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Consistent set of additive biomass functions for eight tree species in Germany fit by nonlinear seemingly unrelated regression

  • Christian Vonderach
  • Gerald Kändler
  • Carsten F. Dormann
Research Paper

Abstract

Key message

Biomass functions are relevant for an easy and quick estimation of tree biomass. Nevertheless, additive biomass functions for different species and different components have not been published for the area of Germany, yet. Now, we present a set of additive biomass functions for estimating component and total mass for eight species and up to nine components.

Context

Biomass functions are relevant for an easy and quick estimation of tree biomass, e.g. for carbon budget calculation. Component-specific functions offer even more detail and can be used to answer questions about, e.g., biomass allocation to different components, (nutrient) element stock and flows or the amount and re-distribution of harvested biomass and its consequences.

Aims

Since there exists no published additive biomass functions in the context of Germany, we aimed at providing such equations for different species and different components using a comprehensive data set from different sources.

Methods

We collected several data sets for eight relevant tree species (Norway spruce, n = 1150 trees; Silver fir, n = 31; Douglas fir, n = 161; Scots pine, n = 460; European beech, n = 918; Oak, n = 313; Sycamore, n = 28 and European ash, n = 37) in Germany and adjacent countries, homogenised the component information, imputed missing values and applied nonlinear seemingly unrelated regression to eight (for deciduous trees species) respectively nine (for conifereous species) components simultaneously.

Results

The collected data set contains trees from 7 cm diameter in breast height to around 80 cm. From this broad data basis, we established two sets of additive biomass functions: a simple model using the predictors diameter in breast height and tree height as well as a more elaborate model using up to six predictors.

Conclusion

Finally, we can present additive models for the eight relevant tree species in Germany. Models for Silver fir, European ash and Sycamore are rather limited in their model range due to their input data; the other models are based on a broad range of predictors and are considered to be broadly applicable.

Keywords

Biomass allocation Component mass Multiple imputation SUR regression Norway spruce–Scots pine–Douglas fir–European beech–Oak 

Notes

Acknowledgements

We thank Emil Cienciala from Institute of Forest Ecosystem Research, Jílové u Prahy, Czech Republic; Rainer Joosten from the Ministry for Environment, Agriculture, Conservation and Consumer Protection of the State of North Rhine-Westphalia, Düsseldorf, Germany; Simon Klinner from Eberswalde forestry state center of excellence, Eberswalde, Germany; Ralf Moshammer from Chair of Forest Growth and Yield Science, Technical University of Munich, Germany; Sabine Rumpf from Northwest German Forest Research Institute, Göttingen, Germany; Wendelin Weis from Bavarian State Institute of Forestry, Freising, Germany and Christian Wirth from the Department of Systematic Botany and Functional Biodiversity, University of Leipzig, Germany for kindly supplying their data to our analysis.

Funding information

This study was funded by BMEL / FNR (FKZ: 22006512).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Affleck DLR, Diéguez-Aranda U (2016) Additive nonlinear biomass equations: a likelihood-based approach. For Sci 62:129–140.  https://doi.org/10.5849/forsci.15-126 Google Scholar
  2. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723.  https://doi.org/10.1109/TAC.1974.1100705 CrossRefGoogle Scholar
  3. Bates D, Kliegl R, Vasishth S, Baayen H (2015) Parsimonious mixed models. ArXiv e-prints p 27. http://adsabs.harvard.edu/abs/2015arXiv150604967B
  4. van Buuren S, Groothuis-Oudshoorn K (2011) Mice: multivariate imputation by chained equations in R. J Stat Softw 45:1–67.  https://doi.org/10.18637/jss.v045.i03 Google Scholar
  5. Cienciala E, Černý M, Apltauer J, Exnerová Z (2005) Biomass functions applicable to European beech. J For Sci (Prague) 51:147–154Google Scholar
  6. Cienciala E, Černý M, Tatarinov F, Apltauer J, Exnerová Z (2006) Biomass functions applicable to Scots pine. Trees 20:483–495.  https://doi.org/10.1007/s00468-006-0064-4, treesCrossRefGoogle Scholar
  7. Cienciala E, Apltauer J, Exnerova Z, Tatarinov F (2008) Biomass functions applicable to oak trees grown in Central-European forestry. J For Sci (Prague) 54:109–120Google Scholar
  8. Dong L, Zhang L, Li F (2015) A three-step proportional weighting system of nonlinear biomass equations. For Sci 61:35–45.  https://doi.org/10.5849/forsci.13-193 Google Scholar
  9. Ellenberg H, Mayer R, Schauermann J (1986) Ökosystemforschung - Ergebnisse des Sollingprojekts : 1966-1986; 145 Tab. Ulmer, Stuttgart, [Hrsg.] Nebent.: Ökosystemforschung - Ergebnisse des Sollingprojekts / Ellenberg ; Mayer ; SchauermannGoogle Scholar
  10. Fahrmeir L, Lang S, Kneib T (2009) Regression. Springer, Berlin.  https://doi.org/10.1007/978-3-642-01837-4 CrossRefGoogle Scholar
  11. Fehrmann L, Kleinn C (2006) General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe. For Ecol Manag 236:412–421.  https://doi.org/10.1016/j.foreco.2006.09.026 CrossRefGoogle Scholar
  12. Good NM, Paterson M, Brack C, Mengersen K (2001) Estimating tree component biomass using variable probability sampling methods. J. Agric. Biol. Environ. Stat. 6:258–267CrossRefGoogle Scholar
  13. Heinsdorf D, Krauß HH (1990) Schätztafeln für Trockenmasse und nährstoffspeicherung von kiefernbeständen, IFE-berichte aus Forschung und Entwicklung / Institut für Forstwissenschaften vol 18. Inst. für Forstwiss., Eberswalde-FinowGoogle Scholar
  14. Henningsen A, Hamann JD (2007) Systemfit: A package for estimating systems of simultaneous equations in R. J. Stat. Softw. 23:40.  https://doi.org/10.18637/jss.v023.i04 CrossRefGoogle Scholar
  15. IPPC (2003) Good practice guidance for land use, Land-Use change and forestry institute for global environmental strategies. IGES, Kanagawa PrefectureGoogle Scholar
  16. Joosten R, Schumacher J, Wirth C, Schulte A (2004) Evaluating tree carbon predictions for beech (Fagus sylvatica L.) in Western Germany. For Ecol Manag 189:87–96.  https://doi.org/10.1016/j.foreco.2003.07.037 CrossRefGoogle Scholar
  17. Krauß HH, Heinsdorf D (2008) Herleitung von Trockenmassen und nährstoffspeicherungen in buchenbeständen, Eberswalder forstliche Schriftenreihe, vol 38 Ministerium für ländliche Entwicklung. Umwelt und Verbraucherschutz des Landes Brandenburg, PotsdamGoogle Scholar
  18. Lehtonen A, Makipaa R, Heikkinen J, Sievanen R, Liski J (2004) Biomass expansion factors (BEFs) for scots pine, Norway spruce and birch according to stand age for boreal forests. For Ecol Manag 188:211–224.  https://doi.org/10.1016/j.foreco.2003.07.008 CrossRefGoogle Scholar
  19. Little RJA, Rubin DB (2002) Statistical analysis with missing data, 2nd edn. Wiley series in probability and statistics, Wiley, HobokenCrossRefGoogle Scholar
  20. Lutz JA, Larson AJ, Swanson ME, Freund JA (2012) Ecological importance of large-diameter trees in a temperate mixed-conifer forest. PLoS One 7:e36,131.  https://doi.org/10.1371/journal.pone.0036131. http://www.ncbi.nlm.nih.gov/pubmed/22567132 CrossRefGoogle Scholar
  21. Maltamo M, Mehtätalo L, Vauhkonen J, Packalén P (2012) Predicting and calibrating tree attributes by means of airborne laser scanning and field measurements. Can J For Res 42:1896–1907.  https://doi.org/10.1139/x2012-134 CrossRefGoogle Scholar
  22. Marklund L (1987) Biomass functions for Norway spruce (Picea abies (L.) Karst) in Sweden Report. Department of Forest Survey, SLUGoogle Scholar
  23. de Miguel S, Mehtätalo L, Durkaya A (2014) Developing generalized, calibratable, mixed-effects meta-models for large-scale biomass prediction. Can J For Res 44:648–656.  https://doi.org/10.1139/cjfr-2013-0385 CrossRefGoogle Scholar
  24. Muukkonen P (2007) Generalized allometric volume and biomass equations for some tree species in Europe. Eur J For Res 126:157–166.  https://doi.org/10.1007/s10342-007-0168-4 CrossRefGoogle Scholar
  25. Oehmichen K, Demant B, Dunger K, Grüneberg E, Hennig P, Kroiher F, Neubauer M, Polley H, Riedel T, Rock J, Schwitzgebel F, Stümer W, Wellbrock N, Ziche D, Bolte A (2011) Inventurstudie 2008 und Treibhausgasinventar Wald. Landbauforschung, Sonderheft, 343Google Scholar
  26. Parresol BR (2001) Additivity of nonlinear biomass equations. Canad J Forest Res-Revue Canadienne De Recherche Forestiere 31:865–878.  https://doi.org/10.1139/cjfr-31-5-865 CrossRefGoogle Scholar
  27. Pellinen P (1986) Biomasseuntersuchungen im Kalkbuchenwald. ThesisGoogle Scholar
  28. Pinheiro JC, Bates DM (2000) Mixed-effects models in S and S-plus statistics and computing. Springer, New York ; Berlin ; Heidelberg [u.a.]  https://doi.org/10.1007/b98882 CrossRefGoogle Scholar
  29. Poudel KP, Temesgen H (2015) Methods for estimating aboveground biomass and its components for Douglas-fir and lodgepole pine trees. Can J For Res, 77–87.  https://doi.org/10.1139/cjfr-2015-0256 CrossRefGoogle Scholar
  30. Pretzsch H, Göttlein A, Block J (2012) Entscheidungsstutzungssystem zum nährstoffentzug im Rahmen der Holzernte - Teil 1: Textteil.̈ Report Lehrstuhl f. Department Ökosystem- u. Landschaftsmanagement Techn. Univ. München, WaldwachstumskundeGoogle Scholar
  31. R Core Team (2014) R: a language and environment for statistical computing. http://www.R-project.org/
  32. Riedel T, Kaendler G (2017) Nationale Treibhausgasberichterstattung: Neue Funktionen zur schatzung̈ der oberirdischen Biomasse am Einzelbaum. Forstarchiv 88:31–38Google Scholar
  33. Rossi P, Allenby G, McCulloch R (2005) Bayesian statistics and marketing. Wiley, New York.  https://doi.org/10.1002/0470863692 CrossRefGoogle Scholar
  34. Rubin DB (1987) Multiple imputation for nonresponse in surveys Wiley series in probability and mathematical statistics : Applied probability and statistics. Wiley, New York [u.a.]  https://doi.org/10.1002/9780470316696 CrossRefGoogle Scholar
  35. Rumpf S, Nagel J, Schmidt M (2011) Biomasseschätzfunktionen von Fichte (Picea abies L.), Kiefer (Pinus sylvestris L.) Buche (Fagus sylvatica L.), Eiche (Quercus robur und petraea L.) und Douglasie (Pseudotsuga menziesii L.) für Nordwestdeutschland. ReportGoogle Scholar
  36. Saborowski J, Gaffrey D (1999) RBS, ein mehrstufiges Inventurverfahren zur Schätzung von Baummerkmalen; II. Modifizierte RBS-Verfahren. Allgemeine Forst und Jagdzeitung 170:223– 227Google Scholar
  37. Schafer JL (1997) Analysis of incomplete multivariate data, Monographs on statistics and applied probability, vol 72, 1st edn. Chapman and Hall, London [u.a.]CrossRefGoogle Scholar
  38. Schröder J (2014) Biomasseschätzung für Wälder mittels Fernerkundung und Modellierung : Ergebnisse des deutsch-polnischen Verbundprojekts “ForseenPOMERANIA”, Eberswalder forstliche Schriftenreihe, vol 56, 1st edn. Ministerium für Infrastruktur und Landwirtschaft des Landes Brandenburg, [Potsdam], [Red.] Bd. 56 doppelt vergebenGoogle Scholar
  39. Skovsgaard JP, Nord-Larsen T (2012) Biomass, basic density and biomass expansion factor functions for European beech (Fagus sylvatica L.) in Denmark. Eur J For Res 131:1035–1053.  https://doi.org/10.1007/s10342-011-0575-4 CrossRefGoogle Scholar
  40. Sprugel DG (1983) Correcting for bias in log-transformed allometric equations. Ecol 64:209–210.  https://doi.org/10.2307/1937343 CrossRefGoogle Scholar
  41. Stagoll K, Lindenmayer DB, Knight E, Fischer J, Manning AD (2012) Large trees are keystone structures in urban parks. Conserv Lett 5:115–122.  https://doi.org/10.1111/j.1755-263X.2011.00216.x CrossRefGoogle Scholar
  42. Ter-Mikaelian MT, Korzukhin MD (1997) Biomass equations for sixty-five North American tree species. For Ecol Manag 97:1–24.  https://doi.org/10.1016/S0378-1127(97)00019-4 CrossRefGoogle Scholar
  43. Von Wilpert K, Vonderach C, Zirlewagen D (2015) Enna - A project for sustainable harvesting wooden biomass. VGB PowerTech 7:83–88Google Scholar
  44. Weis W, Göttlein A (2012) Nährstoffnachhaltige Biomassenutzung. LWF aktuell 90:44–47Google Scholar
  45. Weis W, Gruber A, Huber C, Göttlein A (2009) Element concentrations and storage in the aboveground biomass of limed and unlimed Norway spruce trees at höglwald. Eur J For Res 128(5):437–445.  https://doi.org/10.1007/s10342-009-0291-5 CrossRefGoogle Scholar
  46. Westermann T (2014) Untersuchung auftretender Biomasseverluste entlang der Erntekette bei der Energieholzernte im Buchenholz (Fagus sylvatica L.)Google Scholar
  47. Wirth C, Schumacher J, Schulze ED (2004) Generic biomass functions for Norway spruce in Central Europe - a meta-analysis approach toward prediction and uncertainty estimation. Tree Physiol 24:121–139.  https://doi.org/10.1093/treephys/24.2.121 CrossRefPubMedGoogle Scholar
  48. Wutzler T, Wirth C, Schumacher J (2008) Generic biomass functions for Common beech (Fagus sylvatica) in Central Europe: predictions and components of uncertainty. Canad J Forest Res-Revue Canadienne De Recherche Forestiere 38(6):1661–1675.  https://doi.org/10.1139/x07-194 CrossRefGoogle Scholar
  49. Zell J (2008) Methoden für die Ermittlung, Modellierung und Prognose der Kohlenstoffspeicherung in Wäldern auf Grundlage permanenter Großrauminventuren. ThesisGoogle Scholar
  50. Zellner A (1962) An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J Am Stat Assoc 57(298):348–368.  https://doi.org/10.2307/2281644 CrossRefGoogle Scholar
  51. Zhao D, Kane M, Markewitz D, Teskey R, Clutter M (2015) Additive Tree Biomass Equations for Midrotation Loblolly Pine Plantations. Forest Science.  https://doi.org/10.5849/forsci.14-193 CrossRefGoogle Scholar
  52. Zianis D, Muukkonen P, Makipaa R, Mencuccini M (2005) Biomass and stem volume equations for tree species in Europe. Silva Fennica Monograph 1–2:5–63. https://silvafennica.fi/pdf/smf004.pdf Google Scholar

Copyright information

© INRA and Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Forest Research Institute Baden-WürttembergFreiburgGermany
  2. 2.Department of Biometry and Environmental System AnalysisUniversity of FreiburgFreiburgGermany

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