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

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.


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 longstanding 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 primary originate from French studies, Specifications  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.   Source: [4].   [3]. Table 4 Specifications on analysed yield tables per forest tree species. 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.

Experimental design, materials, and methods
The presented data is used to inform the models described in the following sub-sections.

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 5 Wood density and carbon content per forest tree species. Note: General recommended factors are 0.5 t m À3 for conifers/evergreen and 0.6e0.7 t m À3 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 6
Initial parameter for Chapman-Richards non-linear regression.
where u expresses the potential growth of a tree species i in height and circumference (response growth variables) at age t (independent variable), A ; b ; k ; p are parameters, exp is the basis of natural logarithm and Ɛ the term for random error; with b 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.

Initial parameters to fit non-self-starting non-linear regression model
The statistical model using the CR curve ½u $ f ðt i ; q Þ þ ε] fits the vector of parameters q to the growth variable u; 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.

Allometric equations and specifications
Allometric models presented in Table 7 are used for tree volume estimation. Fig. 1 shows the non-linear mean biomass growth per tree species. For the computation of annual C bio fixation flows [t C bio $yr À1 ] 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.