CO₂ Estimation of Tree Biomass in Forest Stands: A Simple and IPCC-Compliant Approach

Abstract

Background: While forests are pivotal for climate change mitigation, robust CO₂ accounting is required to quantify their climate benefits. However, varying current methodologies complicate this process for practitioners. This study addresses the need for a low-threshold, IPCC-compliant CO₂ estimation method of tree biomass in forest stands. Methods: We developed CO₂ yield tables by integrating segmented allometric biomass functions into fourth-generation yield tables, combining empirical data and simulations for Northwest Germany. Above- and belowground biomass was calculated, converted into CO₂, and compared with estimates from traditional expansion factors. An interactive R Shiny dashboard was designed to visualise results. Results: The main results of this article are the carbon yield tables, covering beech (Fagus sylvatica), oak (Quercus spp.), spruce (Picea abies), pine (Pinus sylvestris) and Douglas fir (Pseudotsuga menziesii), each across various yield classes and starting at age 1, thereby also encompassing the juvenile phase of forest stands. Our comparison with estimates from traditional expansion factors shows that the latter can substantially overestimate carbon content in forest stands compared to our results, ranging from 20% to 35%, with higher estimates for mature stands and improved representation of early growth. The interactive dashboard also allows readers to experiment with their own figures. Conclusions: The choice of CO₂ methodology profoundly affects results. Our yield tables and a calculation tool (dashboard) deliver a transparent, accessible tool for quantifying forest CO₂ stock, supporting sustainable management and carbon market participation.

1. Introduction

Forests play an important role in the global effort to combat climate change. This is primarily due to their ability to sequester carbon dioxide from the atmosphere through photosynthesis, storing it over significant timescales [1]. In order to preserve, maintain, and even expand this climate protection potential, forests must be managed sustainably, which also includes the capacity to monitor the development of their climate mitigation performance.

On a supranational level, the European Union has released comprehensive regulations and laws for a climate-neutral future. Central to these efforts is the “Land Use, Land Use Change, and Forestry (LULUCF)” sector. The EU defines the LULUCF sector broadly:

The land use sector encompasses the management of cropland, grassland, wetlands, forests, settlements, as well as changes in land use including afforestation (i.e., planting trees), deforestation, or draining of peatlands. LULUCF reporting categories comprise various types of carbon pools of living biomass (above and below ground), dead organic matter (CWD and litter), and organic soil carbon. Land-use changes are also reported, for example: deforestation, afforestation, or changes from grassland to arable land or settlements” [2].

This sector is crucial for both emitting and absorbing ${\mathrm{CO}}_2$ from the atmosphere. The European Climate Law (Regulation (EU) 2021/1119 of 30 June 2021) establishes the framework for achieving climate neutrality by 2050 and sets an intermediate target of reducing net greenhouse gas emissions by at least 55% by 2030, compared to 1990 levels [3]. Furthermore, the Commission Implementing Regulation (EU) 2018/2066 of 19 December 2018 details the monitoring and reporting of greenhouse gas emissions. The revised LULUCF Regulation (Regulation (EU) 2023/839) sets an overall EU-level objective of 310 Mt ${\mathrm{CO}}_2$ of net removals in the LULUCF sector by 2030, with Member States responsible for contributing to this target [2,4].

At the national level, EU member states are developing and implementing their own legislative frameworks to align with these EU targets. These national laws often have specific names, such as the “Klimaschutzgesetz” (Climate Protection Act, 2019) in Germany [5]. Other examples of EU countries with national climate protection laws include (i). Finland: Finnish Climate Act (2022), aiming for carbon neutrality by 2035 [6]; (ii). France: Energy and Climate Law (2019), targeting carbon neutrality by 2050 [7]; (iii). Ireland: Climate Action and Low Carbon Development (Amendment) Act (2021), striving for climate neutrality by 2050 [8] and (iv). Portugal: Framework Law on Climate Change (2021), also aiming for climate neutrality by 2050 [9].

While these policies establish clear goals, their effective implementation raises significant questions. There is a lack of knowledge about which forest management strategies are most effective and how the contributions of different land use types, especially forests, can be optimally distributed. In the forest itself, practitioners and policymakers often lack clarity on how specific silvicultural measures affect carbon storage in the short, medium, and long term [10].

The components of the forest carbon budget pools include live biomass, dead biomass, soil, and wood products. Live biomass can be further divided into aboveground and belowground biomass [11,12]. Another significant carbon pool is the carbon stored in wood products over time [13], which ensures carbon storage beyond the forest itself and may also contribute to substitution effects [14,15,16]. However, it should be noted that harvested wood products (HWP) are not included in the scope of our analysis.

The most significant of these pools for reporting purposes is living tree biomass, and its accurate quantification is paramount. This can be approached through the calculation of either the individual tree biomass or the total biomass of a forest stand. The estimation of individual tree biomass typically employs allometric equations, which depend on the diameter and/or height [17]. The accuracy of these functions was enhanced by Riedel and Kändler 2017 [18], who developed new biomass estimation methods based on allometric functions and the Marklund Function in alignment with the “Greenhouse gas (GHG) Reporting”, by assigning different functions for different sectional diameters and heights [18,19,20].

Alternatively, the total biomass for a specific plot or stand can be obtained by summing the biomass of each individual tree on a site or per hectare [17]. The estimation of the total stand biomass is usually done by expanding the standing volume (stock) with specific expansion factors. The development of stand biomass estimates using biomass expansion factors has been undertaken for several tree species, including spruce (Picea abies), pine (Pinus sylvestris), beech (Fagus sylvatica), oak (Quercus robur/petraea), and Douglas fir (Pseudotsuga menziesii) [21,22]. Examples from other countries include pine (Pinus spp.) in Brazil [23], Korean red pine (Pinus densiflora) in South Korea [24] and maple (Acer pseudoplatanus) and ash (Fraxinus excelsior) in the Carpathians [25].

A significant challenge is the methodology for estimating forest carbon stocks. The existence of a wide range of different methods for estimating biomass highlights a clear absence of consensus on the most appropriate approach for calculating biomass and subsequent ${\mathrm{CO}}_2$ stock. This lack of consensus is often a direct result of varying data availability and the resulting methodological choices. It is also important to note that these methodologies can differ significantly among countries preparing their National Inventory Reports, making direct comparisons difficult.

Furthermore, from a forest economics perspective, the potential for carbon sequestration is of considerable importance. This is largely due to the growing relevance of the voluntary carbon market (VCM) as a means of generating revenue from forest-based timber production [26]. In light of these developments on the VCMs, the EU also introduced the Carbon Removal Certification Framework (CRCF) as a voluntary EU initiative in 2024 to create uniform standards for the certification of climate protection activities that remove carbon dioxide from the atmosphere. In light of these developments on the VCMs, the EU also introduced the Carbon Removal Certification Framework (CRCF) as a voluntary EU initiative in 2024 to create uniform standards for the certification of climate protection activities that remove carbon dioxide from the atmosphere [27]. Standards such as the Verified Carbon Standard (VCS) employ models like Faustmann’s approach [28], or the Carbon Budget Model of the Canadian Forest Sector (CBM-CFS3) [29], both of which require substantial expertise and a lengthy familiarisation period due to their complexity. This study also serves as a preparatory analysis for the model used within our department, known as the Forest Economic Simulation Model (FESIM). FESIM is an economic model that integrates a biological production component based on yield tables, a technical production model, and additional submodules—including a habitat tree module and a coarse woody debris decay model [30,31,32,33,34]. The calculations conducted in this study can subsequently be used to assess ${\mathrm{CO}}_2$ levels within FESIM, as both rely on the same yield tables and, therefore, the same underlying biological production model.

The development of an approach that is both simpler and IPCC-compliant has two principal benefits. Firstly, it serves as a pre-study for FESIM development. Secondly, it bridges a threefold knowledge gap that hinders carbon estimation for practitioners: (i). Lack of an accessible estimation tool. Highly accurate methods, such as the single-tree biomass functions by Riedel and Kändler 2017 [18], exist but are not yet integrated into low-threshold, user-friendly tools that forestry practitioners can easily apply in their daily work. This creates a disconnect between state-of-the-art science and practical application. (ii). Inconsistent results from different methods. There is a lack of comparative analysis between common calculation methods. The differences in ${\mathrm{CO}}_2$ estimation results when using precise single-tree biomass functions versus generalised stand expansion factors are not well understood, leading to potential inaccuracies in reporting. (iii). Simplified assumptions in current models. Many estimation methods rely on simplified assumptions about tree morphology, which may not reflect real-world conditions, especially in stands with varying stocking densities. It is therefore the objective of the present article to bridge these gaps by developing a low-threshold estimation tool and conducting a comparative analysis to address the following research questions:

• How can the proposed single-tree biomass functions by Riedel and Kändler 2017 [18] be effectively integrated within yield tables to develop ${\mathrm{CO}}_2$ yield tables that address the existing gap of a low-threshold estimation of the potential ${\mathrm{CO}}_2$ stock in forest stands?
• What are the differences in ${\mathrm{CO}}_2$ estimation results when using single-tree biomass functions compared to those derived from stand expansion factors?
• To what extent does the incorporation of realistic height-diameter (h-d) ratios into single-tree ${\mathrm{CO}}_2$ estimations enhance the accuracy of forest stand ${\mathrm{CO}}_2$ accounting—particularly under varying stocking densities—and support broader applicability of the method?

2. Materials and Methods

2.1. Materials

2.1.1. Input Data: A New Generation of Yield Tables

Yield tables provide valuable information on forest stands. They traditionally serve as planning tools in forestry and are used in various countries, by showing the development of forest stands under variable site qualities and management regimes [35,36,37,38,39]. Common yield tables present detailed information about merchantable timber in a forest stand, separating the “Yield after Thinning” from the “yield from thinning”, based on the age of the stand in years, usually in steps of 5 years. They include data for trees per hectare, mean height (m), top height (m), basal area (${\mathrm{m}}^2$ ${\mathrm{ha}}^{-1}$), mean diameter at breast height (cm), and volume of merchantable timber per hectare (${\mathrm{m}}^3$ ${\mathrm{ha}}^{-1}$). The tables also provide information on the “yield from thinning”, including trees per hectare, basal area ${\mathrm{m}}^2$ ${\mathrm{ha}}^{-1}$, mean diameter (cm), and volume ${\mathrm{ha}}^{-1}$ (${\mathrm{m}}^3$ ${\mathrm{ha}}^{-1}$). Furthermore, they include the total volume production (TVP) (${\mathrm{m}}^3$ ${\mathrm{ha}}^{-1}$), the mean annual increment (MAI) (${\mathrm{m}}^3$ ${\mathrm{ha}}^{-1}$ ${\mathrm{yr}}^{-1}$), and the current annual increment (CAI) (${\mathrm{m}}^3$ ${\mathrm{ha}}^{-1}$ ${\mathrm{yr}}^{-1}$). The data in yield tables has been recorded for various age classes in forest stands, thereby showcasing the development of stand characteristics over time. This enables a comprehensive analysis of forest growth and stand development, including the impact of thinning on the remaining maincrop. As they are based on empirical observations in the past, they also enable projections about future growth and timber yields. Moreover, they take into account different site indices that stand as a proxy for site quality. In this case, the relative site indices here are displayed in Roman numerals, starting at −I (very good site) to VI (very poor site).

For our analysis, we used the new generation of yield tables by Albert et al. (2024) [40] as the database. These are fourth-generation yield tables that are developed both on results from experimental plots and forest growth simulations, i.e., they combine empirical data with modelling. The yield tables of earlier generations were based exclusively on experimental plot data [35]. These trial plots that were used by Albert et al. (2024) [40] were thinned to a high level, thereby representing a staggered high thinning from above, and were extrapolated over a 30-year period using TreeGrOSS, a single-tree growth simulator [41]. High thinning, is a practice involving the removal of trees from the dominant canopy to improve the growing space for selected individuals, (as opposed to low thinning, which involves the removal of suppressed, intermediate, or co-dominant trees from the lower and middle canopy strata—a management approach that has been practiced for long periods in the past, and is partly displayed in the former yield tables by Schober (1995) [35]. The system of staggered high thinning, as depicted by Albert et al. (2024) [40], advocating for intensive early thinning interventions followed by more moderate low thinnings during later stand development stages, is a common and widespread forestry practice nowadays in Germany [40,42].

The youngest stand age reported in yield tables typically starts at the age period in which the stand has attained or surpassed a maximum height of 12 m and should undergo thinning for the first time, corresponding to an age at which the diameter of the tree equals/surpasses 7 cm. In German forestry, this is the threshold, where trees are counted as standing volume. It is important to note that the empirically observed range according to Albert et al. (2024) [40] begins and ends at different minimum and maximum ages. Those minima and maxima are shown in Table 1.

Table 1. Empirically observed and validated minimum and maximum ages of different tree species and site indices [40].

Tree Species/Site Index	−I	0	I	II	III
	Stand age range (years)
Spruce (Picea abies)	20–75	20–95	25–110	30–120	40–120
Pine (Pinus sylvestris)	20–90	20–120	25–120	30–120	40–120
Douglas fir (Douglas fir)	15–95	15–115	20–120	20–120	20–120
Beech (Fagus sylvatica)	25–115	30–125	35–145	40–150	45–150
Oak (Quercus robur/petraea)	15–175	20–180	25–180	30–180	40–180

When utilising yield tables, it is imperative to acknowledge the limitations imposed by the data. It must be kept in mind that yield tables only reflect pure stand composition, even-aged trees, uniform site conditions, homogeneous stocking that is fully stocked with a relative density of 1.0 (B° = 1.0), and comparable silvicultural management, following the criteria established by Kramer et al. (1988) [43]. These limitations, which will be examined in greater detail in the discussion, must be recognised prior to application, in order to ensure a comprehension and effective consideration of the constraints inherent in their utilisation.

Moreover, it must be noted that for the tree species Douglas fir, the number of stems for site index −I is lower than for site index 0. This would lead to a lower ${\mathrm{CO}}_2$ stock in the stand, though the individual trees are larger and individually sequester more ${\mathrm{CO}}_2$.

2.1.2. Foundational Models and Indices

Biomass Equations

In order to calculate the biomass, it is first necessary to ascertain the compartments under consideration. As previously stated, the IPCC delineates five distinct compartments within which biomass is present in forest ecosystems: (i). above-ground tree biomass; (ii). belowground tree biomass; (iii). biomass derived from non-tree vegetation; (iv). soil organic matter extending to a depth of one metre, inclusive of peat; (v). coarse woody debris; and (vi). fine litter [11,12]. In the present analysis, all living above-ground tree compartments are considered, as well as belowground tree biomass. The term ‘above-ground tree biomass’ refers to the entirety of the visible living tree mass, including not only stems up to the root collar, but also branches, bark, fruit, seeds, and leaves. In contrast, ‘belowground tree biomass’ consists of the structural and fine root systems [44]. We employed the term ‘full tree biomass’ to denote the aggregate of both the above-ground and belowground tree biomass. We used BDAT 3.0, which is available in the form of the R-package rBDAT on CRAN [45,46], where the segmented biomass functions by Riedel and Kändler (2017) [18] are fully implemented and depend on diameter and/or height. Coarse woody debris (CWD) will not be part of our analysis. Nevertheless, it should be noted that a fundamental assumption of yield tables is that all recorded mortality is removed and utilised as timber/roundwood. Based on the yield table’s “yield from thinning”, however, the necessary inflows and replenishment rates for establishing and maintaining a defined CWD stock could in principle also be estimated. All the following functions and parameters are derived from the GHG reporting. When other sources have been used, it is declared.

The allometric function (1) is valid for trees under 1.3 m in height, which takes into account the height in meters and species-specific coefficients found in Table 2.

$$B_{H < 1.3 \mathrm{m}}=b_0·H^{b_1}$$

(1)

where $B_{H < 1.3 \mathrm{m}}$ is the above-ground biomass for trees smaller than 1.3 m of height in kg, $b_0$ and $b_1$ are the species-specific coefficients of the function, and H is the tree height in m.

Table 2. Species-specific coefficients of the biomass function for trees H < 1.3 m [18].

Species	${\mathit{b}}_0$	${\mathit{b}}_1$
Coniferous	0.23059	2.20101
Deciduous	0.04940	2.54946

For trees that are at least 1.3 m in height but have a diameter of less than 10 cm, the interpolation function (2) results:

$$B_{d < 10 \mathrm{cm}}=b_0+\left({\displaystyle \frac{b_s-b_0}{d_s^2}}+b_3(d-d_s)\right)d^2$$

(2)

where $B_{d < 10 \mathrm{cm}}$ is the above-ground biomass in kg, $b_{0,s,3}$ are the species-specific coefficients, $d_s$ is the threshold diameter of 10 cm and equals 10 in the equation, and d is the diameter. The species specific coefficients can be found in Table 3.

Table 3. Species-specific coefficients for the biomass function for trees H > 1.3 m, d < 10 cm [18].

Species	${\mathit{b}}_0$	${\mathit{b}}_{\mathit{s}}$	${\mathit{b}}_3$
Spruce (Picea abies)	0.4108	26.63122	0.0137
Pine (Pinus sylvestris)	0.4108	19.99943	0.00916
Beech (Fagus sylvatica)	0.09644	33.22328	0.01162
Oak (Quercus robur/petraea)	0.09644	28.94782	0.01501

For a diameter ≥ 10 cm, the modified Marklund function is used. This includes not only the diameter and the height, but also an upper stem diameter named $D_{03}$, which describes the diameter at 30% of the tree’s height. Equation (3) shows the modified Marklund function. The species specific coefficients can be found in Table 4.

$$B_{d \ge 10 \mathrm{cm}}=b_0·e^{b_1\left({\displaystyle \frac{d}{d+k_1}}\right)}·e^{b_2\left({\displaystyle \frac{D_{03}}{D_{03}+k_2}}\right)}·H^{b_3}$$

(3)

where $B_{d \ge 10 \mathrm{cm}}$ is the above-ground biomass in kg for trees with a diameter greater than 10cm, H is the tree height in m, $b_{0,1,2,3}$, and $k_{1,2}$ are the species-specific coefficients of the function; d is the diameter of the tree in cm, and $D_{03}$ is the diameter of the tree in 30% of its height.

Table 4. Species-specific coefficients for trees with a diameter ≥ 10 cm [18].

Species	${\mathit{b}}_0$	${\mathit{b}}_1$	${\mathit{b}}_2$	${\mathit{b}}_3$	${\mathit{k}}_1$	${\mathit{k}}_2$
Spruce (Picea abies)	0.75285	2.84985	6.03036	0.62188	42	24
Pine (Pinus sylvestris)	0.33778	2.84055	6.34964	0.62755	18	23
Beech (Fagus sylvatica)	0.16787	6.25452	6.64752	0.80745	11	135
Oak (Quercus robur/petraea)	0.09428	10.26998	8.13894	0.55845	400	8

It is important to note that, due to their non-linear nature, there is a risk of unrealistically high values being assigned to extremely strong trees. In order to minimise the effect of overestimation in the extrapolation range above a tree-species-specific threshold diameter, Riedel and Kändler (2017) [18] suggest a linearisation of the Marklund model, where the last slope of the Marklund function is extrapolated linearly. The threshold diameters apply from the following diameter values (Table 5):

Table 5. Species-specific threshold diameters [cm] for the linearisation of the Marklund function, developed by Riedel and Kändler (2017) [18].

Species	d
Spruce (Picea abies)	69 cm
Pine (Pinus sylvestris)	59 cm
Beech (Fagus sylvatica)	86 cm
Oak (Quercus robur/petraea)	94 cm

For the belowground biomass, we also used an allometric function (4), which is presented in the National Inventory Report [20] and takes into account different species-specific coefficients (Table 6). For Douglas fir, coefficients equivalent to those employed for beech were assumed, given their comparable root structure [47].

$$B_u=b_0\ast d^{b_1}$$

(4)

where $B_u$ is the root biomass in kg (belowground), $b_{0,1}$ are the species-specific coefficients, and d is the diameter of the tree in cm.

Table 6. Species-specific coefficients of belowground biomass [18].

Species	${\mathit{b}}_0$	${\mathit{b}}_1$	Source
Spruce (Picea abies)	0.003720	2.792465	[48]
Pine (Pinus sylvestris)	0.006089	2.739073	[49]
Beech (Fagus sylvatica)	0.018256	2.321997	[48]
Oak (Quercus robur/petraea)	0.028000	2.440000	[48,50]
Douglas fir (Pseudotsuga menziesii)	0.018256	2.321997	[47,48]

Biomass Expansion Factors

In order to categorise our results, a comparison was carried out, which required additional calculations. In the field of comparative literature, we have drawn upon the work of Pretzsch (2009) [22], who provided biomass expansion factors for forest stands (1 ha), which can be found in Table 7.

Table 7. Stand expansion factors [22], where R is the specific wood density, $e_{br}$ is the brushwood factor, $e_l$ is the litter factor, and $e_{br}$ and root factor.

Species	R (kg ${\mathrm{m}}^{-3}$)	$e_{\mathit{br}}$	${\mathit{e}}_{\mathit{l}}$	${\mathit{e}}_{\mathit{r}}$
Spruce (Picea abies)	377.1	1.45	1.00	1.25
Pine (Pinus sylvestris)	430.7	1.45	1.00	1.25
Beech (Fagus sylvatica)	554.3	1.45	1.05	1.25
Oak (Quercus robur/petraea)	561.1	1.45	1.03	1.25
Douglas Fir (Pseudotsuga menziesii)	412.4	1.45	1.00	1.25

Total Volume Production and Mean Annual Increment

As a further explanatory model, we would like to list the total volume production (TVP) and also the mean annual increment (MAI), which we used for our calculations. The TVP is defined as the cumulative volume of timber produced by a tree, stand, or forest over time, including both merchantable and non-merchantable timber. The MAI is defined as the average annual growth rate of a tree or stand of trees up to a specified age [43]. For assessing the (additional) climate protection performance, the TVP of managed forests shown is, in our opinion, only partially suitable, as the full TVP cannot be accumulated in the stand long-term if harvesting is forgone. This TVP curve is exclusively for (managed) stands based on the yield table management assumptions of Albert et al. (2024) [40].

h/d-Ratios

In the yield tables, the height and diameter values are shown for the respective basal area centre stem at the respective stand age. However, real individual trees or stands may have different height and diameter values from the yield table. The height (h) and diameter (d) are the central input variables for the dashboard for the ${\mathrm{CO}}_2$ calculation of individual trees and stands, which is why the h/d-ratio is important. To answer the third research question, we also scrutinised which height/diameter ratios (h/d-ratios) are realistic, so that we could also cover data outside of the yield tables. The h/d ratio is a pivotal indicator in forestry that describes the ratio of tree height to diameter at breast height. It functions as a significant indicator for evaluating the stability of individual trees and the stability of entire forest stands. The significance of this phenomenon pertains to the growth behaviour of the trees. In dense forests, competition for light is a driving force that prompts trees to undergo rapid vertical growth, resulting in the development of slender, unstable trunks that exhibit a high h/d ratio. Conversely, free-standing trees can allocate greater energy towards increasing their thickness, resulting in a more compact structure and a lower h/d ratio that is less susceptible to variation and the values are defined as very unstable: h/d ≥ 1, unstable: h/d 0.8 to < 1, stable: h/d 0.45 to < 0.8, solitary tree: h/d < 0.45 [51].

Stand Density Index

In the yield tables, an age-dependent stocking density is shown, which can deviate in real individual stands. The Stand Density Index is an important parameter for making realistic settings for the diameter and stem number of the trees in a stand with regard to the degree of stocking using the dashboard, which will be presented in Section 2.2.2.

To answer the third research question, the SDI should therefore inform the user of the dashboard if settings with overstocking are selected. It must be noted that idealised pure stands from yield tables have a stocking density of $B=1.0$, a metric different from the SDI. The Stand Density Index (SDI) is a metric of stand density in forestry, developed by Reineke in the USA in 1993 [52]. Plotting the logarithm of the number of trees per hectare against the logarithm of the root mean square diameter (or the dbh of the tree with average basal area) of maximum stocked stands generally results in a linear relationship [52].

The model (Equation (5)) is predicated on a constant slope of 1.605. Pretzsch refined those slopes species-specifically (Table 8) [22].

$$SDI=N·{\left({\displaystyle \frac{25}{d_q}}\right)}^{-1.605}$$

(5)

Table 8. Species-specific factors for the Stand Density Index [52].

Species	b
Spruce (Picea abies)	1.664
Pine (Pinus sylvestris)	1.593
Beech (Fagus sylvatica)	1.789
Oak (Quercus robur/petraea)	1.424
Douglas Fir (Pseudotsuga menziesii)	1.664

Stand Density Index [52] is derived from Pretzsch et al. (2009) [22].

Carbon and ${\mathrm{CO}}_2$ Conversion Factors

Plants absorb ${\mathrm{CO}}_2$ from the air through their stomata. Photosynthesis takes place in the mesophyll cells and converts inorganic ${\mathrm{CO}}_2$ into organic compounds, mainly glucose, which forms the basis for the synthesis of other carbohydrates such as cellulose and lignin. This decomposition of ${\mathrm{CO}}_2$ leads to the fixation of carbon in the plant [1]. Consequently, timber consists primarily of carbon (approx. 50%), oxygen (approx. 43%), hydrogen (6%) and nitrogen (<1%). Therefore, a general proportion of 50% carbon is assumed in the conversion of biomass to carbon [53]. The periodic table of chemical elements is used to convert the pure carbon content into ${\mathrm{CO}}_2$. This calculation yields a molar mass of 12.011 g ${\mathrm{mol}}^{-1}$ for carbon (C) and 15.999 g ${\mathrm{mol}}^{-1}$ for oxygen (O). The molecular mass of carbon dioxide is thus 44.009 g ${\mathrm{mol}}^{-1}$ [54]. Utilising these values, the mass of carbon can be converted to the mass of carbon dioxide.

2.2. Methods

2.2.1. Stand ${\mathrm{CO}}_2$ Calculation

Via Equations

The calculation was performed through the utilisation of the relevant formulae from Section Carbon and ${\mathrm{CO}}_2$ Conversion Factors, with the necessary input data being obtained from the yield tables, specifically height and diameter at breast height of the quadratic mean stem. Based on these values, the above- and belowground tree biomass was calculated. This figure represents the single-tree ${\mathrm{CO}}_2$ stock, which was then extrapolated to the entire stand using the corresponding stem numbers (N) from the yield tables. This was undertaken not only for the standing volume, but also for the yield from thinning, in order to calculate the TVP and MAI using these key figures.

Via Expansion

To calculate the above- and belowground tree biomass by expansion factors, we took the stock and expanded it using the species-specific expansion factors from Table 7.

Conversion to ${\mathrm{CO}}_2$

Ultimately, the calculated biomass was multiplied by the conversion factor 0.5 to calculate the carbon content and subsequently by the conversion factor 3.664 to convert it to ${\mathrm{CO}}_2$.

Extrapolation for Younger Stands

The values below the initial age of the yield tables (subject to variation according to the tree species and site index) are extrapolated linearly to allow an approximate estimation of ${\mathrm{CO}}_2$ in younger stands, since they are also able to sequester ${\mathrm{CO}}_2$ [55].

The number of stems was not extrapolated due to the absence of data regarding the stand’s foundation. It can be naturally regenerated or planted. Therefore, numerical data pertaining to the stem count was not provided, as it lay outside the range of the data that had been previously secured through empirical means.

All calculations were carried out in R Studio Version 2024.04.2 Build 764 [56], using the R-packages rBDAT and et.nwfva [46,57]. The codes are provided as rmd files in the Appendix C.

2.2.2. Development of an Online Application (Dashboard)

To test our results, we built a dashboard to estimate above- and belowground ${\mathrm{CO}}_2$ stock in forest stands. The tool avoids manual use of yield tables by implementing the published equations of Riedel and Kändler (2017) [18] within an R Studio application. It uses R-shiny for the interface, dplyr for data processing, and rBDAT for biomass estimation. Users can select tree species and adjust diameter, height, and stem count; the app then calculates tree- and stand-level ${\mathrm{CO}}_2$ storage, h/d ratios, and SDI. Two plausibility checks flag unrealistic h/d ratios and basal areas exceeding one hectare. The dashboard complements existing yield tables and provides a straightforward way of carrying out ${\mathrm{CO}}_2$ accounting for individual trees and forest stands. The dashboard can either be replicated by simply copying the code in the Appendix C and pasting it into an R-shiny document or online: https://easyco2estimation.shinyapps.io/shiny/, accessed on 10 October 2025.

3. Results

3.1. CO₂ Estimates for Forest Stands

3.1.1. Based on Equations

The integration of the Riedel and Kändler (2017) [18] biomass estimation functions was successfully achieved through the utilisation of height and diameter from the yield tables by Albert et al. (2024) [40], as outlined in the Methods section. In the subsequent sections, the stock, TVP and the MAI are presented as illustrative examples for oak (Quercus spec.). The yield tables and other tree species, which have been supplemented with the ${\mathrm{CO}}_2$ figures calculated by the authors, can be found in the Appendix A. Moreover, it should be noted that the starting and end age of each tree species differs, as presented in Table 1, meaning that e.g., for site index −I (oak), the maximum stand age is 175 years.

Figure 1 illustrates the age-related development of stand-level ${\mathrm{CO}}_2$ stock for Quercus spec. across site indices −I to III. The ${\mathrm{CO}}_2$ stock calculation was carried out with single tree equations and is later compared with the upscaling approaches for ${\mathrm{CO}}_2$ stock estimation based on stand expansion factors.

Figure 1. CO₂ stock of Oak for different site indices and different ages.

The trajectories indicate that higher site indices accumulate substantially larger ${\mathrm{CO}}_2$ stocks, ranging from approximately 200 t ${\mathrm{ha}}^{-1}$ on poor sites (Site Index III) to nearly t ${\mathrm{ha}}^{-1}$ on very good sites (site index −I) at advanced stand ages. Across all site classes, ${\mathrm{CO}}_2$ accumulation increases steeply up to about age 60–80 years and then gradually levels off, reflecting the declining increment with stand development. The clear separation of the curves highlights the strong dependence of ${\mathrm{CO}}_2$ storage potential on site productivity.

Figure 2 illustrates the cumulative ${\mathrm{CO}}_2$ (as TVP) stored in oak stands versus their age, differentiated by site quality. Five distinct lines, each representing a site index (from −I to III), show ${\mathrm{CO}}_2$ accumulation. Site Index −I (teal) represents the most productive site, accumulating over 2000 ${\mathrm{t}}^{-1}$ ${\mathrm{ha}}^{-1}$ by 175 years. Site Index III (light green) is the least productive, accumulating just over 1000 ${\mathrm{t}}^{-1}$ ${\mathrm{ha}}^{-1}$ over the same period. Generally, ${\mathrm{CO}}_2$ accumulation increases with age for all sites, with an initial slower growth followed by a more rapid increase. The difference in ${\mathrm{CO}}_2$ storage among the site indices becomes more pronounced as the trees age. For the assessment of additional climate mitigation effects, the TVP of managed forests appears to be of limited suitability, as the full TVP cannot be accumulated in the stand over the long term under a no-management scenario. To avoid potential misinterpretation, it should be clarified that the displayed TVP trajectory refers exclusively to managed stands based on the yield table assumptions of Albert et al., 2024 [40].

Figure 2. Total CO₂ production of Oak for different site indices and different ages.

Figure 3 illustrates the mean annual increment (MAI) of ${\mathrm{CO}}_2$ in oak stands as a function of their age, differentiated by site quality.

Figure 3. Mean annual increment ${\mathrm{CO}}_2$ of oak for different site indices and different ages.

Site Index −I (teal) represents the most productive site, showing the highest MAI, which peaks around 14 t ${\mathrm{ha}}^{-1}$ ${\mathrm{yr}}^{-1}$ at approximately 70 years of age before gradually declining. Site Index III (light green) is the least productive, exhibiting the lowest MAI, which continues to increase slowly throughout the observed period, reaching approximately 6 t ${\mathrm{ha}}^{-1}$ ${\mathrm{yr}}^{-1}$ by 180 years.

For the more productive sites (Site Indices −I, 0, and I), the MAI ${\mathrm{CO}}_2$ curves show a rapid increase in the early years, reach a distinct peak (indicating the age of maximum annual ${\mathrm{CO}}_2$ sequestration), and then gradually decline as the stands mature. The peak MAI is higher and occurs earlier for more productive sites. For less productive sites (Site Indices II and III), the MAI ${\mathrm{CO}}_2$ increases more gradually, and for Site Index III, a clear peak is not reached within the 180-year time frame.

3.1.2. Based on Expansion

While in Figure 1 the ${\mathrm{CO}}_2$ stock was derived by scaling individual-tree estimates and stem numbers following Riedel and Kändler (2017) [18], Figure 4 presents results based on stand expansion factors according to Pretzsch (2009) [22]. Both approaches rely on the identical yield tables provided by Albert et al. (2024) [40], ensuring consistency of the underlying growth assumptions while allowing for a methodological comparison of tree-level versus stand-level upscaling. Figure 4 illustrates the accumulation of carbon dioxide (${\mathrm{CO}}_2$) stock in tonnes per hectare (t ${\mathrm{ha}}^{-1}$) over time (age in years) for oak (Quercus spec.).

Figure 4. CO₂ stock of oak for different site indices and different ages based on stand expansion factors.

Site Index −I shows the highest ${\mathrm{CO}}_2$ accumulation, exceeding 1000 t ${\mathrm{ha}}^{-1}$ by 170–180 years, indicating the most productive site. The orange curve (Site index 0) follows, reaching approximately 1000 t ${\mathrm{ha}}^{-1}$ by 180 years. The purple curve (Site Index I) shows moderate accumulation, reaching around 900 t ${\mathrm{ha}}^{-1}$ at 180 years. The magenta curve (Site Index II) indicates lower accumulation, reaching about 820 t ${\mathrm{ha}}^{-1}$ at 180 years. Finally, the lime green curve (Site Index III) represents the lowest ${\mathrm{CO}}_2$ accumulation, just over 700 t ${\mathrm{ha}}^{-1}$ at 180 years, indicating the least productive site.

All curves exhibit a sigmoidal growth pattern: an initial slow accumulation phase, followed by a period of rapid increase, and finally a gradual levelling off as the stands mature. Differences in ${\mathrm{CO}}_2$ stock among the site indices become more pronounced with increasing age, particularly after 40–50 years.

3.1.3. Comparison of Equation-Based Stock vs. Expansion Factor Stock

Given its central role in comparing tree-level and stand-level upscaling approaches for ${\mathrm{CO}}_2$ stock estimation (Figure 1 and Figure 4), Figure 5 shows the deviation of the methods in percent [%]. These extreme fluctuations highlight the inflexibility of generalised expansion factors when applied to early growth stages. The allometry of young trees changes rapidly and is highly sensitive to site conditions, a dynamic that a single, averaged factor cannot capture. Our single-tree approach, being sensitive to tree height and diameter, could be more suitable in this case.

Figure 5. Deviation of expansion factors to equation-based calculation for the ${\mathrm{CO}}_2$ stock.

3.2. Interactive Online Application

Figure 6 illustrates the interactive application developed for this study, displaying a sample calculation for an oak stand. The application can be found online: https://easyco2estimation.shinyapps.io/shiny/, acessed on 10 October 2025.

Figure 6. Screenshot from the interactive online application.

Based on these inputs, the dashboard displays 120.51 kg of ${\mathrm{CO}}_2$ stock in the above-ground biomass and 38.0 kg in the belowground biomass for the individual tree. At the stand level, the total estimated ${\mathrm{CO}}_2$ stock is 213.04 t ${\mathrm{ha}}^{-1}$, which corresponds to an SDI of 649. As the number of stems per hectare increases, the total ${\mathrm{CO}}_2$ stock increases linearly. The dashboard incorporates validation checks to ensure realistic inputs. If a user enters a biologically implausible height-to-diameter (h/d) ratio, the system flags the input with the warning, “implausible h/d ratio”, indicating an unrealistic combination of parameters.

Similarly, a validation check is in place for stand density. If the number of stems is so high that the cumulative basal area of all trees would exceed the stand area (1 ha), the dashboard triggers a second warning: “SDI is too high! Total basal area exceeds 1 ha”.

4. Discussion

4.1. Discussion of Materials and Methods

The foundation for quantifying potential ${\mathrm{CO}}_2$ stock and sequestration in this study was the fourth generation of yield tables by Albert et al. (2024) [40]. These tables were selected as they are the most contemporary dataset for Northwest Germany, representing a methodological advancement by combining empirical observations with modelling in the single-tree growth simulator TreeGrOSS. A significant limitation, however, is that these tables do not yet account for the future impacts of climate change. The planned updates will be crucial for re-evaluating these findings under future climate scenarios. It should be kept in mind that the data are regionally specific to Northwest Germany, and caution is required when extrapolating the findings to other regions with different growth conditions.

Furthermore, forest thinning practices significantly alter stand dynamics and, consequently, the overall carbon stock by selectively removing trees to guide forest development. Historically, management often favored low thinning, which removes suppressed and intermediate trees from the lower canopy strata, a principle reflected in older yield tables like those by Schober (1995) [35]. In contrast, modern approaches such as high thinning or the now-widespread system of graduated thinning—involving intensive early interventions followed by more moderate low thinnings later on—are employed to more actively guide stand development [40,42]. While any thinning intervention initially reduces the on-site ${\mathrm{CO}}_2$ stock by removing biomass, these practices are designed to reallocate growth to the remaining, often more vigorous, trees. This can accelerate their development and lead to a higher rate of carbon sequestration over the stand’s lifetime; indeed, a global meta-analysis found that thinning, on the whole, significantly increased total tree aboveground biomass and soil organic carbon stocks, enhancing the overall forest ecosystem carbon sink [58]. However, the results are not always straightforward and can be inconsistent [58]. For instance, a 30-year time-series study in Turkey on Brutia pine found no significant difference in total carbon stocks between thinned and unthinned plots, as the faster growth of remaining trees compensated for the removals over time [59]. Furthermore, the specific thinning strategy is critical, as a simulation study in Finland showed that shifting to regimes that allowed higher tree stocking resulted in an increase of up to $11\%$ in the forest ecosystem’s carbon stock and up to $14\%$ in the carbon of harvested timber [60]. This demonstrates that the effect of thinning on the total carbon stock stored in the forest and in timber products is a complex outcome dependent on management intensity, ecosystem response, and regional factors.

A critical methodological constraint is the model’s application to pure stands only. While our single-tree approach can be used to simplify stand data, its direct application to mixed-species forests is problematic. As established in the literature, mixing species fundamentally alters forest dynamics. Interspecific competition leads to significant shifts in individual tree allometry, resource use, and overall productivity, often resulting in higher yields than in monocultures [61,62]. Belowground competition can be equally complex and asymmetric, with species like Fagus showing strong competitive ability for root space [63]. As our model does not capture these interactions, its findings are primarily applicable for pure stands and should be interpreted with caution for more complex stand structures.

For the conversion of tree biomass to carbon, a constant factor of 0.5 was used. This value is a widely accepted standard in European forest carbon accounting, supported by research indicating that the relative error associated with this simplification is typically low, around ±2% [64]. While carbon content can vary within and between species [65], and global averages show a range [66], the 0.5 factor provides a robust and practical estimate for the circumstances of this study. Nevertheless, it remains a simplification that contributes to the overall uncertainty of the absolute carbon stock values.

In our dashboard, we did not set a fixed limit for stems per hectare (at any given age), but it must be noted that the dashboard might give unrealistic outputs when unrealistic inputs are given.

The concept of maximum stand density is not a single, fixed number. Instead, it is a dynamic relationship known as the self-thinning line, which connects the number of trees to their average size [67]. A young stand might have well over 50,000 small seedlings, but as those trees grow, competition causes natural mortality (self-thinning), and the stem count drops. A single threshold fails to capture this fundamental process.

It is influenced by multiple factors that a fixed value ignores:

• Species and Traits: Different tree species have inherently different carrying capacities. For example, self-thinning models for beech and oak have different parameters [67]. A species’ tolerance to drought, shade, or bending stress also directly controls the maximum density a site can support [68].
• Stand Structure: Even in a forest of a single species, the arrangement and size variation of trees matter. Maximum density and yield are often highest in stands with moderate structural diversity, not in those that are perfectly uniform or overly heterogeneous [69].
• Site and Climate: The self-thinning relationship changes based on local conditions. Factors like site quality, solar radiation, temperature, and precipitation all alter a stand’s carrying capacity [70,71]. Therefore, management models based on self-thinning must be adapted for different latitudes and climates [71].

It can thus be concluded that the utilisation of the dashboard necessitates a certain degree of expertise. Realistic maximum basal areas for dense European forests are typically in the range of 37–68 ${\mathrm{m}}^2$ per hectare [72].

4.2. Discussion of Results

Our results reveal a systematic difference between ${\mathrm{CO}}_2$ estimates derived from our single-tree allometric approach and those from the established expansion factors. The interpretation of these deviations provides insight into the strengths and weaknesses of each method.

In mature stands, our approach consistently estimates approximately 20% to more than 35% ${\mathrm{CO}}_2$ stock than the expansion factor method (Figure 4). This substantial, stable deviation can be directly linked to the different methodologies for calculating belowground biomass. Our use of tree-specific allometric functions seems justified by the well-documented variation in root-to-shoot allocation among species. The publication by Dieter and Elsasser (2002) [21] shows that a single, fixed ratio is not able to capture the complexity of the observed data precisely in our case. More importantly, it illustrates that generalised models tend to systematically underestimate root biomass in mature forests, particularly for coniferous species [21]. Our species-specific approach, therefore, provides a more realistic estimation of this crucial carbon pool, avoiding the underestimation inherent in conventional, non-specific methods.

To further assess our model’s foundation, we have categorised our results for single tree estimation with those from Klein and Schulz (2023) [73]. The comparison shows very small deviations, confirming the general accuracy of our underlying allometric functions for individual trees. Minor differences, such as our slightly lower ${\mathrm{CO}}_2$ values for small-dimension pine trees or higher values for large beech trees, do exist. However, the fact that our single-tree estimates align so closely with other recent research, while our stand-level estimates diverge so strongly from the expansion factor method, reinforces our main conclusion: the primary source of the discrepancy very likely is not the basic above- and belowground allometry, but rather the method of aggregating trees to the stand level by multiplying it with the number of stems.

As previously stated, carbon storage in harvested wood products (HWPs) is not addressed in this study; however, it is undeniably an important component of comprehensive carbon accounting. To avoid potential misunderstandings, it is important to emphasise that the utilisation of wood beyond the boundaries of the forest system also plays a significant role. Nonetheless, this aspect is not considered within the scope of the present analysis. The atmospheric impact of wood use can vary depending on its specific application. For instance, when wood is used in construction, it contributes to an increase in the HWP carbon pool. Conversely, when wood is burned for energy, it results in immediate carbon emissions [74]. These outcomes, however, occur outside the system boundaries defined for this study and are therefore excluded from the analysis.

5. Conclusions

This study demonstrates that the choice of methodology for ${\mathrm{CO}}_2$ accounting in forests is not a minor detail but a critical factor that can lead to significant disparities in results, with deviations ranging from 20% to over 35%. These findings underscore the need for accurate and transparent tools for carbon quantification, which have profound implications for forest management, climate policy, and emerging carbon markets.

In this context, tools such as the ${\mathrm{CO}}_2$ yield tables developed here can represent a valuable instrument for practitioners and scientists who need a fast and easy solution for ${\mathrm{CO}}_2$ estimation in forest stands. By facilitating a robust evaluation of their stands’ ${\mathrm{CO}}_2$ storage potential over time, they provide a solid foundation for sustainable management decisions. To further enhance this, the interactive R-shiny dashboard developed in this study offers added value. It moves beyond static tables to provide a user-friendly, and reproducible tool that makes precise ${\mathrm{CO}}_2$ accounting accessible, that neither requires deep statistical expertise nor knowledge in forest growth modelling. This capacity to reliably quantify and project carbon stocks allows forest owners to better engage with mechanisms like the expanding Voluntary Carbon Market (VCM). As companies increasingly seek to offset their emissions, the provision of transparent and verifiable accounting tools is paramount. The credibility and growth of the VCM are thus contingent on the very type of standardised and scientifically sound methodologies that this research seeks to advance.

From a scientific perspective, our results reinforce the call to move away from static, generalised factors towards more dynamic, process-oriented models that capture the underlying biological reality of tree growth. However, our analysis also highlights critical areas where further research is required. The most pressing need is the accounting of carbon in mixed woodlands. The complex interactions between different tree species and their influence on carbon storage are not adequately represented in most existing yield tables. Future research must therefore concentrate on creating carbon yield tables specifically for mixed woodlands to enable a more precise and comprehensive evaluation of carbon potential in these diverse ecosystems. In addition, there is a need for yield tables and carbon accounting approaches that address non-typical forest management concepts, which do not primarily aim at timber production, such as management abstention, set-aside areas, or special silvicultural regimes designed for water or biodiversity protection forests. By providing a more accurate method for estimating carbon, this study adds value not only for practitioners but also for forest-economic modelling. In the future, this will allow for the modelling of yields not only from timber production but also from mechanisms such as the Voluntary Carbon Market (VCM), based on the aforementioned measures. Accordingly, the findings of this study will be directly applied within the FESIM model mentioned above.

Beyond the challenge of mixed stands, future work must also address the impacts of climate change, which will undoubtedly alter growth rates and allometric relationships. But most fundamentally, the ultimate validation for any carbon model lies beyond comparing different equations. It would involve field research to anchor our models in direct, empirical measurements—including destructive sampling of representative trees from various sites and age classes, excavating root systems drying, and weighing each component (stem, branches, foliage, and roots) to determine its actual biomass [75].

In essence, the value of augmenting traditional yield tables with explicit ${\mathrm{CO}}_2$ content lies in their powerful simplicity and accessibility. For forest practitioners, this approach integrates a critical ecosystem service directly into their established planning framework. Instead of navigating separate carbon calculators, they can assess the sequestration potential of a stand ’at a glance’, alongside traditional metrics like timber volume, facilitating intuitive decisions where both economic and ecological outcomes are immediately visible.

For scientists, the innovation lies in lowering the entry barrier to carbon research: These tables support decision-making where both economic and ecological outcomes are immediately visible. For scientists, their innovation lies in lowering the entry barrier to carbon-related research: they offer a standardised, transparent, and readily applicable method for incorporating ${\mathrm{CO}}_2$ dynamics into disciplines that do not typically focus on forest carbon accounting. This enables, for instance, silvicultural researchers to explore how species selection affects both timber production and carbon sequestration, or political scientists to evaluate policy instruments aimed at enhancing forest carbon storage—without the need for specialised carbon models. While not a substitute for detailed simulation approaches—such as those implemented in FESIM—these tables provide a shared empirical foundation that facilitates comparative analysis, interdisciplinary dialogue, and reproducibility. In doing so, they serve as a form of scientific infrastructure that extends the impact of forest carbon research well beyond the forestry domain.

Appendix B.1. Beech

Figure A1. CO ₂ stock of beech for different site indices and different ages.

Figure A2. CO₂ stock of beech for different site indices and different ages based on stand expansion factors by Pretzsch [22].

Figure A3. Single tree CO₂ estimation for beech (above- and belowground biomass).

Figure A4. Total CO₂ production of beech for different site indices and different ages.

Figure A5. Mean annual increment CO₂ of beech for different site indices and different ages.

Appendix B.2. Spruce

Figure A6. CO₂ stock of spruce for different site indices and different ages.

Figure A7. CO₂ stock of spruce for different site indices and different ages based on stand expansion factors by Pretzsch [22].

Figure A8. Single tree CO₂ estimation for spruce (above- and belowground biomass).

Figure A9. Total CO₂ production of spruce for different site indices and different ages.

Figure A10. Mean annual increment CO₂ of spruce for different site indices and different ages.

Appendix B.3. Pine

Figure A11. CO₂ stock of pine for different site indices and different ages.

Figure A12. CO₂ stock of pine for different site indices and different ages based on stand expansion factors by Pretzsch [22].

Figure A13. Single tree CO₂ estimation for Pine (above- and belowground biomass).

Figure A14. Total CO₂ production of pine for different site indices and different ages.

Figure A15. Mean annual increment CO₂ of pine for different site indices and different ages.

Appendix B.4. Douglas Fir

Disclaimer for Douglas fir: We removed the −I site index because, although the ${\mathrm{CO}}_2$ stock of an individual reference stem in the yield tables is higher for better site indices, the total ${\mathrm{CO}}_2$ stock becomes lower when scaled by the lower stem count associated with the −I site index. This scaling effect explains why the overall ${\mathrm{CO}}_2$ stock for −I is less than that of the 0 site index.

Figure A16. CO₂ stock of Douglas fir for different site indices and different ages.

Figure A17. CO₂ stock of Douglas fir for different site indices and different ages based on stand expansion factors by Pretzsch [22].

Figure A18. Total CO₂ production of Douglas fir for different site indices and different ages.

Figure A19. Mean annual increment CO₂ of Douglas fir for different site indices and different ages.

Appendix B.5. Deviation Plots for Other Tree Species

Figure A20. Deviation of Pretzsch’ expansion factors to our results for spruce.

Figure A21. Deviation of Pretzsch’ expansion factors to our results for pine.

Figure A22. Deviation of Pretzsch’ expansion factors to our results for Douglas fir.