainty in individual categories, in theinventory as a whole, and in trends between a year of interest and a base year. The key assumptions,requirements, and procedures are described here.
Approach 1 should be implemented using Table 3.2, Approach 1 Uncertainty Calculation, that can be set up oncommercial spreadsheet software. The table is completed at the category level using uncertainty ranges for
activity data and emission factors consistent with the sectoral good practice guidance9. Different gases should beentered separately as CO2 equivalents.

KEY ASSUMPTIONS OF APPROACH 1
In Approach 1 uncertainty in emissions or removals can be propagated from uncertainties in the activity data,
emission factor and other estimation parameters through the error propagation equation (Mandel, 1984,
Bevington and Robinson, 1992). If correlations exist, then either the correlation can be included explicitly ordata can be aggregated to an appropriate level such that correlations become less important. Approach 1 also
theoretically requires that the standard deviation divided by the mean value is less than 0.3. In practice, however,
the approach will give informative results even if this criterion is not strictly met and some correlations remain.
Approach 1 assumes that the relative ranges of uncertainty in the emission and activity factors are the same in
the base year and in year t. This assumption is often correct or approximately correct. If any of the key
assumptions of Approach 1 do not apply, then either an alternative version of Approach 1 can be developed (e.g.,
see Section 3.4) or Approach 2 can be used instead.
Where the standard deviation divided by the mean is greater than 0.3 the reliability of Approach 1 can be
improved. The section ‘Dealing with Large and Asymmetric Uncertainties in the Results of Approach 1’ in thissection describes how to do this.

KEY REQUIREMENTS OF APPROACH 1
In order to quantify uncertainty using Approach 1, estimates of the mean and the standard deviation for each
input are required, as well as the equation through which all inputs are combined to estimate an output. The
simplest equations include statistically independent (uncorrelated) inputs.
9

Where estimates are derived from models, enter the uncertainty associated with the activity data used to drive the model,
and enter the uncertainty associated with the model parameters instead of the emission factor uncertainty. It may benecessary to use expert judgement, or error propagation calculations associated with the model structure. If it isimpractical to separate the uncertainty estimate obtained from a model for a category into separate activity and emission
factor components, then enter the total uncertainty for the category in the emission factor column and assign zero
uncertainty to the activity factor column.

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Once the uncertainties in the categories have been determined, they may be combined to provide uncertainty
estimates for the entire inventory in any year and the uncertainty in the overall inventory trend over time. As
discussed further below, these uncertainty estimates can be combined using two convenient rules for combining
uncorrelated uncertainties under addition and multiplication.

PROCEDURE OF APPROACH 1
The Approach 1 analysis estimates uncertainties by using the error propagation equation in two steps. First, theEquation 3.1 approximation is used to combine emission factor, activity data and other estimation parameter
ranges by category and greenhouse gas. Second, the Equation 3.2 approximation is used to arrive at the overall
uncertainty in national emissions and the trend in national emissions between the base year and the current year.

Uncertainty of an Annual Estimate
The error propagation equation10 yields two convenient rules for combining uncorrelated uncertainties under
addition and multiplication:•

Where uncertain quantities are to be combined by multiplication, the standard deviation of the sum will be
the square root of the sum of the squares of the standard deviations of the quantities that are added, with thestandard deviations all expressed as coefficients of variation, which are the ratios of the standard deviations
to the appropriate mean values. This rule is approximate for all random variables. Under typicalcircumstances this rule is reasonably accurate as long as the coefficient of variation is less thanapproximately 0.3. This rule is not applicable to division.
A simple equation (Equation 3.1) can then be derived for the uncertainty of the product, expressed inpercentage terms:
EQUATION 3.1
COMBINING UNCERTAINTIES – APPROACH 1 – MULTIPLICATIONU total = U 12 + U 22 + ... + U n2

Where:•

Utotal=the percentage uncertainty in the product of the quantities (half the 95 percent confidence
interval divided by the total and expressed as a percentage);Ui=

the percentage uncertainties associated with each of the quantities.

Where uncertain quantities are to be combined by addition or subtraction, the standard deviation of the sum
will be the square root of the sum of the squares of the standard deviations of the quantities that are addedwith the standard deviations all expressed in absolute terms (this rule is exact for uncorrelated variables).
Using this interpretation, a simple equation (Equation 3.2) can be derived for the uncertainty of the sum,
expressed in percentage terms:
EQUATION 3.2
COMBINING UNCERTAINTIES – APPROACH 1 – ADDITION AND SUBTRACTION
U total =(U 1 • x1 ) 2 + (U 2 • x 2 ) 2 + ... + (U n • x n ) 2
x1 + x2 + ... + x n

Where:
Utotal=xi and Ui =the percentage uncertainty in the sum of the quantities (half the 95 percent confidence
interval divided by the total (i.e., mean) and expressed as a percentage). This term
‘uncertainty’ is thus based upon the 95 percent confidence interval;
the uncertain quantities and the percentage uncertainties associated with them,
respectively.

The greenhouse gas inventory is principally the sum of products of emission factors, activity data and otherestimation parameters. Therefore, Equations 3.1 and 3.2 can be used repeatedly to estimate the uncertainty of the10

As discussed more extensively in Annex 1 of the Good Practice Guidance and Uncertainty Management (GPG2000, IPCC,
2000), and in Annex I of the Revised 1996 IPCC Guidelines (Reporting Instructions) (1996 IPCC Guidelines, IPCC, 1997).

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Chapter 3: Uncertainties

total inventory. In practice, uncertainties found in inventory categories vary from a few percent to orders ofmagnitude, and may be correlated. This is not consistent with the assumptions of Equations 3.1 and 3.2 that thevariables are uncorrelated, and with the assumption of Equation 3.2 that the coefficient of variation is less thanabout 30 percent, but under these circumstances, Equations 3.1 and 3.2 may still be used to obtain an
approximate result.

Uncertainty in the Trend
Trend uncertainties are estimated using two sensitivities:•

Type A sensitivity: the change in the difference in overall emissions between the base year and the current
year, expressed as a percentage, resulting from a 1 percent increase in emissions or removals of a given
category and gas in both the base year and the current year.

•

Type B sensitivity: the change in the difference in overall emissions between the base year and the current
year, expressed as a percentage, resulting from a 1 percent increase in emissions or removals of a given
category and gas in the current year only.

The Type A and Type B sensitivities are merely intermediate variables that simplify the calculation procedure.
The results of the analysis are not constrained to a change of only one percent, but instead depend upon the rangeof uncertainty for each category.
Conceptually, Type A sensitivity arises from uncertainties that affect emissions or removals in the base year andthe current year equally, and Type B sensitivity arises from uncertainties that affect emissions or removals in thecurrent year only. Uncertainties that are fully correlated between years will be associated with Type A
sensitivities, and uncertainties that are not correlated between years will be associated with Type B sensitivities.
Emission factor (and other estimation parameters) uncertainties will tend to have Type A sensitivities, andactivity data uncertainties will tend to have Type B. However, this association will not always hold and it ispossible to apply Type A sensitivities to activity data, and Type B sensitivities to emission factors to reflect
particular national circumstances. Type A and Type B sensitivities are simplifications introduced for theapproximate analysis of correlation.
Once the uncertainties introduced into the national inventory by Type A and Type B sensitivities have been
calculated, they can be summed using the error propagation equation (Equation 3.1) to give the overall
uncertainty in the trend.

Worksheet for Approach 1 Uncertainty Calculation
The columns of Table 3.2, Approach 1 Uncertainty Calculation, are labelled A to M and contain the following
information, of which the derivation of key equations is given in Section 3.7.1 in Section 3.7, TechnicalBackground Information.
•

A and B show the IPCC category and greenhouse gas.

•

C and D are the inventory estimates in the base year and the current year11 respectively, for the category andgas specified in Columns A and B, expressed in CO2 equivalents.

•

E and F contain the uncertainties for the activity data and emission factors respectively, derived from a
mixture of empirical data and expert judgement as previously described in this chapter, entered as half the
95 percent confidence interval divided by the mean and expressed as a percentage. The reason for halving
the 95 percent confidence interval is that the value entered in Columns E and F corresponds to the familiar
plus or minus value when uncertainties are loosely quoted as ‘plus or minus x percent’, so expert judgementsof this type can be directly entered in the spreadsheet. If uncertainty is known to be highly asymmetrical,
enter the larger percentage difference between the mean and the confidence limit.

•

G is the combined uncertainty by category derived from the data in Columns E and F using the error
propagation equation (Equation 3.2). The entry in Column G is therefore the square root of the sum of thesquares of the entries in Columns E and F.

•

H shows the uncertainty in Column G as a percentage of total national emissions in the current year. The
entry in each row of Column H is the square of the entry in Column G multiplied by the square of the entry
in Column D, divided by the square of total at the foot of Column D. The value at the foot of Column H isan estimate of the percentage uncertainty in total national net emissions in the current year, calculated fromthe entries above using Equation 3.1. This total is obtained by summing the entries in Column H and taking
the square root.

11

The current year is the most recent year for which inventory data are available.

2006 IPCC Guidelines for National Greenhouse Gas Inventories

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Volume 1: General Guidance and Reporting•

I shows how the percentage difference in emissions between the base year and the current year changes in
response to a one percent increase in category emissions/removals for both the base year and the current
year. This shows the sensitivity of the trend in emissions to a systematic uncertainty in the estimate (i.e., onethat is correlated between the base year and the current year). This is the Type A sensitivity as defined above.

•

J shows how the percentage difference in emissions between the base year and the current year changes in
response to a one percent increase in category emissions/removals in the current year only. This shows thesensitivity of the trend in emissions to random error in the estimate (i.e., one, that is not correlated, between
the base year and the current year). This is the Type B sensitivity as described above.

•

K uses the information in Columns I and F to show the uncertainty introduced into the trend in emissions byemission factor uncertainty, under the assumption that uncertainty in emission factors is correlated between
years. If the user decides that the emission factor uncertainties are not correlated between years then theentry in Column J should be used in place of that in Column I and the result multiplied by √2.

•

L uses the information in Columns J and E to show the uncertainty introduced into the trend in emissions byactivity data uncertainty, under the assumption that uncertainty in activity data is not correlated between
years. If the user decides that the activity data uncertainties are correlated between years then the entry in
Column I should be used in place of that in Column J and the √2 factor does not then apply.

•

M is an estimate of the uncertainty introduced into the trend in national emissions by the category inquestion. Under Approach 1, this is derived from the data in Columns K and L using Equation 3.2. The entry
in Column M is therefore the sum of the squares of the entries in Columns K and L. The total at the foot of
this column is an estimate of the total uncertainty in the trend, calculated from the entries above using theerror propagation equation. This total is obtained by summing the entries in Column M and taking thesquare root. The uncertainty in the trend is a percentage point range relative to the inventory trend. For
example, if the current year emissions are 10 percent greater than the base year emissions, and if the trend
uncertainty at the foot of Column M is reported as 5 percent, then the trend uncertainty is 10%±5% (or from
5% to 15% increase) for the current year emissions relative to the base year emissions.

•

Explanatory footnotes go at the bottom of the table and give documentary references of uncertainty data(including measured data) or other relevant comments.

An example of the spreadsheet with all the numerical data completed is provided in Section 3.6, Approach 1
uncertainty calculation example. Details of this approach are given in Section 3.7.1 and derivation of theuncertainty in the trend is in Section 3.7.2.

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2006 IPCC Guidelines for National Greenhouse Gas Inventories

Gas

CO2

CO2

…

IPCC
category

E.g.,
1.A.1.
EnergyIndustries
Fuel 1E.g.,
1.A.1.
EnergyIndustries
Fuel 2

Etc...

Gg CO2equivalent

Gg CO2equivalent∑D

Input data

Input data

∑C

Year temissions or
removalsD

Base year
emissionsor removals

C%

E2 + F2

Combined
uncertainty

G

Percentage uncertainty intotal inventory:%

Note A%

Input data

Note A

Emissionfactor /estimation
parameter
uncertainty

F

Input data

Activity
data
uncertainty

E

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Total

B

A

∑H

∑H

%

Note B(G • D )2(∑ D)2Type Asensitivity

I

Contribution
to Varianceby Category
in Year t

H

TABLE 3.2
APPROACH 1 UNCERTAINTY CALCULATION

%

D
∑C

Type Bsensitivity

J%

Trend uncertainty:%

Note DJ•E• 2I•F
Note C

Uncertainty in trend
in national emissions
introduced by activity
data uncertainty

L

Uncertainty in trend
in national emissions
introduced byemission factor /estimation parameter
uncertainty

K

∑M

∑M

%

3.31

K 2 + L2

Uncertainty
introduced into
the trend in total
national
emissionsM

Chapter 3: Uncertainties

Volume 1: General Guidance and Reporting

Note A:

Note B:

If only total uncertainty is known for a category (not for emission factor and activity data
separately), then:•If uncertainty is correlated across years, enter the uncertainty into Column F, and enter 0 inColumn E;•

If uncertainty is not correlated across years, enter the uncertainty into Column E, and enter 0
in Column F

Absolute value of:0.01 • D x + ∑ D i − (0.01 • C x + ∑ C i )∑ Di − ∑ Ci
• 100 −
• 100
(0.01 • C x + ∑ C i )∑ Ci

Where:Cx, Dx = entry from row x of the table from the corresponding column, representing a specificcategory∑ C i , ∑ D i = Sum over all categories (rows) of the inventory of the corresponding column

Note C:In the case where no correlation between emission factors is assumed, sensitivity B should be
used and the result multiplied by √2:
K x = J x • Fx • 2

Note D:In the case where correlation between activity data is assumed, sensitivity A should be used andthe √2 is not required:
Lx = Ix • Ex

DEALING WITH LARGE AND ASSYMMETRIC UNCERTAINTIES
Section 3.7.3 provides details on how the results from Approach 1 can be interpreted if the relative range of
uncertainty is large for a quantity that must be non-negative. The error propagation method that is the basis for
Approach 1 works well if the uncertainties are relatively small, meaning that the standard deviation divided by
the mean is less than 0.3. If the uncertainties are larger, Approach 1 may continue to be used, providing
informative results. However without any corrections, this approach will tend to underestimate uncertainty of themultiplicative (or quotient) terms. Furthermore, if the relative uncertainties are large for non-negative quantities,
then the uncertainty ranges are typically asymmetric, and Approach 1 does not quantify such asymmetry. A
second option is to use Approach 2, however this may not be always feasible. A third option is to use Approach
1 with corrections. For example, as discussed in more detail later in Section 3.7.3, an uncertainty of -65% to+126% relative to the mean might be estimated to be simply plus or minus 100 percent. This example can beproperly addressed with some corrections to the results of Approach 1. The advantage of using the correction
applied to Approach 1 (where applicable), rather than Approach 2, is that relatively simple spreadsheet-based
calculation methods can be used and it is not necessary to use specialised Monte Carlo simulation software.

3.2.3.2

A PPROACH 2: M ONTE C ARLO SIMULATIONThe Monte Carlo analysis is suitable for detailed category-by-category assessment of uncertainty, particularly
where uncertainties are large, distribution is non-normal, the algorithms are complex functions and/or there arecorrelations between some of the activity sets, emissions factors, or both.
In Monte Carlo simulation, pseudo-random samples of model inputs are generated according to the PDFs
specified for each input. The samples are referred to as ‘pseudo-random’ because they are generated by analgorithm, referred to as a pseudo-random number generator (PRNG), that can provide a reproducible series ofnumbers (according to the random seeds assigned as input to the PRNG) but for which any series has propertiesof randomness. Details are available elsewhere (e.g., Barry, 1996). If the model has two or more inputs, thenrandom samples are generated from the PDFs for each of the inputs, and one random value for each input isentered into the model to arrive at one estimate of the model output. This process is repeated over a desired
number of iterations to arrive at multiple estimates of the model output. The multiple estimates are sample valuesof the PDF of the model output. By analyzing the samples of the PDF for the model output, the mean, standard
deviation, 95 percent confidence interval, and other properties of the output PDF can be inferred. Because Monte

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2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

Carlo simulation is a numerical method, the precision of the results typically improves as the number of
iterations is increased. More details regarding the methodology of Monte Carlo simulation, as well as regarding
similar techniques such as Latin Hypercube sampling (LHS), are given by Hahn and Shapiro (1967); Ang andTang (1984); and Morgan and Henrion (1990).

KEY ASSUMPTIONS OF APPROACH 2
Under Approach 2, the simplifying assumptions required for Approach 1 can be relaxed. Thus, numericalstatistical techniques, particularly the Monte Carlo technique, as they can be generally applied, are more
appropriate than Approach 1 for estimating uncertainty in emissions/removals (from uncertainties in activity
measures and emission factors/estimation parameters) when:•

uncertainties are large;•

their distribution are non-Gaussian;•algorithms are complex functions;•correlations occur between some of the activity data sets, emission factors, or both;•

uncertainties are different for different years of the inventory.

KEY REQUIREMENTS OF APPROACH 2
Monte Carlo simulation requires the analyst to specify PDFs (see Fishman, 1996) that reasonably represent eachmodel input for which the uncertainty is quantified. The PDFs may be obtained by a variety of methods, as
described in Section 3.2.2.4 including statistical analysis of data or expert elicitation. A key consideration is todevelop the distributions for the input variables to the emission/removal calculation model so that they are based
upon consistent underlying assumptions regarding averaging time, location, and other conditioning factors
relevant to the particular assessment (e.g., climatic conditions influencing agricultural greenhouse gas emissions).
Monte Carlo analysis can deal with probability density functions of any physically possible shape and width, as well as
handling varying degrees of correlation (both in time and between source/sink categories). Monte Carlo analysis candeal with simple models (e.g., emission inventories that are the sum of sources and sinks, each of which is estimatedusing multiplicative factors) as well as more complex models (e.g., the first order decay for CH4 from landfills).

PROCEDURES OF APPROACH 2
The principle of Monte Carlo analysis is to select random values of emission factor, activity data and otherestimation parameters from within their individual probability density functions, and to calculate the corresponding
emission values. This procedure is repeated many times, using a computer, and the results of each calculation run
build up the overall emission probability density function. Monte Carlo analysis can be performed at the category
level, for aggregations of categories or for the inventory as a whole. Statistical software packages are readily
available – some of which include Monte Carlo algorithms that are very user-friendly12.
Like all methods, Monte Carlo analysis only provides satisfactory results if it is properly implemented. Thisrequires the analyst to have scientific and technical understanding of the inventory. Of course, the results will
only be valid to the extent that the input data, including any expert judgements, are sound.
The Monte Carlo approach consists of four clearly defined steps shown in Figure 3.7. Only the first of theserequires effort from the user, the remainder being handled by the 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 inventory compiler may decide to set up its own programme torun a Monte Carlo simulation; this can be done using statistical software. The Section, ‘Choosing a simulation
technique and sample size’ below contains a short discussion of various software packages.

12

Winiwarter and Rypdal (2001), Eggleston et al. (1998) and Monni et al. (2004) provide examples of Monte Carlo analysis
applied to national greenhouse gas inventories to estimate uncertainties both in overall emissions and emissions trends.
Another example of the use of Monte Carlo analysis is given in McCann et al. (1994). More detailed descriptions andapplications of this method are presented in Bevington and Robinson (1992), Manly (1997), Morgan and Henrion (1990),
and Cullen and Frey (1999). A brief example of the application of Monte Carlo analysis is provided in Box 3.2 based on
Ogle et al. (2003).

2006 IPCC Guidelines for National Greenhouse Gas Inventories

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Volume 1: General Guidance and Reporting

Figure 3.6

Illustration of Monte Carlo method

V alueV alu eV a lue

V alueS o u rce C
Probability

Probability

S o u rc e B
Probability

Probability

S o u rc e A

Probability

Probability

S tep 1 – S p ecify U n ce rtain ties, W id th an d P ro b a b ility D en s ity F u n c tio n s(P D F s) fo r all in p u t d ata

V alu eV a lue

S tep 2 - S e le ct v a lu e s fo r v ariab les fro m th e p ro b ab ility d istrib u tio n s
S e le ct
ran d om va lu eof E m ission
F a ctor fromd istribu tion

S e le ct
ra nd om va lu eof A ctivity
D a ta fro m
d istrib utio n

S elect
ran do m valueo f E m ission
F a ctor fro m
d istrib u tion

S e le ct
ra nd om va lu eof A ctivity
D a ta fro m
distribu tio n

S e le ct
ra nd o m va lu eo f E m ission
F acto r from
distrib utio n

S elect
ran do m valueo f A ctivity
D ata fromd istrib u tion

S tep 3 - C alcu late E m is s io n s in th e co n v en tio n al w a y
E stim ate
E m issio ns M ultiply N um b ers

E stim a te
E m issio ns M u ltiply N u m be rs

E stim a te
E m ission s M u ltiply N u m be rs

A d d se ctor
e m ission s to give
to tal

S tep 4 - Ite rate an d m o n ito r re s u lts
S tore E m ission
T o tal inda tab ase ofre sults

C a lcula te ove ra ll
m ea n a nd
u nce rtain ty fro mda tab ase of re sults

R ep e at S te p 2

M o re ite ra tio ns req u ire d

R e p ea t u n til m ea na n d distrib utio n d o
n ot cha nge

F in is h e d

Step 1: Specify category uncertainties. This includes estimation parameters and activity data, their associatedmeans and PDFs, and any correlations. The uncertainties can be assessed following the guidance in Sections
3.2.1 and 3.2.2. For guidance on assessment of correlations, see ‘Dependence and correlation among inputs’ inthis section and Box 3.2.
Step 2: Select random variables. Select input values. Input values are the estimates applied in the inventory
calculation. This is the start of the iterations. For each input data item, a number is randomly selected from the
PDF of that variable.
Step 3: Estimate emissions and removals. The variables selected in Step 2 are used to estimate annual
emissions and removals based on input values. Correlations of 100 percent are easy to incorporate, and goodMonte Carlo packages allow other correlations to be included. Since the emission calculations should be the

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2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

same as those used to estimate the national inventory, the Monte Carlo process could be fully integrated into theannual emission estimates.
Step 4: Iterate and monitor results. Iterate and monitor results. The calculated total from Step 3 is stored, and theprocess then repeats from Step 2. The results from the repetitions are used to calculate the mean and the PDF.

APPROACH 2 UNCERTAINTIES IN TRENDS
The Approach 2 Monte Carlo method can be used to estimate uncertainties in the trend as well as in the absoluteemission 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 itneeds to be done for both the base year and the current year, and relationships between the data need to beconsidered. 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 selectedfrom it is used for each year in step 3. Changes in the technologies or practices will alter the emission factor overtime. 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 andalso 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 wellenable 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 toestimate 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

2006 IPCC Guidelines for National Greenhouse Gas Inventories

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Volume 1: General Guidance and Reporting

Figure 3.7

Calculation scheme for Monte Carlo analysis of the absolute emissions and thetrend of a single category, estimated as emission factor times an activity rate

Source 1

Source 1

Source 1

Source 1

Source 1

Source 1

Source 1

Emission
Factor 1

Activity
data
Base Year

Activity
dataYear tEmissionfactor 1
Base Year

Emissionfactor 1
Year tActivity
data
Base Year

Activity
dataYear tfind pdf

find pdf

find pdf

find pdf

find pdf

find pdf

find pdf

Selectfrom
pdf

Selectfrom
pdf

Selectfrom
pdf

Selectfrom
pdf

Selectfrom
pdf

Selectfrom
pdf

Selectfrom
pdf

Emission
Base Year =Emis . Factor
x Activity

Emission
Year t =Emis. Factor
x Activity

Emission
Base Year =Emis. Factor
x Activity

Emission
Year t =Emis . Factor
x Activity

Trend =
(Emission Year t Emission in Base Year)/ Emission in Base Year

Trend =
(Emission Year t Emission in Base Year)/ Emission in Base year

Case where the emission factor is
100% correlated between base year andyear t (e.g., the same emission factor isused in each year and there is noyear to year variation expected )Case where the emission factor is notcorrelated between in base year andyear t (e.g., emission factor for coal
where fuel varies from year to year
or where technologies change )CHOOSING A SIMULATION TECHNIQUE AND SAMPLE SIZE
Several commercially available software tools can be used to perform Monte Carlo simulation. These tools canbe stand-alone or used as add-ins to commonly used spreadsheet programs. Many software tools offer an optionof different sampling methods, including random Monte Carlo simulation and variations of Latin Hypercube
Sampling (LHS), which can produce ‘smoother’ looking model output distributions for sample sizes of only a
few hundred samples. The disadvantage of using LHS is that one must decide ahead of time how many iterations
to use. This is because two or more LHS simulations cannot be combined since they will use overlapping strata,
leading to difficulties in interpreting results. In some cases, LHS can yield underestimates of the higher momentsof PDFs, since the stratification method also can preclude clustering of very high or low values as can occur in
random data sets. The overall suggestion is to use random Monte Carlo simulation as the default method,
because it will give flexibility to continue a random simulation to larger and larger simulation sample sizes ifnecessary until the model output distribution converges14 .

14

Cullen and Frey (1999) provide more information on the comparison of LHS and Monte Carlo simulation (pp. 207-213).

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2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

The number of iterations can be determined either by setting the number of model runs, a priori, such as 10,000 andallowing the simulation to continue until reaching the set number, or by allowing the mean to reach a relatively
stable point before terminating the simulation. For example, when the estimate for the 95 percent confidence range
is determined to within ± 1%, then an adequately stable result has been found. This can be checked by plotting afrequency plot of the estimates of the emission. This plot should be reasonably smooth (see Figure 3.8).
Another alternative is to assess the precision of the current number of replicates based on the standard errors of
the percentiles that were used to construct 95 percent confidence intervals. If the range of the confidence
intervals for each percentile (2.5 and 97.5) is less than the reported precision, then the number of iterations
should be adequate (e.g., emissions are reported values to a single digit after the decimal and the percentile
confidence intervals are less than 0.1, such as 0.005). Therefore, the Monte Carlo percentile estimates areunlikely to change in the reported digits for other simulations with the same number of iterations.
Figure 3.8

Example frequency plots of the results of a Monte Carlo simulation

30

Number of cases
Insuffient iterations to give reliable
results.
Enough iterations to give a reliable
estimate of the uncertainty.

20

15

10

5

Total
Emission
01040

3.2.3.3

1060

1080

1100

1120

1140

1160

H YBRID COMBINATIONS OF A PPROACHES 1 AND 2

For some inventories, it may be possible to use Approach 1 for most but not all of the source and sink categories.
For example, many sources and sinks can be quantified using emission factors and activity data, but for some itis necessary to use a model or a more complex calculation procedure. Furthermore, dependencies may be
important for some categories but not others, or the range of uncertainties may be large for some categories andnot others. For these cases, a Monte Carlo-based method is more flexible and would typically produce better
results.
If an inventory compiler has completed Approach 2 for only a subset of categories, the results can be combinedwith Approach 1 to produce an estimate of the uncertainty in national total emissions and the trend. This can beachieved by entering information at a disaggregated level, if correlations do not prevent doing so, into Approach
1. If there are significant correlations among a subset of categories, then the subset could be treated individuallyin Approach 2 but as an aggregation of categories in Approach 1. In the latter case, total emissions for theaggregation of the subset in the base year and in year t is entered in Columns C and D of the Approach 1 table.
The results of the Approach 2 analysis for the uncertainty in total emissions in year t will be entered in Column
G, and the results of the Approach 2 analysis for the contribution to the trend in national total emissions will beentered in Column M. The uncertainty contributions of the affected categories can be combined with those ofother categories using the error propagation rules of Approach 1.
In some cases, most of the category uncertainties in an inventory might be estimated using Approach 2, withrelatively few estimated using Approach 1. It is possible to incorporate Approach 1 estimates of uncertainty for2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.37

Volume 1: General Guidance and Reportingsome categories into an Approach 2 methodology for combining uncertainties for the total inventory. This isdone by using the uncertainty half-range obtained from Approach 1 to specify an appropriate PDF model torepresent uncertainty for each category as part of the Monte Carlo simulation. Typically, a normal distribution
would be a reasonable choice if the uncertainty range is small enough and a lognormal distribution is often
appropriate if the uncertainty range is large. See also the section of ‘Dealing with Large and Asymmetric
Uncertainties in the Results of Approach 1’ in Section 3.2.3.1 for more discussion of normal versus lognormal
distribution assumptions.

3.2.3.4

C OMPARISON BETWEEN A PPROACHESTwo Approaches for uncertainty analysis have been presented:•

Approach 1: Estimation of uncertainties by category using Equations 3.1 and 3.2, and simple combination of
uncertainties by category to estimate overall uncertainty for one year and the uncertainty in the trend.

•

Approach 2: Estimation of uncertainties by category using Monte Carlo analysis, followed by the use ofMonte Carlo techniques to estimate overall uncertainty for one year and the uncertainty in the trend.

Monte Carlo analysis can also be used in a restricted way within Approach 1 to combine activity data andemission factor uncertainties that have very wide or non-normal PDFs or both. This approach can also help deal
with categories within Approach 1 that are estimated by process models, rather than by the classical ‘emission
factor times activity data’ calculation. The choice between Approaches is discussed in Section 3.2.3.5 below.
Use of either Approach will provide insight into how individual categories and greenhouse gases contribute touncertainty in total emissions in any year and to the emissions trend over time.
Application of Approach 2 to the UK inventory (Baggott et al., 2005) suggests that the 95 percent confidence
interval is asymmetric and lies between about 6 percent below and 17 percent above the mean estimated value in2003. The result for the UK takes into account the large relative range of uncertainty for N2O flux from soils aswell as the large contribution to total emissions from fossil fuel combustion. Application of Approach 1 to thesame inventory suggests an uncertainty of about ±17%. On the trend, between 1990 and 2003, UK total net
emissions in CO2 equivalent are estimated to have fallen by 13 percent. Application of the Approach 2 suggeststhat 95 percent confidence interval is roughly symmetrical and lies between -11% and -16%. The corresponding
Approach 1 result gives a range of about ±2% (i.e., -11% to -15%). So both methods give similar magnitudes inthe trend uncertainty.
In the case of Finland, as shown in Section 3.6, year 2003 uncertainty (including both sources and sinks ofgreenhouse gases) was -14 to +15% according to Approach 2, and ±16% with Approach 1. For Finland, carbon
stock changes in the AFOLU Sector are the dominant sources of uncertainty, while fossil fuels contribute thelargest share to total emissions. Since the approximations inherent in Approach 1 mean that it cannot deal withasymmetry, this comparison is encouraging. Physically, the reason for the asymmetry identified under Approach
2 is that the uncertainty range of some very uncertain categories is constrained by the knowledge that theemissions cannot be less than zero. The Approach 2 method can make use of this extra knowledge, but the
Approach 1 method cannot. In case of trend from 1990 to 2003 the uncertainty in Finland was -18 to +23%
(percentage points) with Approach 2 and ±19% (percentage points) with Approach 1.
A separate evaluation of Approach 1 and Approach 2 for case studies based on synthetic inventory data revealed
excellent agreement when the same set of input assumptions were used and when uncertainties were relatively
small (Frey, 2005). For example, in a case study for which Approach 1 produced an estimate of ±6% in thecurrent year inventory, and ±10% in the trend (in terms of percentage points relative to the mean percentagechange), results from Approach 2 for the same input assumptions produced essentially the same result. When theuncertainty ranges were doubled for the emission factors and activity data, the uncertainty in the base estimatescontinued to agree well for Approach 1 and Approach 2, at approximately ±13% of the mean total emissions.
The uncertainty in the trend was approximately ±20% (percentage points) in both cases. However, theuncertainty in the trend was slightly asymmetric in the Approach 2 result, at -19% to +22%. Thus, as the rangesof uncertainty increase, it is expected that Approach 2 will more appropriately characterise the range andskewness of uncertainties than Approach 1.
Although Approaches 1 and 2 focus on propagation of the random component of uncertainty through a model, it
is good practice to combine methods for dealing with model uncertainty with either of the Approaches. An
example of how to deal with model uncertainty in the context of Tier 3 is given in Box 3.3.
Furthermore, although Approach 1 is based upon key simplifying assumptions, it is possible to increase theflexibility of this approach by increasing the complexity of the error propagation equations. For example, error

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2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

propagation equations that contain additional terms can more accurately propagate uncertainty for multiplicativeand quotient models and when uncertainties are skewed.

BOX 3.3
DEALING WITH MODEL UNCERTAINTY IN A PROBABILISTIC ANALYSIS

A Tier 3 modelling approach is designed for flexibility so that a national inventory can be
conducted using a more highly refined model representing national circumstances than in Tier 1 or
2. In particular, it is good practice to address uncertainties attributed to model inputs and structure.
Input uncertainty deals with activity data and possibly other ancillary information that is needed todescribe the environmental setting, such as climate and soil characteristics in an inventory for the
AFOLU Sector. Uncertainty in model structure is attributed to imperfect algorithms andparameterisation. Empirically-based approaches are commonly used for assessing structural
uncertainties (Monte et al. 1996). This approach involves comparing modelled emissions estimateswith measurements from experiments or a national monitoring network, which was designed forvalidation of model-based inventories, addressing both the bias and variance in modelled values(Falloon and Smith 2003).
A statistically-derived relationship may be used to quantify uncertainties in model structural error
for a Tier 3 inventory, addressing imprecision based on the estimated variance, or a similar
measure such as the Root Mean Squared Error, while also dealing with biases based on statisticallysignificant differences between modelled and measured values (Falloon and Smith 2003). In
practice, modelled emissions would be adjusted for biases to more accurately represent emissions
for reporting purposes. Further, a statistically-derived relationship would yield a measure ofvariance for each condition that would be associated with the modelled values, similar to
uncertainties attributed to emission factors in Tier 1 and 2 approaches. To complete theassessment, uncertainties in model inputs, such as activity data, would be combined with model
structural uncertainty using error propagation equations or a Monte Carlo approach.

3.2.3.5

G UIDANCE ON CHOICE OF A PPROACH

Where the conditions for applicability are met (relatively low uncertainty, no correlation between sources except
those dealt with explicitly by Approach 1), Approach 1 and Approach 2 will give identical results. However, andperhaps paradoxically, these conditions are most likely to be satisfied where Tier 2 and Tier 3 methods arewidely used and properly applied in the inventory, because these methods should give the most accurate andperhaps also the most precise results. There is therefore no direct theoretical connection between choice ofApproach and choice of Tier. In practice, when Tier 1 methods are applied, Approach 1 will usually be usedwhile the ability to apply Approach 2 is more likely where Tier 2 and 3 methods are being used, moreover for
quantifying the uncertainty of emissions/removal estimates of complex systems such as in the AFOLU Sector.
When Approach 2 is selected, as part of QA/QC activities inventory agencies also are encouraged to apply
Approach 1 because of the insights it provides and because it will not require a significant amount of additional
work. Where Approach 2 is used, its estimates of overall uncertainty are to be preferred when reporting
uncertainties (see Section 3.2.3.3).

3.3

UNCERTAINTY AND TEMPORALAUTOCORRELATION

Where emission factors, sources of activity data or estimation methods vary within a time series the associatedsources of uncertainty may also change. Approach 2 can take explicit account of this when setting up thecomponent PDFs. In Approach 1 the current percentage uncertainties should be entered in the table, and in cases
where changes throughout the time series mean that the assumption of good correlation of uncertainty inemission factors between years is no longer valid, Type A sensitivity should be used in place of Type B. Ifannual data are autocorrelated, then there will typically be less difference when comparing two years than if they
are not autocorrelated, assuming that the autocorrelation is positive.
The issue of ‘time series’ can refer to inter-annual comparison of emissions in a Year t versus a base year, as has
been set forth in Table 3.2 and the general reporting table given in Table 3.3, or it can refer to a broader set of2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.39

Volume 1: General Guidance and Reporting

statistical methodologies for taking into account temporal autocorrelation. With regard to the latter interpretation,
statistical time series techniques can be used to more accurately take into account temporal autocorrelations inorder to reduce the estimate of uncertainty. For example, if emissions vary on a short term basis, such as for
power plant emissions, the emissions at a given time period often depend on what the emissions were in theimmediately preceding time periods as well as on the emissions at previous points in a cycle. For example, apower plant may require some amount of time in order to achieve a significant change in load. Thus, theemissions in a current hour are constrained somewhat depending on what emissions were in the previous hour.
Furthermore, a power plant may respond to daily fluctuations in load, which are similar from one day to the next.
Thus, the emissions at a given hour of the day may be correlated to those at a given hour of a preceding day.
Likewise, there can be longer-term seasonal cycles, such as from one year to the next, that might induce a
temporal correlation. Statistical time series methods can be fit to an adequate sample of empirical data in order toexplain these temporal correlations. The unexplained portion of the model response is referred to as a random orwhite noise term. The white noise term is an indication of uncertainty in the ability to predict the emissions
output. A detailed example of the application of time series models to emissions estimation is given by AbdelAziz and Frey (2003).

3.4

USE OF OTHER APPROPRIATE TECHNIQUESThe guidance offered here is not meant to preclude the use of other improved methods. For example, in applying
Approach 1, an inventory compiler may wish to derive a similar approach from the generalised error propagation
equations in order to account for more complex correlations or for differences in ranges of uncertainty in year t
versus the base year. Such improvements are consistent with good practice as long as they are appropriately
documented and justified. Furthermore, this document does not cover all situations that may be faced by ananalyst. Therefore, the inventory compiler is encouraged to refer to the references cited in the end of the chapter
for additional suggestions on how to perform uncertainty analyses.

3.5

REPORTING AND DOCUMENTATIONA great deal of effort can be expended in collecting information and data for a quantified uncertainty assessment
and implementing a model to combine uncertainties across parameters, categories, and the entire inventory.
However, all that effort can result in little benefit to a country’s inventory if steps are not also taken to report anddocument the findings of an uncertainty assessment so that they can lead to real improvements in the quality ofdata collected and the inventory as a whole. The integration of a country’s uncertainty assessment efforts with
the implementation of data quality investigations within its QA/QC system can help solve this problem.
Given the large number of inputs and assumptions needed to document an uncertainty analysis, it is not feasible
to report all information. The information reported should be sufficient to provide the key assumptions, choice of
methods and detailed results. Overall, documentation should be sufficient to support the estimates and enable
duplication of the uncertainty estimates. In particular, the documentation should touch upon the following issues(as they pertain to a particular variable):•

Which causes of uncertainty are addressed (see Table 3.1).

•

Which methods for addressing uncertainty were used (see Table 3.1).

•

What is the source of any data or models that were used as the basis for estimating uncertainty.

•

For an estimate of bias, explain what is the magnitude of the error expressed on a relative or absolute basis
as appropriate (specify which and give proper units).

•

If uncertainty was estimated based upon data, explain how uncertainty was distinguished from variability
and how the appropriate geographic extent, averaging time (e.g., annual), and other representativenessconsiderations were addressed in selecting and analyzing data. Provide a brief summary of the data itself,
including the mean, sample standard deviation, and sample size. Provide additional detail as appropriate if
data were stratified or contain other components of uncertainty (e.g., precision and accuracy of measurement
methods used to obtain the data).

•

For an estimate of random error in the form of a range or a distribution, provide sufficient information touniquely specify the range (e.g., plus or minus percentage variation relative to the mean, or parameters of a
PDF).

3.40

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties•

For estimates of uncertainty based upon expert judgement, the following information should be documented
and archived:(i)reference number for judgement;

(ii)

date;

(iii)

name of expert(s) involved;(iv)

experts’ background (references, roles, etc.);(v)

the variable being judged;(vi)

the logical basis for judgement, including any data taken into consideration. This should include therationale for the high end, low end, and central tendency of the distribution;(vii)

the resultant PDF, or the range and most likely value and the PDF subsequently inferred;(viii)

identification of any external reviewers;(ix)

results of any external review;(x)

approval by inventory compiler, specifying date and person.

•

Explanation of any correlation or dependencies that were accounted for between two or more inputs or withrespect to autocorrelation.

•

Explanation of any special considerations that might be unique to a particular country or situation, such as
the use of various statistical techniques for dealing with non-detects, mixture distributions, extrapolation,and so on.

•

Explanation of differences in results between Approach 1 and 2.

In addition to documentation of the uncertainty estimates for inputs to an inventory, documentation should be
provided regarding the general approach used and whether it is based primarily on Approach 1 or Approach 2.
Any modifications to these Approaches should be explained and appropriately justified.
The reporting of uncertainties also requires a discussion of limitations and caveats for any quantitative
uncertainty estimates produced that are suspected to present an incomplete representation of all causes of
uncertainty. During the process of collecting information on inputs for an uncertainty assessment (e.g., empiricalor expert judgement as a basis for PDFs, characterisations of conceptualisation and model uncertainty), the likely
causes of the various uncertainties identified—including potential biases—should be documented. These likely
causes should be documented whether or not they were quantified and include any specific recommendations
available regarding how they can be reduced.
Similarly, when reporting and interpreting the results from a quantitative uncertainty assessment, it is importantto keep in mind the limitations of the approach used to combine uncertainties. For example, although Approach 1
can address some causes of correlation, any possible biases associated with other causes of correlations thatmight exist (e.g., between categories) that are identified in the course of an uncertainty assessment should be
documented.
Table 3.3 is a generalised table for reporting uncertainty of an inventory, regardless of the Approach followed. If
the point estimate and the mean estimate of emissions/removals are not the same value, it is good practice for theuncertainty ranges shown in Columns E, F, G, and J to be estimated relative to point estimates used whenreporting the national inventory. If the point estimate and the mean estimates differ, then it is advisable toconsider why they differ and possibly revisit the point estimate in order to identify and account for bias.

2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.41

Gas

CO2

CO2

…

IPCC
category

E.g.,
1.A.1.
EnergyIndustries
Fuel 1E.g.,
1.A.1.
EnergyIndustries
Fuel 2

Etc...

Year temissions/removals

Gg CO2equivalent

Gg CO2equivalentD

Base year
emissions/removals

C(-)%

Activity data
uncertainty

E

(+)%

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Total

B

A

Volume 1: General Guidance and Reporting

(-)%

(+)%

Emissionfactor/estimation
parameter uncertainty(combined if more than
one estimation parameteris used)F(-)%

Combined
uncertainty

G

(+)%

H

1.000

(fraction)

Contribution
to variancein Year t

TABLE 3.3
GENERAL REPORTING TABLE FOR UNCERTAINTY(% of base year)

Inventory trend innational emissions
for year t increase
with respect to base
year

I

(-)%

(+)%

Uncertainty
introduced into thetrend in total nationalemissions withrespect to base year

J

Approach andComments

K

3.42

Chapter 3: Uncertainties

Notes:
Column C: Base year emissions in Gg CO2 equivalent by category and gas.
Column D: Year t emissions in Gg CO2 equivalent by category and gas. Year t is the year of interest or the current
year.
Columns E and F: Uncertainties in activity and emission factor estimates (Columns E and F) should be reported
where possible, but it is understood that some calculation methods for some categories may not be
amenable to this type of reporting. Thus, where this information is not available, the table entry canbe left blank.
Column G: An uncertainty estimate for each category should be reported, relative to the mean estimate, even if
uncertainties cannot be further disaggregated by activity and emission factor in a particular case. For
the foot of the table, report the uncertainty in the total inventory. This must be obtained through theApproach 1 or 2 calculations, and cannot be determined simply by summing quantities in the columns.
Column H: Report the ‘contribution to uncertainty’. It is estimated dividing the variance of each category by
the total variance of the inventory ( σ x2 ∑ σ x2 ). If Approach 1 has been used, it is calculated
dividing each entry in Column H of Table 3.2 by the value, in the same column, in the line ‘Total’of Table 3.2. General methodology to be applied when Approach 2 is used and when uncertainty isasymmetric is provided in Section 3.2.3.
Column I: Report the inventory trend, estimated as:⎛ Year t emissions − Base year emissions ⎞⎟⎟ • 100 .
Mean Trend (%) = ⎜⎜Base year emissions⎝⎠

Report separately for each category by row and report for the total inventory at the foot of the column.
Column J: This is the uncertainty in the trend by category. For the ‘total’ at the foot of the table, the overall
uncertainty in the trend for the entire inventory should be given. The uncertainty in the trend isbased on percentage points with respect to the inventory trend. For example, if the inventory trend
is -5%, and if the 95% probability range of the trend is -8% to -3%, then the uncertainty in trend isreported as -3% to +2%.
Column K: Indicate whether Approach 1 or Approach 2 was used, and include any other comments that might
help clarify the methodology or information sources.
General Comments on Columns E, F, G, and J: For each of these columns, two subcolumns are provided tofacilitate reporting of uncertainty ranges that are asymmetric. For example, if the uncertainty range is -50% to+100%, then ‘50’ should be reported the subcolumn headed as ‘(-)%’ and ‘100’ should be reported in the column
headed as ‘(+)%’.

3.6

EXAMPLESThis section presents two examples of uncertainty estimates for inventories, both based upon the Finnish 2003
greenhouse gas emission inventory. These examples are country-specific and are shown here only for the purpose ofillustrating procedures and general insights. The specific uncertainty estimates and results will differ among countries.
The example of Table 3.4 is based upon Approach 1, and is shown in the general format of the Approach 1 worksheet(Table 3.2). The results indicate that the net emissions in year t, which is 2003 in this example, is 67,730 Gg CO2
equivalent with an uncertainty of ±15.9%, which corresponds to a 95 percent probability range of 56,970 to 78,490 Gg
CO2 equivalent. Based upon the total base year and year t inventories reported in the table, the average trend is a 42
percent increase in emissions from 1990 to 2003. The uncertainty in the trend is ±19% (percentage points), whichcorresponds to a 95 percent probability range for the trend of 24% to 61% with respect to the base year emissions.
The example of Table 3.5 is based upon Approach 2, and is shown in the format of the General Reporting Table for
Uncertainty shown in Table 3.3. The results indicate that the net emissions in year t are 67,730 Gg CO2 equivalent
with an uncertainty range of -14 to +15 percent, which corresponds to a 95 percent probability range of 58,490 to
78,130 Gg CO2 equivalent. Based upon the total base year and year t inventories reported in the table, the averagetrend is a 42 % increase in emissions from 1990 to 2003. The uncertainty in the trend is -18 to +23% (percentage
points) which corresponds to a 95 percent probability range for the trend of 25% to 65% with respect to the baseyear emissions.
These examples illustrate that the results from Approaches 1 and 2 can be very similar when the overall
uncertainty is relatively small. However, Approach 2 is a more flexible approach that enables quantification ofasymmetry in probability ranges, such as for the year t inventory.

2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.43

Gas

IPCC category

5

141

CH4

N2O

2

10

CH4

N2O

4

18

CH4

N2O

9

85

CH4

N2O

6

E

4

108

CH4

N2O

9

39

CH4

N2O
90

2

41

7

226

7

80

31

51

9

162

16

30

7

10 6769 350

22 75327 640

2%

2%

2%

2%

5%

5%

20%

20%

1%

1%

2%

2%

2%

2%

4%

1%

2%

2%

%

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Solid

Liquid

1.A.2 Manufacturing Industries and Construction

Peat

Biomass

Gas

Solid

Liquid

5 656

5 073

26

CO2

Peat

15 72227 232

Gg CO2 Gg CO2
equivalent equivalent

CH4

CO2

Gas

D

F

G

H

I

J

50%

75%

75%

75%

150%

50%

150%

50%

50%

75%

50%

75%

75%

75%

5%

1%

3%

2%

%

50%

75%

75%

75%

150%

50%

151%

54%

50%

75%

50%

75%

75%

75%

7%

1%

3%

3%

%

0.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00010.00000.00010.00010.00130.00010.00030.00010.00050.00000.00140.00060.00050.00010.00090.00010.00010.00000.05520.04470.00800.2320%0.00190.00010.00090.00010.00470.00020.00170.00060.00110.00020.00340.00030.00060.00010.22430.19640.47800.5806%

Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationororsource/sink
uncertainty
sensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty

C

N2O

CO2

Solid

1.A.1 Energy Industries

CO2

Liquid

1.A Fuel Combustion Activities

B

A

0.07%

0.01%

0.02%

0.01%

0.08%

0.00%

0.21%

0.03%

0.03%

0.01%

0.04%

0.01%

0.01%

0.00%

0.28%

0.04%

0.02%

0.46%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

0.01%

0.00%

0.00%

0.00%

0.03%

0.00%

0.05%

0.02%

0.00%

0.00%

0.01%

0.00%

0.00%

0.00%

1.36%

0.28%

1.08%

1.64%

%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.02%

0.00%

0.01%

0.03%

%

3.44

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Volume 1: General Guidance and Reporting

4

N2O

E

0.2

2

CH4

N2O

1

0.2

0.0

2

84

6

22

410

40

4

0.3

29

3

81

19

19

6

5%

5%

1%

1%

1%

1%

1%

1%

1%

5%

5%

5%

5%

15%

15%

1%

1%

2006 IPCC Guidelines for National Greenhouse Gas Inventoriesc. Railways

0.0

N2O

N2O

68

CH4

Diesel

0.0

12

N2O

CH4

59

N2O

Natural gas

32

CH4

Cars with Catalytic
Converters
Cars without Catalytic
Converters

78

0.4

56

N2O

CH4

4

111

CH4

N2O

17

20

N2O

CH4

5

Gasolineb. Road Transportation

a. Civil Aviation

1.A.3 Transport

Peat

D

F

G

H

I

J

150%

110%

150%

50%

158%

50%

259%

378%

50%

150%

100%

150%

50%

150%

50%

50%

75%

150%

110%

150%

50%

158%

50%

259%

378%

50%

150%

100%

150%

50%

151%

52%

50%

75%

0.00000.00000.00000.00000.00000.00000.00000.00050.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00030.00020.00130.00760.00150.00000.00000.00110.00010.00160.00020.00010.00000.00000.00000.00000.00000.00180.00010.00050.00860.00080.00010.00000.00060.00010.00170.00040.00040.0001

Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationoror
uncertainty
source/sinksensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty
Gg CO2 Gg CO2
%
%
%
%
%
equivalent equivalent

C

CH4

Gas

IPCC category

Biomass

Gas

B

A

0.00%

0.00%

0.00%

0.00%

0.04%

0.01%

0.34%

2.89%

0.07%

0.01%

0.00%

0.16%

0.00%

0.24%

0.01%

0.01%

0.00%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.01%

0.00%

0.00%

0.00%

0.00%

0.00%

0.04%

0.01%

0.00%

0.00%

%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.08%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

%

3.45

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4 (CONTINUED)
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Chapter 3: Uncertainties

E

1

1

N2O

56

N2O

CH4

282

1

CH4

0.1

CH4

N2O

2

0.5

CH4

56

N2O

19

2

1

61

307

1

0.3

0.3

0.6

47

15

4

1

6

0.6

4

3

1

25%

25%

15%

15%

5%

5%

10%

10%

3%

3%

30%

30%

30%

20%

20%

10%

10%

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Peat

Biomass

Gas

Solid

Liquid

CH4

N2O

1.A.4 Other Sectors

N2O

4

N2 O

Gasoline

Diesel

1

CH4

5

0.4

N2O

2

7

N2O

CH4

0.5

Gasoline&Diesel

e. Other Transportation

Gasoline

Residual Oil & Gas/Diesel
Oil

D

F

G

H

I

J

150%

50%

150%

150%

50%

75%

50%

75%

75%

75%

150%

150%

50%

150%

100%

150%

100%

152%

56%

151%

151%

50%

75%

51%

76%

75%

75%

153%

153%

58%

151%

102%

150%

100%

0.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00040.00200.00000.00000.00000.00010.00070.00020.00000.00000.00000.00000.00010.00000.00000.00000.00000.00130.00640.00000.00000.00000.00000.00100.00030.00010.00000.00010.00000.00010.00010.0000Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationororsource/sink
uncertainty
sensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty
Gg CO2 Gg CO2
%
%
%
%
%
equivalent equivalent

C

CH4

Gas

IPCC category

d. Water-borne Navigation

B

A

0.00%

0.00%

0.06%

0.30%

0.00%

0.00%

0.00%

0.00%

0.05%

0.02%

0.01%

0.00%

0.00%

0.00%

0.01%

0.00%

0.00%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

0.00%

0.00%

0.03%

0.14%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.01%

0.00%

0.00%

0.00%

0.00%

%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

%

3.46

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4 (CONTINUED)
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Volume 1: General Guidance and Reporting

CO2

CO2

N2O

CH4

CO2

CH4

2.A.2 Lime Production

2.A.3 and 2.A.4
Limestone and Dolomite Use1

2.A.3 and 2.A.4
Soda Ash Use1

2.B.2 Nitric Acid Production

2.B.8.b Ethylene

2.B.10 Other

2.C.1 Iron and Steel Production

E

5

60

4

1 595

18

99

383

9

147

5

1 396

20

148

513

500

3%

12%

5%

5%

7%

7%

2%

2%

5%

3%

2%

50%

13%

13%

7%

7%

2006 IPCC Guidelines for National Greenhouse Gas Inventories

CO2

CO2

2.A.1 Cement Production

786

40

0

CH4

2 Industrial Processes and Product Use

12

4

10

63

CH4

8

b.iii.4 Natural Gas Transmission and Storageb. iii.5 Natural gas Distribution

CO2

CH4

Oil – Flaring

2

0.4

9

2

a.iii.4 Oil – Refining

a.ii.

1.B.2 Oil and Natural Gas

123

1

N2O

6

0.3

N2O

CH4

2

1.B Fugitive Emissions from Fuels

Gas

Liquid

D

F

G

H

I

J

20%

5%

20%

100%

2%

9%

3%

5%

0%

0%

90%

0%

50%

75%

75%

75%

20%

13%

21%

100%

7%

11%

4%

5%

5%

3%

90%

50%

52%

76%

75%

75%

0.00000.00000.00000.00040.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00130.00000.01840.00010.00020.00070.01300.00080.00010.00000.00240.00000.00000.00000.00000.00020.00310.00010.02930.00040.00310.01080.01050.00080.00030.00020.00130.00000.00000.00020.0000Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationororsource/sink
uncertainty
sensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty
Gg CO2 Gg CO2
%
%
%
%
%
equivalent equivalent

C

CH4

Gas

IPCC category

1.A.5 Non-Specified

B

A

0.00%

0.01%

0.00%

1.84%

0.00%

0.00%

0.00%

0.06%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

0.00%

0.05%

0.00%

0.21%

0.00%

0.03%

0.03%

0.03%

0.01%

0.00%

0.00%

0.09%

0.00%

0.00%

0.00%

0.00%

%

0.00%

0.00%

0.00%

0.03%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

%

3.47

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4 (CONTINUED)
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Chapter 3: Uncertainties

215

623

CH4

N2O

3.A.2 Manure Management

3.A.2 Manure Management

CO2

CO2

net carbon stock change inorganic soils

E

1 813

-535

-23 798

1 324-1 113-21 354

461

222

1 537

21

40

22

63

25

578

830

20%

0%

0%

0%

0%

0%

38%

30%

88%

10%

24%

26%

50%

2006 IPCC Guidelines for National Greenhouse Gas Inventories

CO2

net carbon stock change inmineral soils

3.B.2.a Cropland Remaining Croplandcarbon stock change in biomass

3.B.1.a Forest Land Remaining Forest Land

1 868

CH4

3.A.1 Enteric Fermentation

3 AFOLU

8

HFCs,
PFCs,
SF6

87

0

0

2.H.3 Other (grouped data of fgases)

HFCs

2.F.4 Aerosols

62

HFCs

2.F.2 Foam Blowing Agents

0

SF6

HFCs

2.F.1 Refrigeration and Air
Conditioning

640

N2O

CO2

2.D Non-Energy Products from
Fuels and Solvent Use

2.G.3.a Medical Applications

Gas

IPCC category

D

F

G

H

I

J

90%

100%

35%

83%

16%

31%

0%

20%

0%

0%

0%

0%

5%

92%

100%

35%

83%

16%

31%

38%

36%

88%

10%

24%

26%

50%

0.00030.00030.01220.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.02640.00740.26400.00890.00180.02350.00020.00100.00210.00130.00050.01210.00170.02780.02340.44860.00970.00470.03230.00040.00080.00050.00130.00050.01210.0174Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationororsource/sink
uncertainty
sensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty
Gg CO2 Gg CO2
%
%
%
%
%
equivalent equivalentC

2.G.1 Electrical Equipment

B

A

2.37%

0.74%

9.24%

0.74%

0.03%

0.72%

0.00%

0.02%

0.00%

0.00%

0.00%

0.00%

0.01%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

0.79%

0.00%

0.00%

0.00%

0.00%

0.00%

0.02%

0.04%

0.06%

0.02%

0.02%

0.45%

1.23%

%

0.06%

0.01%

3.48

0.85%

0.01%

0.00%

0.01%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.02%

%

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4 (CONTINUED)
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Volume 1: General Guidance and Reporting

Gas

IPCC category

D

91
8

180

16

2

618

CO2

CH4

CO2

CH4

N2O

CO2

3.B.4.ai Peatlands Remaining
Peatlands

3.B.4.ai Peatlands Remaining
Peatlands

3.C.1.a Biomass Burning in
Forest Lands
3.C.1.a Biomass Burning in
Forest Lands

3.C.1.a Biomass Burning in
Forest Lands

3.C.2 Liming

CH4

N2O

3 678

735

27.0

N2O

2 497

592

11.3

2 608

277

1

6

0%

0%

10%

0%

20%

10%

10%

10%

15%

15%

30%

0%

2006 IPCC Guidelines for National Greenhouse Gas Inventories

4.A Solid Waste Disposal

4 Waste

3.C.5 Indirect N2O Emissions
from Managed Soils

3 486

N2O

5

547

67

109

CO2

503

2 907

-1 181

CO2

3.C.4 Direct N2O Emissions
from Managed Soils:
Agricultural Soils
3.C.4 Direct N2O Emissions
from Managed Soils: N
Fertilizers Application, Forest
Land

E

F

G

H

I

J

43%

334%

380%

227%

20%

70%

70%

70%

208%

208%

90%

100%

43%

334%

380%

227%

28%

71%

71%

71%

208%

208%

95%

100%

0.00030.00090.00000.00770.00000.00000.00000.00000.00000.00030.00000.00180.05740.00950.00060.04940.01270.00000.00030.00350.00000.00360.00190.09640.05250.01240.00020.05480.00580.00000.00020.00190.00010.01150.00140.0611

Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationororsource/sink
uncertainty
sensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty
Gg CO2 Gg CO2
%
%
%
%
%
equivalent equivalentC

net carbon stock change inmineral soils
net carbon stock change inorganic soils

3.B.3.a Grassland Remaining Grassland

B

A

2.47%

3.18%

0.22%

11.23%

0.25%

0.00%

0.02%

0.24%

0.01%

0.74%

0.17%

9.64%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

0.00%

0.00%

0.00%

0.00%

0.16%

0.00%

0.00%

0.03%

0.00%

0.08%

0.06%

0.00%

%

3.49

0.06%

0.10%

0.00%

1.26%

0.00%

0.00%

0.00%

0.00%

0.00%

0.01%

0.00%

0.93%

%

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4 (CONTINUED)
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Chapter 3: Uncertainties

21

84

N2O

sparsely populated areas

F

G

H

I

J

67 730

3

17

19

66

18

13

95

10%

5%

10%

5%

10%

5%

15%

380%

380%

105%

380%

380%

105%

35%

Percentage uncertainty
in total inventory

380%

380%

104%

380%

380%

104%

32%

15.9%

0.02520.00000.00000.00000.00000.00000.00000.00000.00020.00050.00030.00110.00020.00010.00150.00010.00040.00040.00140.00040.00030.0020

Uncertainty assessment was made at the aggregation level used by Finland in 2003 inventory, and therefore glass production could not be separated.

47 604

8

N2O

Total

28

N2O

4.D.2 Industrial Wastewater
Treatment and Discharge
4.E Other: N input from Fish
Farming

22

CH4

4.D.2 Industrial Wastewater
Treatment and Discharge

12

CH4

N2 O

densely populated areas

118

CH4

sparsely populated areas

densely populated areasE

2006 IPCC Guidelines for National Greenhouse Gas Inventories

1

Gas

IPCC category

D

Emission
Base year Year tContribution to
Activityfactoremissions emissions
variance by
Combined
Type A
Type Bdata/estimationororsource/sink
uncertainty
sensitivity sensitivity
uncertainty parameter
removals removals
category in year t
uncertainty
Gg CO2 Gg CO2
%
%
%
%
%
equivalent equivalentC

4.D.1 Domestic Wastewater Treatment and Discharge

B

A

0.07%

0.17%

0.03%

0.43%

0.09%

0.01%

0.05%

%

Uncertainty in trend innational emissions
introduced by emission
factor / estimation
parameter uncertainty

K

M

Trend uncertainty

0.00%

0.00%

0.01%

0.01%

0.01%

0.00%

0.04%

%

3.50

18.7%

0.0349

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

0.00%

%

Uncertainty in trend
Uncertainty
in national emissions introduced into
introduced by
the trend in total
activity data
national
uncertainty
emissionsL

The aggregation level and uncertainty estimates are country-specific for Finland, and do not represent recommended uncertainties or level of aggregation for other countries.

TABLE 3.4 (CONTINUED)
EXAMPLE OF AN APPROACH 1 UNCERTAINTY ANALYSIS FOR FINLAND (BASED ON STATISTICS FINLAND, 2005)

Volume 1: General Guidance and Reporting

5
141

N2O

10

N2O

CH4

2

18

N2O

CH4

4

85

N2O

CH4

9

CH4

6

9
39

CH4

N2O

41

7

226

7

80

31

51

9

162

16

30

7

10 6769 350

22 7532006 IPCC Guidelines for National Greenhouse Gas Inventories

Liquid

1.A.2 Manufacturing Industries and Construction

Peat

Biomass

Gas

Solid

Liquid

5 656

26

CO2

Peat

5 073

CH4

CO2

Gas

15 72227 640Year temissionsorremovals
Gg CO2equivalent

Base year
emissionsorremovals
Gg CO2equivalent
27 232

D

C

N2O

CO2

1.A.1 Energy Industries

CO2

Solid

Gas

B

Liquid

1.A Fuel Combustion Activities

IPCC category

A

F

G

H

I

J

K

2

2

5

5

20

20

1

1

2

2

2

2

4

1

2

2

2

2

5

5

20

20

1

1

2

2

2

2

4

1

2

2

75

75

70

50

70

50

50

75

50

75

75

75

5

1

3

2

10

10

150

50

150

50

50

10

50

10

10

10

5

1

3

2

Activity data Emission factor
uncertainty
uncertainty

75

75

70

50

71

52

51

76

50

75

75

75

6

1

3

3

12

12

148

50

154

57

50

11

50

12

12

12

7

1

3

3

Combined
uncertainty

0.00000.00000.00070.00000.00010.00000.00000.00000.00010.00000.00000.00000.00500.00020.00610.0061

4

-19

60

37

729

1 370

188

140

91

91

15

18

89

84

45

1

-25

-21

-33

-18

-260

-398

-37

-57

-23

-43

-30

-32

-11

-3

-3

-3

30

27

41

21

374

544

39

87

25

59

39

39

11

3

3

3

3.51

Inventory trend in
Uncertainty introduced
ApproachContribution
national emissions for into the trend in totalandto varianceyear t increase with national emissions withaComments
in year t
respect to base year
respect to base year(-)% (+)% (-)% (+)% (-)% (+)%
(fraction)(% of base year)
(-)%
(+)%
Approach 2

E

TABLE 3.5
EXAMPLE OF REPORTING OF APPROACH 2 UNCERTAINTY ANALYSIS USING GENERAL REPORTING TABLE FOR UNCERTAINTY
Emissions, removals and uncertainties are from National Inventory of Finland for year 2003 (Statistics Finland, 2005). The aggregation level and uncertainty estimates are country-specific forFinland, and do not represent recommended uncertainties or level of aggregation for other countries.

Chapter 3: Uncertainties

4

68

N2O

CH4

N2O

Cars without Catalytic Converters

Diesel

6

40

4

0.3

29

3

81

19

19

2

N2O

1

0.2

0.0
0.2

N2O

CH4

2

84

6

22

CH4

59

2
90

410

2006 IPCC Guidelines for National Greenhouse Gas Inventoriesc. Railways

Natural gas

12

N2O

Cars with Catalytic Converters

32

CH4

78

0.4

CH4

N2O

4
56

CH4

N2O

20
111

CH4

N2O

5
17

CH4

N2O

4
108

CH4

N2O

5

5

1

1

1

1

1

1

1

5

5

5

5

15

15

1

1

2

2

5

5

1

1

1

1

1

1

1

5

5

5

5

15

15

1

1

2

2

70

60

70

50

99

50

86

94

50

70

57

70

50

70

50

50

75

50

75

150

110

150

50

158

50

259

378

50

150

100

150

50

150

50

50

10

50

10

(-)% (+)% (-)% (+)% (-)% (+)%

Gg CO2equivalent

Gg CO2equivalent

70

60

70

49

99

50

86

94

50

70

57

70

50

70

51

50

75

50

74

149

110

149

50

157

50

259

392

50

148

100

150

50

151

53

50

11

50

12

Combined
uncertainty

G

Activity data Emission factor
uncertainty
uncertainty

F

Gas

E

D
Year temissionsorremovalsC
Base year
emissionsorremovalsB

Gasolineb. Road Transportation

a. Civil Aviation

1.A.3 Transport

Peat

Biomass

Gas

Solid

IPCC category

A

I

J

0.00000.00000.00010.00000.00000.01740.00000.00000.00000.00000.00000.00010.00000.00000.00000.00000.0000(fraction)

-30

-30

23

-51

-63

1 176

-49

-1

-12

-49

-29

-28

-7

13

35

-17

-44

(% of base year)

-13

-11

-59

-5

-11

-446

-6

-17

-12

-11

-9

-20

-20

-14

-35

-11

-13

(-)%

17

13

94

5

16

643

6

21

15

14

11

27

26

16

45

12

20

(+)%

Inventory trend in
Uncertainty introduced
Contribution
national emissions for into the trend in total
to varianceyear t increase with national emissions within year ta
respect to base year
respect to base year

H

3.52

Approach 2

ApproachandComments

K

TABLE 3.5 (CONTINUED)
EXAMPLE OF REPORTING OF APPROACH 2 UNCERTAINTY ANALYSIS USING GENERAL REPORTING TABLE FOR UNCERTAINTY
Emissions, removals and uncertainties are from National Inventory of Finland for year 2003 (Statistics Finland, 2005). The aggregation level and uncertainty estimates are country-specific forFinland, and do not represent recommended uncertainties or level of aggregation for other countries.

Volume 1: General Guidance and Reporting

2
6

CH4

1

N2O

1

CH4

56

N2O

282

CH4

1

N2O

0.1

CH4

N2O

2
0.5

CH4

56

N2O

19

CH4

1

0.3

0.3

1

47

15

4

1

6

1

4

3

1

9

2

2

1

61

307

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Liquid

1.A.5 Non-Specified

Peat

Biomass

Gas

Solid

Liquid

N2O

4

N2O

1.A.4 Other Sectors

Diesel

1

CH4

N2 O

Gasoline

5

7
0.4

CH4

2

N2O

1

CH4

N2O

7

7

25

25

15

15

5

5

10

10

3

3

30

30

30

20

20

10

10

7

7

25

25

15

15

5

5

10

10

3

3

30

30

30

20

20

10

10

75

75

70

50

70

70

50

75

50

75

75

75

70

70

50

70

57

70

57

10

10

150

50

150

150

50

10

50

10

10

10

150

150

50

150

100

150

100

(-)% (+)% (-)% (+)% (-)% (+)%

Gg CO2equivalent

Gg CO2equivalent

75

75

71

53

71

71

50

75

51

76

76

74

72

72

54

71

59

70

57

17

17

155

60

150

151

50

15

52

20

13

13

158

156

63

154

104

149

99

Combined
uncertainty

Activity data Emission factor
uncertainty
uncertainty

Year temissionsorremovalsG

Base year
emissionsorremovals

F

Gas

E

D

C

B

Gasoline & Diesel

e. Other Transportation

Gasoline

Residual Oil & Gas/Diesel Oil

d. Water-borne Navigation

IPCC category

A

I

J

0.00000.00000.00000.00000.00000.00130.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000(fraction)

45

43

13

1

9

9

124

132

-27

-72

-15

-19

-5

9

15

56

-42

36

2

(% of base year)

-33

-31

-38

-32

-28

-28

-27

-49

-12

-6

-21

-18

-37

-41

-43

-49

-16

-30

-19

(-)%

43

46

57

46

38

38

32

62

14

8

25

20

60

67

67

71

22

39

22

(+)%

Inventory trend in
Uncertainty introduced
Contribution
national emissions for into the trend in total
to varianceyear t increase with national emissions within year ta
respect to base year
respect to base year

H

3.53

Approach 2

ApproachandComments

K

TABLE 3.5 (CONTINUED)
EXAMPLE OF REPORTING OF APPROACH 2 UNCERTAINTY ANALYSIS USING GENERAL REPORTING TABLE FOR UNCERTAINTY
Emissions, removals and uncertainties are from National Inventory of Finland for year 2003 (Statistics Finland, 2005). The aggregation level and uncertainty estimates are country-specific forFinland, and do not represent recommended uncertainties or level of aggregation for other countries.

Chapter 3: Uncertainties

CH4

CH4

b.iii.5 Natural Gas - Distribution

640
0

CO2

CO2

CO2

N2O

CH4

CO2

CH4

CO2

HFCs,
PFCs

HFCs

HFCs

2.A.2 Lime Production

2.A.3 and 2.A.4 Limestone and Dolomite
Use

2.A.3 and 2.A.4 Soda Ash Use

2.B.2 Nitric Acid Production

2.B.8.b Ethylene

2.B.10 Other

2.C.1 Iron and Steel Production

2.D Non-Energy Products from Fuels andSolvent Use

2.F.1 Refrigeration and Air Conditioning

2.F.2 Foam Blowing Agents

2.F.4 Aerosols

40

12

10

63

2

0.4

63

25

578

830

9

147

5

1 396

20

148

513

500

2006 IPCC Guidelines for National Greenhouse Gas Inventories

5

60

4

1 595

18

99

383

CO2

786

0

4

8

123

2.A.1 Cement Production

2 Industrial Processes

CH4

CO2

1

N2O

b.iii.4 Natural Gas - Transmission andstorage

Oil – Flaring

0.3

CH4

50

3

8

5

5

4

4

2

2

2

13

13

50

3

12

5

5

7

7

2

2

2

13

13

5

20

5

20

57

2

9

3

5

90

50

75

5

20

5

20

100

1

5

3

5

90

50

10

(-)% (+)% (-)% (+)% (-)% (+)%

Gg CO2equivalent

Gg CO2equivalent

10

24

11

50

20

10

20

57

5

10

4

5

5

3

90

50

51

75

10

24

26

50

20

13

21

100

7

10

4

5

5

3

90

50

52

23

Combined
uncertainty

Activity data Emission factor
uncertainty
uncertainty

Year temissionsorremovalsG

Base year
emissionsorremovals

F

Gas

E

D

C

B

a.iii.4 Oil – Refining

a.ii

1.B.2 Oil and Natural Gas

1.B Fugitive Emissions from Fuels

Gas

IPCC category

A

I

J

0.00000.00000.0001

0.002

0.00000.00000.00000.01260.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000(fraction)

4 584 122

30

85

145

32

-13

10

50

34

-36

236

27

-49

64

64

(% of base year)-519 745

-71

-8

-35

-9

-7

-9

-13

-4

-2

-113

-41

-29

-31

-41

(-)%

1 206 234

156

8

40

10

8

10

14

4

2

334

53

85

37

55

(+)%

Inventory trend in
Uncertainty introduced
Contribution
national emissions for into the trend in total
to varianceyear t increase with national emissions within year ta
respect to base year
respect to base year

H

b,c

b,c

b

d

d

b,c

b

b

3.54

Approach 2

ApproachandComments

K

TABLE 3.5 (CONTINUED)
EXAMPLE OF REPORTING OF APPROACH 2 UNCERTAINTY ANALYSIS USING GENERAL REPORTING TABLE FOR UNCERTAINTY
Emissions, removals and uncertainties are from National Inventory of Finland for year 2003 (Statistics Finland, 2005). The aggregation level and uncertainty estimates are country-specific forFinland, and do not represent recommended uncertainties or level of aggregation for other countries.

Volume 1: General Guidance and Reporting

8

HFCs,
PFCs,
SF6

2.H.3 Other (grouped data of f-gases)

5
180
16
2
618

CH4

CO2

CH4

N2O

CO2

3.A.4.ai Peatlands Remaining Peatlands

3.C.1.a Biomass Burning in Forest Lands

3.C.1.a Biomass Burning in Forest Lands

3.C.1.a Biomass Burning in Forest Lands

3.C.2 Liming

277

1

8

91

6

547

2006 IPCC Guidelines for National Greenhouse Gas Inventories

503

67

109

CO2

CO2

net carbon stock change in organic soils

2 907

1 324

-1 113-2 1354

461

222

1 537

21

40

22

-1 181

1 813

CO2

CO2

-535

CO2

3.B.4.ai Peatlands Remaining Peatlands

net carbon stock change in mineral soils

3.B.3.a Grassland Remaining Grassland

net carbon stock change in organic soils

net carbon stock change in mineral soils

3.B.2.a Cropland Remaining Croplandcarbon stock change in biomass-2 3798

623

N2O

3.A.2 Manure Management

CO2

215

CH4

3.A.2 Manure Management

3.B.1.a Forest Land remaining Forest Land

1 868

CH4

3.A.1 Enteric Fermentation

3 AFOLU

62

N2O

2.G.3.a Medical Applications

87

SF6

20

10

10

10

15

15

30

20

30

20

10

10

10

15

15

30

20

30

20

70

70

70

80

80

90

90

20

3

70

70

70

208

208

90

90

20

(-)% (+)% (-)% (+)% (-)% (+)%

Gg CO2equivalent

Gg CO2equivalent

25

70

70

71

80

80

90

99

89

99

35

83

16

20

38

34

88

22

72

71

71

208

212

103

100

95

101

35

27

16

31

38

38

88

Combined
uncertainty

Activity data Emission factor
uncertainty
uncertainty

Year temissionsorremovalsG

Base year
emissionsorremovals

F

Gas

E

D

C

B

2.G.1 Electrical Equipment

IPCC category

A

I

J

0.00000.00000.00000.00000.00000.00740.00000.08520.01520.01250.56620.00060.00000.00150.00000.00000.0000(fraction)

-55

-50

-49

-50

6

9

-39

-346

-27

108

-10

-26

3

-18

164

-36

-75

(% of base year)

-11

-11

-12

-12

-32

-32

-29

-2223

-32

-242

-19

-15

-4

-3

-123

-23

-22

(-)%

15

15

15

15

46

48

50

1067

54

393

25

17

5

3

292

35

41

(+)%

Inventory trend in
Uncertainty introduced
Contribution
national emissions for into the trend in total
to varianceyear t increase with national emissions within year ta
respect to base year
respect to base year

H

b

b

b

b

b

b

b

b

3.55

Approach 2

ApproachandComments

K

TABLE 3.5 (CONTINUED)
EXAMPLE OF REPORTING OF APPROACH 2 UNCERTAINTY ANALYSIS USING GENERAL REPORTING TABLE FOR UNCERTAINTY
Emissions, removals and uncertainties are from National Inventory of Finland for year 2003 (Statistics Finland, 2005). The aggregation level and uncertainty estimates are country-specific forFinland, and do not represent recommended uncertainties or level of aggregation for other countries.

Chapter 3: Uncertainties

N2O

3.C.5 Indirect N2O Emissions fromManaged Soils

67 73047 604

42

-62

-37

-15

-21

-13

9

-20

-32

-19

-58

-18

-12

-19

-17

-25

-29

-16

-16

-14

-19

-17

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Trend not calculated, when base year emissions are zero

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.012

0.03030.0000

Uncertainty assessment was made in the aggregation level used by Finland in 2003 inventory, and therefore glass production could not be separated.

15

391

388

109

378

378

109

27

43

334

386

d

14

94

94

61

94

94

60

34

43

81

94

-19

c

380

380

380

380

20

380

-25

(-)%

Entries to Column H are obtained by dividing the variance of each category (obtained from the Monte Carlo simulation tool) by the total variance of the inventory.

94

94

94

94

32

94

0.2170(% of base year)

A more complex method for estimation of uncertainties is used, and therefore activity data and emission factor uncertainties are left blank. The resulting uncertainty is shown in Column G

10

5

5

10

15

10

227

(fraction)

b

10

5

5

10

15

10

76

I

J

23

18

27

22

34

40

20

20

16

25

32

29

(+)%

Inventory trend in
Uncertainty introduced
Contribution
national emissions for into the trend in total
to varianceyear t increase with national emissions within year ta
respect to base year
respect to base year

H

a

Total

3

8

N2O

4.E Other: N input from Fish Farming

17

19

66

18

28

22

84

21

N2O

densely populated areas

1395

4.D.2 Industrial Wastewater Treatment
and Discharge

N2O

N2O

sparcely populated areas

12

118

2 497

592

11

2 608

CH4

CH4

densely populated areas

3 678

735

27

3 486

4.D.2 Industrial Wastewater Treatment
and Discharge

CH4sparcely populated areas

4.D.1 Domestic Wastewater Treatment and Discharge

4.A Solid Waste Disposal

CH4

N2O

3.C.4 Direct N2O Emissions fromManaged Soils: N Fertilizers Application,
forest land

4 WasteN2O(-)% (+)% (-)% (+)% (-)% (+)%

Gg CO2equivalent

Gg CO2equivalent

Combined
uncertainty

Activity data Emission factor
uncertainty
uncertainty

Year temissionsorremovalsG

Base year
emissionsorremovals

F

Gas

E

D

C

B

3.C.4 Direct N2O Emissions fromManaged Soils: Agricultural Soils

IPCC category

A

b

b

b

b

b

3.56

Approach 2

ApproachandComments

K

TABLE 3.5 (CONTINUED)
EXAMPLE OF REPORTING OF APPROACH 2 UNCERTAINTY ANALYSIS USING GENERAL REPORTING TABLE FOR UNCERTAINTY
Emissions, removals and uncertainties are from National Inventory of Finland for year 2003 (Statistics Finland, 2005). The aggregation level and uncertainty estimates are country-specific forFinland, and do not represent recommended uncertainties or level of aggregation for other countries.

Volume 1: General Guidance and ReportingChapter 3: Uncertainties

3.7

TECHNICAL BACKGROUND INFORMATION

3.7.1

Approach 1 variables and equations

This section covers the basis for the statistical calculation methods used in Approach 1 as complementary
information to Section 3.2.3.1, Approach 1: Propagation of Error, and Table 3.2, Approach 1 Uncertainty
Calculation. Key variables and equations used for the calculation are defined in this section.
Explana t ion of t he variables
Cx, = Value of an entry in Column C and row x, emissions or removals of each category of base year inventory∑ C i = Sum of emissions and removals over all categories (rows) of the base year inventory
Dx, = Value of an entry in Column D and row x, emissions or removals of each category of the year of inventory t∑ D i = Sum of emissions and removals over all categories (rows) of the year of inventory t
Co lumn A-F
Input data of emissions and removals, activity data and emission factor uncertainties of each category
Co lumn G
Combined uncertainty using error propagation equation. See Equation 3.1 in Section 3.2.3.1.
G x = E x 2 + Fx 2

Co lumn H
Contribution to uncertainty. See also Equation 3.2 in Section 3.2.3.1.
Hx =(G x • D x )2(∑ D i )2

The total emission uncertainty is obtained using the error propagation equation:∑ (Gi • Di )= ∑ Hi∑ Di
2

Co lumn I
Entries in Column I show how the difference in emissions between the base year and the year t changes in
response to a 1 percent increase in emissions of category x emissions in the base year and year t. This shows thesensitivity of the trend in emissions to a systematic uncertainty in the emission estimate – i.e., one that iscorrelated between the base year and year t. This sensitivity is described as Type A sensitivity.
Ix = percentage trend if category x is increased by 1 percent in both years – percentage trend without increase=

0.01 • D x + ∑ D i − (0.01 • C x + ∑ C i )∑ D i − ∑ C i • 100• 100 −
(0.01 • C x + ∑ C i )∑ Ci

Co lumn J
Entries in Column J show how the difference in emissions between the base year and year t changes in response
to a 1 percent increase in the emissions of category x in year t only. This shows the sensitivity of the trend inemissions to random uncertainty error in the emissions estimate – i.e., one that is not correlated between the baseyear and year Y. This sensitivity is described as Type B sensitivity.
Jx = percentage trend if category x is increased by 1 percent in year t – percentage trend without increase=

0.01 • D x + ∑ D i − ∑ C i∑ D i − ∑ C i • 100• 100 −
∑ Ci
∑ Ci

=

Dx
∑ Ci

2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.57

Volume 1: General Guidance and Reporting

Co lumn K
Under the assumption that the same emission factor is used in both years and the actual emission factors are fully
correlated, the percent error introduced by it is equal in both years. Therefore the formula for the uncertainty
introduced on the trend by the emission factor is:K x = sensitivity A • uncertainty of emission factor= I x • Fx
In case no correlation between emission factors is assumed, sensitivity B should be used and the result needs to
be increased by √2 for the reason given below in the main derivation for Column L:
K x = sensitivity B • uncertainty of emission factor • 2= J x • Fx • 2

Co lumn L
The trend is the difference between the emissions in the base year and in the year t. Therefore the uncertainty of
the activity data of the base year and year t has to be taken into account. The two uncertainties combined using
the error propagation equation and the assumption that the uncertainty is the same in the base year and year t is:=(uncertainty (activity data, base year))2 + (uncertainty (activity data, year t ))2≈(uncertainty (activity data, year t ))2 • 2= Ex • 2
Since activity data in both years are assumed to be independent, Column L equals:
Lx = sensitivity B • combined uncertainty of activity data of both years= Jx • Ex •2

In case correlation between activity data is assumed, sensitivity A should be used and the √2 factor does not apply.
Lx = Ix • Ex

Co lumn M
Uncertainty introduced on the trend by the uncertainty in the activity data and the emissions factor.
M x = K 2x + L2x

The entries Mi in Column M are combined to obtain the total uncertainty of the trend using the error propagation
equation as follows:
Total uncertainty of the trend =

3.7.2

∑ Mi

Approach 1 – details of the equations for trend
uncertainty

The following steps show how to calculate trend uncertainty using Types A and B sensitivities (see also Section
3.2.3.1).
1) The method for assessing level uncertainty in year Y assumes that categories and gases are uncorrelated, orare aggregated until the aggregated categories can be treated as uncorrelated.
2) The uncertainty in the trend in total emissions from the country (the quantity at the foot of Column M) is
estimated as:
UT =N∑ U i2i =1

where UT is the uncertainty in the trend in total emissions from the country and Ui is the uncertainty introduced
into UT by the category i and gas.

3.58

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

3) We takeU i = (U E2 ,i + U A2 ,i )where UE,i is the uncertainty introduced into Ui by the uncertainty associated with the emission factor of thecategory i and gas, and UA,i is the uncertainty introduced into Ui by the uncertainty associated with the activity
data of the category i and gas.
4) We know from Columns E and F what the uncertainties related to activity data and emission factors for the
category i and gas are in percentage terms, but we do not yet know how these uncertainties affect the trend in the
total emissions, which is what we need for UE,i and UA,i. For this we write

U E ,i = Ai u e,iand

U A,i = Bi u a ,iWhere Ai is the Type A sensitivity associated with the category i and gas, and ue,i the percentage uncertainty
associated with the emission factor in Column F, and Bi is the Type B sensitivity associated with the category i
and gas, and ua,i the percentage uncertainty associated with the activity data in Column E. Essentially Type A
and Type B sensitivities are elasticities relating respectively a percentage difference that is self-correlated
between the base year and year Y, and one which is uncorrelated, to the percentage change in total emissions.
The method allows for this assumption to be inverted, or for both emission factor and activity data to be selfcorrelated between years, or for neither to be self-correlated.
5) The Type A and Type B sensitivities are calculable from formulae for the trend in terms of sums over
categories and gases in the base year and in year Y. The additional factor of √2 is introduced because an
uncorrelated uncertainly might affect either the base year or the year Y. The current formulation assumes forType B sensitivity that the emissions in year Y are not too different from those in the base year; if this were notthe case we would have to introduce separate consideration of the base year and year Y for the uncorrelated
uncertainties, rather than using the √2 factor.

DERIVATION OF TYPE A SENSITIVITY
The trend can be written as (assuming that 1990 is a base year):N⎞⎛N⎜ ∑ ei , y − ∑ ei ,1990 ⎟⎟100 • ⎜ i =1 N i =1⎟⎜
∑ ei ,1990
⎟
⎜
i =1
⎠
⎝

If the category i and gas is increased by 1 percent throughout (consistent with the assumption that Type A
sensitivity captures the effect of uncertainties which are correlated between years) the trend becomes:
⎛ N
⎛N
⎞⎞
⎜ ∑ ei , y + 0.01 ei , y − ⎜⎜ ∑ ei,1990 + 0.01 ei,1990 ⎟⎟ ⎟⎜⎝ i =1⎠⎟100 • ⎜ i =1⎟
N⎜⎟
ei ,1990 + 0.01 ei ,1990
∑
⎜
⎟
i =1
⎝
⎠

and the sensitivity Ai becomes:
N
⎛ N
⎛N
⎞⎞
⎛ N
⎞
⎜ ∑ ei , y + 0.01 ei , y − ⎜⎜ ∑ ei,1990 + 0.01 ei ,1990 ⎟⎟ ⎟⎜ ∑ ei , y − ∑ ei ,1990 ⎟⎜⎝ i =1⎠ ⎟ − 100 • ⎜ i =1
i =1⎟100 • ⎜ i =1
⎟
N
N
⎜
⎟
⎟
⎜
∑ ei,1990 + 0.01 ei,1990∑ ei,1990
⎜
⎟
⎟
⎜
i =1
i =1
⎝
⎠
⎠
⎝

This is the same as the expression given for the Type A sensitivity in Note B on page 6.18 of the GPG2000.

TYPE B SENSITIVITY
The Type B sensitivity we assume that the category i and gas is increased by 1 percent in year y only. In thiscase the trend becomes:

2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.59

Volume 1: General Guidance and ReportingN⎛ N⎞⎜ ∑ ei , y + 0.01 ei , y − ∑ ei,1990 ⎟i =1⎟100 • ⎜ i =1
N⎜⎟
∑ ei ,1990
⎜
⎟
i =1
⎝
⎠

So the sensitivity Bi becomes:
N
N
⎞
⎛N
⎛ N
⎞
⎜ ∑ ei , y − ∑ ei,1990 ⎟⎜ ∑ ei , y + 0.01 ei , y − ∑ ei ,1990 ⎟
i =1
⎟
i =1
⎟ − 100 • ⎜ i =1
100 • ⎜ i =1
N
N
⎟
⎜
⎜
⎟
∑ ei ,1990∑ ei,1990
⎟
⎜
⎜
⎟
i =1
i =1
⎝
⎠
⎠
⎝

All the terms on the numerator cancel out between the brackets except for 0.01 ei , y which becomes ei,y when
multiplied by 100. So the expression for Bi simplifies to

ei , yN∑ ei,1990

which is the expression at the top of

i =1

Column J on page 6.16 of the GPG2000.

3.7.3

Dealing with large and asymmetric uncertainties in
the results of Approach 1

This section provides guidance on how to correct for biases in large estimates of uncertainty from Approach 1
and how to convert the uncertainty ranges into asymmetric 95 percent probability ranges based upon a lognormal
distribution.
Correction of uncertainty estimate for large uncertainties: The approximate error propagation method ofApproach 1 produces an estimate of the uncertainty half range (U), expressed as a percentage relative to themean, of the inventory results. As the uncertainty in the total inventory uncertainty becomes larger, the error
propagation approach systematically underestimates the uncertainty unless the model is purely additive.
However, most inventories are estimated based upon the sum of terms, each of which is a product (e.g., ofemission factors and activity data). The error propagation approach is not exact for such multiplicative terms.
Results from empirical studies show that in some cases uncertainty estimated using Approach 1 could beunderestimated; the analyst could use a correction factor, for example that proposed in Frey (2003). Frey (2003)
evaluated the performance of an analytical approach for combining uncertainty in comparison to a Monte Carlosimulation with large sample sizes for many cases involving different ranges of uncertainty for additive,
multiplicative, and quotient models. Error propagation and Monte Carlo simulated estimates of the uncertainty
half-range of the model output agreed well for values of less than 100 percent. As the uncertainty in the total
inventory increased to higher levels, there was a systematic under-estimation of uncertainty in the total inventory
by the error propagation approach. The relationship between the simulated and error propagation estimates wasfound to well-behaved. Thus, a correction factor was developed from the comparison that is applicable if U for
the total inventory uncertainty is large (e.g., greater than 100 percent) and is given by:
EQUATION 3.3
CORRECTION FACTOR FOR UNCERTAINTY HALF-RANGE()⎡ − 0.720 + 1.0921U −1.63 • 10 −3 U 2 + 1.11 • 10 −5 U 3 ⎤FC = ⎢
⎥
U
⎣⎢
⎦⎥

2

Note: Use if U > 100% and if the model contains multiplicative or quotient terms

Not necessarily reliable for U > 230%
Not necessary for models that are purely additive.
Where:
U

3.60=½-range for uncertainty estimated from error propagation, in units of percent

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

Fc=

Correction factor for analytical estimate of the variance, dimensionless ratio of corrected touncorrected uncertainty

The empirically-based correction factor produces values from 1.06 to 1.69 as U varies from 100% to 230%. The
correction factor is used to develop a new, corrected, estimate of the total inventory uncertainty half-range,
Ucorrected, which in turn is used to develop confidence intervals.
EQUATION 3.4
CORRECTED UNCERTAINTY HALF-RANGE
U corrected = U • FC

Where:
Ucorrected=

Corrected ½-range for uncertainty estimated from error propagation, in units of %The errors in the analytical estimate of the variance are generally small for uncertainty half-ranges (U) of less thanapproximately 100 percent. If the correction factor is applied for U > 100% for values of U up to 230%, the typicalerror in the estimate of U is expected to be within plus or minus 10 percent in most cases. The correction factor will
not necessarily be reliable for larger uncertainties because it was calibrated over the range of 10% to 230%.
Calculation of asymmetric confidence intervals for large uncertainties: In order to calculate confidence
intervals for the model output based upon only the mean and half-range for uncertainty, a distribution must be
assumed. For models that are purely additive, and for which the half range of uncertainty is less thanapproximately 50 percent, a normal distribution is often an accurate assumption for the form of the model output.
In this case, a symmetric uncertainty range with respect to the mean can be assumed. For multiplicative models,or when the uncertainty is large for a variable that must be non-negative, a lognormal distribution is typically an
accurate assumption for the form of the model output. In such cases, the uncertainty range is not symmetric withrespect to the mean, even though the variance for the total inventory may be correctly estimated from Approach
1. Here, we provide a practical methodology for calculating approximate asymmetric uncertainty ranges based
upon the results of error propagation, based upon a methodology developed by Frey (2003). A key characteristicof the 95 percent confidence intervals is that they are approximately symmetric for small ranges of uncertainty
and they are positively skewed for large ranges of uncertainty. The latter result is necessary for a non-negative
variable.

The parameters of the lognormal distribution can be defined in several ways, such as in terms of the geometricmean and geometric standard deviation. The geometric mean can be estimated based upon the arithmetic mean
and the arithmetic standard deviation:
EQUATION 3.5
ASYMMETRIC CONFIDENCE INTERVALS – GEOMETRIC MEAN
⎧⎪

1
2

⎛

2
⎡ U ⎤ ⎞⎟⎫⎪
⎥ ⎬⎣ 200 ⎦ ⎟⎠⎪⎭

μ g = exp⎨ln(μ ) − ln⎜1 + ⎢⎪⎩⎜⎝Where:

μg=

geometric meanμ=arithmetic mean

The geometric standard deviation is given by:
EQUATION 3.6
ASYMMETRIC CONFIDENCE INTERVALS – GEOMETRIC STANDARD DEVIATION⎧ ⎛2 ⎫⎪ ⎜ ⎡ U ⎤ ⎞⎟ ⎪σ g = exp⎨ ln 1 + ⎢⎥ ⎬⎪ ⎜⎝ ⎣ 200 ⎦ ⎟⎠ ⎪⎩⎭Where:

σg=geometric standard deviation

2006 IPCC Guidelines for National Greenhouse Gas Inventories

3.61

Volume 1: General Guidance and Reporting

A confidence interval can be estimated based upon the geometric mean, geometric standard deviation, and theinverse cumulative probability distribution of a standard normal distribution (with a logarithmic transformation):
EQUATION 3.7
LOWER/UPPER UNCERTAINTY HALF-RANGE FROM ERROR PROPAGATION

{( )

( )}

{( )

( )}

⎛ exp ln μ g − 1.96 ln σ g − μ ⎞⎟ × 100
U low = ⎜⎜⎟μ⎝⎠⎛ exp ln μ g + 1.96 ln σ g − μ ⎞⎟ × 100
U high = ⎜⎜⎟μ⎝⎠Where:
Ulow =

Lower ½-range for uncertainty estimated from error propagation, in units of %.

Uhigh =

Upper ½-range for uncertainty estimated from error propagation, in units of %.

To illustrate the use of these equations, consider an example. Suppose the mean is 1.0 and the ½-range of
uncertainty estimated from error propagation is 100 percent. In this case, the geometric mean is 0.89 and thegeometric standard deviation is 1.60. The 95 percent probability range as a percentage relative to the mean isgiven by the interval from Ulow to Uhigh of Equations 3.7. In the example, the result is -65% to +126%. In contrast,
if a normal distribution had been used as the basis for uncertainty estimation, the range would have been
estimated as approximately ±100% and there would be a probability of approximately two percent of obtaining
negative values. Figure 3.9 illustrates the sensitivity of the lower and upper bounds of the 95 percent probability
range, which are the 2.5th and 97.5th percentiles, respectively, calculated assuming a lognormal distribution based
upon an estimated uncertainty half-range from an error propagation approach. The uncertainty range isapproximately symmetric relative to the mean up to an uncertainty half-range of approximately 10 to 20 percent.
As the uncertainty half-range, U, becomes large, the 95 percent uncertainty range shown in Figure 3.9 becomeslarge and asymmetric. For example, if U is 73 percent, then the estimated probability range is approximately 50% to +100%, or a factor of two.
Estimates of asymmetric ranges of uncertainty with respect to the arithmetic
mean assuming a lognormal distribution based upon uncertainty half-range
calculated from a propagation of error approach
Uncertainty Relative to Mean (%)

Figure 3.9

350
300
250

97.5th Percentile, Uhigh

200
150

95 Percent Range

100
50

2.5th Percentile, Ulow

0
-50
-100
0

3.7.4

50

100
150
Uncertainty Half-Range (%)

200

250

Methodology for calculation of the contribution to
uncertainty

The methodology for calculation of contribution to uncertainty is based upon apportioning the variance of theinventory to the variance of each category.
If the uncertainty is symmetric, then the variance is estimated, on a category basis, as:3.62

2006 IPCC Guidelines for National Greenhouse Gas Inventories

Chapter 3: Uncertainties

EQUATION 3.8
CONTRIBUTION OF CATEGORY X – VARIANCE FOR SYMMETRIC UNCERTAINTY⎛

σ x2 = ⎜⎜ D x
⎝

Ux ⎞
⎟
200 ⎟⎠

2

Where:
Ux=

uncertainty half-range for category x, in units of percent;Dx=

the total emissions or removals for category x, corresponding to the entries in Column D of
Table 3.5.

σx2=

the variance of emissions or removals for category x.

Even if the uncertainty is asymmetric, the variance can be estimated based on the arithmetic standard deviationor the coefficient of variation. The variance is simply the square of the arithmetic deviation. The variance for the
category can be estimated from the coefficient of variation, νx, as:
EQUATION 3.9
CONTRIBUTION OF CATEGORY X – VARIANCE FOR ASYMMETRIC UNCERTAINTY

σ x 2 = (Dxυ x )2

Once the variance is known for a category, the variances should be summed over all categories. The result is theapproximate total variance in the inventory. However, this result is not likely to agree exactly with a Monte
Carlo simulation result for the inventory for at least one and possibly more reasons: (1) because of sample
fluctuations in the Monte Carlo simulation, the Monte Carlo estimate of the variance may differ somewhat fromthe true value; (2) the analytical calculation is based upon assumptions of normality or lognormality of the
distributions for combined uncertainty for individual categories, whereas Monte Carlo simulation canaccommodate a wide variety of distribution assumptions; and (3) the Monte Carlo simulation may account for
nonlinearities and dependencies that are not accounted for in the analytical calculation for contribution tovariance. If the emission inventory calculations are linear or approximately linear, without any substantial
correlations, then the results should agree fairly well. Furthermore, methods for estimating ‘contribution tovariance’ for Monte Carlo methods are approximate. For those methods that potentially can account for all
contributions to variance (e.g., Sobol’s method, Fourier Amplitude Sensitivity Test), the measures of sensitivity
are more complex (e.g., Mokhtari et al., 2006). Thus, the methodology described here is a practical compromise.

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