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. 2024 Jun 21;28(4):953–965. doi: 10.1111/jiec.13511

Robust modeling of material flows to end-uses under uncertainty: UK wood flows and material efficiency opportunities

R L Anspach 1,3,✉, S R Allen 2,3, R C Lupton 1,3
PMCID: PMC13100019  PMID: 42027597

Abstract

In this study we quantify wood flows from raw materials to end-uses for the United Kingdom in a robust way using a new material flow analysis (MFA) model with uncertainty. This is important to identify opportunities for efficiency given constraints on wood supply. We have developed a new “ProbPACTOT” MFA model which introduces a systematic method to handle mixed units during reconciliation and uncertainty in data observations, conversion factors, and process recipes. This makes it possible to track material flows all the way to end-uses, which is otherwise difficult because the diverse materials, data types, and units used to quantify end-products are hard to integrate into standard allocation-based MFA models. We apply the model for the case of wood in the United Kingdom by defining 56 process recipes and reconciling 117 data observations from various sources. The results quantify upstream production and trade flows, through to 19 specific end-uses of wood fibers. We use this to show the potential scale of savings by enhancing material efficiency; for example, if pallets were used 25% more intensively, 0.49 Inline graphic0.2 Inline graphic of wood fibers could be saved, corresponding to 4%–7% of the total soft sawnwood consumption of the United Kingdom. Judging the scale of opportunities for wood material efficiency in the United Kingdom is important domestically, and has global significance as the United Kingdom is the second largest net importer of wood products in the world. Moreover, this study proposes an important advancement in MFA giving a structure for modeling uncertain material flows up to end-uses, applicable to any material. This article met the requirements for a gold-gold JIE data openness badge described at http://jie.click/badges.

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Supplementary Information

The online version of this article (doi:10.1111/jiec.13511) contains supplementary material, which is available to authorized users.

Keywords: end-uses, industrial ecology, material efficiency, material flow analysis (MFA), uncertainty, wood

INTRODUCTION

Demand for global industrial roundwood is predicted to quadruple by 2050, exceeding the capacity of sustainable supply (Gresham House, 2019; O’Brien & Bringezu, 2017; World Bank, 2016). As a consequence, there is an increasing need to plan for the use of national and imported wood resources (World Bank, 2016). This planning cannot be done at the level of individual projects or products, but must be considered as a higher level, to determine where limited resources should be used most efficiently and for the greatest benefit. Robust information about the production, trade, processing, and use of timber and timber-containing products is essential for doing this successfully.

Material flow analysis (MFA) is a method to quantify mass flows and stocks of material occurring in a system, usually national or global. It is commonly used to assist with the quantification of timber-related resource flows to inform choices about sustainable uses of timber. MFA has been applied to quantify wood mass flows at a country level (Brownell et al., 2023; Gonçalves et al., 2021; Höher, 2020; Hekkert et al., 2000; Kayo et al., 2019; Lenglet et al., 2017; Mantau, 2015; Parobek et al., 2014; Sokka et al., 2015; Szichta et al., 2022), at a European level (Cazzaniga et al., 2022), and to understand carbon flows (Brunet-Navarro et al., 2018; Aryapratama & Pauliuk, 2019). A particular focus has been using MFA to show the potential for improved “cascading use” of wood, that is, keeping the natural resource in the production and use cycles for as long as possible by making use of resources in order of value (Babuka et al., 2020; Brownell et al., 2023; Gonçalves et al., 2021; Höglmeier et al., 2015; Mantau, 2015; Mehr et al., 2018; Suter et al., 2017; Szichta et al., 2022).

Material efficiency opportunities, that is, the potential to fulfill the required function of a product with less material input (Allwood et al., 2011), are another important means to optimize use of the limit supply of timber. MFA has been used to investigate the material-saving potential at national or global scale of material efficiency measures in finished products for several materials (Cullen & Allwood, 2013; Shanks et al., 2019; Westbroek et al., 2021), but this has not been done for wood products. Material efficiency measures were investigated for wood at the level of products such as timber structures from waste materials (Llana et al., 2022), designing for disassembly (Yan et al., 2022), and repair and re-use (Pronk et al., 2022; Russell et al., 2022); but these findings have not been combined with MFA-based knowledge of the magnitude of wood flows linked to each product to understand their contribution on the system scale.

These analyses all depend on a robust analysis of timber flows through the system. In particular, the wider scope of opportunities for material efficiency and cascading use requires not only a good understanding of timber flows within the core timber-processing industries, but also of the eventual role of timber, in diverse forms and in diverse end-use products, where many of the opportunities for increasing material efficiency reside. Such detailed mapping of wood flows would enable targeted industry-specific recommendations on material efficiency, and reveal the drivers behind timber demand to understand the consequences of changes in one part of the system on another.

Modeling material flows to cover this wider scope—that is, extending all the way to final products—relies on introducing a wider range of production and trade data. This brings significant additional challenges, as there is limited information published on timber in finished products, which must therefore be estimated from a variety of sources.

It is difficult to accurately track the mass of forest products due to the varying form, shape, moisture content, and densities that wood products come in, and this becomes even harder further downstream, where different types of semi-finished wood products get mixed into finished products (O’Brien & Bringezu, 2018). Most of the studies of wood flows referenced above avoid the problem by focusing on semi-finished products and aggregate end-use into one flow (Babuka et al., 2020; Cazzaniga et al., 2022; Gonçalves et al., 2021; Hekkert et al., 2000; Kayo et al., 2019; Lenglet et al., 2017; Parobek et al., 2014; Sokka et al., 2015). Other studies give details on the sectoral use of wood products. Szichta et al. (2022), Brownell et al. (2023), and Brownell et al. (2023) aggregate end-uses into four main sectors (furniture, construction, packaging, and others, for material application industries other than paper), while Aryapratama and Pauliuk (2019) differentiate between furniture and packaging, buildings, agriculture, infrastructure, and other sectors. However, knowledge of the sectoral uses of wood is insufficient for identifying opportunities for enhancing material efficiency where greater product-level detail is needed on end-uses.

Bösch et al. (2015) and Brownell et al. (2023) reconcile their whole model by mass balancing inflows and outflows of wood up to end-uses. Bösch et al. (2015) assembles and balances diverse data from various sources in a physical input–output table without giving details on how the challenges of dealing without diverse data were dealt with. Brownell et al. (2023) build on existing Danish monetary and physical input–output tables, avoiding this problem. Three other papers (Aryapratama & Pauliuk, 2019; Brunet-Navarro et al., 2018; Szichta et al., 2022) determine the allocation of semi-finished products to their sectoral applications by using sector splits, which does not allow for combining diverse types of product-specific data. Aryapratama and Pauliuk (2019) allocates semi-finished products into their sectoral use using an inter-industry transaction matrix, while Brunet-Navarro et al. (2018) uses the “FAOSTAT” allocation scheme’ which applies universal allocation factors to semi-finished products. However, these are homogeneous approaches applied to all flows in the model which do not allow for incorporating and reconciling a mixture of upstream and downstream data where available. For example, if additional data on wood inputs to a specific sector such as furniture is available, that cannot be considered in a model based purely on downstream allocation of semi-finished products to sectors. Therefore, more flexible modeling approaches are needed to manage the complexity, uncertainty, and heterogeneity of data related to the full scope of wood flows.

This study’s aim is therefore to improve the robustness of understanding how and where wood is used, by:

  • Extending MFA tools to deal with varied and uncertain data and limited details on finished products (Section 2.1)

  • Applying these methods to the United Kingdom, as a case study to demonstrate the method (Section 2.2)

  • Showing how wood is used in the United Kingdom, and how much uncertainty remains in results (Section 3)

  • Discussing what this analysis tells us about key areas to use wood more efficiently in the United Kingdom (Section 4)

The United Kingdom is a relevant case study as even though it is a small country, the United Kingdom is the second largest net importer of wood products in the world (World Bank, 2016). Timber is also at the heart of national-level discussions on decarbonization in the United Kingdom (Forestry Comission, 2022; HM Government, 2021a, 2021b) which makes it timely to understand the system scale use of this material and inform national and institutional decision making on material efficiency.

METHOD AND APPROACH

We first introduce the existing MFA reconciliation modeling approach used, and how it is developed to account for uncertainty. The following two subsections then focus on the case study of wood flows for the United Kingdom, describing the wood system’s structure, and the specific data sources used.

MFA reconciliation model developed for uncertainty analysis

Tracking material flows through production processes to finished products is challenging as it requires fitting a large variety of potentially inconsistent data into the material flow model, with each step down the supply chain adding a level of uncertainty into the results. In general, this is solved by defining an MFA system, and applying data reconciliation procedures to find a solution which satisfies mass balance constraints while matching the available data as well as possible (Brunner & Rechberger, 2016). Within this general approach, much is left to the modeler to determine how specifically the data should be organized and the model equations set up. For this study, we use an existing implementation of MFA data reconciliation known as “PACTOT” (Process ACTivity - Object Trade) (Lupton, 2021), described later, which helps to manage and reconcile observed data points from across the supply chain. The basic PACTOT model does not handle uncertainty, so here we develop the new “probabilistic PACTOT” (ProbPACTOT) model used for the subsequent case study.

The PACTOT model structure

The PACTOT reconciliation model is an implementation of MFA data reconciliation, targeted at situations where flow data is relatively scarce, so assumptions about process characteristics are important both to fill in unmeasured flow values and where heterogeneous systems are being modeled. It is therefore convenient to build a model in terms of “mixed units” rather than everything being directly defined in mass units.

In the model, processes are defined by their “recipes,” which are a fixed set of input/use and output/supply quantities (left-hand side of Figure 1). Materials, products, and other entities flowing between processes are referred to as “objects.” Each object can optionally allow for trade flows, and can be measured in whatever way is most convenient (e.g., sawnwood could be measured by volume, but end-products such as construction wall panels can be measured in the units in which they are generally quantified, such as square meters). These process and object definitions define the possible flows in the model, and are used to assemble the constraint matrices to ensure conservation of mass of all objects (Lupton, 2021).

FIGURE 1.

FIGURE 1

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The structure of the ProbPACTOT model. The elements of the original PACTOT reconciliation model are shown on the left, where Inline graphic identifies an object; Inline graphic identifies a process; Inline graphic is the input (use) of object Inline graphic into process Inline graphic; Inline graphic is the output (supply) of object Inline graphic into process Inline graphic. Here, in the present study, the model is developed into the ProbPACTOT model, shown on the right-hand side, where uncertainty in process recipes and observations are described by probability density functions (PDFs).

Input data points, called generally “observations,” are collected in a database and linked to the specific part of the model structure they are referring to, consistent with the approach described by Germano et al. (2021) for tracking the meaning and provenance of data points using Semantic Web technologies. Observations can measure different aspects of the system, such as the input or output quantity of an object into/out of a process, or trade flows across the system boundary (Lupton, 2021). An observation can refer to single objects, or aggregates of objects which are grouped because of their common features (e.g., wooden bedroom furniture or sawnwood).

The observations are used to set up a least-square optimization which reconciles any conflicting input data within the constraints of the model structure (defined by the objects, processes, and their recipes). Depending on the input data available, the model can be under-constrained, meaning that there are several possible solutions to achieve mass balance, or over-constrained, in which case data reconciliation is necessary.

The ProbPACTOT model

A well-reconciled model does not mean that the results are reliable, because observations can be erroneous or contain partial data. Conversely, when there is insufficient data and the reconciliation finds multiple possible solutions, there is clearly uncertainty about the correct solution. To quantify the effect of data and parameter uncertainty, the PACTOT model was further developed to include statistical uncertainty analysis using a Monte Carlo approach, resulting in the ProbPACTOT model (right-hand side of Figure 1). The ProbPACTOT model gives the option to:

  • Enhance transparency and re-traceability in data reporting by inputting observations into the model in their original unit of measure before being converted to a common unit, when needed, during calculation steps.

  • Assign a coefficient of variation to each observation, used to define observations as normal distributions from which samples can be retrieved.

  • Reflect the uncertainty in recipe mixes by sampling input and output mixes from defined probability distributions.

After the uncertainty characterization of observations, conversion factors, and recipes, in each Monte Carlo sample the model is re-reconciled, giving a set of sampled solution to the model.

Data reconciliation stems from the assumption that the observed values inevitably contain small random errors which have to be adjusted to achieve mass balance. However, when the adjustments made during reconciliation become large, this may indicate a more fundamental problem with the observed data or with the model. Detecting this situation is known as gross error detection (Narasimhan, 2000). Using the ProbPACTOT model, possible gross errors can be identified when more than half of the reconciled values fall outside the 95% confidence interval estimated for the original observed value. This may indicate that the uncertainty range estimated for the observed data was underestimated, or that there is a missing flow in the model structure for which other flows compensate by increasing or decreasing their value during reconciliation. Cases where possible gross errors are flagged by this test can then be reviewed by the modeler.

Choice of process types for modeling different situations

The model structure can be summarized by the following three modeling principles with detailed examples of each given in Section 2.2.4. When only the output of a production process is known, recipe mixes are used to constrain process inputs and yields. Alternatively, when data is available on the production process inputs, separate sub-processes, called transfer processes, are defined for known inputs to avoid over-constraining the model by the use of recipe mixes. Finally, when data is only available on material intensities, the recipe can be defined as the amount of material consumed in relation to some other unit of measurement.

Proposed framework for uncertainty characterization in MFA models

Various studies report difficulties in characterizing uncertainty, because information is often missing on the methods used to generate the data (Laner et al., 2016). Therefore a Bayesian approach was proposed by Lupton and Allwood (2018) to characterize the uncertainty behind values tailored to MFA studies. The Bayesian approach represents unknown parameters as random variables, using objective and subjective knowledge to define probability in a way that reflects the current knowledge of the system and which can be updated later as more information becomes available. The first step of this, uncertainty characterization, involves determining a suitable probability distribution to represent whatever the current knowledge about the parameter is.

For the specific data values (observations), uncertainty was characterized using the pedigree matrix method described by Laner et al. (2016). This approach includes five indicators that are scored from one to four according to the reliability, completeness, geographical, temporal, and other correlation of the data. Each indicator is given a coefficient of variation (CV) based on their expected level of impact on results. The final value for uncertainty for an observation is calculated as the square root of the sum of the squared CVs for each of the indicators.

For the ProbPACTOT model, additional uncertainty characterization is needed for the other key model parameters, specifically conversion factors and process recipes:

  1. Conversion factors: Often, observations must undergo a harmonization process to ensure they are presented in a consistent and standardized unit of measurement (e.g., converting volume into a standardized unit of mass). Additionally, it is often necessary to perform conversions to eliminate materials that are not relevant to the focus of the study (binders and water in the case of wood). Observations can refer to a single material/product, or an aggregate category of different sub-products. Ideally, a representative average conversion factor for the unit and material content is defined for each observation. If the precise mix of sub-objects is known, the weighted average conversion factor can be found based on specific conversion factors for each sub-object contained within the observation, but this detailed information is often not available. Therefore, we model average conversion factors as uniform distributions with a lower and a upper bound:
    graphic file with name d33e580.gif 1
    where CF is the desired representative conversion factor for the aggregated observation; Inline graphic is the observation value in its original units; Inline graphic and Inline graphic are the upper and lower bounds of the unit conversion factor (e.g., Inline graphic); Inline graphic and Inline graphic are the upper and the lower bound of the share of non-analyzed material content Inline graphic (as a fraction). This is a general approach for any material, which is further developed in Section S.3, equation S5, of the Supporting Information S2 to take into account consideration particular to wood, such as moisture content.

  2. Recipe input and output mixes: The operation of processes should ideally refer to the average input and output mixes of the process in the studied system boundary (in this case, a country). Like observations, a recipe can be an aggregate of different production processes, in which case the average input and output mixes should be estimated for all the processes before calculating the average for the whole. But this is often challenging because of the lack of data. To reflect the uncertainty behind recipe mixes, input and output mixes are modeled in a dependent manner to respect the constraint on the total, meaning that the distribution has to create Inline graphic positive numbers that add up to 1, as shown in Figure 1 in uncertain recipe mixes. This is done by defining recipe inputs and outputs using Dirichlet distributions. An adapted pedigree matrix method was developed to determine the parameters of the Dirichlet distribution. A high Inline graphic parameter, defined in Section S.2.1, of the Supporting Information S2, means a high concentration of possible solutions around the best-estimate value and therefore a low uncertainty (Lupton & Allwood, 2018).

    It is not always clear how to choose the parameters for the probability distribution to reflect qualitative knowledge about uncertainty in the process recipes. Occasionally some quantitative information is given about uncertainty input or output mixes, which can then be used to calibrate the Dirichlet distribution (Paoli et al., 2018), but this is not common. Therefore we developed a simple new version of a pedigree matrix, aimed at consistently characterizing uncertainty in process recipes (Table Table 1). To illustrate the level of variation given for different situations, for a recipe with three inputs of 20%, 30%, and 50%, respectively, the percentage point variation due to the three Inline graphic values are shown in Table Table 1. The variation refers to the full range of values.

TABLE 1.

Pedigree matrix to determine alpha values, defined in Section S.2.1 of the Supporting Information S2, with an example for baseline share of 20%–30%–50%.

Uncertainty level Inline graphic value Percentage-point variation
No data available 10 33
Incomplete data valid for one product 100 11
Representative average available 1000 3
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The UK wood system

To constitute a map of wood material flows in the United Kingdom, a static bottom-up substance flow analysis approach (Brunner & Rechberger, 2016) was taken from the delivery of wood fibers into semi-finished product manufacturing to the production of finished goods including wood embedded in trade.

The system boundary

The system boundary includes the territorial activities of wood-processing industries and wood product trade flows in the United Kingdom as shown in Figure 2. The focus of the analysis is on the production of finished products where there can be potential to implement material efficiency measures (e.g., paper, construction, and commercial product industries). The energy industry was included into the analysis to quantify the amount of fibers directly incinerated, as opposed to being used for material applications.

FIGURE 2.

FIGURE 2

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System boundary of the study. C, consumption; EOL, end-of-life; FP, finished products; FR, forest residues; M, manufacturing; SPF, semi-finished products.

Unit of measure

To make the MFA consistent, a uniform unit has to be defined for the mass flows of wood fibers only, accounting for the wood content of products. In principle, wood fibers can be measured as dry mass, or as volume of wood fiber equivalent, which expresses products’ wood content in terms of equivalent roundwood (soft and hard) volume at fiber saturation point, before any shrinkage due to loss in moisture occurs (green volume). MFA studies of wood flows typically measure flows using volume of wood fiber equivalent (Inline graphic(f)) (Gonçalves et al., 2021; Lenglet et al., 2017; Mantau, 2015; O’Brien & Bringezu, 2018; Szichta et al., 2022). In addition, country-specific conversion factors are available from FAO, ITTO, and United Nations (2020) to convert between reported units of products by ONS (2019) and UN (2023) and, wood fiber equivalent for all semi-finished products. Therefore, in this study, flows of wood are reported in wood fiber equivalents.

Object types and observations

Raw fibers, semi-finished, and finished products are defined in Section S.1 of the Supporting Information S2. Observations on their input, trade, and production quantity with references is further detailed in Table S1–S2 of the Supporting Information S1.

Model structure

The three modeling principles of recipes, presented in Section 2.1.3, were applied in the following instances in the case of wood flows:

  • Recipe mixes: The yield of production processes are expressed as output mixes, for example, sawmills are modeled with an average yield of 50% (FAO, ITTO and UNECE, 2020). As no observation is available on the input of packaging manufacturing, this is modeled with a 63% input of recycled pulp (Van Ewijk et al., 2018). Other input and output mixes used in the model are detailed in Section S.2.2 of the Supporting Information S2.

  • Transfer processes: Observation on the input of roundwood, by-products and fibers for recycling into pulpmills and wood-based panel mills is available. To avoid over-constraining the model, six sub-processes are defined for each of these input quantities resulting in two outputs, respectively: fibers to be consumed by pulpmills and fibers to be consumed by wood-based panel manufacturers, as shown in Figure S1 of the Supporting Information S2.

  • Wood fiber intensities: To estimate the wood fiber content embodied into the structure of new residential buildings, data on the area of residential houses constructed by typology in 2019 is used. The interlink of processes, based on equation S4 of the Supporting Information S2, express wood fiber intensities embodied into an area of building element (e.g., kilograms of wood per square meter of floor area) which are then consumed by the different typologies (e.g., square meter of wooden floor area consumed by a square meter of detached house).

Sources of uncertainty in the wood MFA

The following sources of uncertainty were identified in the model:

  1. Observations: There are two main sources of uncertainty in the observed data. First, data on process inputs are often collected from surveys (Forest Research UK, 2021), so that uncertainty is affected by response rates, errors in measurements, and non-responses. There can be reporting, completeness, and classification inconsistencies in production (ONS, 2019) and trade (UN, 2023) quantities. Moreover, in the construction industry, wood products are often finished on site which means that objects identified as construction products are incomplete as they only represent the fraction of products that were sold in their finished state at the time of reporting. The pedigree score assigned to each observation is detailed in Table S1–S2 of the Supporting Information S1.

  2. Conversion factors: There are ongoing efforts and research to calculate average conversion factors to volume of wood fiber equivalent on a country level for semi-finished products (FAO, ITTO and UNECE, 2020) and for finished products (O’Brien & Bringezu, 2018); where the average country-specific volume, softwood and hardwood content, other material content, and moisture content of the object have to be estimated. In other instances representative mixes are missing, in which case conversion factors to wood fiber equivalent can be calculated based on equation S5–S6 or life-cycle databases can be used as sources for conversion factors. The difference between the two approaches is explained in Section S.3 of the Supporting Information S2. In this study we use equation S5–S6 using data from Table S5–S7 in the Supporting Information S2.

  3. Recipe input and output mixes: Process input and output mixes are ideally derived from industry reports on national-scale quantities of semi-finished products used by industries as in TRADA (2005) which can be outdated or not available. If they are not available, the input and output mixes are estimated from the production of one typical product, however, this present completeness issues. To reflect these uncertainties, recipe mixes are defined as Dirichlet distributions detailed in Section S.2.2 of the Supporting Information S2.

  4. Missing data: Input and production quantities can be incomplete with data missing on objects within an object group which is reflected in the completeness indicator of the pedigree matrix score defined in Section 2.1.4. Other missing data is revealed after reconciliation and shown with a higher level of aggregation in results.

RESULTS

Figure 3 shows the results of the MFA, and describes wood flows in the United Kingdom in 2019. The numerical results discussed in the following sections represent the mean average results, with a bound corresponding to the minimum and maximum values of the Monte Carlo runs excluding outliers calculated as data points beyond 1.5 times the interquartile range. The unit of wood fiber equivalent is abbreviated as Inline graphic in the results later for readability.

FIGURE 3.

FIGURE 3

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Volumes of wood flows measured in Inline graphic(f) in the United Kingdom for the year of 2019 from a territorial perspective. Each flow of the Sankey diagram corresponds to the mean value of the Monte Carlo simulation. The uncertainty in finished products consumption is shown by violin plots. The box plots indicate the minimum without outliers, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum values without outliers. The outliers are calculated as data points beyond 1.5 times the interquartile range. The black vertical bars correspond to the mean values. The relative uncertainty in results, calculated as the difference between the maximum and mean value divided by the mean and expressed as a %, is shown on the right-side bar. Trade flows are represented by the dark grey inflows and outflows. The vertical bars represent manufacturing and trade processes which in some cases are an aggregate of several other sub-processes. Underlying data for this figure are available in the UK-wood-end-use-flows repository at doi.org/10.5281/zenodo.10834953 with their specific location within the repository specified in the README file. FP-C, finished products consumption; cst, construction; F-D, fibers deliveries; eng, engineered; F, fibers; FP-M, finished products manufacturing; NB, new-builds; oth other; prod, production; refurb, refurbished; resid, residential; SFP-M, semi-finished products manufacturing; struct, structure; U, uncertainty.

Reliance on importations

Figure 3 highlights that the United Kingdom is a net importer of wood products; direct material input was of 80.28 Inline graphic4 Inline graphic in 2019 of which 42.10 Inline graphic1.7 Inline graphic of fibers were sourced from imports. Domestic extraction totaled 38.18 Inline graphic3.7 Inline graphic with 9.87 Inline graphic0.8 Inline graphic of fibers extracted as roundwood, 8.55 Inline graphic2.2 Inline graphic as pre- and post-consumer fibers for recycling, 11.70 Inline graphic1.07 Inline graphic as paper for recycling, and 8.07 Inline graphic4.4 Inline graphic as forest residues directly used for energy. On average 81% of the direct material input was consumed in the United Kingdom resulting in a domestic material consumption of 69.16 Inline graphic4.5 Inline graphic and only 19%, 10.16 Inline graphic0.48 Inline graphic of fibers were exported. Direct material input into wood material applications was 47.39 Inline graphic2.67 Inline graphic of which 27.62 Inline graphic1.35 Inline graphic was sourced from imports and 19.77 Inline graphic1.61 Inline graphic was extracted nationally.

Uses of wood in the United Kingdom

Among the total fibers consumed domestically (domestic material consumption), on average, 42% was directly used for energy, equaling 28.44 Inline graphic3.2 Inline graphic (“Pellets” and “Other feedstocks” in Figure 3). The other 58% was consumed as products, equaling 40.72 Inline graphic2.4 Inline graphic, of which 5.39 Inline graphic1.3 Inline graphic as industrial residues.

The 14.69 Inline graphic1.3 Inline graphic of paper products was consumed in the United Kingdom with 6.85 Inline graphic0.5 Inline graphic of raw fibers processed by UK pulpmills. The 2.19 Inline graphic0.1 Inline graphic of fibers was imported as pulp and 9.05 Inline graphic0.9 Inline graphic as finished paper products. Imports of finished paper products covered on average 62% of the total national consumption.

The 12.42 Inline graphic2.1 Inline graphic of wood fibers was used as construction products, of which only 0.60 Inline graphic0.4 Inline graphic was imported in their finished state (i.e., almost all wood fibers for construction underwent processing into final products within the United Kingdom). The construction industry was the largest consumer of sawnwood and particleboard in the United Kingdom in 2019, consuming 5.50 Inline graphic1.3 and 4.48 Inline graphic0.6 Inline graphic of these products, respectively. Timber Trends UK (2010) estimates that between 2008 and 2013, around 5 Inline graphic of soft sawnwood was consumed per year by the construction industry, which is in line with our estimates. Other engineered wood-based panels such as glue-laminated panels only represented 0.14 Inline graphic0.1 Inline graphic of consumption. Concerning the final destination of these fibers, it is estimated that 0.59 Inline graphic0.1 Inline graphic of sawnwood was used for structural applications—such as roof trusses, frames, and floor beams—in newly built residential buildings. Joinery products such as windows, doors, and thresholds, and moldings are estimated to represent 1.22 Inline graphic0.8 Inline graphic of consumption.

The 1.98 Inline graphic0.7 Inline graphic of new flat pallets and 2.45 Inline graphic0.8 Inline graphic refurbished pallets were consumed in the United Kingdom mainly from national sources with only 0.14 Inline graphic0.0 Inline graphic imported. The 2.05 Inline graphic0.8 Inline graphic of soft sawnwood was purchased by pallet manufacturers to make new and refurbished pallets.

The 3.04 Inline graphic1.0 Inline graphic of wood fiber was consumed in the United Kingdom as furniture products with 1.72 Inline graphic0.4 Inline graphic, more than half being imported as furniture in its finished state.

Fencing products are mainly manufactured in the United Kingdom using locally produced roundwood and sawnwood products corresponding to a total consumption of 1.30 Inline graphic0.4 Inline graphic of fencing products.

Robustness of results

There are two ways to evaluate the robustness of results: by looking at how well the algorithm reconciled the model (i.e., how far the flows in the final results differ from the original observation data), and by assessing the uncertainty in results. In this section, the robustness of the calculated and observed flow values of 10,000 Monte Carlo runs were analyzed.

Model diagnostics

To check for possible gross errors in the model or data, the overlap between the original observed data points and the reconciled data was checked following the method in Section 2.1.1. The results, shown in Figure S2–S4 of the Supporting Information S2, reveal that 22% of the reconciled data fall outside the 95% confidence interval of the original observed data points. To evaluate the significance of the discrepancies, the minimum and maximum relative difference that occurred in the 10 000 runs between the observed and reconciled values for a flow were calculated. The ones that show significant discrepancy from the observed range are shown in Table 2. Significant corrections were made in semi-finished product production processes. The inputs of pulpmills, wood pellet mills, and wood-based panel mills were all adjusted by the reconciliation algorithm to higher volumes.

TABLE 2.

Most significant discrepancies between original observed data values and reconciled values in Inline graphic.

Observed value Reconciled value Min and max
Type Source Target in Inline graphic in Inline graphic relative diff (%)
Production Sawmills Soft sawnwood 3.67 Inline graphic 1.4 2.97 Inline graphic 1.9 13–24
Fiberboard mfg Fiberboard 1.39 Inline graphic 0.4 0.97 Inline graphic 0.8 24–36
Pellets mfg Pellets 1.05 Inline graphic 0.1 0.78 Inline graphic 0.1 23–29
Input By-products Fibers for WBP mfg 1.41 Inline graphic 0.2 1.83 Inline graphic 0.1 16–35
Roundwood Fibers for WBP mfg 1.28 Inline graphic 0.1 1.66 Inline graphic 0.1 21–36
Fiber for recycling Fibers for WBP mfg 0.94 Inline graphic 0.1 1.32 Inline graphic 0.1 28–51
By-products Pulpmills 0.05 Inline graphic 0.0 0.32 Inline graphic 0.1 298–671
Roundwood Pulpmills 0.45 Inline graphic 0.0 0.62 Inline graphic 0.0 23–51
By-products Pellet mfg 0.23 Inline graphic 0.0 0.41 Inline graphic 0.1 41–154
Roundwood Pellet mfg 0.30 Inline graphic 0.0 0.49 Inline graphic 0.0 54–75
Import Pulp Pulp 1.88 Inline graphic 0.1 2.19 Inline graphic 0.1 10–21
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Note: Underlying data for this table are available in the UK-wood-end-use-flows repository at doi.org/10.5281/zenodo.10834953 with their specific location within the repository specified in the README file.

Abbreviations: diff, difference; mfg, manufacturing; WBP, wood-based panel.

Uncertainty

A 45% uncertainty corresponding to Inline graphic1.8 Inline graphic, remains in the volume of sawnwood used in construction for applications other than the structural parts of residential new-builds. Similarly, the volume of fibers in joinery products could only be determined with a 65% relative uncertainty corresponding to a variation of Inline graphic0.8 Inline graphic. Other semi-finished products used as construction products were calculated with a lower relative uncertainty of 16%–32% with absolute variations lower than Inline graphic0.8 Inline graphic. While there is a relative uncertainty of 50%–79% in the volume of fibers incorporated into commercial product applications, it is evident that the highest volume of fibers is embodied into industrial packaging, 4.56 Inline graphic1.3 Inline graphic, followed by furniture, 3.04 Inline graphic1.0 Inline graphic, and fencing products, 1.29 Inline graphic0.4 Inline graphic. The mixes of semi-finished products consumed by finished product manufacturing processes is also tied to high uncertainties in some cases. The type of fibers used by the furniture industry could be determined with an uncertainty between 64% and 123% with an estimate of 0.73 Inline graphic0.5 Inline graphic of sawnwood and 0.77 Inline graphic0.4 Inline graphic of particleboard being consumed by the industry. The consumption of pallets, new and refurbished, could be calculated with a 36% of uncertainty while the source of fibers in these pallets, whether from virgin or recycled sources, was estimated with a higher uncertainty of 77%–81%. All in all, even if there are intersections in uncertainty ranges, it is still possible to establish a ranking of wood fiber volumes in end-uses.

Sources of uncertainty in results and approaches to mitigate them

The main area of uncertainty in the analysis is tied to the construction industry, due to the difficulty in achieving a detailed breakdown on the destination of semi-finished products in non-structural applications. There is one part of the wood used in construction which can be mapped relatively precisely with a low uncertainty of 11%: structural elements in residential buildings, as these have standard dimensions and information could be obtained on the share of wood structures by typologies in the United Kingdom from Drewniok et al. (2023). However, given the limited data available, the MFA was not able to give more precise mapping of semi-finished products into construction applications. In many cases, although the quantity of semi-finished products is relatively well known, their destination applications are not (e.g., plywood is mainly used in construction applications, hence having a low uncertainty of 33%, but a higher resolution on the destination of plywood than this is challenging to achieve). In other cases, there is data mainly on finished products, so there is greater uncertainty about the mix of semi-finished products used to make them (e.g., the volume of sawn and panel products going into joinery products could only be estimated with a 65% uncertainty).

Non-structural, repair and maintenance work can only be covered by a top-down approach lacking the resolution needed for understanding the specific applications of the wood products used. To achieve greater resolution in the destinations of wood products in construction, building stock studies like the one conducted in a London Borough by Romero Perez de Tudela et al. (2020), when scaled up, provide insights into wood intensities in various structural and non-structural applications. However, these studies lack resolution on the year of installation which could be enhanced by surveying contractors who could offer the detailed breakdown needed to understand the specific destinations of the yearly inflows of semi-finished wood products.

OPPORTUNITIES FOR MATERIAL EFFICIENCY

In this section, the order of magnitude of wood savings achieved by implementing material efficiency measures in finished products are discussed. Further opportunities to analyze the consequences of these measures on the supply chain are then proposed.

Direct measurement of material efficiency

Pulpmills have a recycled input rate of 55%–69%, calculated as the ratio between paper for recycling and total input into pulpmills. However, the country still produces and collects paper for recycling which it does not have the capacity to process. This means that action for material efficiency has to be taken on the side of finished product demand if the processing capacity of paper for recycling cannot increase. If packaging demand was to decrease by 20% by implementing strategies such as avoiding overpackaging or by lightweighting product packaging, 1.41 Inline graphic0.1 Inline graphic of wood fibers could be saved, corresponding to 8%–9% of fibers consumed as paper product in the United Kingdom.

The construction industry produces 1.94 Inline graphicInline graphic of industrial residues of which 0.86 Inline graphic0.6 Inline graphic are in the form of solid wood products, and 0.93 Inline graphicInline graphic as fiber and particle-based products. Although research is looking into the recycling of contaminated wood (Faraca et al., 2019), particle and fiber-based products are currently challenging to recycle into material applications as they are contaminated with binders. Due to this, these waste residues are currently a low-value downcycled output of the original wood fiber, so they should be a priority for using wood more efficiently. Reducing residues by 15% in construction activities could lead to a saving of 0.14 Inline graphic0.1 Inline graphic of these fiber and particle-based products.

The industrial packaging industry has a high potential for closed-loop recycling as wooden pallets can be dismantled and reassembled into refurbished pallets at their end-of-life. Although more than half of industrial pallets are refurbished, the industry still consumes 25% of the total sawnwood supply in the Unite Kingdom. Sawnwood demand can be reduced by manufacturing pressed pallets (Inka Paletten, 2023) by chipping unusable wooden boards instead of incinerating them. Another strategy to enhance material efficiency is increasing intensity of use. If new pallets were used a quarter more intensively during their lifetime, 0.49 Inline graphic0.2 Inline graphic of wood fibers would be saved annually, which corresponds to 4%–7% of the total soft sawnwood consumption in the UK.

The furniture industry is an indirect user of recycled fibers and industrial by-products through its consumption of particleboard and fiberboard. As furniture manufacturers cannot have direct control on the recycled content of their products, other end-use material efficiency strategies have to be investigated. Product lightweighting is a design stage efficiency strategy which aims to embody less material into a product while ensuring the same function and structural integrity (Allwood et al., 2011). There are industry examples of lightweighted wood panel products in the furniture industry (Ikea, 2023). If furniture products are made 30% lighter weight, as done by (Ikea, 2023), 0.91 Inline graphic0.3 Inline graphic of fibers could be saved, corresponding to 6%–13% of the UK soft sawnwood consumption but more analysis would be needed to test the feasibility of this measure across components and products. The impact of lightweighting wood panels on product lifetime and durability has to be further investigated to avoid unintended consequences such as a shorter product life, undermining the saving potential of the strategy.

The treatment of wood in fencing products with chemicals to protect them from insects and decay poses challenges for end-of-life recycling, resulting in fencing products being incinerated. Anticipated decay of wood fences, especially fence posts, is an issue raised by the Association of Fencing Industries (2006). We estimate that if product durability is increased by 20%, 0.13 Inline graphic0.0 Inline graphic of fibers could be saved by the industry.

Further considerations for material efficiency

The analysis reveals the importance for the United Kingdom to engage with global supply chains at each processing stage. It shows that 59%–61% of the domestic material input of the paper, product, and construction industries was sourced from imports on which UK-based decisions on material efficiency do not have direct impact. Pathways for cooperative actions toward sustainability in international supply chains could be facilitated by conducting supply and trade network analysis studies (Han et al., 2021; Tang et al., 2023).

Moreover, material efficiency measures implemented at the finished product level result in larger savings upstream in the supply chain compared to the savings that can be estimated at the level of finished product manufacturers. However, the upstream consequences on the supply chain of these downstream measures are complex to measure because of complex inter-industry interactions that take place. This study can serve for further in-depth analysis of measuring the consequences of implementing change in the supply chain on material savings and on environmental impacts throughout all processing stages. For this, consequential life-cycle assessment (Brandão et al., 2017) has the potential to be linked with this MFA study to provide a physically consistent consequential map of wood flows.

CONCLUSION

In this study, we present the new ProbPACTOT model that paves the way to model material flows with a higher resolution by proposing a systematic method to deal with the uncertainty related to data observations, conversion factors, and recipe mixes in a transparent manner integrated in separate calculations steps. This is important because tracking material content and mixes in products becomes increasingly difficult when the number of processing stages increases, and because a lack of methods to integrates various types of uncertain data can prevent modelers from achieving the resolution needed in their MFA.

The ProbPACTOT model is demonstrated on a case study of wood flows in the United Kingdom in 2019. This is an appropriate case study because: (1) wood is similar to many materials in the sense that it is a complex material prone to inaccurate accounting and used in various forms and applications and (2) wood is at the heart of national-level discussions on decarbonization in the United Kingdom while also being a limited supply.

The analysis reveals a territorial map of wood flows in the United Kingdom and shows how much wood is used in different pathways and finished products, which indicates the areas where greater material efficiency would have the greatest impact. We estimate that by reducing over-packaging 1.41 Inline graphic0.1 Inline graphic of fibers would be saved corresponding to 8%–9% of the domestic paper product consumption. Increasing the intensity of use of pallets and lightweighting furniture would result in 0.49 Inline graphic0.2 and 0.91 Inline graphic0.3 Inline graphic of fibers saved corresponding to 4%–7% and 6%–13% of the national soft sawnwood consumption, respectively.

This study highlights the importance for the United Kingdom to engage with global wood supply chains at each processing stage due to the dependence of the UK’s wood supply chain on international trade. In this study, the focus has been on estimating the detailed flows of wood to end-use products within the national boundary, so these international connections have not been quantified further, but this could be done in future by linking to global input–output databases. Finally, this MFA and estimations of savings by material efficiency set the basis for future in-depth analysis on the upstream consequences of downstream change in the supply chain which is instrumental for consequential life-cycle assessment.

Supplementary Information

44498_2024_2804022_MOESM1_ESM.xlsx (45.6KB, xlsx)

Supporting Information S1: This supporting information provides quantitative observation data, serving as input into the ProbPACTOT model, and information on the uncertainty characterisation of these data observations following the pedigree matrix method of Laner (2016). It also contains a table detailing the references used to specify the input and output mixes of process recipes.

44498_2024_2804022_MOESM2_ESM.pdf (6.8MB, pdf)

Supporting Information S2: This supporting material provides information on the definition of object types and observations in Section S.1, process recipes and their uncertainty characterisation in Section S.2, conversion factors with their uncertainty characterisation in Section S.3 and the results of the model reconciliation in Section S.4.

ACKNOWLEDGMENTS

This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant No. EP/T518013/1. The authors of the paper would like to thank Matt Roberts from the University of California, Berkeley and Michal Drewniok from the University of Leeds for their inputs in the initial stages of this work.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are openly available in UK-wood-end-use-flows at https://doi.org/10.5281/zenodo.10834953.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.

Footnotes

Editor Managing Review: Stefan Pauliuk

Anspach, R. L., Allen, S. R., & Lupton, R. C. (2024). Robust modeling of material flows to end-uses under uncertainty: UK wood flows and material efficiency opportunities. Journal of Industrial Ecology, 28, 953–965. 10.1111/jiec.13511

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

44498_2024_2804022_MOESM1_ESM.xlsx (45.6KB, xlsx)

Supporting Information S1: This supporting information provides quantitative observation data, serving as input into the ProbPACTOT model, and information on the uncertainty characterisation of these data observations following the pedigree matrix method of Laner (2016). It also contains a table detailing the references used to specify the input and output mixes of process recipes.

44498_2024_2804022_MOESM2_ESM.pdf (6.8MB, pdf)

Supporting Information S2: This supporting material provides information on the definition of object types and observations in Section S.1, process recipes and their uncertainty characterisation in Section S.2, conversion factors with their uncertainty characterisation in Section S.3 and the results of the model reconciliation in Section S.4.

Data Availability Statement

The data that support the findings of this study are openly available in UK-wood-end-use-flows at https://doi.org/10.5281/zenodo.10834953.

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