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

  • Christian VonderachEmail author
  • Gerald Kändler
  • Carsten F. Dormann
Research Paper


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.


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.


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.


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.


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.


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.


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



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.


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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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