Dimitra Ioannidou

Régis Pommier

Guillaume Habert

Guido Sonnemann

Evaluating the risks in the construction wood product system through a criticality assessment framework

The increasing use of wood in product eco-design focuses on the environmental merits of wood.

Nevertheless, forest cover loss and other threats may hamper the supply of certain wood species, hence significantly impacting the economic sector. Supply risk has been intensively studied in the field of mineral resources; this has led to the emergence of the criticality concept, which evaluates the supply risks and main impacts of limited accessibility. In the case of biotic, renewable resources, lack of sustainable management can result in supply shortage. We developed here a criticality framework for wood to assess the risk of supply shortage of different wood species in different regions. Our motivation to look at wood is that it is the biotic resource most used in construction. The indicators used in the framework express all factors that can disturb the forest growth, such as fire and diseases, the sustainable supply of harvested wood, such as trade barriers and country governance, as well as the

Introduction

The last few years have seen a steady increase in the use of wood as a building material in Europe, China and North America (Food and Agriculture Organization and UNECE, 2018;[START_REF] Howard | U.S. forest products annual market review and prospects, 2013-2017[END_REF]. The multifaceted properties of wood justify the recent enthusiasm of architects and engineers to use this material in their projects; in addition to its aesthetic quality, wood is considered an environmentally friendly material, extracted from a renewable resource with a replenishment rate of a few decades. Furthermore, construction wood fares well in environmental analyses due to its carbon sequestration properties and the climate benefits associated with the sustainable management and regrowth of forests [START_REF] Bellassen | Carbon sequestration: managing forests in uncertain times[END_REF]. Many research endeavors have dealt with the environmental impacts of wood products and the benefits of wood along the value chain [START_REF] Bösch | Physical input-output accounting of the wood and paper flow in Germany[END_REF][START_REF] González-García | Combined application of LCA and eco-design for the sustainable production of wood boxes for wine bottles storage[END_REF][START_REF] Gustavsson | Variability in energy and carbon dioxide balances of wood and concrete building materials[END_REF][START_REF] Suter | Life Cycle Impacts and Benefits of Wood along the Value Chain: The Case of Switzerland[END_REF]. Moreover, the value of the forest ecosystem services, their evolution over time and the disturbances they face is a thriving field of research [START_REF] Costanza | Changes in the global value of ecosystem services[END_REF][START_REF] Lawler | Projected land-use change impacts on ecosystem services in the United States[END_REF][START_REF] Ojea | Ecosystem Services and REDD: Estimating the Benefits of Non-Carbon Services in Worldwide Forests[END_REF][START_REF] Ouyang | Improvements in ecosystem services from investments in natural capital[END_REF][START_REF] Thom | Natural disturbance impacts on ecosystem services and biodiversity in temperate and boreal forests[END_REF]. Ecosystem services range from regulating services such as the regulation of water quality and provision of hedge against natural hazards, such as flood and soil erosion [START_REF] Hlásny | Sustainable forest management in a mountain region in the Central Western Carpathians, northeastern Slovakia: the role of climate change[END_REF] to cultural services such as recreation and spiritual fulfillment and to supporting services such as soil formation, nutrient cycling and a habitat for threatened or endangered species [START_REF] Balmford | Economic Reasons for Conserving Wild Nature[END_REF]. These forest services may be of utmost importance to the local population [START_REF] Uhde | Hybrid MCDA Methods to Integrate Multiple Ecosystem Services in Forest Management Planning: A Critical Review[END_REF].

However, despite the rich literature around wood and forests, the criticality of wood and the supply risk of some popular wood species for the construction industry has not been studied yet.

As a renewable resource, wood is rarely considered at risk by businesses, government or the public.

However, actual data about wood may present a different story. A recent study based on satellite data documented the increasing deforestation in the tropical and boreal forests over the course of the last decade [START_REF] Hansen | High-Resolution Global Maps of 21st-Century Forest Cover Change[END_REF]. Forests are faced with different types of deforestation and forest degradation challenges, depending on the location of a forest and the economic and socio-political situation of the supplying country [START_REF] Kissinger | Drivers of Deforestation and Forest Degradation. A synthesis report for REDD+ Policymakers[END_REF]. Intense competition for available land leads to forest clearing in order to use the space for other economic activities, such as agriculture, biofuel plantations or urban expansion [START_REF] Bradshaw | Little left to lose: deforestation and forest degradation in Australia since European colonization[END_REF][START_REF] Defries | Deforestation driven by urban population growth and agricultural trade in the twenty-first century[END_REF][START_REF] Kissinger | Drivers of Deforestation and Forest Degradation. A synthesis report for REDD+ Policymakers[END_REF].

Intensive harvesting and extraction of other forest products (fuelwood, charcoal) as well as other types of disturbances, including fires, adverse weather conditions and pathogen attack, degrade the forest quality [START_REF] Hosonuma | An assessment of deforestation and forest degradation drivers in developing countries[END_REF]. The impact of the aforementioned drivers is amplified by weak governance conditions, which fail to ensure a sustainable forest management and to impede illegal trading of wood products [START_REF] Lukumbuzya | Overview of the Timber Trade in East and Southern Africa: National Perspectives and Regional Trade Linkages[END_REF].

Coupled with these general risks pertaining to deforestation are more specific supply constraints of the different wood species. Some types of wood are extracted only from a handful of countries and can serve competing uses (e.g. use as lumber versus use as pulpwood). In addition, the variety of ecosystem services provided by forests restricts the logging activities to a percentage of the existing forest. As a result, different wood species used in the construction and furniture manufacturing sector can present different supply constraints, which can impact the cost and even the timely production of the final product.

In the present article, we study wood from an economic sustainability point of view and we examine whether the current wood supply chains can satisfy human needs in construction and furniture manufacturing. This approach of the interactions between natural and social systems, which is at the core of the sustainability science [START_REF] Kates | What kind of a science is sustainability science?[END_REF], provides a new, complementary perspective to the study of the environmental impacts of wood. We develop a new framework, based on the criticality concept, to study the aforementioned interactions. Our point of departure is that not only abiotic (nonrenewable) but also renewable resources need to be sustainably managed to avoid supply constraints.

While for the former resources, sustainable management just delays their (unavoidable) exhaustion, for the latter it makes it possible to avoid their exhaustion that would occur under unsustainable conditions. With the exception of the methodology developed by [START_REF] Bach | Assessing the Availability of Terrestrial Biotic Materials in Product Systems (BIRD)[END_REF], no other framework has been developed for the assessment of the availability of biotic resources. Therefore, the present framework is setting the foundation for the criticality assessment of wood, one of the main resources in construction and manufacturing. The value of the framework and of the observations that can be derived from such an assessment is shown through application to four different wood species.

Methodology

Framework and Concepts

The use of the term "critical" indicates resources for which at least one indicator or attribute surpasses a threshold value [START_REF] Bradshaw | The potential scarcity of rare elements for the Energiewende[END_REF]. Common criticality assessment methodologies developed evaluate the performance of a resource over two dimensions: how imminent is the risk of not having the resource in the future and what would be the repercussions of such a shortage on a social and economic level (Ioannidou et al., 2019;European Commission, 2010;National Research Council, 2007). The concept of criticality was first developed for evaluating non-fuel minerals which are not domestically available and whose importation is subject to geopolitical risk. Although the initial field of application was the metals, the concept is slowly expanding to other resources, such as water [START_REF] Sonderegger | Criticality of Water: Aligning Water and Mineral Resources Assessment[END_REF] and gravel [START_REF] Ioannidou | Is gravel becoming scarce? Evaluating the local criticality of construction aggregates[END_REF]. At the policy level, the European Commission has lately included in the periodically updated criticality tables published, in addition to metals, biotic materials, such as natural rubber (evaluated as critical), natural cork, natural teak wood and sapele wood (European Commission, 2014). In addition, in 2017, the European Commission published a report providing some general guidelines about the assessment of biotic materials, however no concrete indicators were defined [START_REF] Blengini | Assessment of the Methodology for Establishing the EU List of Critical Raw Materials[END_REF]. Previous research endeavors have addressed the issue of availability of biotic resources, however no study has been performed on the criticality of wood [START_REF] Bach | Assessing the Availability of Terrestrial Biotic Materials in Product Systems (BIRD)[END_REF]. Although the essence of the criticality concept remains the same, the nature and attributes of biotic resources radically change the challenges related to their supply. Nevertheless, the criticality concept can contribute to the understanding of the supply chain risks related to the family of wood, which is a renewable and biotic resource and to the identification of potential measures to counteract supply shortages.

We herein developed a framework for criticality assessment of different wood species based on the methodology of metal criticality determination developed by [START_REF] Graedel | Criticality of metals and metalloids[END_REF][START_REF] Graedel | Methodology of metal criticality determination[END_REF]. This methodology accounts for a multitude of socio-economic and environmental factors that can influence the supply of a resource and the reaction to a supply restriction [START_REF] Graedel | Methodology of metal criticality determination[END_REF]. The criticality framework has been applied to many minerals, such as iron [START_REF] Nuss | Criticality of iron and its principal alloying elements[END_REF] and the geological copper family [START_REF] Nassar | Criticality of the Geological Copper Family[END_REF]. The indicators of the modified framework for wood are selected based on observed problems, are in sync with the guidelines of the European Commission and account for the characteristics of the biotic resources. We adhered to the rationale of the initial methodology to aggregate the indicators to components which express a particular area of focus and subsequently the components into the two criticality dimensions, Supply Risk and Vulnerability to Supply Restriction (Figure 1). The third dimension of Environmental Implications, foreseen in the initial methodology of [START_REF] Graedel | Methodology of metal criticality determination[END_REF], is included in the framework of Figure 1 but is out of the scope of the current study. Wood is a very peculiar material; it differs from the minerals in that the forests, which supply the wood, are multifunctional and provide several environmental (and not only) functions and services other than wood production. Furthermore, while for the metals we generally talk about environmental impacts, wood production and use do not only hold negative impacts but also benefits (e.g. contribution to climate change mitigation, water, soil and biodiversity conservation). The multiparametric dimension of Environmental Implications should be the topic of further study, building upon existing work in the current literature related to the environmental properties of wood.

Inside each component, all indicators are equally factored and similarly all components inside one dimension have the same weight. The indicators are either country-specific, depicting the environmental and socio-economic context of a country supplying the specific wood, or speciesspecific, accounting for the attributes of the particular tree which define its economic use and its adaptability to supply risks.

The functional unit of the study is the harvested volume of a wood species that is used in construction and furniture manufacturing. Other uses of wood, such as pulpwood or charcoal, were only considered in the indicator of Competing end uses, while non-monetary services provided by the forest were out of the scope of the current study.

Supply Risk

This dimension accounts for the challenges encountered in the supply chain of a wood species (Figure 2). These challenges are then translated into indicators in the modified framework, which are categorized in three components: the Biological, Technological, Economic and Land availability (BTEL) component, the Social and Regulatory component and the Geopolitical component (Figure 1).

We provide here an overview of the different wood-related challenges and the corresponding indicators of the framework; a detailed explanation of the indicators is included in the Supplementary Information. The wood-related challenges are distinguished into two groups: the threats at the forest level and the possible constraints in the supply chain of wood (Figure 2). Two main challenges at the forest level, particularly for tropical forests, are deforestation and forest degradation [START_REF] Blaser | Initial analysis on the mitigation potential in the forestry sector[END_REF].

Deforestation is connected to the permanent loss of forest area in favor of other economic activities, such that the forest is not expected to naturally regrow [START_REF] Ramage | The wood from the trees: The use of timber in construction[END_REF]. Deforestation is primarily due to an increased pressure for available land. The expansion of commercial and subsistence agriculture activities, including the rapid increase of biofuel and palm oil plantations, the creation of infrastructure projects, the urban expansion and the mining activities intensify the land competition, which negatively impacts the less economically profitable forestry. Furthermore, although wood is usually considered a regional resource, many species are globally traded, due to their unique mechanical and aesthetic properties. Global trade increases the pressure on these species and is highly associated with deforestation dynamics, especially in the case of tropical forests [START_REF] Henders | Trading forests: Land-use change and carbon emissions embodied in production and exports of forest-risk commodities[END_REF].

Degradation may be a temporary condition of the forest, as it allows the possibility for natural or artificial regeneration. In tropical forests providing furniture grade wood such as mahogany (Swietenia macrophyla King), degradation is primarily due to overharvesting [START_REF] Shearman | Are we approaching 'peak timber' in the tropics?[END_REF]. Moreover, other disturbances, including fire, adverse weather, storms or floods deteriorate the forest quality, thus limiting the wood available for harvesting. Another challenge leading to degradation is related to pathogens and diseases, which can jeopardize the economic yields of the forest and thus significantly impact provisioning service providers, such as farmers or forest owners [START_REF] Boyd | The Consequence of Tree Pests and Diseases for Ecosystem Services[END_REF]. The impact of biological threats on forest provisioning and ecosystem services depends on the sensitivity of the wood species and the environmental conditions in the forest, which can favor or hamper the spread of a pest.

The risk of deforestation and forest degradation is expressed in the framework through the indicators of Land Availability and Other disturbances. The indicator Other disturbances includes biological and climatic threats that can affect the growth of a wood species. It is calculated from the percentage of forest area affected by these threats based on historical data from the national reports of the Food and Agriculture Organization (FAO) (Food and Agriculture Organization, 2015). The indicator Land availability expresses the land limitations due to most deforestation and forest degradation drivers (Figure 2) and the land competition with the protective function (conservation of forest area as a natural reserve) (eq. 1). The latter component is not a forest threat, but a risk for the wood supply chain, as land use regulation can reduce the harvested wood by promoting conservation of some forests as natural reserve and a habitat for flora and fauna.

(1)

where Change in areas of forest and other wooded land is calculated from the percentage of change in the forested and wooded area between 2010 and 2015 (Food and Agriculture Organization, 2015; [START_REF] Keenan | Dynamics of global forest area: Results from the FAO Global Forest Resources Assessment 2015[END_REF] and the percentage of Forest protected is provided by FAO. As the change calculated in the first part of this indicator refers to a period of 5 years, a multiplication by 20 ensures a hierarchist perspective [START_REF] Hofstetter | Modelling the valuesphere and the ecosphere: Integrating the decision makers' perspectives into LCA[END_REF]. When the change in the forested and wood area is positive (forest growth), the first part of the equation 1 is assumed 0. If the indicator of Land availability is calculated as greater than 100, a value of 100 is assumed.

Another forest challenge is related to climate change, which can alter the climate conditions in a way that only specific wood species can survive and by providing a favorable environment for insect and pathogen outbreaks and for extreme weather events [START_REF] Hanewinkel | Climate change may cause severe loss in the economic value of European forest land[END_REF][START_REF] Seidl | Climate change vulnerability of sustainable forest management in the Eastern Alps[END_REF]. In literature, there exist forest models and studies which consider C change effects on forest [START_REF] Kirilenko | Climate change impacts on forestry[END_REF][START_REF] Nabuurs | Stemwood volume increment changes in European forests due to climate change-a simulation study with the EFISCEN model[END_REF]. Despite the significance of this factor, it has not been included in the framework, because the study adopts a static rather than dynamic criticality approach. This means that a reevaluation of the criticality of the different wood species is required periodically. This static approach is commonly adopted by many criticality studies [START_REF] Achzet | How to evaluate raw material supply risks-an overview[END_REF][START_REF] Graedel | Six Years of Criticality Assessments: What Have We Learned So Far?[END_REF] and by the European Commission (2018). A dynamic criticality framework however should account for the climate change impact on forestry.

In addition to the direct forest challenges, the socio-economic context in a country can significantly influence the forest management regime; illegal wood trading is an example of how weak governance can fail to manage forest harvesting. The case of aucoumea klaineana (okoumé), a tropical hardwood from Congo rainforest, shows that the increased demand for a popular wood from a country with a loose legal framework and controlling systems can bypass the recent European Union Timber Regulations [START_REF] Rowe | Has the EU fallen for Congo rainforest logging scam? BBC[END_REF]. In the framework, the indicator Corruption Perceptions Index, which was developed by the Transparency International Organization, is used as a proxy for illegal trading.

Furthermore, the level of economic development is associated to the forest exploitation; satellite data corroborate the existence of the first half of the Environmental Kuznets Curve, meaning that the higher the per capita income until the curve turning point the more pronounced the forest loss [START_REF] Crespo Cuaresma | Economic Development and Forest Cover: Evidence from Satellite Data[END_REF] Regarding the constraints related to the supply chain of wood, a main factor is the competing end uses of a wood species; not all harvested wood can end up in construction as structural material or parquet flooring. For example, large volumes of picea mariana (black spruce) are used in paper production, as the species can give high quality pulpwood. The indicator of Competing End Uses expresses the economic incentives in using a wood species in different sectors. This indicator is associated to the value of the corresponding industrial sectors [START_REF] Blengini | Assessment of the Methodology for Establishing the EU List of Critical Raw Materials[END_REF] and is based on an economic allocation of the harvested amount of a wood species to the different end uses. When an economic allocation is not possible, an allocation based on the volumes of the wood for the different end uses is followed, similarly to the mass allocation in Life Cycle Assessment (International Organization for Standardization, 2006).

In addition, export restrictions and trade barriers imposed to particular wood species, which are considered endangered, increase the risk of use of these species. The indicator Export Restrictions is based on the Appendices of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) (UNEP, 2017).

Another factor affecting the supply is the mean annual increment (MAI), which expresses the longterm productivity of a plant or stand on a given site [START_REF] Pretzsch | Forest Dynamics, Growth and Yield, Forest Dynamics, Growth and Yield[END_REF]. It is obtained by dividing the yield at a given time by the age of the stand. The indicator of Mean annual increment is given by dividing the maximum mean annual volume increment in the FAO report (FAO, 2001), which is 89.5m 3 /ha/yr for eucalyptus saligna, by the MAI for the specific wood species (eq. 2):

( As a metric of the sensitivity of our results for Supply Risk and a possible alternative for Environmental Kuznets Curve, we also used forest certification as an indicator. The risk for the wood supply chain increases with the increase in the percentage of non-certified forests in every country.

Certification is based mainly on the two international labels, the Program for the Endorsement of Forest Certification (PEFC) and the Forest Stewardship Council (FSC).

Vulnerability to supply restriction

In the criticality framework, the Vulnerability to Supply Restriction expresses the gravity of impacts of a potential cease of supply of a wood species. This dimension looks at the components of Importance, Substitutability and Susceptibility (Figure 1). The Importance component includes the indicators of National Economic Importance and Percentage of Population Utilizing. The former indicator accounts for the economic significance of a species for a country, based on importation data from the International Tropical Timber Organization, data from FAO about the importance of domestic forestry and the Gross Domestic Product of the country, according to the World Bank Database. These data refer to the end wood products and do not account for products that contain wood but are not classified under the categories of FAO (Food and Agriculture Organization, 2018).

In terms of Gross Domestic Product, forests generate 1% of the global economic activities (FAO, 2014). However, this percentage is significantly higher if the entire contribution of the forest and the value of non-timber forest products and services is considered. Forests are an important employer, with more than 13 million people involved in forest-related activities and around 1-1.5 billion people deriving direct and indirect benefits from forests [START_REF] Agrawal | Economic contributions of forests[END_REF]. The importance of forestry to local economies is accentuated in forested areas where the population subsistence largely depends on the exploitation of the forest products. For example, in Gambia, even though the forestry sector officially contributes to 0.5 percent of the country's GDP, forests determine the fate of more than three quarters of the population through the provision of food, construction materials and energy resources (FAO, 2016).

The indicator Percentage of Population Utilizing (PPU) considers the per capita consumption of wood in a country. Countries that have a high score of PPU are more likely to experience problems in the case of shortage of wood because they are more dependent on the specific resource. For this category, we consider specific types of wood that are used in the construction and furniture manufacturing sector, namely plywood, sawlogs and veneer logs, sawnwood and veneer sheets to estimate the per capita construction wood consumption in every country over the years (Food and Agriculture Organization, 2018). The Percentage of Population Utilizing (PPU) follows the transformation in eq. 3:

(3) Where is the per capita construction wood consumption in the country studied, is the median value of the per capita construction wood consumption worldwide and and respectively the 10 th and the 90 th percentile. The per capita consumption of construction wood in every country is given by the Forestry Production and Trade dataset (FAO, 2018).

In the Substitutability component, the indicators assess the potential of using alternative wood species to cover the same uses provided by the main species. The Substitute Performance follows a quantitative evaluation of the attributes of the substitute as opposed to the attributes of the main species. A wood species has to serve a threefold function related to mechanical performance, durability and aesthetics. For the purposes of this study, the selection of the potential substitute was based on the available literature review. However, a more comprehensive procedure should include classification of all species to homogeneous clusters ("families") with similar physical and mechanical properties. This classification can underpin the selection of adequate substitutes from within the same family. The creation of these quite homogeneous clusters of species can be achieved following either a deterministic or a fuzzy approach to define the technological proximity among the species [START_REF] Lissouck | Clustering for preservation of endangered timber species from the Congo Basin Forest[END_REF]. The indicator of Substitute Availability expresses the Supply Risk of the substitute species.

The indicator of Net Import Reliance Ratio (NIRR) compares the Net Import Reliance of a wood

species to its substitute. The Net Import Reliance of a wood species is defined in eq. 4:

(4)

The another one [START_REF] Pommier | Comparative environmental life cycle assessment of materials in wooden boat ecodesign[END_REF], a design-level intervention can optimize resource use in a project.

Finally, the Long Term versus Short Term Normative Orientation indicator was developed by

Hofstede to depict the dimensions of national culture [START_REF] Hofstede | Dimensionalizing Cultures: The Hofstede Model in Context[END_REF]. The culture and traditions in a country as well as the temporal view and attitude of its people can influence the acceptance of innovative technologies. Societies with a long term orientation tend to adopt a more pragmatic stance and adapt more easily to a shifting environment and the use of alternative materials [START_REF] Hofstede | Dimensionalizing Cultures: The Hofstede Model in Context[END_REF].

Innovation and willingness to accept and adopt change can be key factors in addressing the shortage of specific wood species, especially in the construction sector, which is by definition more conservative and slow moving. This indicator shows the capacity of a community to adapt and use other building materials than the ones traditionally used.

Results

To evaluate the general applicability of the criticality framework to different species and its capacity to address different challenges, we applied it to four wood species, two used in France (aucoumea klaineana and pinus pinaster) and two in the USA (pinus contorta and picea mariana). Our goal in selecting these species was to cover a wide range of factors that can play a role in the supply chain, namely to account for different climate regions by including both tropical and boreal species, which face different types of threats, to address the impacts in two different economies, to include both domestic and imported species and to study species with different supply constraints; aucoumea klaineana is classified as vulnerable and is subject to illegal trading, pinus contorta and picea mariana are threatened by wood-boring beetles and the spruce budworm respectively [START_REF] Arbellay | Cambial injury in lodgepole pine (Pinus contorta): mountain pine beetle vs fire[END_REF][START_REF] Salomón | Natural root grafting in Picea mariana to cope with spruce budworm outbreaks[END_REF] while pinus pinaster was severely hit by the Klaus Storm. We studied the supply distribution of each species (Figure 3) and weighed the indicators corresponding to each sourcing country by the percentage of harvested wood provided by that country. The goal of the case studies was not to perform an extensive assessment of wood species but to go more in depth in the selected species. In the case of aucoumea klaineana (okoumé), the criticality framework highlighted the significant supply risk for this tropical wood (Figure 4 and Tables 1,2). Okoumé is a hardwood used mainly for plywood construction. It is extracted from the Congo Basin Forest and the main supplying country is Gabon. However, the lack of systematic control in the exporting countries encourages illegal trade and unsustainable harvesting practices. As a result, there is no clear legal and political framework ensuring a sustainable forest management in the supplying countries. In the criticality indicators used here, the weak governance conditions in the countries of the Congo rainforest were expressed by the Corruption Perceptions Index and the World Governance Indicator. In addition, the Extinction Risk for this species is high, as it is classified as vulnerable because of the reduction in the species population size due to increased felling. For this reason, okoumé has the highest Supply Risk among the studied species.

Regarding the ranking of the species in the vulnerability axis (Figure 4), it is evident that the use of non-domestic species (aucoumea klaineana, picea mariana) increases the risk of dependence of an economy to other countries for importing the wood, while at the same time reduces the contribution to the Gross Domestic Product. The harvesting and treatment of local wood (pinus pinaster in France) yields a series of indirect benefits to the local economy, associated with the employment of local workforce for the harvesting and treatment of wood and the impact on the sectors affiliated to forestry.

On a cross-country comparison, the popularity in the use of wood in the USA amplifies the importance of ensuring a sustainable supply of the most demanded wood species.

Discussion

The importance of a criticality framework for wood is multifold. First of all, it can be a useful tool for companies and local authorities that want to ensure an economically sustainable supply of wood in construction. An additional benefit of the application of this framework is not only the absolute value of the two dimensions, but also the value of the different indicators, in order to define the specific issues related to a wood species and be able to effectively address them. Such a framework offers two points of intervention; at a country and species-level. In the first case, we can identify which issues (e.g. insect attacks, absence of solid governance and legal framework)t may threaten the forest and the wood extraction activity in a specific country. I In the second case, we can substitute a species by another one that is less critical or research the possibility of a design-level substitution. For example, one of the main risks in the supply chain of aucoumea klaineana is the increased value of Corruption Perceptions Index. The unstable regulatory framework in the producing countries does not ensure the sustainable supply of this wood species and more effective rules should be applied to avoid overharvesting and seeking short-term profit. In the case of picea mariana, we observe that more than half of the harvested amount goes to other uses and not for construction. That means that if demand for the other uses increases, the price for this wood may go up or the quantity available for construction may decrease, which will affect the construction planning. From an impact point of view, the use of non-domestic wood species that are mainly or entirely imported (such as aucoumea klaineana) raises the risk for manufacturing and construction, considering that the trade map and the trade restrictions can easily change.

The use of this framework in the design with wood should be coupled with the environmental assessment of the impacts of the harvesting and treatment of the specific wood species. A point that should be considered is that wood production, provided done sustainably, does not hold only negative impacts, but also a lot of benefits, arising from the harvesting patterns, especially in plantation forests [START_REF] Brockerhoff | Plantation forests and biodiversity: oxymoron or opportunity?[END_REF][START_REF] Vangansbeke | Spatially combining wood production and recreation with biodiversity conservation[END_REF]. The "paradox" in wood is that, even though a natural material, it is submitted to considerable treatment before it is used in construction. Such a chemical (polymer) treatment converts a versatile material to a certified material possessing specific properties and complying with codes and regulations.

Moreover, the use of the criticality framework allows a localization of problems and can indicate preferable sources of supply. From the study of picea mariana, we observe that the value of the Supply Risk indicators is lower for wood coming from the Canadian forests, because the disturbances that the Canadian forests faced in the last decade are significantly lower than the corresponding value for USA (table in SI). Depending on the species, this observation can also lead to the decision for plantations of a wood species in a country.

Limitations

The current study focused on setting the foundations for considering the constraints in the supply of different wood species and promoting an economically sustainable procurement, which should be considered at a design level. Nonetheless, due to the pioneering character of the topic, the research has some limitations and further work could be directed to enhance the framework with additional features.

The current framework does not account for the value of the ecosystem services other than wood production, since the perspective adopted here is from the wood supply chain point of view. Defining the balance between ecosystem services of a forest and wood extraction needs to be aligned with the principles of sustainable development; human needs to create value from nature not by acting against it but by accounting for its complexity and its role and significance.

Moreover, no metric for climate change has been included in the framework. Climate change leads to variations in temperature and rainfall and can even affect the pathogens in a way that the environment is more positive to their diffusion [START_REF] Sturrock | Climate change and forest diseases[END_REF]. However, as mentioned earlier, the current study adopted a static criticality approach and therefore the inclusion of such a dynamic factor was out of the scope of this framework. With respect to forest certification, an alternative framework included in the Supplementary Information uses the percentage of certified forest as an indicator. Nevertheless, there is some caution and mistrust toward existing certification systems and their effectiveness on battling deforestation [START_REF] Blackman | Does Eco-certification Stem Tropical Deforestation? Forest Stewardship Council Certification in Mexico. Resources for the Future[END_REF]. For this reason, certification was not integrated in the final framework, considering the criticism against the labels because the evaluation is based on auditor expertise and there is a lack of a robust auditing system [START_REF] Lopatin | Assessment of Compliance with PEFC Forest Certification Indicators with Remote Sensing[END_REF]. Moreover, forest certification is criticized for commodification of natural resources [START_REF] Kopnina | Commodification of natural resources and forest ecosystem services: Examining implications for forest protection[END_REF], which disadvantages the local populations, and for failure to address the primary environmental issues related to forests [START_REF] Blackman | Does forest certification in developing countries have environmental benefits? Insights from Mexican corrective action requests[END_REF]. A more transparent certification system is required that can provide an accurate overview of the forest stands and address the challenge of field assessment. To this end, satellite monitoring can provide a powerful tool; the use of remote sensing technology is evidenced to have contributed to reducing deforestation [START_REF] Mcdermott | Forest certification and legality initiatives in the Brazilian Amazon: Lessons for effective and equitable forest governance[END_REF]. The use of satellite imaging and the interpretation of the data in combination with the implementation of the developed framework can be used to define harvesting strategies and ensure sustainable forestry.

Finally, the framework used the indicator "Environmental Kuznets Curve" to address the importance of the local environment in defining optimal forest management strategies; local conditions can affect the dynamic behavior of a system and the magnitude of the impact of socio-economic pressure on deforestation [START_REF] Brander | The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use[END_REF]. However, the "Environmental Kuznets Curve" is a global approach in linking cause and effect in forest cover loss and further research in the field of environmental economics may need to consider additional local parameters in defining the social pressure -deforestation relationship.

Conclusion

In this article, we developed a criticality framework for evaluating the supply risks and the impacts of a potential supply disruption in the wood supply chain. Our point of departure was that not only abiotic resources but also resources that regenerate need to be sustainably managed to avoid supply constraints. We considered in the criticality framework direct threats related to forest cover loss and degradation and indirect threats related to the socio-economic environment of the supplying countries.

The application of the framework to four case studies indicated risks and points of intervention for these wood species. The impact of robust regulations and a solid legal context which can protect the forests from illegal harvesting and trading is important in order to decrease the Supply Risk of a wood species. In addition, for the species studied, the use of local species decreased the risk related to import restrictions and at the same time had a more significant contribution to the local economy. The framework facilitates the comparison across different raw materials and can complement existing environmental tools used in the design phase of construction and manufacturing.

Figure 1 .

 1 Figure 1. Criticality framework for wood and indicators included in the two dimensions, Supply Risk

Figure 2 .

 2 Figure 2. Forest threats and wood supply constraints and their components. Deforestation and forest

  2) Apart from the aforementioned indicators, the framework includes some additional indicators. The Extinction Risk expresses the risk due to decrease in the population of a tree and is based on the Red List of Threatened Species of the International Union for Conservation of Nature and Natural Resources (IUCN) (International Union for Conservation of Nature and Natural Resources, 2000). The indicator of Global Supply Concentration (GSC) follows the Herfindahl-Hirschman Index (HHI) and is calculated from the squares of each country's annual production share. The Worldwide Governance Indicator -Political Stability & Absence of Violence/Terrorism (WGI-PV) is given by a database that assesses the governance conditions.

  Susceptibility component represents the ability to innovate in order to overcome a supply restriction. It consists of the indicators Net Import Reliance (explained above), Global Innovation Index and Long Term versus Short Term Orientation. The Global Innovation Index is a metric developed by INSEAD in collaboration with Cornell University and the World Intellectual Property Organization and is annually updated. It represents the out-of-the-box thinking and the investigation of non-conventional technologies and applications. Instead of a direct substitution of a wood species with

Figure 3 .

 3 Figure 3. Supply distribution in percentages of the four species studied in this article: aucoumea

Figure 4 .

 4 Figure 4. Values of Supply Risk and Vulnerability to Supply Restriction for the four species studied.

  . The calculation of the indicator Environmental Kuznets Curve is based on data from Cuaresma et al. (Crespo Cuaresma et al., 2017) and the PPP-adjusted per capita Gross Domestic product values from the Penn World Table from the University of Groningen. Countries with a GDP less than 5500 int. $ follow the model of Cuaresma et al. (Crespo Cuaresma et al., 2017) while countries with a higher GDP are assumed to follow a linear regression model.

Table 1 .

 1 The figure presents also the sensitivity of the results if instead of the Environmental Kuznets Indicators inside the Supply Risk dimension and values for the four species studied.Aucoumea klaineana has the highest values for Corruption Perceptions Index and World GovernanceIndicator, because of the inadequate legal and political framework in the supplying countries. BTEL stands forBiological, Technological, Economic and Land availability component.

	Curve indicator (EKC), we consider the forest certification. A high score in both dimensions indicates
	high risk. The highest score in each axis is 100.

Aucoumea klaineana has the highest score in both dimensions, because it is a vulnerable species with weak governance conditions in its supplying countries and it is fully imported from the African countries.

Table 2 .

 2 Indicators inside the Vulnerability to Supply Restriction dimension and values for the four species studied. Import Reliance Ratio is 100% for aucoumea klaineana, while pinus pinaster has the highest significance for the national economy.

	Wood species

Acknowledgement

D.I. thanks the Swiss National Science Foundation (project P2EZP2_175297). We thank S. Cahoon, G. Christensen, C. Barnett and C. Toney from U.S. Forest Service for provision of data on spruce.


Ali Mokh

Julien De Rosny

George C Alexandropoulos

Ramin Khayatzadeh

Abdelwaheb Ourir

Mohamed Kamoun

Arnaud Tourin

Mathias Fink

Time Reversal Precoding at SubTHz Frequencies: Experimental Results on Spatiotemporal Focusing

Keywords: Time reversal, receive spatial modulation, terahertz communications, spatiotemporal focusing

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

The last decade has witnessed a tremendous growth in the global mobile data traffic, and by 2030, the trend of exponential data rate increase will continue, overcoming the capabilities of the fifth Generation (5G) networks. To confront the shortcomings of 5G, initial requirements for the future 6G communication networks are being discussed dealing with wider frequency bands as well as the needs for increasing the maximum transmission rate, better spectrum efficiency, extremely massive network connections and antenna deployments, shorter delays, increased coverage, and improving anti-interference capability [START_REF] Zhao | A survey of 6G wireless communications: Emerging technologies[END_REF], [START_REF] Shlezinger | Dynamic metasurface antennas for 6G extreme massive MIMO communications[END_REF]. The initial discussions indicate that the frequencies in the range of Sub-TeraHertz (SubTHz) and above are highly probable to be considered for 6G, since there are plenty of available bands suitable to satisfy those early demanding requirements [START_REF] Saad | A vision of 6G wireless systems: Applications, trends, technologies, and open research problems[END_REF], [START_REF] Tariq | A speculative study on 6G[END_REF]. In fact, it appears that 6G will utilize spectrum beyond 140 GHz with particular applications in very short-range communication, or the so-called whisper radio [START_REF] Xing | Propagation measurement system and approach at 140 GHz-Moving to 6G and above 100 GHz[END_REF]. However, because of the current technological limits, it is difficult to apply in SubTHz the signal processing currently in use for millimeter wave communications, such as Orthogonal Frequency-Division Multiplexing (OFDM). In this paper, we consider the Time Reversal (TR) technique [START_REF] Fink | Time-reversed acoustics[END_REF] as the pre-processor for robust data transmissions, which can be paired with a simple receiver implementing basic reception signal processing.

A TR mirror is an apparatus that is capable of focusing waves both in time and in space, i.e., of offering spatiotemporal focusing. It is based on the time-reversal symmetry of propagating media. Thirty years ago, it has been first applied to focus ultrasonic waves in water, tissues, and solids. The TR mirror is very efficient in complex media such as multiple scattering media [START_REF] Derode | Robust acoustic time reversal with high-order multiple scattering[END_REF] or cavities [START_REF] Draeger | One-channel time reversal of elastic waves in a chaotic 2D-silicon cavity[END_REF], because it takes benefit of wave propagation reflections to enhance its spatiotemporal focusing. In acoustics, the main application of TR has been non-destructive control, imaging, and therapy [START_REF] Fink | Time-reversed acoustics[END_REF]. In 2004, the concept of the TR mirror was extended to electromagnetic waves [START_REF] Lerosey | Time reversal of electromagnetic waves[END_REF] realized at 2.4 GHz. Two years later, capitalizing on the fact that the larger the transmission bandwidth the better the focusing is, wideband TR was successfully realized [START_REF] Lerosey | Time reversal of wideband microwaves[END_REF]. In [START_REF] Qiu | Detection of physics-based ultrawideband signals using generalized RAKE with multiuser detection (MUD) and time-reversal mirror[END_REF], TR was considered for ultra-wideband communications. The improvement in the Signal-to-Noise (SNR) ratio, thanks to the TR-based temporal focusing, has been experimentally verified with a multi-antenna transmitter in [START_REF] Qiu | Time reversal with MISO for ultrawideband communications: Experimental results[END_REF], [START_REF] Mokh | Indoor experimental evaluation of ultra-wideband MU-MISO TRDMA[END_REF]. The concept of TR division multiple access was introduced in [START_REF] Han | Timereversal division multiple access over multi-path channels[END_REF] for multi-user communication. Very recently, [START_REF] Alexandropoulos | Indoor time reversal wireless communication: Experimental results for localization and signal coverage[END_REF] demonstrated indoor cm-level localization accuracy with TR at 3.5 GHz using up to 600MHz bandwidth channel sounding signals.

In this paper, we experimentally study the spatiotemporal focusing properties of time-reversed electromagnetic waves centered at 273.6 GHz with a bandwidth up to 4 GHz in multipath complex media realized with a leaking reverberation cavity. The experimental measurements are followed by a simulation evaluation intending to verify the possibility of data transmission towards a simple non-coherent receiver equipped with two antenna elements. In particular, we deploy a Receive Spatial Modulation (RSM) chain based on a simple power detector to realize wireless communications at the considered subTHz frequency band.

The rest of the paper is organized as follows. In Section II, the principle of TR-based precoding is described. In Section III, we present our subTHz experimental setup to realize and measure TR-precoded signals. In Section IV, we present our simulated evaluation of the Bit Error Rate (BER) performance of a communication scheme based on RSM using the measured signals. Finally, the concluding remarks of the paper are included in Section V.

II. TIME REVERSAL PRECODING

Let us consider a multiple access wireless communication system comprising one single-antenna transmitter that wishes to communicate in the downlink direction with N singleantenna receivers. We represent by h i [k] the baseband Channel Impulse Response (CIR) at discrete time k between the transmitter and the i-th (i = 1, 2, . . . , N ) receiving antenna. The TR precoding utilizes the time reversed CIR, i.e., h * i [L-k] with L denoting the number of the significant channel taps, to focus the information-bearing electromagnetic field on the ith receiving antenna. In mathematical terms, the TR-precoded signal sent by the transmit antenna in order to focus each baseband information message x i [l] on its respective receiving antenna is given by the following expression:

s[k] = N i=1 L l=1 x i [l]h * i [L + l -k] L l=1 |h i [l]| 2 . ( 1
)
The normalization factor ensures that the power emitted toward each single-antenna receiver is the same. By using the latter expression, the baseband equivalent of the signal at each j-th (j = 1, 2, . . . , N ) receiving antenna can be expressed as

y j [k] = L l=1 N i=1 x i [l]R j,i [L + l -k] + n j [k], (2)
where R j,i [k] represents the correlation function between the CIRs of the j-th and i-th receiving antennas, which is given as follows:

R j,i [k] = k h * i [k -k ]h j [k ] L l=1 |h i [l]| 2 . ( 3
)
In the latter expression, n j [•] denotes the zero-mean additive white Gaussian noise at the j-th receiver having standard deviation σ. In multipath wireless communication channels, when applying TR precoding with the CIR toward the ith receiving antenna, the time-reversed field focuses in time and in space at this antennas, exhibiting a signal peak. The amplitude of this peak is given by the CIR's autocorrelation function at lag 0, i.e., by R i,i [0].

III. SUBTHZ EXPERIMENTAL MEASUREMENTS

In this section, we present the experimental setup used to investigate the TR spatiotemporal focusing in the considered subTHz frequency band. In such frequencies, the attenuation of the channel becomes very high, and it is difficult to realize a multipath channel even for indoor application. Since such a channel is prerequisite for TR, we have designed a specific setup for each experiment that results in rich scattering fading conditions. Finally, we present the experimental results for the spatiotemporal focusing capability of the considered TR-based precoding scheme.

A. Experiment Setup

Our experimental subTHz setup operating at the central frequency f c = 273.6 GHz using a 5 cm × 5 cm × 2.5 cm closed metallic box is depicted in Fig. 1. The box behaves as a rich multipath medium. To emit inside the cavity, the Transmit (Tx) antenna is inserted into the box through a small hole. To be able to focus outside the box, there are multiple small holes with a diameter of 1 mm on the other side of the box. The Receive (Rx) antenna is positioned in front of this side of the box at a distance of 5 cm on a motorized axis, which is parallel to the face (see Fig. 1). Both the Tx and Rx antennas are identical. They operate between 260 and 400 GHz and are omnidirectional. The point x = 0 on the axis faces the box's center.

To create transmitted signals at subTHz, we have generated a reference sinusoidal signal at the desired frequency f c , as follows. The deployed local oscillator R&S SGMA produces a sinusoid at 5.7 GHz, which was then up-converted for transmission using a WR2.2 VDI SAX WM570 harmonic mixer (operating at 260-400 GHz with -10 dBm transmit power) with a multiplication factor set to 48 (note that 5.7 × 48 = 273.6). At the Rx side, a harmonic mixer with the same multiplication factor was deployed for down-conversion back to 5.7 GHz. Both the Arbitrary Waveform Generator (AWG) to produce the 3 GHz baseband signal and the digital sampling oscilloscope to record the field were connected to the same reference clock working at 10 MHz. The estimation of the CIR and the TR precoding were performed, as follows. was transmitted by the Tx with B denoting the transmission bandwidth. Synchronously, the signal was probed by the Rx antenna. A desktop computer performed the CIR estimation by correlating the recorded signal with the chirp signal. Even if TR generated high amplitude pulses, the gain was not sufficient to directly probe the pulse with the Rx antenna. For this reason before emission, the CIR flipped in time was also convoluted with the same chirp signal. Similarly to the CIR estimation, the TR-focused signal was reconstructed in the computer using cross correlation.

B. Performance Results

We have measured the CIR for different positions of the Rx antenna spaced by 0.3 mm, in particular, between the positions x = -6.2 mm and 6.2 mm, where x = 0 is the position facing the center of the metallic box. We have used a transmission bandwidth of B = 4 GHz. Figure 2(a) demonstrates the CIRs for those different Rx positions. In Fig. 2(b), the amplitude of the electromagnetic field is plotted versus the Rx antenna placement when the CIR probed at position x = -1.8 mm is flipped in time and emitted. Both figures show the capability of the TR technique to focus the signal in time and space at the targeted Rx position.

To investigate the TR capability for multiple access scenarios, i.e., spatiotemporal focusing of different signals towards different spatial positions, we applied the TR precoding considering the two Rx positions x 1 = -2.7 mm and x 2 = -1.8 mm. The signals have been normalized in such a way that the 2 received powers are identical. To transmit data, the pulses were modulated either in amplitude or phase. Each pulse was separated by D channel taps. For this case, the duration of each symbol is actually T s = D B . From the probing of the 2 TRprecoded field with respect to the intended Rx positions, we deduced the maximum received signal strengths. Note that the signal strength at the position of the unintended RX antenna provides the Inter-User Interference (IUI). The Inter-Symbol Interferences (ISI) is deduced from the analysis of the temporal secondary lobes. The result for the received signal strengths are included in Fig. 3 considering D = 15. It can be concluded that, for multiple access transmission, the focusing signal at each Rx position is affected by the sum of all interference, namely, teh IUI of the other focusing signal and the two ISI contributions. The resulted signals and corresponding interference will be used in the following section for computing the BER of a multiple access transmission scheme.

IV. RECEIVE SPATIAL MODULATION WITH TR

In this section, we make use of the measured subTHz signals to simulate a transmission scheme between the single-antenna transmitter and a receiver with two receive antenna elements. The scheme implements TR-based precoding and an RSM technique based on Receive Antenna Shift Keying (RASK), which targets a specific Rx antenna to transmit data.

A. System Description

The idea is to use TR precoding to target one of two Rx antenna elements [START_REF] Mokh | Time reversal receive antenna shift keying on MIMO LOS channel[END_REF]: target the first antenna to transmit a bit '0' and the second antenna to transmit an '1' bit. On the Rx side, the receiver needs to understand which antenna has been targeted, and this can be realized with a simple power detector [START_REF] Mokh | Theoretical performance of coherent and incoherent detection for zero-forcing receive antenna shift keying[END_REF]. Depending on the estimation of the index of the antenna with the largest received signal strength, one can estimate the transmitted symbol. The block diagram of this simple communication scheme is illustrated in Fig. 4. It is noted that a variant of the RASK scheme was proposed in [START_REF] Mokh | Extended receive antenna shift keying[END_REF] for increasing the spectral efficiency. This scheme was termed as Extended RASK (ERASK), where more combinations can be used, and hence, each Rx antenna can be targeted or not. The only detection requirement here is to estimate if each Rx antenna has been targeted or not, which requires a certain threshold for the received signal strength.

The motivation to use the latter RSM-based schemes lies on our intention to verify the capability of TR to offer spatial multiplexing in the subTHz frequency band, while adopting a very simple receiver that does not need phase detection or synchronization between each receiving antennas.

B. Simulation Results

We have used the signals from Section III with the experimental measurements, and calculated the received signal strength and the interference at the two Rx positions x 1 = -2.7 mm and x 2 = -1.8 mm, considering different values for D. Figure 5 depicts the corresponding BER when using the RASK and ERASK schemes. Note that the ERASK scheme has a double spectral efficiency (2 bits are sent per symbol, while only one bit is sent in the case of RASK). As expected, the greater D is, the better the performance of both two schemes, with the effect of reducing the error performance with increasing SNR σ -2 . These results showcase the capability of our designed TR-based scheme in subTHz frequencies for multiple access applications, offering the very low spatial separation distance of 0.9 mm.

V. CONCLUSION

In this paper, we experimentally investigated the performance of TR precoding in the subTHz frequency band. An experimental setup has been designed to estimate the CIR at the central carrier frequency 273.6 GHz with a 4 GHz bandwidth, which was then used to realize TR-based spatiotemporal focusing. Our measured signals were also used in a simulated data communication scenario including RASK-based reception with simple power detectors. The performance evaluation results showcased the capability of TR to focus transmitted signals in both space and time, thanks to the SubTHz signal wavelength. In addition, our simulation results verified the TR capability for realizing multiple access transmissions towards two receive antennas separated by 0.9 mm. For future work, we intend to experiment video communication at subTHz considering reconfigurable intelligent surfaces [START_REF] Alexandropoulos | Reconfigurable intelligent surfaces for rich scattering wireless communications: Recent experiments, challenges, and opportunities[END_REF] for reprogrammable rich scattering conditions.

Figure 1 .

 1 Figure 1. Photo and schematic illustration of the designed experimental setup centered at the subTHz frequency 273.6 GHz with up to B = 4 GHz bandwidth.

Figure 2 .

 2 Figure 2. (a) Baseband modulus of the CIRs probed at different positions; (b) Baseband modulus of the field probed at different positions when focusing by TR toward the position x = -1.8 mm.

Figure 3 .

 3 Figure 3. The amplitude of the received signal strength and interference from each TR-precoded signal over all possible Rx positions for D = 15.

Figure 4 .

 4 Figure 4. Block diagram of the proposed transmission scheme between a single-antenna Tx and an Rx with two antenna elements, which adopts TR precoding and RASK modulation/demodulation with simple power detection.

Figure 5 .

 5 Figure 5. BER of RASK and ERASK transmission in subTHz domain towards locations x = -2.7 and -1.8 mm, with different D