We developed a model to estimate carbon stored in different categories of wood products at time t. The model is simple, consisting of two parameters (average lifespan (l
i
) and recycling rate (r
i
)) and a single state variable (C
p) which represents the carbon content in an unique product commodity (p) (e.g. sawn wood, wood-based panels or paper and paperboard). The variable C
p is defined by the sum of sub-variables (c
i
), which represent the carbon stored in products produced at different years (i) from harvested (H
i
) and recycled wood (R
i
) (Eqs. 1, 2 and 3). We used the distributed approach as described by Marland et al. (2010). The parameters of average lifespan and recycling rate are time-dependent and define the removal rate of the product produced at time t. We used time steps of 1 year.
$$ {C}_{\mathrm{p}}(t)=\sum {c}_i\left({t}_i\right) $$
(1)
$$ {c}_i\left({t}_i\right)=\left({H}_i+{R}_i\right)\times \left({1-CDF}_i\left({t}_i\right)\right) $$
(2)
$$ {R}_i={r}_i\times \sum \left({c}_{1\to i}\left({t}_i-1\right)-{c}_{1\to i}\left({t}_i\right)\right) $$
(3)
The product removal rate was defined using the cumulative distribution function (CDF) of a normal distribution, also used in other studies (e.g. Muller et al. (2004)). The normal distribution is defined with a mean and a standard deviation. The mean corresponds to the average lifespan of the product under analysis produced at year i. The standard deviation was arbitrarily defined as one third of the average lifespan (Eq. 4) (Supplementary Information 1). The normal distribution was calculated using the function dnorm (in the package stats version 3.2.0) in R software version 3.0.1.
In the literature, besides using the normal distribution to define the cumulative distribution function, other distributions have been used such as linear (Winjum et al. 1998), exponential (Karjalainen et al. 1994) or gamma distributions (Klein et al. 2013). All of them have been proposed using expert knowledge, but none of them have ever been validated due to lack of data. We omitted linearly and exponentially distributed functions, because we assume a maximum rate of decay over a product’s average lifespan, but not immediately after production. In other words, most of the products designed to be in use, for example 25 years, will be removed around 25 years after production, but not the next year after their production. We believe that gamma distribution is the closest to reality because it allows representation of asymmetric behaviour. However, it was excluded because it is difficult to estimate the required parameters for each average lifespan included in this study due to lack of data. Moreover, wood products’ removal rates defined using normal distributions are similar to gamma distributions because they are not very asymmetric as can be seen in studies that applied it (e.g. Marland and Marland (2003) or Klein et al. (2013)).
Avoided emissions of carbon dioxide equivalents are assumed to be equal to carbon stocks increments once they are transformed using a correction factor (1 t C equals 44/12 t CO2).
Theoretical simulation exercise
When selecting scenarios, the focus was placed on covering all possible combinations of average lifespan and recycling rate. Recycling scenarios ranged from 0 to 95 %. Higher recycling rates were avoided because they would be impossible to achieve in reality. Average lifespan scenarios ranged from 5 to 100 years. The maximum average lifespan value of 100 years was selected from the list of half-life values (equivalent to the average lifespan when using normal distribution) compiled in the review study of Pingoud et al. (2003).
Since the interval between minimum and maximum average lifespan and recycling rates included 95 units each, we decided to split them with the same number of intervals (19), thus using increments of 5 years and 5 %, respectively, which are obviously different units that cannot be directly compared. The model was run for 400 combinations of scenarios (20 different recycling rates combined with 20 different average lifespan).
Special attention was placed on the three selected product commodities of sawn wood, wood-based panels and paper and paperboard. According to the IPCC recommendations (IPCC, 2014), the average lifespan of the selected products are 35, 25 and 2 years, respectively. Since an average lifespan of 2 years was not included in this simulation exercise, we represented the average lifespan of paper and paperboards with 5 years. The recycling percentages estimated were 30, 10 and 70 % for sawn wood, wood-based panels and paper and paperboards, respectively. These percentages were approximated from other studies: sawn wood from Eggers (2002) and Schelhaas et al. (2004), wood-based panels from Eggers (2002); Schelhaas et al. (2004) and Skog (2008) and paper and paperboards from Eggers (2002) and Mantau (2012). However, these studies used different groups to classify products, which make comparisons difficult.
In a first phase, we estimated carbon stock in wood products at steady state under the assumption of constant production (Fig. 1). The total amount of carbon was the sum of carbon stock in products produced in successive years. The steady state was achieved when the total carbon stock increased less than 1 % of the input. This threshold was defined to avoid excessive time with very low carbon stock increments.
In a second phase, we estimated the carbon stock oscillation during the switch from old product characteristics to new ones (higher average lifespan or higher recycling rate) (Fig. 1). We first estimated the carbon stock curve derived by the production stop of products with old characteristics. Then, we estimated the curve representing the carbon stock of products with new characteristics. The sum of both curves represented the total carbon stock of this product commodity.
Finally, we calculated the difference between carbon stock at time zero of the second phase and subsequent years to estimate the temporal development of carbon stock changes.
Application to the European wood sector
We applied the same model approach with real data from Europe (EU-28). We used annual production of the three selected products, their average lifespan and their recycling rate to estimate the current carbon stock in wood products.
The annual production of a given product was estimated using the United Nations Food and Agriculture Organization Statistics (FAOSTAT) online database (Food Agriculture Organization of the United Nations 2014). Each product category used in this study is an aggregate of different items as shown in Table 1. Information on annual production was available from 1961 to 2014. The last value reported for fibreboard category was on 1994. From 1995 onwards, this category was split into medium density fibreboards and hardboards. We started running the model from year 1800 for the spin-up. At this year, the estimated annual production was zero t C for all products. The production of successive years was estimated with a linear increase until the first value reported by FAOSTAT was achieved at year 1961. Future production was estimated using the forecast increases in percentages from Mantau and Saal (2010). This report estimated that till 2020 wood consumption would increase by 15.4 % compared to 2010 values. The last year of production estimations available from FAOSTAT was 4 years later (2014). Therefore, we estimated a proportional increase for the last 6 years (2014–2020) of 9.24 %. The same production increase from 2020 to 2030 of 17.2 % estimated by Mantau and Saal (2010) was used for the last simulated years of this study (2020–2046). Conversion factors to estimate carbon content from volumes reported in FAOSTAT were extracted from IPCC (2014) (Table 1).
Table 1 Description of the FAOSTAT data used to estimate wood production
FAOSTAT data includes recycled products. Therefore, we had to estimate the production with virgin wood. This transformation was performed for each product type using its recycling rate. The factor of virgin wood production over the total production was estimated by extracting the recycling value to 100 %. For example, for wood-based panels with 10 % of recycling rate, we estimated that only 90 % (100 minus 10) of the volume reported from FAOSTAT was produced with virgin wood.
In this practical exercise, instead of simulating stepwise increments of average lifespan and recycling rate as in the theoretical exercise, we defined a target of GHG emission reduction and calculated how much the average lifespan or the recycling rate should increase to achieve it. Product characteristics of average lifespan and recycling rate were assumed to improve abruptly in 2017. Since a European target of GHG emission reduction for the land use, land use change and forestry sector does not exist, we defined an arbitrarily one of additional reduction of 5 Mt. of CO2 in 2030. The year 2030 was chosen because the targets in the Intended Nationally Determined Contributions of EU are defined for this year. Average lifespan increments (inc
l
) were defined applying the same proportion to current values of all products (e.g. an increment of 1.1 times on current average lifespan (l
c
) of wood-based panels will suppose a rise from 25 to 27.5 years) (Eq. 5). The increments on recycling rate (inc
r
) were calculated differently because of two reasons. Firstly, they are limited at 100 %. Secondly, we assume that the effort to increase it on a product with a high recycling rate is bigger than the effort to increase it on another product with a low recycling rate. Thus, we added to the current value of recycling rate (r
c
) a portion of the percentage needed to achieve 100 % (e.g. an increment of 0.1 on current recycling rate of wood-based panels will suppose a rise from 10 to 19 %) (Eq. 6).
$$ {l}_{\mathrm{n}}={l}_{\mathrm{c}}\times {inc}_l $$
(5)
$$ {r}_{\mathrm{n}}={r}_{\mathrm{c}}+\left(100-{\mathrm{r}}_{\mathrm{c}}\right)\times {inc}_r $$
(6)
where l
n and r
n are new average lifespan and new recycling rate values, respectively. We also estimated the climate change mitigation effect if both increases were combined. All calculations were performed using R software (version 3.0.1).