Chapter 5: Time Series Consistency

CHAPTER 5

TIME SERIES CONSISTENCY

2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories

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Volume 1: General Guidance and Reporting

Authors
Jongikhaya Witi (South Africa), Daniela Romano (Italy)
Francesco Tubiello (USA and Italy), Justin Goodwin (UK)Contributing Authors
Suvi Monni (Finland), Cody Alsaker (USA), Sandro Federici (Italy)

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Chapter 5: Time Series Consistency

Contents
5Time Series Consistency ............................................................................................................................... 5.5
5.1

Introduction .......................................................................................................................................... 5.5

5.2

Ensuring a consistent time series .......................................................................................................... 5.5

5.3

5.2.1

Recalculations due to methodological changes and refinements ................................................. 5.5

5.2.2

Adding new categories ................................................................................................................. 5.6

5.2.3

Tracking increases and decreases due to technological change and other factors ....................... 5.7

Resolving data gaps .............................................................................................................................. 5.8
5.3.1

Issues with data availability ......................................................................................................... 5.8

5.3.2

Non-calendar year data ................................................................................................................ 5.9

5.3.3

Splicing techniques ...................................................................................................................... 5.9

5.4

Reporting and Documentation of trend information........................................................................... 5.17

5.5Time series consistency QA/QC......................................................................................................... 5.18

References…………………………………………………………….. ............................................................ 5.19

Equations
Equation 5.1

Recalculated emission or removal estimate computed using the overlap method 5.10

FiguresFigure 5.1

Consistent overlap ................................................................................................. 5.11

Figure 5.2

Inconsistent overlap .............................................................................................. 5.11

Figure 5.3

Linear interpolation ............................................................................................... 5.13

TablesTable 5.0 (New)

Examples of surrogate data by sector .................................................................... 5.13

Table 5.1 (Updated)

Summary of splicing techniques ........................................................................... 5.17

Table 5.2 (Updated)

Category-specific documentation of recalculations .............................................. 5.18

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Boxes
Box 5.1 (Updated)

Recalculation in the Agriculture, Forestry and Other Land Use (AFOLU) Sector . 5.6

Box 5.1a (New)Time series consistency when using facility level data from new legislation (e.g.
data from emissions trading scheme or other national data reporting programmes) 5.9

Box 5.1b (New)

Case study of overlap method for methane emissions from charcoal production inGodonia ................................................................................................................. 5.12

Box 5.2a (New)

Case study of interpolating data for carbon dioxide emissions from fossil liquidincineration in Godonia ......................................................................................... 5.14

Box 5.2b (New)

Case study of non-linear interpolation of data direct soil N2O emissions frommanure on non-federal grasslands ......................................................................... 5.16

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Chapter 5: Time Series Consistency

5

TIME SERIES CONSISTENCY

Users are expected to go to Mapping Tables in Annex 1, before reading this chapter. This is required to correctly
understand both the refinements made and how the elements in this chapter relate to the corresponding chapter
in the 2006 IPCC Guidelines.

5.1

INTRODUCTION

No refinement.

5.2

ENSURING A CONSISTENT TIME SERIES

5.2.1

Recalculations due to methodological changes andrefinements

A methodological change in a category is a switch to a different tier from the one previously used. Methodologicalchanges are often driven by the development of new and different data sets. An example of a methodologicalchange is the new use of a higher tier method instead of a Tier 1 default method for an industrial category becausea country has obtained site-specific emission measurement data that can be used directly or for development of
national emission factors.
A methodological refinement occurs when an inventory compiler uses the same tier to estimate emissions but
applies it using a different data source or a different level of aggregation. An example of a refinement would be if
new data permit further disaggregation of a livestock enteric fermentation model, so that resulting animal
categories are more homogenous or applies a more accurate emission factor. In this case, the estimate is still being
developed using a Tier 2 method, but it is applied at a more detailed level of disaggregation. Another possibility
is that data of a similar level of aggregation but higher quality data could be introduced, due to improved datacollection methods.
Both methodological changes and refinements over time are an essential part of improving inventory quality. It isgood practice to change or refine methods when:• Available data have changed: The availability of data is a critical determinant of the appropriate method, andthus changes in available data may lead to changes or refinements in methods. As countries gain experienceand devote additional resources to preparing greenhouse gas inventories, it is expected that data availability
will improve. 1
0F• The previously used method is not consistent with the IPCC Guidelines for that category: Inventory compilers
should review the guidance for each category in Volumes 2-5.
• A category has become key: A category might not be considered key in a previous inventory year, dependingon the criteria used, but could become key in a future year. For example, many countries are only beginning tosubstitute HFCs and PFCs for ozone depleting substances being phased out under the Montreal Protocol.
Although current emissions from this category are low, they could become key in the future based on trend orlevel. Countries anticipating significant growth in a category may want to consider this possibility before it
becomes key.
• The previously used method is insufficient to reflect mitigation activities in a transparent manner: As
techniques and technologies for reducing emissions are introduced, inventory compilers should use methods
that can account for the resulting change in emissions or removals in a transparent manner. Where thepreviously used methods are insufficiently transparent, it is good practice to change or refine them. See Section
5.2.3 for further guidance.
• The capacity for inventory preparation has increased: Over time, the human or financial capacity (or both) to
prepare inventories may increase. If inventory compilers increase inventory capacity, it is good practice tochange or refine methods to produce more accurate, complete and transparent estimates, particularly for key
categories.
1 Sometimes collection of data may be reduced which can result in a less rigorous methodological outcome.

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Volume 1: General Guidance and Reporting• New inventory methods become available: In the future, new inventory methods may be developed that takeadvantage of new technologies or improved scientific understanding. For example, remote-sensing technology
improvements in emission monitoring technology may make it possible to monitor directly more types ofemission sources.
• Availability of new EFs in the IPCC Guidelines that could be different from previous IPCC Guidelines: From
time to time, the IPCC GHG Inventory Guidelines are to be subjected to a refinement process in an effort tointroduce new methodologies and emission factors based on the latest available science. Under thesecircumstances, the inventory compiler has to carefully consider the emission factors presented in the mostrecent available IPCC Guidelines and make a determination of the appropriateness of such emission factors to
the category in question for the full time series. If the emission rate changes over time, the inventory compiler
might consider the appropriateness of the EF in relation to changes in the emission rate for specific periods ofthe time series. When such changes occur, they should be properly documented. Changes in emission rates
might be triggered by changes in process/technology changes. In such cases, it is possible for the inventory
compiler to apply the old EFs in one set of the time series and the latest EFs for other parts of the time series.
• Correction of errors: It is possible that the implementation of the QA/QC procedures described in Chapter 6,
Quality Assurance and Quality Control and Verification, will lead to the identification of errors or mistakes in
the inventory. As noted in that chapter, it is good practice to correct errors in previously submitted estimates.
In a strict sense, the correction of errors should not be considered a methodological change or refinement. Thissituation is noted here, however, because the general guidance on time series consistency should be taken into
consideration when making necessary corrections.
BOX 5.1 (UPDATED)RECALCULATION IN THE AGRICULTURE, FORESTRY AND OTHER LAND USE (AFOLU) SECTOR

It is anticipated that the use of recalculation techniques in the AFOLU Sector will be particularly
important. The development of inventory methods and interpolation/extrapolation tools (models) for
this sector is ongoing and it is anticipated that changes to the methods of many countries will occur
over time due to the complexity of the processes involved. In simple cases, sampling orexperimentation may provide country-specific emission factors, which might require a time series
recalculation. Situations that are more complicated can also arise. For example:•

The instruments used to collect activity data may change through time, and it is impossible togo back in time to apply the new instrument. For example, land-clearing events can be estimatedby the use of satellite imagery, but the satellites available for this work change or degrade
through time. In this case, the overlap method described in Section 5.3.3.1 is most applicable.

•

Some data sources such as forest inventories required for AFOLU categories may not be
available annually because of resource constraints. In this case, interpolation between years or
extrapolation for years external to the available times series of data may be the most appropriate
method to apply, possibly using a proxy. Extrapolated data may be recalculated when final data
become available (see Sections 5.3.3.3 and 5.3.3.4 on interpolation and extrapolation).

•

Emissions and removals in AFOLU typically depend on past land use activity (GPG-LULUCF
2003). Thus, data must cover a large historical period (20-100 years), and the quality of such data
will often vary through time. Overlap, interpolation or extrapolation techniques may be necessary
in these cases.

•

The calculation of emission factors and other parameters in AFOLU may require a combinationof sampling and modelling work. Time series consistency must be applied to the modelling
work as well. Models can be viewed as a way of transforming input data to produce output
results. In most cases where changes are made to the data inputs or mathematical relationships
in a model, the entire time series of estimates should be recalculated. In circumstances where
this is not feasible due to available data, variations of the overlap method could be applied.

5.2.2

Adding new categories

The addition to the inventory of a new category or subcategory requires the calculation of an entire time series,and estimates should be included in the inventory from the year emissions or removals start to occur in the country.
A country should make every effort to use the same method and data sets for each year. It may be difficult tocollect data for previous years, however, in which case countries should use the guidance on splicing in Section
5.3.3 to construct a consistent time series.

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Chapter 5: Time Series Consistency

A country may add new categories or new gases to the inventory for a variety of reasons:• A new emission or removal activity is occurring: Some emission processes, particularly in the IPPU Sector,
only occur as a result of specific technological processes. For example, the use of substitutes for ozonedepleting substances (ODS substitutes) has been phased in at very different rates in different parts of the world.
Some applications may only now be starting to occur in some countries.
• Rapid growth in a very small category: A category that previously was too small to justify resources forinclusion in the national inventory, could experience sudden growth and should be included in future
inventories.
• New IPCC categories: The 2006 IPCC Guidelines contain some categories and subcategories that were notcovered in the Revised 1996 IPCC Guidelines (IPCC, 1997). As a result, countries may include new estimatesin future national inventories. Countries should include estimates for new categories and subcategories for theentire time series.
• Country-specific categories: In cases where the 2006 IPCC Guidelines and its 2019 Refinement do not provide
guidance on allocation and methodological guidance for a specific category and country deems the category to
be significant (according to its national definition) to its national emissions total (e.g. CH4 emissions from andremovals by agricultural soils or forest ecosystem in low forest cover countries).
• Additional inventory capacity: A country may be able to use more resources or employ additional experts overtime, and thus include new categories and subcategories in the inventory.
If a new emission-causing activity began after the base year, or if a category previously regarded as insignificant,for reasons of not estimating emissions/removals from an existing source/sink, has grown to the point where it
should be included in the inventory, it is good practice to document the reason for not estimating the entire timeseries.

5.2.3

Tracking increases and decreases due to technologicalchange and other factors

Emission inventories can track changes in emissions and removals through changing activity levels or changing
emission rates, or both. The way in which such changes are included in methodologies can have a significant
impact on time series consistency.

Changes in activity levels

National statistics typically will account for significant changes in activity levels. For example, fuel switchingfrom coal to natural gas in electricity generation will be reflected in the national fuel consumption statistics. Further
disaggregation of activity data can provide more transparency to indicate specifically where the change in activity
is occurring. This approach is relevant when changes are taking place in one or more subcategories, but not
throughout the entire category. To maintain time series consistency, the same level of disaggregation into
subcategories should as far as possible be used for the entire time series, even if the change began recently.

Changes in emission rates

Research may indicate that the average rate of emissions/removals per unit of activity has changed over the timeseries. In some cases, the factors leading to a technological change may also make it possible to use a higher tiermethod. For example, an aluminium plant manager who introduces measures to reduce the frequency and intensityof anode effects may also collect plant-specific parameters that can be used to estimate a new emission factor. This
new factor might not be appropriate for estimating emissions for earlier years in the time series, before thetechnological change occurred. In these cases, it is good practice to use the updated emission factor or otherestimation parameters or data to reflect these changes. Since a general assumption is that emission factors or otherestimation parameters do not change over time unless otherwise indicated, countries should clearly document thereason for using different factors or parameters in the time series. This is particularly important if sampling or
surveying occurs periodically and emission factors or estimation parameters for years in between are interpolated
rather than measured. Changes in process/management practices/technologies can be used as a guide to trigger
commissioning of periodic surveys.

Changes in data sources for different years of the time series

A change in data availability or a gap in data is different from periodically available data because there is unlikely
to be an opportunity to recalculate the estimate later using better data. In some cases, countries will improve theirability to collect data over time, so that higher tier methods can be applied for recent years, but not for earlier years.
This is particularly relevant to categories in which it is possible to implement direct sampling and measurement

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programs because these new data may not be indicative of conditions in past years. Some countries may find thatthe availability of certain data sets decreases over time as a result of changing priorities within governments,
economic restructuring, or limited resources. For example, a land cover map for the latest time step in the timeseries might be developed from a new satellite imagery product with higher imagery resolution and different image
processing procedures to derive land cover classes compared to the satellite imagery used to generate a land covermap in the base year or other year within a time series. This implies that different land cover maps produced forthe time series will have varying resolution and methods for deriving land cover classes. Differences in these
attributes (imagery resolution and image processing procedures, etc.) might introduce inconsistencies and errors
in activity data derived from various land cover maps used in the time series. Changes in livestock management
techniques will have an impact on annual emissions and assumptions and EFs. In such cases, EFs should be applied
from the year the changes took place (i.e. they cannot be applied prior to the year of change). Technologies andpractices of livestock management may be applied to different levels for different years but have to be applied
appropriately across the time series. Section 4.4.2 in Volume 4, Chapter 4 provides an example on how to ensure
methodological consistency when more sophisticated extrapolation is done in the forest land category, based on“functional relationships” among various interrelated variables.

Capture, destruction, or combustion of emissions

Larger point sources such as chemical manufacturing facilities or power plants might generate emissions but
prevent them from being released to the atmosphere through capture and storage (e.g., CO2), destruction (e.g.,
HFC-23) or combustion (e.g., CH4). These activities do not necessarily change the average emissions generated
per unit of activity, and therefore it is not good practice to use different emission factors for different years. Instead,the inventory compiler should estimate total emissions generated and emissions reduced separately, and thensubtract reductions from the total generation to arrive at an estimate for total emissions to the atmosphere. However,for mitigation actions that take place across numerous facilities in the same way, a stratification of the facility
population into two groups, one with mitigation and another group without mitigation, should be considered andseparate emission factors applied for each group. For example, methane emissions from the oil and gas systems
are impacted by flaring and other activities/technologies. The fraction of oil or gas production with and without
these activities/technologies can be determined and distinct emission factors can be applied to each population.

5.3

RESOLVING DATA GAPS

5.3.1

Issues with data availability

For a complete and consistent time series, it is necessary to determine the availability of data for each year.
Recalculating previous estimates using a higher tier method, or developing estimates for new categories will bedifficult if data are missing for one or more years. Examples of data gaps are presented below:• Periodic data: Natural resource or environmental statistics, such as national forest inventories and waste
statistics, may not cover the entire country on an annual basis. Instead, they may be carried out at intervals suchas every fifth or tenth year, or region-by-region, implying that national level estimates can only be directly
obtained once the inventory in every region has been completed. When data are available less frequently thanannual, several issues arise. First, the estimates need to be updated each time new data become available, andthe years between the available data need to be recalculated. The second issue is producing inventories foryears after the last available data point and before new data are available. In this case, new estimates should be
extrapolated based on available data, and then recalculated when new data become available.
• Changes and gaps in data availability: A change in data availability or a gap in data is different fromperiodically available data because there is unlikely to be an opportunity to recalculate the estimate later using
better data. In some cases, countries will improve their ability to collect data over time, so that higher tiermethods can be applied for recent years, but not for earlier years. This is particularly relevant to categories inwhich it is possible to implement direct sampling and measurement programs because these new data may not
be indicative of conditions in past years. Some countries may find that the availability of certain data sets
decreases over time as a result of changing priorities within governments, economic restructuring, or limited
resources. Some countries with economies in transition no longer collect certain data sets that were available
in the base year, or if available, these data sets may contain different definitions, classifications and levels of
aggregation. Box 5.1a presents an example of time series consistency associated with using available industrial
reporting information.

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BOX 5.1A (NEW)
TIME SERIES CONSISTENCY WHEN USING FACILITY LEVEL DATA FROM NEW LEGISLATION (E.G. DATA FROMEMISSIONS TRADING SCHEME OR OTHER NATIONAL DATA REPORTING PROGRAMMES)

Availability of data and details of information may change over the period of the time series due to
new legislation establishing regular data collection and emission monitoring systems at facility level.
Examples are the requirements of data collected in the context of the European Emissions Trading
Scheme, the European Pollutant Release and Transfer Register, other facility monitoring programsin Australia and the USA. Therefore, inventory compilers will be able to implement higher tiermethods for recent years but have difficulty in applying the same methods historically.
As far as feasible, the inventory compiler should make use of the most accurate emissions and otherparameters collected within the relevant contexts. In addition, it is important that when using these
data, either partially or totally, the consistency of time series in the preparation of the national
inventory is ensured to the extent practicable.
Something to check is whether the sectoral coverage of the category to be estimated is complete andthe data collected have undergone a validation process before communication.
Then the expert should decide how to integrate these data in the national inventory (graduating froma Tier 1 to a Tier 2, or from a Tier 2 to a Tier 3), and from which point of the time series the use ofsuch data starts.
The most recent information is usually more accurate or at least can be more transparently
documented than the older one so judgement from sectoral experts, relevant associations and otherexperts in the field should be taken into account to decide if new data and information apply also to
the past. For instance, discrepancies from old and new emission factors may be justified by thechange in technologies and/or best practices, or they may be affected by incorrect assumptions andmethods to ensure data consistency that need to be applied. When the same method is not used along
the time series relevant techniques should be selected to ensure the consistency of the time series (orthe appropriate documentation has been provided to justify the trend, e.g. change in technicalconditions due to the introduction of mitigation technology/recovered emissions).
This issue is relatively common in the IPPU sector. Although the relationship between emissions
estimated from the Tier 3 and the Tier 2 methods should be relatively constant over time for a given
plant this may vary if the industry has changed significantly over time. In some cases if technologies
and practices in the industry have not changed much, the expert should evaluate if emission factors
derived from recent data may also be appropriate for historical years or if a splicing technique should
be applied to ensure time series consistency.
For instance, if emissions and other data are collected from a certain point of the time series onwards
in the context of a facility level reporting program, the expert should evaluate if an average emission
factor or parameter deriving from this collection may also be applied to the time series backward(ensuring the consistency of the time series). There may be cases where the expert uses two different
tiers (Tier 2 and Tier 3), and the expert should clearly document that the use of two different methods
does result in the most appropriate EFs.

5.3.2

Non-calendar year data

No refinement.

5.3.3

Splicing techniques

Splicing in this context refers to the combining or joining of more than one method to form a complete time series.
Several splicing techniques are available if it is not possible to use the same method or data source in all years.
This section describes techniques that can be used to combine methods to minimise the potential inconsistencies
in the time series. Each technique can be appropriate in certain situations, as determined by considerations such asdata availability and the nature of the methodological modification. Selecting a technique requires an evaluationof the specific circumstances, and a determination of the best option for the particular case. It is good practice toperform the splicing using more than one technique before making a final decision and to document why aparticular method was chosen. The principal approaches for ensuring time series consistency are summarised inTable 5.2.

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5.3.3.1 O VERLAPThe overlap technique is often used when a new method is introduced but data are not available to apply the new
method to the early years in the time series, for example when implementing a higher tier methodology. If the new
method cannot be used for all years, it may be possible to develop a time series based on the relationship (oroverlap) observed between the two methods during the years when both can be used. Essentially, the time series
is constructed by assuming that there is a consistent relationship between the results of the previously used andnew method. The emission or removal estimates for those years when the new method cannot be used directly aredeveloped by proportionally adjusting the previously developed estimates, based on the relationship observed
during the period of overlap. In this case, the emissions or removals associated with the new method are estimatedaccording to Equation 5.1: 2
1F

EQUATION 5.1
RECALCULATED EMISSION OR REMOVAL ESTIMATE COMPUTED USING THE OVERLAP METHOD
n

y 
1
y0 =
x0 • 
•∑ i 
 n − m + 1 i = m xi 

Where:y0= the recalculated emission or removal estimate computed using the overlap methodx0= the estimate developed using the previously used method

yi and xi are the estimates prepared using the new and previously used methods during the period of overlap,
as denoted by years m through n
A relationship between the previously used and new methods can be evaluated by comparing the overlap between
only one set of annual estimates, but it is preferable to compare multiple years. This is because comparing only
one year may lead to bias and it is not possible to evaluate trends.
Figure 5.1 shows a hypothetical example of a consistent overlap between two methods for the years in which bothcan be applied. In Figure 5.2, there is no consistent overlap between methods and it is not good practice to use theoverlap technique in such a case.
Other relationships between the old and new estimates may also be observed through an assessment of overlap.
For example, a constant difference may be observed. In this case, the emissions or removals associated with the
new method are estimated by adjusting the previous estimate by the constant amount equal to the average
difference in the years of overlap.

2Overlap Equation 5.1 is preferred to the equation described in Good Practice Guidance for National Greenhouse Gas
Inventories (GPG, 2000; IPCC, 2000):n n
y0 = x0  ∑ yi ∑ xi =
 i m=i m because the latter gives more weight to overlapping years with the highest emissions. However in practical cases the results
will often be very similar and continued use of the previous equation is consistent with good practice where its use gives
satisfactory results.

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Figure 5.1 Consistent overlap

Figure 5.2 Inconsistent overlap

Before applying the overlapping technique, the expert should be aware of the relationship between the old and the
new method applied to estimate emissions and able to understand the differences to be sure that the new method
actually improves the accuracy of emission estimates.
Box 5.1b provides a practical example were the inventory compiler should evaluate the application of the overlap
approach to estimate GHG emissions for the years 2001–2003.

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BOX 5.1B (NEW)CASE STUDY OF OVERLAP METHOD FOR

METHANE EMISSIONS FROM CHARCOAL PRODUCTION IN GODONIA

Consider the example below where we should evaluate the application of the overlap approach toestimate GHG emissions for the years 2001–2003.

Tier 1 quantified

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

4,000

4,000

4,100

4,200

4,800

4,900

5,000

4,800

4,900

5,000

4,035

4,598

4,410

4,500

4,320

4,513

4,790

Tier 2 quantified

Step 1. For each year, calculate the ratio between Tier 2 and Tier 1 (e.g. in 2010: 4790/5000 = 0.96):
2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

4,000

4,000

4,100

4,200

4,800

4,900

5,000

4,800

4,900

5,000

Tier 2 quantified

4,035

4,598

4,410

4,500

4,320

4,513

4,790

Ratio Tier 2:Tier 1

0.96

0.96

0.90

0.90

0.90

0.92

0.96

Tier 1 quantified

Step 2. Calculate average and standard deviation of the differences:
1
 4035 4598 4410 4500 4320 4513 4790  
0.93
•
+
+
+
+
+
+

 =
(2010
−
2004
+
1)
4200 4800 4900 5000 4800 4900 5000  •

Average = 0.93 (correction factor to be multiplied by the estimate developed based on thepreviously used method as per equation 5.1). For simplicity, the average has been rounded totwo decimal places.
1((0.96 − 0.93) 2 + (0.96 − 0.93) 2 + (0.90 − 0.93) 2 + (0.90 − 0.93) 2 + (0.90 − 0.93)2 + (0.92 − 0.93)2 + (0.96 − 0.93)2 ) =
0.028
7

•

Standard deviation = 0.028 (low variability  overlap approach seems appropriate). Please referto Box 3.0a in Chapter 3, Volume 1 for guidance in the interpretation of standard deviation fora normal distribution.

Step 3. Apply average to calculate missing data:•

Year 2001: 4,000 • 0.93 = 3,720•

Year 2002: 4,000 • 0.93 = 3,720•

Year 2003: 4,100 • 0.93 = 3,813
2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Tier 1 quantified

4,000

4,000

4,100

4,200

4,800

4,900

5,000

4,800

4,900

5,000

Tier 2 quantified

3,720

3,720

3,813

4,035

4,598

4,410

4,500

4,320

4,513

4,790

0.96

0.96

0.90

0.90

0.90

0.92

0.96

Ratio Tier 2:Tier 1

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Chapter 5: Time Series Consistency

5.3.3.2

S URROGATE DATA

Table 5.0 presents examples of surrogate data that could be applied when using the surrogate data method.
TABLE 5.0 (NEW)EXAMPLES OF SURROGATE DATA BY SECTOR
Energy
•
•
•
•

•

IPPU

Gross-domestic
product
Population statistics
Vehicle fleet
Fuel sales data(taking into account
import/export)
Annual Income•••

Commodity
Production statistics
Gross-domestic
product (of eachspecific category
where available)
Plant-specificparameters

AFOLU
•

•
•
•
•

•

5.3.3.3

Crop sales data(taking into account
import/export)
Crop productivity
and harvested area
Milk production data
Animals slaughtered
Gross-domestic
product of eachspecific category
Fuelwood
consumption data(taking into account
import/export)

Waste
•
•
•
•
•

Gross-domestic product
Population statistics
Annual Income
Protein intake data
Ratio of domestic/
industrial wastewater

I NTERPOLATION

In some cases, it may be possible to apply a method intermittently throughout the time series. For example,
necessary detailed statistics may only be collected every few years, or it may be impractical to conduct detailed
surveys on an annual basis. In this case, estimates for the intermediate years in the time series can be developed
by interpolating between the detailed estimates. If information on the general trends or underlying parameters isavailable, then the surrogate method is preferable.
Figure 5.3 shows an example of linear interpolation. In this example, data for 1994 and 1995 are not available.
Emissions were estimated by assuming a constant annual growth in emissions from 1993-1996. This technique isappropriate in this example because the overall trend appears stable, and it is unlikely that actual emissions for1994 and 1995 are substantially different from the values predicted through interpolation. For categories that havevolatile emission trends (i.e., they fluctuate significantly from year to year), interpolation will not be according togood practice and surrogate data will be a better option. It is good practice to compare interpolated estimates withsurrogate data as a QA/QC check.
Figure 5.3 Linear interpolation

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BOX 5.2A (NEW)CASE STUDY OF INTERPOLATING DATA FOR

CARBON DIOXIDE EMISSIONS FROM FOSSIL LIQUID INCINERATION IN GODONIA

Annually, the Statistical Office of Godonia collects activity data on the amounts of fossil liquid
waste incinerated by all industrial waste incineration companies. The Statistical office uses thisactivity data to estimate CO2 emissions from incineration of fossil liquid waste. However, these data
were not available for the years 2004-2006 due to temporary closure of the unit with the Statistical
Office responsible for collecting waste data. Hence, the time series emission estimates for thiscategory are incomplete in the national GHG inventory of Godonia and require that a data gap filling
method is applied. The steps involved in filling the data gaps in the time series are described below.

GHG emission source x

1999

2000

2001

2002

2003

3,800

3,920

4,030

4,135

4,235

2004

2005

2006

2007

2008

2009

2010

4,655

4,770

4,880

4,975

Step 1. Determine whether any factors might have affected the activities that give rise to emissions
for the emission category of interest. This step is important to ensure that the interpolation method
is not applied in cases where the activity was prohibited for certain years of the time series (e.g. due
to legislation prohibiting certain activities, disruptions such as conflicts/economic performance,etc.).
Step 2. Analyze data and assess applicability and type of interpolation technique desired. This
exercise can be achieved by fitting a trend line on the data and assessing the value of R2 (theregression coefficient). The closer to unity the regression coefficient is, the more appropriate theinterpolation methodology is. In the example above, fitting a linear trend line is more appropriate as
the time series is linear.
Step 3. Calculate difference in GHG emissions between last year before the gap and first year after
the gap:

GHG emission source x

1999

2000

2001

2002

2003

3,800

3,920

4,030

4,135

4,235

2004

2005

2006

2007

2008

2009

2010

4,655

4,770

4,880

4,975

4,655 (2007) – 4,235 (2003) = 420

Step 4. Calculate the length of the gap: 2007 – 2003 = 4 years.
Step 5. Calculate average change in emissions per gap year = 420/4 = 105 Gg CO2.
Step 6. Calculate total emissions for gap year by adding the average change per year.
Step 7. Use results obtained in step 6 to calculate the missing emissions data in the time series:•

year 2004: 4,235 + 105 = 4,340 Gg CO2•

year 2005: 4,340 + 105 = 4,445 Gg CO2•

year 2006: 4,445 + 105 = 4,550 Gg CO2

Step 8. Transparently report results:

GHG emission source x

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

3,800

3,920

4,030

4,135

4,235

4,340

4,445

4,550

4,655

4,770

4,880

4,975

5.3.3.4 T REND EXTRAPOLATIONNo refinement.

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Chapter 5: Time Series Consistency

5.3.3.5 O THER TECHNIQUESNo refinement.

5.3.3.5 A N ON - LINEAR TREND ANALYSIS
In some cases, particularly for emission categories influenced by economic activity, time series consistency is best
represented by multiplicative (exponential) rather than additive (linear) relationships. In these cases, it is better toconstruct a polynomial through all the given data points. The resultant polynomial can be used to fill data gaps in
the time series. There are a number of non-linear methods for interpolating within a set of known data. For example,
inventory compilers can apply the Newton’s interpolation method or the Lagrange’s interpolation method. Bothmethodologies are widely available in literature and yield the same interpolating polynomial (Ouyed & Dobler2010). The Richard extrapolation and Padé approximation methods can also be applied for trend extrapolation.
Inventory compilers should exercise caution when applying trend extrapolation methods. For example, a highorder polynomial may provide a very good fit to a data set over its range of validity. However, if higher powers
than needed are included, the polynomial may diverge rapidly from smooth behaviour outside range of the data.
When countries use models or measurements to estimate GHG emissions the X2 statistical method would be usefulfor testing whether a difference is significant from a statistical perspective or not. Such testing would help toincrease accuracy and time-series consistency of imputing missing data.
An example of filling data gaps with a non-linear trend is given in Box 5.2b. In this example, there is one year of
missing data for direct soil N2O emissions from manure on non-federal grasslands. However, a plot of the data
indicates that a linear trend fit is clearly inappropriate. Therefore, a polynomial will be fit to the data and used to
impute the missing year.

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BOX 5.2B (NEW)CASE STUDY OF NON-LINEAR INTERPOLATION OF DATADIRECT SOIL N2O EMISSIONS FROM MANURE ON NON-FEDERAL GRASSLANDS

The annual greenhouse gas inventory requires direct soil N2O emissions in kt N2O-N from manure
on non-federal grasslands to be part of the emission estimates. This annual greenhouse gas inventory
is calculated for the years 1990 to the most recent year and is reported to the United Nations
Framework Convention on Climate Change. However, the time series for N2O emissions below is
missing data for 2002. To fill this data gap a non-linear trend analysis is conducted. All of the steps
required to complete the time series are described below.
Step 1. Plot the known data to determine the most appropriate gap-filling method to apply. The
figure below contains a plot of the data. However, the data do not follow a linear trend, but apolynomial should fit the data well.
Step 2. Determine the order of the polynomial most appropriate for the data. The goal is to find apolynomial with the lowest order that still adequately fits the data. Start by fitting a polynomial oforder 2 then incrementally increase the order until an adequate fit is found. Beware of overfitting thedata. Statistical tests comparing the nth and the (n+1)th order polynomial fit can be useful. For these
data, a fourth order polynomial is the most appropriate fit.
Step 3. Use the polynomial determined in Step 2 to estimate the missing data. The polynomial
obtained via least-squares regression is given by:
7.8752 + 3.986t − 0.4072t 2 + 0.023t 3 − 0.0013t 4
Emissions

1990
11.34

1992
14.89

1994
16.23

1996
18.22

1998
19.78

2000
20.89

2002
19.69

2004
19.57

2006
19.21

2008
16.43

2010
14.23

2012
9.32

Step 4. Transparently report results:

Non-linear Trend
25

Emissions

20
15
10
5
0

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

Year

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Chapter 5: Time Series Consistency

5.3.3.6 S ELECTING THE MOST APPROPRIATE TECHNIQUE
A number of splicing techniques are presented below to address time series consistency issues. The choice of
splicing technique involves expert judgement, and depends on an expert assessment of the volatility of emissions
trend, the availability of data for two overlapping methods, the adequacy and availability of surrogate data sets,
and the number of years of missing data. Table 5.1 summarises the requirements for each technique and suggests
situations in which they may or may not be appropriate. Countries should use Table 5.1 as a guide rather than aprescription.
TABLE 5.1 (UPDATED)SUMMARY OF SPLICING TECHNIQUESSplicing TechniqueApplicability

Comments

Overlap

Data necessary to apply both thepreviously used and the new method
must be available for at least one year,
preferably more.

•

Emission factors, activity data or otherestimation parameters used in the new
method are strongly correlated withother well-known and more readily
available indicative data.

•

Data needed for recalculation using the
new method are available forintermittent years during the timeseries.

•Data for the new method are notcollected annually and are not available
at the beginning or the end of the timeseries.

••Surrogate Data

Interpolation

Trend Extrapolation

•

•

•

•
Non-Linear Trend
Analysis(Interpolation/
Extrapolation)

In cases where time series consistency
is best represented by multiplicative(exponential) rather than additive(linear) relationships•

Other Techniques

The standard alternatives are not valid
when technical conditions are changing
throughout the time series (e.g., due tothe introduction of mitigation
technology).

•
•

5.4

•

Most reliable when the overlap between two or
more sets of annual estimates can be assessed.
If the trends observed using the previously
used and new methods are inconsistent, thisapproach is not good practice.
Multiple indicative data sets (singly or in
combination) should be tested in order todetermine the most strongly correlated.
Should not be done for long periods.
Estimates can be linearly interpolated for theperiods when the new method cannot beapplied.
The method is not applicable in the case oflarge annual fluctuations.
Most reliable if the trend over time is constant.
Should not be used if the trend is changing (inthis case, the surrogate method may be more
appropriate).
Should not be applied for long periods.
Most reliable for trend analysis of model
outputs.
Applicable in the case of large annual
fluctuations with observed high standard
deviations (see Box 3.0a, Chapter 3, Volume 1of the 2019 Refinement for guidance on
standard deviation values.
Document customised approaches thoroughly.
Compare results with standard techniques.

REPORTING AND DOCUMENTATION OF
TREND INFORMATION

If the same method and data sources are used throughout the time series, and there have been no recalculations,then following the reporting guidance for each category should be sufficient to ensure transparency. Generally,
countries should explain inventory trends for each category, giving particular attention to outliers, trend changes,
and extreme trends. Countries should provide additional documentation if they have recalculated previous
estimates and if they have used the techniques in this chapter to splice methodologies.
Recalculations: In addition to following the category-specific guidance on each category provided in Volumes 25, countries should clearly document any recalculations. The documentation should explain the reason for therecalculation and the effect of the recalculation on the time series. Countries can also include a graph that shows2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories

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Volume 1: General Guidance and Reporting

the relationship between the previous data trend and the new data trend. Table 5.3 provides an example of how
recalculations can be documented either for reporting purposes or for internal tracking.
TABLE 5.2 (UPDATED)CATEGORY-SPECIFIC DOCUMENTATION OF RECALCULATIONSEmissions and Removals (Gg)

Category/Gas

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Previous Data (PD)
Latest Data (LD)
Difference in percent=100●[(LD–PD)/PD]
Documentation:••••

Reason for application of time-series splicing techniques (e.g. gap filling, revised AD, new methodology);
Data source used;
Selection and justification of the method employed;
Assumptions used to reconstruct time series (e.g. rationale for choice of surrogate data).

Splicing techniques: Countries should provide documentation of any splicing techniques used to complete a timeseries. The documentation should identify the years in which data for the method were not available, the splicing
technique used, and any surrogate or overlap data used. Graphical plots, such as those shown in Section 5.3 canbe useful tools for documenting and explaining the application of splicing techniques.
Mitigation: The category-specific guidance in Volumes 2-5 provide targeted guidance on specific informationthat should be reported for each category, including mitigation and reductions. Generally, countries should
document the approach used to track mitigation activities and provide all relevant parameters such as abatement
utilisation, destruction efficiency, updated emission factors etc.

5.5

TIME SERIES CONSISTENCY QA/QC

No refinement.

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Chapter 5: Time Series Consistency

References
References copied from the 2006 IPCC Guidelines
IPCC (1997). Revised 1996 IPCC Guidelines for National Greenhouse Inventories, Houghton, J.T., Meira Filho,
L.G., Lim B., Tréanton, K., Mamaty, I., Bonduki, Y., Griggs, D.J. and Callander, B.A. (Eds). Intergovernmental
Panel on Climate Change (IPCC), IPCC/OECD/IEA, Paris, France.
IPCC (2000). Good Practice Guidance and Uncertainty Management in National Greenhouse Gas Inventories,
Penman, J., Kruger, D., Galbally, I., Hiraishi, T., Nyenzi, B., Emmanuel, S., Buendia, L., Hoppaus, R.,
Martinsen, T., Meijer, J., Miwa, K. and Tanabe, K. (Eds). Intergovernmental Panel on Climate Change (IPCC),
IPCC/OECD/IEA/IGES, Hayama, Japan.
IPCC (2003). Good Practice Guidance for Land Use, land-Use Change and Forestry, Intergovernmental Panel on
Climate Change, Penman, J., Gytarsky, M., Hiraishi, T., Kruger, D., Pipatti, R., Buendia, L., Miwa, K., Ngara,T., Tanabe, K. and Wagner, F. (Eds), IPCC/IGES, Hayama, Japan.
US EPA (2004). Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990-2003, United States Environmental
Protection Agency (US EPA), National Service Center for Environmental Publications (NSCEP).
http://www.epa.gov/globalwarming/publications/emissions.

References newly cited in the 2019 Refinement
Ouyed, R. and Dobler, W. (2010) Computational Physics: Chapter 4 - Interpolation/Extrapolation Techniques.
(1st Edition): 47-68. 3
2F

3 Available at: https://www.coursehero.com/file/23549186/Ouyed-Chapter-4-Interpolation-Extrapolation-Techniques/.

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