REDD+ Uncertainty Training

Foundational Training on Uncertainty Statistics in Carbon Accounting for Jurisdictional ART-TREES Programs (V2.0)

Preface

This training resource was commissioned by Winrock International under its JTAP portfolio (20065-2025-ICA-03) as a Foundation Module for uncertainty quantification training in jurisdictional REDD+ carbon accounting. The following training curriculum provides methodological guidance for quantifying, reporting, and reducing uncertainty in REDD+ carbon accounting in accordance with ART-TREES Standard (V2.0) requirements and the IPCC 2019 guidelines (ART, 2021; IPCC, 2019).

Rather than viewing estimation uncertainty as a penalty to manage, this framework treats it as a strategic metric for identifying dominant error sources and optimizing credit issuance (Camara et al., 2024; Duncanson et al., 2021; Simoes et al., 2021). Projects investing in targeted uncertainty reduction can achieve improved crediting revenue through minimizing penalty deductions, as well as through stronger pricing from enhanced credibility and lower verification and monitoring costs (Köhler & Huth, 2010).

Uncertainty Potential

Recent analyses have identified opportunities to strengthen uncertainty reporting across REDD+ programs. According to Butler et al. (2024), while 91% of participating countries report activity data uncertainty, only 4-14% report emission factor and allometric uncertainty. This pattern presents an opportunity for jurisdictions to enhance methodological completeness and improve credit issuance outcomes. Research demonstrates that comprehensive uncertainty quantification, including emission factors and modeling assumptions contribute to significant variance across reference levels ranging from 4.2% to 262.2% (Pelletier et al., 2013).

Comprehensive uncertainty reporting serves multiple strategic objectives beyond regulatory compliance. When jurisdictions systematically quantify and report all uncertainty sources, they establish baseline metrics for improvement and unlock pathways to enhanced credit revenue. Butler et al. (2024) note that comprehensive assessment can initially produce wider confidence intervals, but this transparency enables targeted methodological refinements that systematically reduce actual uncertainty over time, a process that directly increases credit issuance and revenue. Recognizing the importance of incentivizing comprehensive reporting, results-based payment programs have implemented supportive mechanisms. The FCPF Carbon Fund uses a capped uncertainty deduction schedule that removes disincentives for comprehensive reporting:

FCPF Uncertainty Deduction Conservativeness Factors:¹

• No deduction if uncertainty is ≤15%
• 4% deduction if uncertainty is 15–30%
• 8% deduction if uncertainty is 30–60%
• 12% deduction if uncertainty is 60–100%
• 15% maximum deduction if uncertainty is >100%

This structure ensures that programs with very high initial uncertainty face the same maximum 15% deduction, removing the penalty for reporting comprehensive uncertainty while maintaining incentives to improve. The ART-TREES Standard goes further by allowing participants to recover over-deducted credits when cumulative uncertainty decreases across multi-year crediting periods (Section 8, V2.0). These provisions reward demonstrable improvements and create positive incentives for methodological investment.

Uncertainty Compliance

Section 8 of the ART Standard V2.0 mandates the following criteria (ART, 2021, p. 45):

1. Monte Carlo simulations: Minimum 10,000 iterations for uncertainty propagation
2. 90% confidence intervals: Half-width calculation for adjustment factors
3. Conservative bias: Systematic underestimation acceptable, overestimation prohibited
4. Whole-chain integration: Combine activity data + emission factor uncertainties
5. Crediting period aggregation: Flexibility to sum uncertainty deductions across years
6. Allometry Exemption: Allometric modelling uncertainty is excluded as non-mandatory.

Equation 10: Uncertainty deduction

\[ UNC_t = (GHGER_t + GHGREMV_t) \times UA_t \]

Equation 11: Uncertainty adjustment factor

\[ UA_t = 0.524417 \times \frac{HW_{90\%}}{1.645006} \]

Primer on Uncertainty Statistics

Forest carbon inventory fundamentally relies on making inferences about true population estimates from limited samples of observed data. But a forest is complex, and our measuring tools and samples are never perfect. For example, when we measure 50 field plots across a million-hectare jurisdiction, we expect that our sample mean will vary from the true mean. Uncertainty is simply how much doubt we have that our measured average is close to the true average.

Fundamentally, this difference between our sampled average and the assumed true population average² is what informs the metrics of statistical uncertainty. For instance, this dispersion in estimates is computed using:

• Standard deviation (DescTools::SD()):³ Measures the spread of observed points around the sample mean, a property of our field sample itself describing how spread out our observations are from one another and their mean.
• Standard error (DescTools::MeanSE()): Measures how much the sample mean is expected to deviate from the true population estimates that are assumed to follow the universal law of large numbers when at critical mass. In effect, this property characterizes our subsample’s precision according to that assumed truth. Expressed as \(\text{se} = \frac{\sigma}{\sqrt{n}}\), this also implies standard errors will ultimately decrease the more we increase our sample size.

The distinction is critical: standard deviation quantifies data variability, while standard error quantifies estimation precision. For example, under the ART-TREES Standard (V2.0), the 90% confidence interval uses a z-value of 1.645, meaning we can be 90% confident the true mean lies within ±1.645 standard errors of our sample mean.

Root Mean Squared Error (DescTools::RMSE(); Armstrong (1978)) measures a slightly different dimension of uncertainty by estimating prediction accuracy rather than sampling precision. While standard error decreases with larger sample sizes, RMSE measures model performance and remains constant unless the model itself improves:

\[ RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\text{ref}_i - x_i)^2} \]

In forest carbon accounting, RMSE quantifies how much model predictions deviate from observed reference values. Common applications include allometric equations, remote sensing models predicting forest attributes, and land cover classification accuracy assessments. While ART-TREES v2.0 exempts allometric uncertainty from mandatory reporting, RMSE values inform emission factor uncertainty and sampling design decisions.

Primer on Monte Carlo Methods

Monte Carlo simulation traces its roots to the Markov Chain, developed by Andrey Markov in the early 1900s (Sheynin, 1989). At the time, Markov publicly feuded with Pavel Nekrasov, who claimed statistical laws required independent events, arguing this supported divine free will. To disprove this, Markov analyzed the first 20,000 letters of a poem by Pushkin finding 8,638 vowels and 11,362 consonants. He demonstrated that the probability of the next letter depends on the current letter, vowels tend to follow consonants and vice versa, yet aggregated over thousands of letter sequences, the system still converged to a stable distribution (43% vowels, 57% consonants). This proved statistical predictability holds even with strong causal dependence.

The technique remained theoretical until 1948, when Nicholas Metropolis, John von Neumann, and Stanislaw Ulam at Los Alamos developed the Monte Carlo method and named it after Ulam’s uncle’s love for the roulette casions of Monte Carlo (Metropolis & Ulam, 1949). Metropolis rewired the ENIAC computer to perform the first Monte Carlo simulations of nuclear core criticality. They discovered that rather than generating random configurations and weighting by the Boltzmann factors, they sampled configurations with probability and weighted globally dramatically reducing computational cost.

A key to its success in nuclear science related to its distinction of one-sided and two-sided error distributions that enabled the design of false-biased simulation algorithms. Specifically, the study of nuclear reactivity required false-bias metrics to more definitively estimate critical levels of neuron activity for achieving a nuclear chain reaction. It is worth noting how the Monte Carlo method emerged from the statistics of critical systems where different rules of dependency are assumed. Critical systems are characterized by self-organizing populations that exist dynamically between steady-state thresholds and unpredictable tipping points, such as in patterns of mega-fires, the spread of beetle outbreaks, or in disease epidemics (Sornette, 2006) where assumption of causal dependence prevails. These approaches also play an increasing role in the spatial and temporal modelling of plant ecology and remote sensing of forest ecosystems (Schrodt et al., 2025).

Operationally, the Monte Carlo method involves three core mathematical principles:

1. Pseudo-random Number Generation
2. Markov-Rule of Memory-less Dependence
3. Law of Large Numbers & Convergence

Pseudo-random Number Generation: Monte Carlo simulations use pseudo-random number generators (PRNG’s) producing deterministic sequences that appear random. The mathematical foundation mirrors prime number distributions, simulating local unpredictability combined with global statistical regularity. There are four different kinds of randomization algorithms that meet Monte Carlo simulation requirements. Randomization compliance can be verified using primality tests published as coded scripts (Baillie & Wagstaff, 1980; Murray, 2003; Solovay & Strassen, 1977).

Markov Property Memory-less Dependence: The system “remembers” only the immediate previous state. For example, this limits temporal bounds of resampling so that each year’s carbon stock projection requires only the current year’s state, not 30 years of history, dramatically reducing computational complexity.

\[ P(X_{t+1} | X_t, X_{t-1}, ...) = P(X_{t+1} | X_t) \]

Law of Large Numbers: As iterations increase, sample statistics converge to population parameters. Standard error decreases by \(\sqrt{m}\) when samples increase by factor \(m\). This informs ART requirement for minimum 10,000 iterations.

Causal Dependence in Forest Ecology

This concept of causal dependence is crucial in forest carbon science because ecosystems are not a series of independent coin flips. They are dynamic systems where the state of the forest in Year ^t+1 is heavily dependent on the state in Year ^t.

• Tipping Points and Disturbances: Markovian principles model system transitions, which are vital for understanding disturbance regimes, such as wildfire and pest outbreaks, and potential for ecological tipping points. For example, the probability of a forest transitioning to a degraded state this year is dependent on its current health, not its health 50 years ago.

• Modeling Uncertainty: By incorporating these dependent, causal relationships, Monte Carlo models can more realistically simulate the path-dependent uncertainty of carbon stocks over time, rather than treating all uncertainty sources as randomly independent variables

Training Curriculum

This curriculum addresses the four primary sources of uncertainty in REDD+ carbon accounting: allometric equations, emission factors, activity data, and their combined error propagation. Winrock International works with partner jurisdictions to implement targeted interventions using Monte Carlo simulation frameworks tailred to each domain.⁴ The curriculum draws on real-world examples and practical exercises from this ongoing work:

• Chapter 1 Allometric Uncertainty: Strategic interventions in allometric estimation are presented that reduce uncertainty by 30-50%, including: development of localized equations (Tier 2) through destructive sampling; model ensemble approaches using Bayesian averaging; integration of wood density and height data from LiDAR or field measurements; and implementation of standardized measurement protocols with quality assurance/quality control (QA/QC) procedures.
• Chapter 2 Emission Factor Uncertainty: Multiple methodological interventions and strategic data selections offer important uncertainty reductions in emission factors, including: field validation campaigns, laboratory quantification of organic carbon and soil profiles; seasonal modelling of fuel loads, moisture content, and disturbance severity sampling; and analysis of stand regeneration and updated growth curves. Additionally, the strategic selection of IPCC default emission factors across land conversions represents an often-overlooked resource in emissions accounting. This chapter presents typical default emission factors ranked by their associated uncertainty levels.
• Chapter 3 Activity Data Uncertainty: Significant uncertainty reductions can be achieved through enhanced reference data collection and data cube processing informing improved image classification algorithms; multi-temporal validation datasets and noise signal seperation; systematic accuracy assessment protocols.
• Chapter 4 Monte Carlo Aggregation: Effective Monte Carlo simulation frameworks incorporate sensitivity analyses to identify uncertainty sources and quantify their contribution to overall credit deductions. Winrock provides technical assistance in implementing these strategies, drawing on use cases to help jurisdictions prioritize cost-effective improvements and quality assurance measures tailored to their specific forest conditions and monitoring infrastructure.

Armstrong, J. S. (1978). Long-range forecasting: From crystal ball to computer (2nd ed.). Wiley.

ART. (2021). The REDD+ environmental excellence standard (2.0 ed.). https://www.artredd.org/wp-content/uploads/2021/12/TREES-2.0-August-2021-Clean.pdf

Baillie, R., & Wagstaff, S. S. (1980). Lucas pseudoprimes. Mathematics of Computation, 35(152), 1391–1417.

Butler, B. J., Sass, E. M., Gamarra, J. G., Campbell, J. L., Wayson, C., Olguıń, M., Carrillo, O., & Yanai, R. D. (2024). Uncertainty in REDD+ carbon accounting: A survey of experts involved in REDD+ reporting. Carbon Balance and Management, 19(1), 22.

Camara, G., Simoes, R., Souza, F., Menino, F., Pelletier, C., Andrade, P. R., Ferreira, K., & Queiroz, G. (2024). Uncertainty and active learning analysis. In Satellite time series on earth observation data cubes. https://e-sensing.github.io/sitsbook/uncertainty-and-active-learning.html#uncertainty-and-active-learning

Duncanson, L., Disney, M., Armston, J., Nickeson, J., Minor, D., & Camacho, F. (2021). Aboveground woody biomass product validation good practices protocol. https://doi.org/10.5067/DOC/CEOSWGCV/LPV/AGB.001

IPCC. (2019). 2019 refinement to the 2006 IPCC guidelines for national greenhouse gas inventories (Agriculture, Forestry and Other Land Use, Vol. 4). Intergovernmental Panel on Climate Change. https://www.ipcc-nggip.iges.or.jp/public/2019rf/vol4.html

Köhler, P., & Huth, A. (2010). Towards ground-truthing of spaceborne estimates of above-ground life biomass and leaf area index in tropical rain forests. Biogeosciences (Online), 7(8), 2531–2543.

Metropolis, N., & Ulam, S. (1949). The monte carlo method. Journal of the American Statistical Association, 44(247), 335–341.

Murray, S. H. (2003). The schreier-sims algorithm. Essay Submitted to the Department of Mathematics of the Australian National University.

Pelletier, J., Martin, D., & Potvin, C. (2013). REDD+ emissions estimation and reporting: Dealing with uncertainty. Environmental Research Letters, 8(3), 034009.

Schrodt, F., Beck, M., Estopinan, J., Bowler, D. E., Fontaine, C., Gaüzère, P., Goury, R., Grenié, M., Martins, I. S., Morueta-Holme, N., & al., et. (2025). Advancing causal inference in ecology: Pathways for biodiversity change detection and attribution. Methods in Ecology and Evolution, 16(10), 2276–2304.

Sheynin, O. B. (1989). AA markov’s work on probability. Archive for History of Exact Sciences, 39(4), 337–377.

Simoes, R., Camara, G., Queiroz, G., Souza, F., Andrade, P. R., Santos, L., Carvalho, A., & Ferreira, K. (2021). Satellite image time series analysis for big earth observation data. Remote Sensing, 13(13), 2428.

Solovay, R., & Strassen, V. (1977). A fast monte-carlo test for primality. SIAM Journal on Computing, 6(1), 84–85.

Sornette, D. (2006). Critical phenomena in natural sciences: Chaos, fractals, selforganization and disorder: Concepts and tools. Springer.

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1. https://www.forestcarbonpartnership.org/sites/default/files/documents/fcpf_buffer_guidelines_v4.2_clean_cf28.pdf

2. The fundamentals of parametric statistics are all based on the calculation of mean estimates of large populations. Key to this, however, is the empirical assumption that true populations, when large enough numbers are sampled, all begin to converge around a specific shape in distribution that follows the dimensions of a bell-curve.

3. The package::function()notation (e.g., DescTools::SD()) explicitly identifies which package each function belongs to, helping users verify package installations and resolve naming conflicts.

4. i.e., https://seamusmurphy.shinyapps.io/winrock-monte-carlo/