## Uncertainty [MGD Sections]

UNFCCC decisions and requirements

IPCC good practice guidance

Significance and key category analysis

Design decisions relevant to national forest monitoring systems

Quality assurance and quality control

Practical considerations in choosing an integration tool

Estimating uncertainty of area and change in area

Estimating total emissions/removals and its uncertainty

Guiding principles – Estimation and uncertainty

Reporting and verification of emissions and removals

Financial considerations

Sampling

Relative efficiencies

Developing and using allometric models to estimate biomass

IPCC good practice guidance

Significance and key category analysis

Design decisions relevant to national forest monitoring systems

Quality assurance and quality control

Practical considerations in choosing an integration tool

Estimating uncertainty of area and change in area

Estimating total emissions/removals and its uncertainty

Guiding principles – Estimation and uncertainty

Reporting and verification of emissions and removals

Financial considerations

Sampling

Relative efficiencies

Developing and using allometric models to estimate biomass

## Remote Sensing Observations [MGD Sections]

UNFCCC decisions and requirements

IPCC good practice guidance

Relationship to UNFCCC

GHGI coverage, approaches, methods and tiers

Design decisions relevant to national forest monitoring systems

Land cover, land use and stratification

Forest reference emission levels and forest reference levels

Quality assurance and quality control

Guiding principles – Requirements and design decisions

Estimation methods for REDD+ activities

Integration frameworks for estimating emission and removals

Selecting an integration framework

Activity data x emission/removal factor tools

Fully integrated tools

Practical considerations in choosing an integration tool

Guiding principles – Methods and approaches

Remote sensing observations

Coarse resolution optical data

Medium resolution optical data

High resolution optical data

L-band Synthetic aperture radar

C-band and X-band SAR

LIDAR

Global forest cover change datasets

Ground-based observations

National forest inventories

Auxiliary data

Guiding principles – Remote sensing and ground-based observations

Activity data

Methods for estimating activity data

Maps of forest/non-forest, land use, or forest stratification

Detecting areas of change

Additional map products from remote sensing

Estimating uncertainty of area and change in area

Estimating total emissions/removals and its uncertainty

REDD+ requirements and procedures

Reporting forest reference emission levels and forest reference levels

Technical assessment of forest reference emission levels and forest reference levels

Reporting results of REDD+ activities

Technical analysis of the REDD+ annex to the BUR

Additional advice on REDD+ reporting and verification

Guiding Principles – Reporting and verification of emissions and removals

Financial considerations

Country examples – Tier 3 integration

Use of global forest change map data

Relative efficiencies

Developing and using allometric models to estimate biomass

IPCC good practice guidance

Relationship to UNFCCC

GHGI coverage, approaches, methods and tiers

Design decisions relevant to national forest monitoring systems

Land cover, land use and stratification

Forest reference emission levels and forest reference levels

Quality assurance and quality control

Guiding principles – Requirements and design decisions

Estimation methods for REDD+ activities

Integration frameworks for estimating emission and removals

Selecting an integration framework

Activity data x emission/removal factor tools

Fully integrated tools

Practical considerations in choosing an integration tool

Guiding principles – Methods and approaches

Remote sensing observations

Coarse resolution optical data

Medium resolution optical data

High resolution optical data

L-band Synthetic aperture radar

C-band and X-band SAR

LIDAR

Global forest cover change datasets

Ground-based observations

National forest inventories

Auxiliary data

Guiding principles – Remote sensing and ground-based observations

Activity data

Methods for estimating activity data

Maps of forest/non-forest, land use, or forest stratification

Detecting areas of change

Additional map products from remote sensing

Estimating uncertainty of area and change in area

Estimating total emissions/removals and its uncertainty

REDD+ requirements and procedures

Reporting forest reference emission levels and forest reference levels

Technical assessment of forest reference emission levels and forest reference levels

Reporting results of REDD+ activities

Technical analysis of the REDD+ annex to the BUR

Additional advice on REDD+ reporting and verification

Guiding Principles – Reporting and verification of emissions and removals

Financial considerations

Country examples – Tier 3 integration

Use of global forest change map data

Relative efficiencies

Developing and using allometric models to estimate biomass

## Record Keeping [MGD Sections]

Measurement, reporting and verification processes

Operational requirements

Guiding principles – Institutional arrangements

GHGI coverage, approaches, methods and tiers

Significance and key category analysis

Design decisions relevant to national forest monitoring systems

Quality assurance and quality control

Reporting and verification of emissions and removals

REDD+ requirements and procedures

Reporting forest reference emission levels and forest reference levels

Technical assessment of forest reference emission levels and forest reference levels

Reporting results of REDD+ activities

Technical analysis of the REDD+ annex to the BUR

Additional advice on REDD+ reporting and verification

Guiding Principles – Reporting and verification of emissions and removals

Operational requirements

Guiding principles – Institutional arrangements

GHGI coverage, approaches, methods and tiers

Significance and key category analysis

Design decisions relevant to national forest monitoring systems

Quality assurance and quality control

Reporting and verification of emissions and removals

REDD+ requirements and procedures

Reporting forest reference emission levels and forest reference levels

Technical assessment of forest reference emission levels and forest reference levels

Reporting results of REDD+ activities

Technical analysis of the REDD+ annex to the BUR

Additional advice on REDD+ reporting and verification

Guiding Principles – Reporting and verification of emissions and removals

## Integration + Estimation [MGD Sections]

GHGI coverage, approaches, methods and tiers

Design decisions relevant to national forest monitoring systems

Guiding principles – Requirements and design decisions

Estimation methods for REDD+ activities

Integration frameworks for estimating emission and removals

Selecting an integration framework

Activity data x emission/removal factor tools

Fully integrated tools

Practical considerations in choosing an integration tool

Guiding principles – Methods and approaches

Reporting forest reference emission levels and forest reference levels

Technical assessment of forest reference emission levels and forest reference levels

Reporting results of REDD+ activities

Guiding Principles – Reporting and verification of emissions and removals

Financial considerations

Country examples – Tier 3 integration

Design decisions relevant to national forest monitoring systems

Guiding principles – Requirements and design decisions

Estimation methods for REDD+ activities

Integration frameworks for estimating emission and removals

Selecting an integration framework

Activity data x emission/removal factor tools

Fully integrated tools

Practical considerations in choosing an integration tool

Guiding principles – Methods and approaches

Reporting forest reference emission levels and forest reference levels

Technical assessment of forest reference emission levels and forest reference levels

Reporting results of REDD+ activities

Guiding Principles – Reporting and verification of emissions and removals

Financial considerations

Country examples – Tier 3 integration

## Ground Based Observations [MGD Sections]

UNFCCC decisions and requirements

IPCC good practice guidance

GHGI coverage, approaches, methods and tiers

Significance and key category analysis

Design decisions relevant to national forest monitoring systems

Land cover, land use and stratification

Forest reference emission levels and forest reference levels

Quality assurance and quality control

Guiding principles – Requirements and design decisions

Estimation methods for REDD+ activities

Integration frameworks for estimating emission and removals

Selecting an integration framework

Activity data x emission/removal factor tools

Fully integrated tools

Practical considerations in choosing an integration tool

Guiding principles – Methods and approaches

Ground-based observations

National forest inventories

Intensive monitoring sites

Auxiliary data

Guiding principles – Remote sensing and ground-based observations

Emissions/removals factors

Above- and belowground biomass

Dead wood and litter pools

Soil organic carbon

Emissions from prescribed fires and wildfires

National choices in emissions and removals factor estimation

Emission and removal factor uncertainties

Estimating total emissions/removals and its uncertainty

Guiding principles – Estimation and uncertainty

Reporting and verification of emissions and removals

Financial considerations

Sampling

Country examples – Tier 3 integration

Brief review of the potential for estimation of biomass by remote sensing

mgd_Appendix_H

IPCC good practice guidance

GHGI coverage, approaches, methods and tiers

Significance and key category analysis

Design decisions relevant to national forest monitoring systems

Land cover, land use and stratification

Forest reference emission levels and forest reference levels

Quality assurance and quality control

Guiding principles – Requirements and design decisions

Estimation methods for REDD+ activities

Integration frameworks for estimating emission and removals

Selecting an integration framework

Activity data x emission/removal factor tools

Fully integrated tools

Practical considerations in choosing an integration tool

Guiding principles – Methods and approaches

Ground-based observations

National forest inventories

Intensive monitoring sites

Auxiliary data

Guiding principles – Remote sensing and ground-based observations

Emissions/removals factors

Above- and belowground biomass

Dead wood and litter pools

Soil organic carbon

Emissions from prescribed fires and wildfires

National choices in emissions and removals factor estimation

Emission and removal factor uncertainties

Estimating total emissions/removals and its uncertainty

Guiding principles – Estimation and uncertainty

Reporting and verification of emissions and removals

Financial considerations

Sampling

Country examples – Tier 3 integration

Brief review of the potential for estimation of biomass by remote sensing

mgd_Appendix_H

## 5.2.6.2 Method 2: Calculation of emissions/removals factors from change-over-time

For the second method, the same strata are monitored through time, and if change occurs (such as clearing or degradation) then an emissions/removals factor can be calculated from the observed change,

Where and correspond to the carbon density of the forest before and after the change, respectively.

The calculation of the uncertainty of the emission/removal factor in this case depends upon the sampling design, and in particular whether there were permanent plots that were surveyed at both

*t*_{1}and*t*_{2}. In the simple case when there were no permanent plots and the carbon density estimates were obtained from independent samples at*t*_{1}and*t*_{2}, then the overall uncertainty can be calculated in an analogous way to Equation 28,In contrast, if the plots were permanently located and if all of the sample plots measured at

*t*_{1}were re-measured at*t*_{2}, then the samples are correlated, and this correlation should be taken into account. In this case the uncertainty in is given by,where

*r*is the correlation in biomass density from*t*_{1}to*t*_{2}across the sample plots.When biomass density is positively correlated between

*t*_{1}and*t*_{2}, then the final term of Equation 31 acts to reduce the overall variance, and thus to increase the precision. More generally, Equation 30 and Equation 31 can also be used to determine the uncertainty of any change in measured biomass between two time periods, such as in the analysis of general forest monitoring. In this case and in the absence of significant disturbance the correlation is likely to be high, and typically greater than 0.8 (Köhl et al., 2006) especially if*t*_{1}and*t*_{2}are relatively close together in time (< 10 years apart).Equation 30 and Equation 31 represent two extreme cases where either all of the original plots were re-surveyed Equation 31), or none of the original plots were re-surveyed (Equation 30). The intermediate situation occurs when only a fraction of the plots are permanent, with some plots only measured at

*t*_{1}, and some plots only measured at*t*_{2}. This can occur if e.g. some plots were lost or destroyed after*t*_{1}but were replaced by other plots at*t*_{2}, or if there were difficulties with re-locating plots in the field. Ensuring a mixture of both permanent and temporary plots can also be built into the survey design to provide some insurance against the situation where, over time, permanent plots become non-representative, thus potentially introducing bias.A sampling design with a mixture of temporary and permanent plots is known as sampling with replacement (Loetsch & Haller, 1964), with the calculation of the estimate of being more complex than either of the extreme cases. Köhl et al., (2015) provide a more complete description of sampling with replacement in the context of REDD+, and also present the calculations required to estimate for this situation. These calculations use linear regression to update the mean carbon density at

*t*_{1}based on information embedded within the*t*_{2}survey results, and therefore the estimate for the mean change in carbon density no longer equals the simple difference given in Equation 21. If this is considered undesirable, then an alternative estimate for under sampling with replacement (Päivinen & Yli-Kojola, 1989) can be used instead. The calculation is described in Box 27.*Reducing uncertainties*

Uncertainties in the estimation of emission/removal factors can be reduced by:

- increasing sampling density without further sub-stratification
- further sub-stratification to focus sampling on forest areas likely to be affected by REDD+ activities, after as well as before the transfers between strata or land use change has occurred. If further stratification is adopted then the estimates for and may need to be calculated using the estimators appropriate for a stratified sampling design, as described under ‘
*Stratified estimators*’ in Section 5.1.5. No more than 6-8 strata are generally recommended (Cochran 1977, p134). - retaining the same stratification and sampling density but using auxiliary information to verify the direction of change. For example in the case of degradation, if the direction of transfer was consistent with advancing forest fragmentation, then increased forest carbon density would be unlikely and the probability distribution of the degradation estimate should be considered truncated so as to eliminate the possibility of increases.
- Increasing the number of permanent sample plots, if using Method 2 to estimate the change in carbon density over time.

*Other uncertainties*

The calculation for the uncertainty of the emissions factor given in Equation 28 and Equation 30 includes only error due to sampling, and although it is typically the most important source of error, there are a number of other error sources, such as measurement errors, errors associated with the use of allometric models used to predict tree biomass, or errors in expansion factors such as root:shoot ratios for estimating below-ground biomass. These additional errors can be considered independent from the sampling error, and thus the total error variance can estimated by adding them to . Of these additional error sources, uncertainty arising from the prediction of each individual from the biomass model, and uncertainty resulting from a choice of alternative suitable models, are likely the major additional terms that should be considered for inclusion. The former of these diminishes with increasing sample size, and hence its importance is partially a function of the total number of individuals estimated. The latter error source is independent of sample size, and thus cannot be reduced by increased field effort. If alternative allometric models are available for a given situation, then it is recommended that the uncertainty due to model choice be considered for inclusion in the total error estimate. Measurement errors, such as errors in the estimation of stem diameter, are generally small so long as standard forestry protocols have been used.

A wide range of different methods can be used to estimate these additional allometric model error terms, including analytical approximations (e.g. Lo 2005, Ståhl et al., 2014), Monte-Carlo methods (e.g. Molto et al., 2013, Picard et al., 2015) and hybrid approaches (e.g. Chave et al., 2004). These additional error sources can combined into a single variance term, , and added to to provide an estimate of total error.

### Box 27: Calculation of the uncertainty of emissions/removals factors under sampling with replacement

Sampling with replacement is a survey design where the measured change over time involves a combination of permanent and temporary sample plots. The estimate of the uncertainty of the difference between two time periods requires the following quantities:

n12: The number of ‘common’ or permanent plots across both t1 and t2.

n1: The total number of plots at t1.

n2: The total number of plots at t2.

n1- : The number of plots unique to t1.

n-2 : The number of plots unique to t2.

: The variance of the measured carbon density at times t1 and t2.

*r*The plot-level correlation in carbon density between t1 and t2.

From this information two weighting parameters are calculated:

and the uncertainty of the estimate of the emissions/removals factor is given by:

When all of the plots measured at t1 are also measured at t2, then A = B = 1, and Equation 34 reduces to Equation 31. When there are no plots in common between t1 and t2, then A = B = 0, and Equation 34 reduces to Equation 30. In this latter case n12 = 0, and the first term in Equation 34 is undefined.