Environmental and Ecological Statistics

, Volume 25, Issue 2, pp 199–219 | Cite as

Unbiased emission factor estimators for large-area forest inventories: domain assessment techniques

  • Luca Birigazzi
  • Javier G. P. Gamarra
  • Timothy G. GregoireEmail author


Large-area forest inventories are often undertaken following a stratified random or systematic design. Yet the strata rarely correspond to the reporting areas of interest (domains) over which the country wants to report specific variables. The process is exemplified by a country aiming to use national forest inventory data to obtain average biomass estimates per forest type for GHGI international reporting, where activity data (areas of land use or land use changes) and emission factors (carbon coefficients) are typically compiled from disparate sources and estimated using different sampling schemes. This study aims to provide a decision tree for the choice of the estimator to be used in forest surveys to draw conclusions about population sub-groups created after (and independently of) the sample selection. This manuscript describes two unbiased estimators that can be used to estimate reporting-strata means, regardless of the sampling design adopted, and extends the result to the common situation in which the reporting-strata are spatially explicit, where a nested group estimator outperforms in terms of both bias and precision other more traditional estimators. From this estimator, an optimal sample allocation scheme is also derived.


Emission factors Forest Reference Levels Greenhouse Gas Inventory National Forest Inventory REDD\({+}\) Survey sampling 



The authors want to thank specially Becky Tavani and Julian Fox from the Forestry Department in FAO, and the whole UN-REDD program for their comments and continuous support in the preparation of this document. Two anonymous reviewers provided deep insights to improve the clarity of the manuscript.


  1. Bechtold WA, Patterson PL (2005) The Enhanced Forest Inventory and Analysis Program—National Sampling Design and Estimation Procedures. USDA Forest Service General Technical Report SRS-80:85Google Scholar
  2. Bey A, Sánchez-Paus Díaz A, Maniatis D, Marchi G, Mollicone D, Ricci S, Bastin JF, Moore R, Federici S, Rezende M, Patriarca C, Turia R, Gamoga G, Abe H, Kaidong E, Miceli G (2016) Collect Earth: land use and land cover assessment through augmented visual interpretation. Remote Sens Basel 8(10):807. CrossRefGoogle Scholar
  3. Chambers RL (2011) Which sample survey strategy? A review of three different approaches. Pak J Stat 27(4):337–357Google Scholar
  4. Cochran WG (1977) Sampling techniques, 3rd edn. Wiley publication in applied statistics. Wiley, New YorkGoogle Scholar
  5. Gasparini P, Di Cosmo L (2015) Forest carbon in italian forests: stocks, inherent variability and predictability using nfi data. For Ecol Manag 337:186–195CrossRefGoogle Scholar
  6. Gregoire TG, Valentine HT (2008) Sampling strategies for natural resources and the environment. Chapman and Hall/CRC, New YorkGoogle Scholar
  7. Holt D, Smith TF (1979) Post stratification. J R Stat Soc Ser A Gen 142(1):33–46. CrossRefGoogle Scholar
  8. Husch B, Beers T, Kershaw J (2002) Forest mensuration. John Wiley & Sons, Hoboken, NJGoogle Scholar
  9. IPCC (2003) Good practice guidance for land use. Land-use change and forestry. Institute for Global Environmental Strategies, KanagawaGoogle Scholar
  10. IPCC (2006) Guidelines for National Greenhouse Gas Inventories, vol 4. Agriculture, forestry and other land use. Institute for Global Environmental Strategies, KanagawaGoogle Scholar
  11. Kish L (1980) Design and estimation for domains. Stat 29(4):209–222. CrossRefGoogle Scholar
  12. Kleinn C, et al. (2003) New technologies and methodologies for national forest inventories. Unasylva-FAO, pp 10–15Google Scholar
  13. Köhl M, Magnussen S (2014) Sampling in forest inventories. In: Köhl M, Pancel L (eds) Tropical forestry handbook. Springer, Berlin, pp 1–50Google Scholar
  14. Köhl M, Magnussen SS, Marchetti M (2006) Sampling methods, Remote Sensing and GIS Multiresource Forest Inventory. Tropical Forestry. Springer, Berlin.
  15. Lehtonen R, Pahkinen E (2004) Practical methods for design and analysis of complex surveys. John Wiley & Sons, Chichester, England.
  16. Lohr SL (2009) Sampling: design and analysis. Advanced (Cengage Learning). Brooks/Cole Publishing Company, BostonGoogle Scholar
  17. Mandallaz D (2008) Sampling techniques for Forest Inventories. Chapman & Hall, London. CrossRefGoogle Scholar
  18. Maniatis D, Mollicone D (2010) Options for sampling and stratification for national forest inventories to implement REDD\({+}\) under the UNFCCC. Carbon Balance Manag 5(1):9. CrossRefPubMedPubMedCentralGoogle Scholar
  19. McDonald TL (2003) Review of environmental monitoring methods: survey designs. Environ Monit Assess 85(3):277–292. CrossRefPubMedGoogle Scholar
  20. Morales-Hidalgo D, Kleinn C, Scott C (2017) Voluntary guidelines on national forest monitoring. FAO, RomeGoogle Scholar
  21. Neyman J (1934) On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. J R Stat Soc 97(4):558–625. CrossRefGoogle Scholar
  22. Pacificador AY Jr (1997) The sample mean under stratified random sampling. Philipp Stat 46:73–82Google Scholar
  23. R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  24. Rao JN, Molina I (2015) Small area estimation. John Wiley & Sons, Hoboken, NJ.
  25. Revolution Analytics, Weston S (2015) doParallel: Foreach Parallel Adaptor for the ’parallel’ Package, R package version 1.0.10.
  26. Särndal CE, Lundström S (2005) Estimation in surveys with nonresponse. John Wiley & Sons, Hoboken, NJ.
  27. Särndal CE, Swensson B, Wretman J (1992) Model assisted survey sampling. Springer, New York.
  28. Schreuder H, Gregoire T, Wood G (1993) Sampling methods for Multiresource Forest Inventory. John Wiley & Sons, New YorkGoogle Scholar
  29. Schreuder HT, Ernst R, Ramírez-Maldonado H (2004) Statistical techniques for sampling and monitoring natural resources. USDA Forest Service General Technical Report RMRS-GTR-126Google Scholar
  30. Schulz B, Bechtold W, Zarnoch S (2009) Sampling and estimation procedures for the vegetation diversity and structure indicator. General technical report PNW, U.S. Deptartment of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, ORGoogle Scholar
  31. SEPAL (2016) System for earth observation data access, processing and analysis for land monitoring. Accessed 14 April 2017
  32. Thompson SK (2012) Sampling. Wiley, Hoboken. CrossRefGoogle Scholar
  33. Tubiello F, Salvatore M, Cóndor Golec R, Ferrara A, Rossi S, Biancalani R, Federici S, Jacobs H, Flammini A (2014) Agriculture, forestry and other land use emissions by sources and removals by sinks. FAO Statistics Division, Food and Agriculture Organization, Rome ESS/14-02:89Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Luca Birigazzi
    • 1
  • Javier G. P. Gamarra
    • 1
  • Timothy G. Gregoire
    • 2
    Email author
  1. 1.Forestry DepartmentFAORomeItaly
  2. 2.School of Forestry and Environmental StudiesYale UniversityNew HavenUSA

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