# Data and non-linear models for the estimation of biomass growth and carbon fixation in managed forests

Ariane Albers, Pierre Collet, Anthony Benoist, Arnaud Hélias

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Ariane Albers, Pierre Collet, Anthony Benoist, Arnaud Hélias. Data and non-linear models for the estimation of biomass growth and carbon fixation in managed forests. Data in Brief, 2019, 23, pp.103841. 10.1016/j.dib.2019.103841. hal-02118935v2

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Data Article

# Data and non-linear models for the estimation of biomass growth and carbon fixation in managed forests

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Ariane Albers<sup>a, b, c, *</sup>, Pierre Collet<sup>a</sup>, Anthony Benoist<sup>c, d</sup>, Arnaud Hélias<sup>b, c, e</sup>

## ARTICLE INFO

**Article history:**

Received 27 January 2019

Received in revised form 28 February 2019

Accepted 6 March 2019

Available online 16 March 2019

**Keywords:**

Biogenic carbon modelling

Carbon fixation

Forestry biomass

Non-linear growth

## ABSTRACT

The data and analyses presented support the research article entitled "Coupling partial-equilibrium and dynamic biogenic carbon models to assess future transport scenarios in France" (Albers et al., 2019). Carbon sequestration and storage in forestry products (e.g. transport fuels) is sought as a climate change mitigation option. The data presented support and inform dynamic modelling approaches to predict biomass growth and carbon fixation dynamics, of a tree or forest stand, over specific rotation lengths. Data consists of species-specific yield tables, parameters for non-linear growth models and allometric equations. Non-linear growth models and allometric equations are listed and described. National statistics and surveys of the wood supply chain serve to identify main tree species, standing wood volumes and distributions within specific geographies; here corresponding to managed forests in France. All necessary data and methods for the computation of the annual fixation flows are presented.

© 2019 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

<footnote><sup>a</sup> IFP Energies Nouvelles, 1 et 4 Avenue de Bois-Préau, 92852 Rueil-Malmaison, France</footnote>

<footnote><sup>b</sup> LBE, Montpellier SupAgro, INRA, UNIV Montpellier, Narbonne, France</footnote>

<footnote><sup>c</sup> Elsa, Research Group for Environmental Lifecycle and Sustainability Assessment, Montpellier, France</footnote>

<footnote><sup>d</sup> CIRAD – UPR BioWooEB, Avenue Agropolis, F-34398, Montpellier, France</footnote>

<footnote><sup>e</sup> Chair of Sustainable Engineering, Technische Universität Berlin, Berlin, Germany</footnote>

<footnote>DOI of original article: https://doi.org/10.1016/j.apenergy.2019.01.186</footnote>

<footnote>* Corresponding author. IFP Energies Nouvelles, 1 et 4 Avenue de Bois-Préau, 92852 Rueil-Malmaison, France.
E-mail address: ariane.albers@ifpen.fr (A. Albers).</footnote>
Specifications table

<table><tr><td>Subject area</td><td>Biology, Ecological modelling</td></tr><tr><td>More specific subject area</td><td>Dynamic modelling of forest biomass growth and annual carbon fixation</td></tr><tr><td>Type of data</td><td>Text, figures, tables</td></tr><tr><td>How data was acquired</td><td>Combination of secondary sources from public datasets available online and peer-reviewed literature, including national statistics and surveys, yield tables, non-linear growth parameters and allometric relations.</td></tr><tr><td>Data format</td><td>Filtered and analysed secondary data.</td></tr><tr><td>Experimental factors</td><td>Some data was re-expressed into different units when necessary to inform the models.</td></tr><tr><td>Experimental features</td><td>Non-linear growth was computed using data retrieved from yield tables. Initial parameters were compiled from literature to fit the non-self-starting non-linear regression model used for growth. Allometric equations were compiled and selected for tree volume estimations. Finally, mean biomass growth and carbon fixation was computed per one tonne of forestry biomass of interest.</td></tr><tr><td>Data source location</td><td>Managed forest systems in France or from other regions when data was not available for France (see Table 1).</td></tr><tr><td>Data accessibility</td><td>All data used and generated is included in this article and in its Supplementary Material</td></tr><tr><td>Related research article</td><td>A. Albers, P. Collet, D. Lorne, A. Benoist, A. Hélias, Coupling partial-equilibrium and dynamic biogenic carbon models to assess future transport scenarios in France, Appl. Energy. 239 (2019) 316–330. https://doi.org/10.1016/j.apenergy.2019.01.186</td></tr></table>

Value of the data

* A large compilation of secondary data, useful to facilitate dynamic carbon modelling of biomass growth and carbon fixation in managed forest systems.

* Part of the data is generic enough to be used to model stands of unknown or mixed species.

* The proposed modelling approach is flexible and applicable to any tree species and management practice (R script to fit non-self-starting non-linear regression growth parameters included).

* Annual carbon stocking factors are provided for all tree species of the French wood supply chain.

1. Data

The data presented provides the basis for a non-linear forestry biomass growth model, whose outputs were used for modelling time-dependent carbon fixation in forest biomass [1]. This data article aggregates data from various datasets, including national statistics and surveys, yield tables, non-linear growth parameters and allometric relations (Table 1). The wood supply chain in France is represented by 12 main forest tree species (Table 2). National surveys and statistical results describe the distribution per tree species, used for weighted mean estimates (Table 3). Yield tables tabulate the age-dependent mean tree development and productivity of fully stocked managed stands, measured largely from long-standing experimental forest stand surveys. Yield table data is used to estimate i) initial parameters to fit non-self-starting non-linear regression models to predict tree growth, ii) age-dependent growth variables, and iii) site-dependent management practices (e.g. thinning periods, rotation cycles). Allometric models are used for volume estimation. All data sources primarily originate from French studies,

<table><caption>**Table 1**

General sources.</caption><thead><tr><td>Specific data</td><td>Databases</td><td>Source</td></tr></thead><tbody><tr><td>Species traits</td><td>Global TRY Plant Trait Database (https://www.try-db.org/TryWeb/Home.php)</td><td>[3]</td></tr><tr><td>National forestry inventories</td><td>National Institute of Geographic and Forest Information, Ministry of Agriculture, Agro-food and Forests</td><td>[4]</td></tr><tr><td>Wood density</td><td>International DRYAD Global Wood Density Database (http://datadryad.org/)</td><td>[5]</td></tr><tr><td>Allometric equations</td><td>GlobAllomeTree international database platform (http://www.globallometree.org/about/)</td><td>[6]</td></tr><tr><td>Carbon content</td><td>Food and Agricultural institute (FAO), Forestry Commission, and other</td><td>[7,8]</td></tr></tbody></table>
<table><caption>**Table 2**

Species traits of forest species wood supply chain in France.</caption><thead><tr><th>Common name</th><th>Species botanical name</th><th>Family</th><th>Genus</th><th>Species epithet</th><th>Leaf type</th><th>Leaf Phenology</th></tr></thead><tbody><tr><td>Douglas fir</td><td><i>Pseudotsuga menziesii</i></td><td>Pinaceae</td><td>Pseudotsuga</td><td>menziesii</td><td>needle</td><td>evergreen</td></tr><tr><td>Norway spruce</td><td><i>Piceaabies</i></td><td>Pinaceae</td><td>Picea</td><td>abies</td><td>needle</td><td>evergreen</td></tr><tr><td>Maritime pine</td><td><i>Pinus pinaster</i></td><td>Pinaceae</td><td>Pinus</td><td>pinaster</td><td>needle</td><td>evergreen</td></tr><tr><td>Silver fir</td><td><i>Abies alba</i></td><td>Pinaceae</td><td>Abies</td><td>Alba</td><td>needle</td><td>evergreen</td></tr><tr><td>Scots pine</td><td><i>Pinus sylvestri</i></td><td>Pinaceae</td><td>Pinus</td><td>sylyvestri</td><td>needle</td><td>evergreen</td></tr><tr><td>Sweet chestnut</td><td><i>Castanea sativa</i></td><td>Fagacea</td><td>Castanea</td><td>sativa</td><td>broadleaf</td><td>deciduous</td></tr><tr><td>Hornbeam</td><td><i>Carpinus betulus</i></td><td>Corylaceae</td><td>Carpinus</td><td>betulus</td><td>broadleaf</td><td>deciduous</td></tr><tr><td>Ash</td><td><i>Fraxinus excelsior</i></td><td>Oleaceae</td><td>Fraxinus</td><td>excelsior</td><td>broadleaf</td><td>deciduous</td></tr><tr><td>European beech</td><td><i>Fagus sylvatica</i></td><td>Fagacea</td><td>Fagus</td><td>syhvatica</td><td>broadleaf</td><td>deciduous</td></tr><tr><td>Sessile oak</td><td><i>Quercus petraea</i></td><td>Fagacea</td><td>Quercus</td><td>petraea</td><td>broadleaf</td><td>deciduous</td></tr><tr><td>English oak</td><td><i>Quercus robur</i></td><td>Fagacea</td><td>Quercus</td><td>robur</td><td>broadleaf</td><td>deciduous</td></tr><tr><td>White oak</td><td><i>Quercus pubescens</i></td><td>Fagacea</td><td>Quercus</td><td>pubescens</td><td>broadleaf</td><td>deciduous</td></tr></tbody></table>

Source: Global TRY Plant Trait Database [3].

<table><caption>**Table 3**

National inventory (2012–2016) and distribution of living standing volume per forest tree species in France.</caption><thead><tr><th>Common name</th><th>Species</th><th>Distribution standing volume [Bm³]</th><th>Distribution standing volume [%]</th></tr></thead><tbody><tr><td>Douglas fir</td><td><i>P. menziesii</i></td><td>106</td><td>4</td></tr><tr><td>Norway spruce</td><td><i>P. abies</i></td><td>213</td><td>8</td></tr><tr><td>Maritime pine</td><td><i>P. pinaster</i></td><td>133</td><td>5</td></tr><tr><td>Silver fir</td><td><i>A. alba</i></td><td>213</td><td>8</td></tr><tr><td>Scots pine</td><td><i>P. sylvestri</i></td><td>160</td><td>6</td></tr><tr><td>Other conifers</td><td><i>Pinaceae spp</i></td><td>146</td><td>6</td></tr><tr><td>Sweet chestnut</td><td><i>C. sativa</i></td><td>135</td><td>5</td></tr><tr><td>Hornbeam</td><td><i>C. betulus</i></td><td>108</td><td>4</td></tr><tr><td>Ash</td><td><i>F. excelsior</i></td><td>108</td><td>4</td></tr><tr><td>European beech</td><td><i>F. sylvatica</i></td><td>297</td><td>11</td></tr><tr><td>Sessile oak</td><td><i>Q. petraea</i></td><td>297</td><td>11</td></tr><tr><td>English oak</td><td><i>Q. robur</i></td><td>297</td><td>11</td></tr><tr><td>White oak</td><td><i>Q. pubescens</i></td><td>108</td><td>4</td></tr><tr><td>Other broadleaved</td><td><i>Fagacea spp</i></td><td>365</td><td>14</td></tr></tbody></table>

Source: [4].

<table><caption>**Table 4**

Specifications on analysed yield tables per forest tree species.</caption><thead><tr><th>Common name</th><th>Species</th><th>Country</th><th>Eco-region</th><th>Geographical specifications</th><th>Yield class</th><th>Source</th><th>Page in source document</th></tr></thead><tbody><tr><td>Douglas fir</td><td><i>P. menziesii</i></td><td>France</td><td>West Massif Central</td><td>Creuse, Corrèze et Haute-Vienne</td><td>2</td><td>[9]</td><td>50</td></tr><tr><td>Norway spruce</td><td><i>P. abies</i></td><td>France</td><td>South Massif Central</td><td>Montagne Noire, Monts de Lacune-Sommail-Espinouse, Levezou and Aigoual</td><td>16</td><td>[9]</td><td>134</td></tr><tr><td>Maritime pine</td><td><i>P. pinaster</i></td><td>France</td><td>South-West</td><td>Landes de Gascogne</td><td>3</td><td>[9]</td><td>54</td></tr><tr><td>Silver fir</td><td><i>A. alba</i></td><td>France</td><td>Jura</td><td>N/A</td><td>12</td><td>[9]</td><td>112</td></tr><tr><td>Scots pine</td><td><i>P. sylvestri</i></td><td>France</td><td>Sologne</td><td>N/A</td><td>3</td><td>[9]</td><td>20</td></tr><tr><td>Other conifers</td><td><i>C. sativa</i></td><td>Spain</td><td>North Spain</td><td>N/A</td><td>4</td><td>[10]</td><td>131</td></tr><tr><td>Sweet chestnut</td><td><i>C. betulus</i></td><td>N/A</td><td>European part</td><td>Eco-regions of deciduous forests and forest steppe</td><td>2</td><td>[11]</td><td>375</td></tr><tr><td>Hornbeam</td><td><i>F. excelsior</i></td><td>N/A</td><td>Northern Eurasia</td><td>N/A</td><td>2</td><td>[11]</td><td>108</td></tr><tr><td>Ash</td><td><i>F. sylvatica</i></td><td>France</td><td>North-West</td><td>N/A</td><td>6</td><td>[9]</td><td>84</td></tr><tr><td>European beech</td><td><i>Q. petraea</i></td><td>France</td><td>Loire</td><td>N/A</td><td></td><td>[9]</td><td></td></tr><tr><td>Sessile oak</td><td><i>Q. robur</i></td><td>N/A</td><td>European part</td><td>Eco-regions of mixed forests, deciduous forests and forest steppe</td><td>1a</td><td>[11]</td><td>294</td></tr><tr><td>English oak</td><td><i>Q. pubescens</i></td><td>N/A</td><td>European part</td><td>Eco-regions of mixed forests, deciduous forests and forest steppe</td><td>2</td><td>[11]</td><td>295</td></tr></tbody></table>
for geographical coherence. However, adequate European studies were retained when French data was unavailable (Table 4). Biomass yield and carbon content were obtained by applying specific conversion factors (Table 5). The *Supplementary Material* provides technical guidance and data for all assessed tree species concerning selected yield tables, regression analysis and parameters, biomass yield calculations, and annual carbon stocking factors. It includes a R [2] script to compute the regression parameters for running the growth model, applicable to future studies.

## 2. Experimental design, materials, and methods

The presented data is used to inform the models described in the following sub-sections.

### 2.1. Modelling non-linear growth

The cumulative tree growth is represented by the non-linear Chapman-Richards (CR) curve. The CR equation (Eq. (1)) is based on species- and site-dependent parameters and one independent variable, with the following notation [13]:

<table><caption>**Table 5**

Wood density and carbon content per forest tree species.</caption><thead><tr><th>Common name</th><th>Species</th><th>Wood density [t·m<sup>-3</sup>]</th><th>Carbon content [C·t<sup>-1</sup>]</th></tr></thead><tbody><tr><td>Douglas fir</td><td><i>P. menziesii</i></td><td>0.4533</td><td>0.5280</td></tr><tr><td>Norway spruce</td><td><i>P. abies</i></td><td>0.3700</td><td>0.4980</td></tr><tr><td>Maritime pine</td><td><i>P. pinaster</i></td><td>0.4140</td><td>0.5212</td></tr><tr><td>Silver fir</td><td><i>A. alba</i></td><td>0.3530</td><td>0.4750</td></tr><tr><td>Scots pine</td><td><i>P. sylvestri</i></td><td>0.4219</td><td>0.5036</td></tr><tr><td>Other conifers</td><td><i>Pinaceae</i> spp</td><td>0.4024</td><td>0.5052</td></tr><tr><td>Sweet chestnut</td><td><i>C. sativa</i></td><td>0.4400</td><td>0.5010</td></tr><tr><td>Hornbeam</td><td><i>C. betulus</i></td><td>0.7060</td><td>0.4899</td></tr><tr><td>Ash</td><td><i>F. excelsior</i></td><td>0.5597</td><td>0.4918</td></tr><tr><td>European beech</td><td><i>F. sylvatica</i></td><td>0.5855</td><td>0.4709</td></tr><tr><td>Sessile oak</td><td><i>Q. petraea</i></td><td>0.5597</td><td>0.4970</td></tr><tr><td>English oak</td><td><i>Q. robur</i></td><td>0.5597</td><td>0.5016</td></tr><tr><td>White oak</td><td><i>Q. pubescens</i></td><td>0.5597</td><td>0.4948</td></tr><tr><td>Other broadleaved</td><td><i>Fagaceae</i> spp</td><td>0.5672</td><td>0.4924</td></tr></tbody></table>

Note: General recommended factors are 0.5 t m⁻³ for conifers/evergreen and 0.6–0.7 t m⁻³ for broadleaves/deciduous. The carbon content for all tree organs (different tree compartments), can be estimated with a factor of 0.5, by neglecting the lower carbon concentration in the needles/leaves [12].

<table><caption>**Table 6**

Initial parameter for Chapman-Richards non-linear regression.</caption><thead><tr><th rowspan="2">Common name</th><th rowspan="2">Species</th><th colspan="3">Initial parameters</th></tr><tr><th>A</th><th>k</th><th>p</th></tr></thead><tbody><tr><td>Douglas fir</td><td><i>P. menziesii</i></td><td>140</td><td>0.03</td><td>2</td></tr><tr><td>Norway spruce</td><td><i>P. abies</i></td><td>172</td><td>0.03</td><td>2</td></tr><tr><td>Maritime pine</td><td><i>P. pinaster</i></td><td>140</td><td>0.03</td><td>2</td></tr><tr><td>Silver fir</td><td><i>A. alba</i></td><td>326</td><td>0.03</td><td>2</td></tr><tr><td>Scots pine</td><td><i>P. sylvestri</i></td><td>180</td><td>0.03</td><td>2</td></tr><tr><td>Other conifers</td><td><i>Pinaceae</i> spp</td><td>172</td><td>0.03</td><td>2</td></tr><tr><td>(Sweet) Chestnut</td><td><i>C. sativa</i></td><td>120</td><td>0.03</td><td>2</td></tr><tr><td>Hornbeam</td><td><i>C. betulus</i></td><td>200</td><td>0.02</td><td>2</td></tr><tr><td>Ash</td><td><i>F. excelsior</i></td><td>320</td><td>0.03</td><td>2</td></tr><tr><td>European Beech</td><td><i>F. sylvatica</i></td><td>300</td><td>0.02</td><td>2</td></tr><tr><td>White oak</td><td><i>Q. petraea</i></td><td>240</td><td>0.04</td><td>2</td></tr><tr><td>English oak</td><td><i>Q. robur</i></td><td>320</td><td>0.02</td><td>2</td></tr><tr><td>Sessile oak</td><td><i>Q. pubescens</i></td><td>400</td><td>0.04</td><td>2</td></tr><tr><td>Other broadleaves</td><td><i>Fagaceae</i> spp</td><td>300</td><td>0.04</td><td>2</td></tr></tbody></table>

Sources: A. Pommerening, pers. comm.; H. Pretzsch, pers. comm.
<table><caption>**Table 7**

Overview of retained allometric equations for volume estimations.</caption><thead><tr><th rowspan="2">Species</th><th rowspan="2">Allometric equation</th><th colspan="5">Coefficients</th><th rowspan="2">Volume</th><th rowspan="2">Location</th><th rowspan="2">Creator</th><th rowspan="2">Source</th></tr><tr><th>α</th><th>β</th><th>γ</th><th>δ</th><th>ε</th></tr></thead><tbody><tr><td>P. menziesii</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) × (1 + δ/(Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>5.3E-1</td><td>-5.3E-4</td><td>—</td><td>5.7E+1</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>P. abies</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>6.3E-1</td><td>-9.5E-4</td><td>—</td><td>—</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>P. pinaster</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) + γ × Ci<sup>2</sup>/H × (1 + (δ/Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4E + 0.4<sup>4</sup> × π)</td><td>2.4E-1</td><td>9.7E-4</td><td>4.0E-1</td><td>2E+2</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>A. alba</td><td>V<sub>stem</sub> = (a + β × (Ci/π)<sup>2</sup>) × H + γ × (Ci/π)<sup>2</sup></td><td>-2.8E+0</td><td>3.4E-2</td><td>8.4E-2</td><td>—</td><td>—</td><td>Stem UB</td><td>ITA</td><td>CMCC</td><td>[16]</td></tr><tr><td>P. sylvestri</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) + γ × Ci<sup>2</sup>/H × (1 + (δ/Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>3.0E-1</td><td>3.2E-4</td><td>3.8E-1</td><td>2E+2</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>Pinaceae spp</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) + γ × Ci<sup>2</sup>/H × (1 + (δ/Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>3.0E-1</td><td>3.2E-4</td><td>3.8E-1</td><td>2E+2</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>C. sativa</td><td>V<sub>stem</sub> = α × (Ci/π)<sup>2</sup> × H + β</td><td>3.8E-2</td><td>8.5E-1</td><td>—</td><td>—</td><td>—</td><td>Stem UB</td><td>FRA</td><td>FCBA</td><td>[17]</td></tr><tr><td>C. betulus</td><td>V<sub>stem</sub> = α × (Ci/π)<sup>2</sup> × H + β</td><td>3.3E-2</td><td>3.0E+0</td><td>—</td><td>—</td><td>—</td><td>Stem UB</td><td>FRA</td><td>FCBA</td><td>[17]</td></tr><tr><td>F. excelsior</td><td>V<sub>stem</sub> = (Ci/π)<sup>α</sup> × H<sup>β</sup> × e<sup>-γ</sup></td><td>2.0E+0</td><td>7.7E-1</td><td>2.5E+0</td><td>—</td><td>—</td><td>Stem UB</td><td>NDL</td><td>CMCC</td><td>[18]</td></tr><tr><td>F. sylvatica</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) + γ × Ci<sup>2</sup>/H × (1 + (δ/Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>4.0E-1</td><td>2.7E-4</td><td>4.2E-1</td><td>4.5E+1</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>Q. petraea</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) + γ × Ci<sup>2</sup>/H × (1 + (δ/Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>4.7E-1</td><td>-3.5E-4</td><td>3.8E-1</td><td>—</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr><tr><td>Q. robur</td><td>V<sub>stem</sub> = (Ci/π)<sup>α</sup> × H<sup>β</sup> × e<sup>-γ</sup></td><td>2.0E+0</td><td>8.6E-1</td><td>2.9E+0</td><td>—</td><td>—</td><td>Stem UB</td><td>NDL</td><td>CMCC</td><td>[18]</td></tr><tr><td>Q. pubescens</td><td>V<sub>stem</sub> = α × 10<sup>β</sup> × LOG(Ci/π) × γ × LOG(Ci/π)<sup>2</sup> × δ × LOG(H) + ε × LOG(H)<sup>2</sup></td><td>3.5E-4</td><td>1.1E+0</td><td>3.1E-1</td><td>5.4E-1</td><td>2.1E-1</td><td>Stem UB</td><td>ROU</td><td>CMCC</td><td>[19]</td></tr><tr><td>Fagaceae spp</td><td>V<sub>T<sub>above</sub></sub> = (a + β × Ci) + γ × Ci<sup>2</sup>/H × (1 + (δ/Ci<sup>2</sup>)) × Ci<sup>2</sup> × H/(4x10<sup>4</sup> × π)</td><td>4.7E-1</td><td>3.5E-4</td><td>3.8E-1</td><td>—</td><td>—</td><td>Total AG</td><td>FRA</td><td>INRA</td><td>[15]</td></tr></tbody></table>

Acronyms: H: top height; DBH: Diameter breast height; Ci: Circumference; Total AG: total aboveground; Stem UB: stem under bark; FRA: France; ITA: Italy; NDL: Netherlands; ROU: Romania.

Note: Equations are all expressed in Ci and the given units needed respective conversions to be expressed in common units. The volume is expressed in stem under bark (i.e. bark and wood) or total aboveground tree volume. The total aboveground volume includes stem under bark, needles/leaves and branches. The group "other conifers" (Pinaceae spp) and "other broadleaved" (Fagaceae spp) use the same volume relations as Scots pine and Sessile oak respectively, due to their representativeness.

Source: Allometric equations analysed and selected from Ref. [6]; and respective references in the table.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Mean biomass growth in tonnes of carbon per tree species.</figcaption></figure>

$$ \omega(t_i) = A(1 - \beta \exp^{-kt})^p + \varepsilon \quad (1) $$
with $p = 1/(1 - m)$

where $\omega$ expresses the potential growth of a tree species i in height and circumference (response growth variables) at age t (independent variable), A, $\beta$, k, p are parameters, exp is the basis of natural logarithm and $\varepsilon$ the term for random error; with $\beta$ is fixed to 1 [14], and the allometric constant m fixed to 0.5 ($0 < m < 1$) [13]. CR forms a sigmoid and asymptotic curve with a point of inflection determined by the allometric constant p, approaching a maximum threshold of the response variable, the asymptote A. The empirical growth parameter k scales the absolute growth, governing the rate at which A approaches its potential maximum.

## 2.2. Initial parameters to fit non-self-starting non-linear regression model

The statistical model using the CR curve [$\omega \sim f(t_i, \theta) + \varepsilon$] fits the vector of parameters $\theta$ to the growth variable $\omega$; whereby the function f represents a non-linear combination of the parameters. Initial parameters to fit the non-self-starting non-linear regression model (Table 6) were developed for k and p. Values for k lie between 0.02 and 0.04, depending on the studied species and for p 2. The acceptable values for k range between 0.2 and 2.5. A is estimated as twice the maximum value given for age in the species-specific yield tables.

## 2.3. Allometric equations and specifications

Allometric models presented in Table 7 are used for tree volume estimation.

## 2.4. Mean biomass growth development of all species

Fig. 1 shows the non-linear mean biomass growth per tree species. For the computation of annual Cbio fixation flows [t Cbio·yr⁻¹] in biomass (as presented with the stocking factors in the Supplementary material) see section 2.3.1. in the companion research article [1]. Data from Table 3 to Table 7 are used for these calculations.
Acknowledgments

The authors would like to acknowledge the valuable inputs from Prof. Hans Pretzsch (TU Munich) and Prof. Arne Pommerening (Swedish University of Agricultural Sciences). This work is part of a Ph.D. research work of Ariane Albers supported by IFP Energies nouvelles doctoral grant.

Transparency document

Transparency document associated with this article can be found in the online version at https://doi.org/10.1016/j.dib.2019.103841.

**Appendix A. Supplementary data**

Supplementary data to this article can be found online at https://doi.org/10.1016/j.dib.2019.103841.

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