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Methods to estimate uncertainties EU Workshop on uncertainties in greenhouse gas inventories. 5 to 6 th September 2005, Helsinki, Finland. John Watterson 1 , Justin Goodwin 1 , Melissa Downes 1 , Alistair Manning 2 , and Lorna Brown 3. With thanks to John Abbott 1 and Neil Passant 1.

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Methods to estimate uncertaintiesEU Workshop on uncertainties in greenhouse gas inventories

5 to 6th September 2005, Helsinki, Finland.

John Watterson1, Justin Goodwin1, Melissa Downes1,Alistair Manning2, andLorna Brown3

With thanks to John Abbott1 and Neil Passant1

1National Environmental Technology Centre - Netcen - Harwell Science Park, Didcot, Oxfordshire, OX11 0QJ, UK.

2The Met Office, FitzRoy Road, Exeter, Devon, EX1 3PB, UK.

3Institute of Grassland and Environmental Research (IGER), North Wyke Research Station, Okehampton, Devon, EX20 2SB, UK.

What is in this presentation


  • Overview of methods and guidance – initial thoughts

  • Estimation of uncertainties in activity data (AD)

  • Use of IPCC default uncertainties in national inventories

  • Estimation of uncertainty in national emission factors (EFs)

  • Verification of emission data: How can comparison of different models/methods be used to estimate uncertainties?

  • Estimation of uncertainties in models

  • Combining uncertainties

  • Treatment of correlations

Some general problems with uncertainty analysis

  • Strictly uncertainties in inventories cannot be exactly quantified

    • Unknown sources

    • Gaps in understanding of existing sources

    • Measurement for emission factors are inadequate to quantify uncertainties

    • Emission factors may be inappropriate for specific sources

    • Expert elicitation has a role – workshops later this afternoon


  • We need to understand the likely magnitude of uncertainties and their impacts

  • But there is hope!!

    • We do have some knowledge and understanding of uncertainties

    • We need to identify major uncertainties to direct improvements in GHG inventories

Overview of methods and guidance

  • ‘Approach 1’

    • emission sources aggregated up to level similar to IPCC Summary Table 7A

    • uncertainties then estimated for these categories

    • uncertainties calculated based on error propagation equations

    • Provides basis for Key Source analysis

  • ‘Approach 2’

    • corresponds to Monte Carlo approach

    • Can use software such as @RISK and MS excel spreadsheets – or write your own MC code

  • Recommend reading the 2006 IPCC Guidelines – Volume 1 Chapter 3 “Uncertainties”

Estimation of uncertainties in Activity Data

Estimation of uncertainties in activity data (AD) - examples


Digest of UK Energy Statistics(UK Department for Trade and Industry)

Energy statistics for the UK (imports, exports, production, consumption, demand) of liquid, solid and gaseous fuels

Calorific values of fuels and conversion factors


UK Defra - Institute of Grassland and Environmental Research (IGER)

Estimation of uncertainties in activity data (AD)

Pollution Inventory(Environment Agency)

Scottish Environmental Protection Agency

United Kingdom Petroleum Industry Association

United Kingdom Offshore Operators Association

Iron and Steel Statistics Bureau




Uncertainties in UK fuel activity data

  • Fuel activity data taken from Digest of UK Energy Statistics

  • Uncertainties used for the fuel activity data estimated from the statistical difference between supply and demand for each fuel

  • Effectively the residuals when a mass balance is performed on the production, imports, exports and consumption of fuels

  • For solid and liquid fuels both positive and negative results are obtained indicating that these are uncertainties rather than losses

Uncertainties in UK fuel activity data

  • Quoted uncertainty refers to the total fuel consumption rather than the consumption by a particular sector, e.g. residential coal

  • To avoid underestimating uncertainties, it was necessary to correlate the uncertainties used for the same fuel in different sectors

Uncertainties in UK fuel activity data

  • For gaseous fuels uncertainties include losses and tended to be negative. For natural gas, a correction was made to take account of leakage from the gas transmission system but for other gases this was not possible.

  • The uncertainties in activity data for minor fuels (colliery methane, orimulsion, SSF, petroleum coke) and non-fuels (limestone, dolomite and clinker) were estimated based on judgement comparing their relative uncertainty with that of the known fuels.

Time series of variability in the supply and demand of coal

Difference in supply and demand of coal

Trend suggests improvement in accuracy of estimates of supply and demand over time?

Difference in supply and demand of natural gas

Supply greater than demand – is this all due to losses (fugitive emissions) in the gas transmission system?

Could apply a correction if estimated fugitive emissions are known

Decline in difference reflects measures implemented in the UK to reduce fugitive emissions in the gas transmission system

Uncertainty in coal activity data

Some general comments on using statistical differences derived from energy balance data

  • Uncertainties in the fuel combustion data for specific sectors or applications, are probably higher than the uncertainty suggested by the statistical difference between supply and demand

  • Warning - if a statistical difference is zero it is likely that the data are of uncertain quality and this does not imply zero uncertainty. In these instances, the data quality should be examined for QA/QC purposes and the relevant statistical agencies should investigate

Use of IPCC default uncertainties in national inventories

Using IPCC default uncertainties

  • Where possible, uncertainty data for EFs should be derived from published country specific studies

    • estimate values of uncertainties

    • you may be able to derive the PDF from available data

  • If such data are unavailable, then use default values from guidelines

    • suggest it will be best to refer to the 2006 IPCC guidelines which should be available in early 2006

    • unless you have other evidence, assume PDF normal

    • before using defaults, try using expert judgement / elicitation to produce more applicable data

Typical data available in 2006 IPCC guidelines

  • Data above taken from Stationary Combustion Chapter in 2006 Guidelines

    • Derived from EMEP/CORINAIR Guidebook

    • Very limited sector specific information and wide range of uncertainty quoted

  • GLs suggest an overall uncertainty value of 7 % for the CO2 emission factors of Energy

Using uncertainties in the IPCC guidelines

e.g. Uncertainties in CH4 emissions from Table 2.12 in previous slide

Probability Distribution




 = 1 standard deviation of the mean, E

2 = 50

95% CI = 2 / E

= 50 / 100

= 50 %

Using uncertainties in the IPCC guidelines

e.g. uncertainties in N2O emissions from Table 2.12

These are order of magnitude uncertainties – need to use Approach 2 (i.e. MC simulation) and define a suitable PDF

Estimation of uncertainty in national emission factors (EFs)

Example from data to support UK review of carbon emission factors (CEF)

Large number of samples used to estimate CEF

Checks to see if a weighted mean approach produces a more accurate CEF estimate

Uncertainty values can be used directly from this report

Verification of emission data: how can comparison of different models/methods be used to estimate uncertainties?

Initial considerations

  • One a very basic level comparisons using different models/methods can be used to assess uncertainties by

    • (a) The closeness of the estimates gives a feel for potential gross errors. It depends on how independent the methods are and the potential errors in each method ‑ both estimation and modeling approaches could have problems, but for different reasons.

    • (b) By comparison across a wide number of pollutants a qualitative feel for the uncertainty for any particular pollutant can be gauged.

Verification of the UK GHG inventory

  • The approach uses the Lagrangian dispersion model NAME (Numerical Atmospheric dispersion Modelling Environment)

  • Sorts the observations made at Mace Head into those that represent Northern Hemisphere baseline air masses and those that represent regionally-polluted air masses arriving from Europe. The Mace Head observations and the hourly air origin maps are applied in an inversion algorithm to estimate the magnitude and spatial distribution of the European emissions that best support the observations

  • The technique has been applied to 2-yearly rolling subsets of the data and used to estimate longer term averages

Verification of the UK GHG inventory

  • The inversion (best-fit) technique, simulated annealing, is used to fit the model emissions to the observations.

  • It assumes that the emissions from each grid box are uniform in both time and space over the duration of the data. This in turn implies that the release

    • is assumed independent of meteorological factors such as temperature and diurnal or annual cycles, and

    • that, in so far as the emission relates to industrial production or other anthropogenic activity, use there is no definite cycle or intermittency.

  • The estimated releases will include any natural release as well as anthropogenic emissions.

Based on meteorological analyses

NAME model derived air origin maps

Darker shade – Greater contribution from area

All possible surface sources over previous 10 days

Maps generated for each hour 1995-2004

Baseline analysis

Mace Head

Inverse modelling

  • Aim: generate emission estimates from ‘polluted’ observations (above baseline)

  • Use NAME to predict concentration time series at Mace Head from each source

  • Scale emissions to obtain best match between model and observations

    • Simulated Annealing

    • Iterative technique

    • No prior information

  • Apply to all monitored species

  • Independent verification of emissions

Equation: Ae = m

Minimise: m - Ae

A: the dilution matrix

m: observed concentrations

(- baseline)

e: emissions

NAME model predictions of emissions of N2O across Europe

Nitrous oxide – comparison of GHG inventory estimates and model estimates

Thermal oxidiser abatement system fitted to adipic acid plant

Quality of agreement between UK GHGI estimates and model

  • Reasonable agreement between modelled and measured which gives confidence of the inventory estimates

  • But fitment of abatement to adipic acid plant not reflected in NAME model trend

  • This problem investigated with representatives from the adipic acid plant and the meteorological office

  • Where was the problem – GHG inventory or model?

Answer – probably mostly the model, but check the GHG inventory also

  • The NAME model assumes no definite cycle or intermittency in emissions – this was not the case – periods were the adipic acid plant was shut down and periods where abatement not operating

    • So, make adjustments to the model

  • The oxidised nitrogen from wastewater is not currently included in the GHG – this (small) source could be added to improve the accuracy of the N2O estimate

    • So, make checks on the inventory

Estimation of uncertainties in models

Initial considerations

  • Model is a representation of a ‘real world’ system – but can never exactly mimic the ‘real world’

  • Key considerations in model uncertainty

    • Has the correct ‘real world’ been identified – for example, the ‘real world’ in a GHG inventory would be a complete and unbiased inventory

    • Is the model an accurate representation of this ‘real world’?

Example using N2O from agriculture in the UK GHG inventory

Recent detailed study into the uncertainty of the model used to estimate emissions from the UK GHG inventory

An inventory of nitrous oxide emissions from agriculture using the IPCC methodology: emission estimate, uncertainty and sensitivity analysis (2001). Brown, L., Amstrong Brown, S., Jarvis, S.C., Syed, B., Goulding, K.W.T., Philips, V.R., Sneath, R.W. and Pain, B.F. Atmos Environ., 35, 1439-1449.


  • Monte Carlo approach used to estimate the uncertainty in the model

    • 26 parameters were included

    • For some parameters, a beta pert distribution used derived from IPCC minima, maxima and most likely (default) values. No information in IPCC GLs to suggest alternative distribution.

  • Sensitivity analysis performed using multivariate stepwise regression using @RISK software


  • N2O emissions from UK agriculture were estimated to be 87 Gg N2O-N for both 1990 and 1995 using the IPCC default EFs

  • Total estimate shown to have high overall uncertainty of 62%

  • Comparisons of results from this study and other UK-derived inventories suggests the default IPCC inventory may overestimate emissions

  • Uncertainty in individual components determined

  • This has identified the components of the model where improvements could be made since

    • emissions are a significant fraction of the total and

    • the associated uncertainties are high

Uncertainty associated with parameters

Treatment of correlations


When to use a correlation

  • Activity Data are calculated via mass balance

    • Supply and demand of fuels in energy statistics

  • Emission Factors are shared across activities

    • Natural gas or gas/diesel oil used by different sources

  • Emission Factors are calculated or extrapolated across a time series

    • Methane from livestock

Correlations (ii)

How to use a correlation

  • Can be used in combination

    • Activity and EF’s correlated

  • If correlations occur, the easiest and most effective method is to use a Monte Carlo Simulation

  • NB: Correlations may not have an effect. Will only affect areas where the inventory is sensitive and/or the dependencies are very strong

Combining uncertainties

Combining uncertainties

  • For Tier 2 analysis - a  Monte Carlo approach is necessary.

    • Uncertainties are set and the correlations marked. The software is then set up and run and automatically takes these into account.

  • For component uncertainties <60%, a sum of squares approach can be used.

    • UT = (UE2 + UA2)

  • For component uncertainties >60% all that is possible is to combine limiting values to define an overall range

    • U% = (E+A+E*A/100) and L% = (E+A-E*A/100)

  • U=Uncertainty, T=total, E=Emission Factor, A=Activity Data, U%=upper limit, L%= lower limit

Example Monte Carlo model

Calculating uncertainties




Fuel/Activity Uncertainty

Emission Uncertainty

Emission Factor Uncertainty


Probability Distribution





Distribution Types:


Tier 2 - Monte-Carlo Method

Input 2



Input 1

Tier 2 - Monte-Carlo Method












  • Step 1: Assess component uncertainties

    • Expert Judgement & Data

      • Maximum, Minimum

      • Distribution type

  • Step2: Run the analysis

    • up to 20,000 iterations

  • Step 3: Results

    • 5th - 95th percentile = Range as % of the mean





  • Correlations do affect the overall uncertainty result – suggest approach is to start identifying inputs that are correlated, rather than setting up the model with the input level at the lowest level of aggregation and examining the correlations in each parameter individually

  • It is easy to produce MC output that superficially looks credible – but carefully check underlying assumptions

  • You can write a programme to complete a MC analysis – you do not need to use an expensive commercial package

Demonstration of MC model

  • UK has set up MC model to illustrate certain key points

    • Suggested layout of a simple MC model

    • Defining non-correlated PDFs

    • Considering correlations

    • How to deal with emissions and associated uncertainty where individual EF and AD uncertainties are unknown

    • Example output table

Final thoughts





  • Read the IPCC guidance

  • Consider comments made by Expert Reviewers and in Peer Reviews

  • Gather country specific information on EFs and AD

  • Use IPCC defaults only if sufficient information cannot be found

  • Careful with Monte Carlo analysis – easy to produce poor quality work

  • Get the help of a statistician

  • Ask for peer review

  • Reflect on output of the uncertainty analysis – is it sensible?

Background reading first!

Gather sufficient information

Follow IPPC Good Practice

Try to be open to criticism!


  • The UK GHG inventory is funded by UK Defra and the Devolved Administrations

  • UK Defra

    • Jim Penman – Head Response Strategies

    • Susan Donaldson – GHG Science Advisor

    • Joanne Halliday – GHG Science Advisor

    • Steve Cornellius - GHG Science Advisor

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