concepts, modelling, and

Supplementary Information, for: Integrating material stocks into economy-wide material flow accounting: concepts, modelling, and global application for 1900-2050 Wiedenhofer, D. 1*, Fishman, T.2, Haas, W.1, Lauk, C.1, Krausmann, F.1 1

... University of Natural Resources and Life Sciences, Vienna. Institute of Social Ecology,

Department for Economics and Social Sciences. Schottenfeldgasse 29, 1090 Vienna, Austria. 2

... Yale University, Center for Industrial Ecology, School of Forestry and Environmental Studies, 195 Prospect St. New Haven 06511 USA *

... corresponding author: [email protected]

Summary of contents This supplementary information contains the ‘details’ of the MISO-model, (Müller et al., 2014)including equations, specific data sources and parameters used as well as the methodological documentation for the attribution of uncertainty and sensitivity assessments. Additionally, the SI contains extensive validations of the modeling results against the available literature. Detailed materials-specific sensitivity and uncertainty results are also shown, which are complementary to the more aggregate results shown in the main manuscript. Table of Contents Details of the MISO-model ..................................................................................................................... 2 Initial Condition .................................................................................................................................. 2 Model Input Data (exogenous data) .................................................................................................... 2 Data on biophysical additions to stocks .......................................................................................... 2 Model parameters and sources for stock-building materials, processing waste, manufacturing and construction waste, lifetime distributions, recycling rates and uncertainty ranges ......................... 4 Choosing appropriate lifetime distributions .................................................................................. 11 Uncertainty – specifying the Monte-Carlo Simulations module ................................................... 11 Model Output Data ............................................................................................................................ 13 Evaluation...................................................................................................................................... 13 Detailed model description .................................................................................................................... 13 Validating MISO results: systematic comparison with the literature .................................................... 16 SI -1

Robustness of Monte-Carlo Simulations and uncertainty attribution ................................................... 21 Testing for local model sensitivity ........................................................................................................ 24

Details of the MISO-model This section contains detailed information on all the data, assumptions and calculation procedures required to quantify all relevant parameters required for the modeling. It follows the basic “overview, design, details” protocol adapted for dynamic MFA by (Müller et al., 2014).

Initial Condition To estimate the starting dynamics of stocks and flows a spin-up module is implemented. This spin-up utilizes data starting in 1820 to estimate dynamics until 1900. This time span covers the longest mean lifetime assumptions. Initially in 1820 the model starts with zero stocks and only a biophysical input flow of stock building materials, which initiates the dynamic MFA.

Model Input Data (exogenous data) Data on biophysical additions to stocks The main reference for data on materials inputs are comprehensive economy-wide material and energy flow accounts (ew-MFA), which provide long-term data on global extraction and consumption of materials and energy carriers. These accounts are compiled following standardized accounting principles and methodological guidelines (Eurostat, 2012; Krausmann et al., 2015). In the utilized database global annual time series for the period 1850-2014 and national level data for the period 19502014 are available (Krausmann et al., 2017, 2016, 2009a, (in revision); Schaffartzik et al., 2014). For the spin-up period data for the time period 1820 – 1900 is required. Materials input data for the years not covered by the MFA database (1820-1850 and for some materials, e.g. wood, bricks, also for the period 1820-1900), we assumed constant per capita material use from 1850 - 1900, and extrapolated total inflows by multiplying per capita flows with population estimates from the Maddison Project (Bolt and van Zanden, 2014). The ew-MFA database provides data for 40-65 materials and enables the identification of all important stock-building materials, i.e. those materials which accumulate in stocks of infrastructure and buildings, typically with lifetimes longer than one year (Table S1). Sand and gravel used as sub-base and base course layers in the construction of roads and buildings are currently not fully covered in ew-MFA databases and need to be estimated on the basis of concrete, brick and asphalt use and specific multipliers (Miatto et al., 2016). Quantitatively the coverage of material inputs to stocks is high (>98% of mass), although for a few materials (e.g. building stone, slate) no data are available or could not be estimated.

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Table S1: Correspondence of stock-building materials from the ew-MFA database (Eurostat, 2012; Krausmann et al., 2009b, (in revision); Schaffartzik et al., 2014) and stock-building materials as handled in the MISO model. The “Additional Source” lists the main sources used to specify the differences between raw materials extraction and stock building materials. ew- MFA classification

ew-MFA

Stock-building material as

identifier

handled in the MISO-model

Additional data sources used

Industrial roundwood

A.1.4.1.

Solidwood products

(FAO, 2015)

Industrial roundwood

A.1.4.1.

Paper and paperboard

(FAO, 2015) (Cullen et al., 2012; Kelly and Matos,

Iron ore

A.2.1.

Iron and steel

2014; Modern Casting Staff, 2015; USGS, 2015; Worldsteel Association, 2015)

Copper ore

A.2.2.1.

Copper

Bauxit

A.2.2.7.

Aluminum

Nickel ores,

A2.2.2.

Lead ores,

A.2.2.3.

Zinc ores,

A.2.2.4.

Tin ores,

A.2.2.5.

Handled as

Gold, silver, platinum and other

A.2.2.6.

other metals and minerals

(Glöser et al., 2013; Kelly and Matos, 2014; USGS, 2015) (Kelly and Matos, 2014; USGS, 2015; World Aluminium, 2015)

(Krausmann et al., 2009a; USGS, 2015)

precarious metals, Uranium and thorium ores,

A.2.2.8.

Other metal ores

A2.2.9.

Crude oil

A.4.3.

Crude oil

A.4.3.

Limestone

A.3.2.

Clays and kaolin

A.3.5.

Sand and gravel

A.3.4.

Sand and gravel

A.3.4.

Limestone

A.3.2.

Silica sands

A.3.4.

Soda ash

A.3.8.

Limestone

A.3.2.

Silica sands

A.3.4.

Soda ash

A.3.8.

Plastics

(PlasticsEurope, 2012)

Bitumen, together with sand

(Abraham, 1945; IEA, 2015; UNSD,

and gravel handled as asphalt

2013)

Cement, together with sand and gravel handled as concrete Bricks Sand and gravel required to produce concrete and asphalt

(CEMBUREAU, 2013, 1998) (UNSD, 2010) Using fixed technical coefficients from (Krausmann et al., 2015; Miatto et al., 2016)

Sand and gravel used as sub-

Additional estimates based on concrete,

bases in buildings and base-

asphalt and bricks going into use, utilizing

course layers in roads

the procedures from (Miatto et al., 2016) (Butler and Hooper, 2011; Glass Alliance

Container glass

Europe, 2017; NSG Group and others, 2011; Ruth and Dell’Anno, 1997) (Butler and Hooper, 2011; Glass Alliance

Flat glas

Europe, 2017; NSG Group and others, 2011; Ruth and Dell’Anno, 1997)

Because the ew-MFA database covers raw materials and traded goods in physical units, additional information from industry and production statistics and specific literature were required to quantify the physical additions to stocks as required for the MISO model. For example, in ew-MFA gross iron ore extraction is reported with specific contents of metallic iron. Data on metal contents (Kelly and Matos, 2014; Worldsteel Association, 2015) and production losses in blast furnaces and direct reduction (Cullen SI -3

et al., 2012) the mass flow of iron and steel that is actually an input to in-use stocks was quantified. This procedure ensures full consistency between material flow accounts and the MISO model. The differences between the amount of extracted raw materials and the inputs into stocks can be accounted for as wastes (e.g. waste rock from metal production), emissions (e.g. CO2 from burning limestone) or changes in moisture content (e.g. brick production) in material flow accounts.

Model parameters and sources for stock-building materials, processing waste, manufacturing and construction waste, lifetime distributions, recycling rates and uncertainty ranges For the MISO modelling ideally, we would be able to assemble a complete set of parameters for each year, stock-building material input and in-use stock. We have conducted an extensive literature research to assemble time specific data on the global scale, however reliable information about developments over time are quite scarce and could only be found for some parameters. Wherever we could not identify global parameters from previous studies on specific materials or processes, we used world-regional studies to specify a global average. If no time-specific parameters are available, we held the parameter constant over time. In this section and table S4 we briefly summarize the findings of the literature survey and the assumptions we made for global average values. We describe the parameters for the lifetimes and the respective normal distribution in terms of mean lifetime ± years (expressed as 99.7% range or three standard deviations for the probability that the stock comes to the end of its lifetime in these years). For the uncertainty ranges used in the Monte-Carlo Simulations we express the error range as a percentage of the respective parameter value, containing 99.7% (or three standard deviations) of the stochastic realizations of these variables throughout the 104 Monte-Carlo Simulations (MCS). Table S4 provides an overview of the assumptions we made for normal lifetime distributions and global average recycling/down-cycling rates as well as assumed uncertainty ranges for the years 1900 and 2014. An overview on the values assumed for processing waste as well as manufacturing and construction waste is provided in Table S2. We conceptually distinguish certain stock types based on material characteristics, to inform our reviewing of the literature for parameters. Each stock type may comprise stocks with rather different lifetimes (e.g. steel is used in cars, machinery, reinforced concrete, transport infrastructure) and in some cases physical interrelations between stock types exist (e.g. reinforced concrete is a combination of concrete and steel). As far as detailed enough information was available, we have calculated average lifetimes for stock types as weighted averages of the different stocks and applications included in the stock type, taking interdependencies between stock types (e.g. steel and concrete) into account. Solidwood, paper and paperboard: For industrial roundwood we assume processing losses (bark) of 10% (Eurostat, 2012). Based on data reported in FAO forestry statistics we estimate that losses during SI -4

manufacturing and construction of solidwood products and paper amount to 27% (incl. changes in moisture content) (FAO, 2015). Average lifetimes for solidwood products and paper/paperboard are based on the tier 1 approach of the IPCC guidelines for harvested wood products (Pingoud et al., 2006). These parameters have been confirmed by a review of case studies in previous work of some of the authors (Lauk et al., 2012). The recycled amount of paper and paperboard is based on data from FAOSTAT (FAO, 2015) for 1961 to 2014; recycling rates were calculated from modeled end-of-life outflows from stocks and the reported amount of recycled paper products. Prior to 1961, we keep recycling rates constant at the level of 1961. For solidwood products, we assume material recycling to be negligible and therefore set recycling rates to zero. Thermal energy generation from end-of-life waste of wood and paper has not been considered as re- or down-cycling and is not taken into account. Iron and steel: According to the ew-MFA database (Krausmann et al., 2009a) the global average ore grade of iron ore fluctuates between 58% and 42%; manufacturing and construction losses were estimated at 17.5% (Cullen et al., 2012). A study on global iron flows (Müller et al., 2011) reports a sectoral split of global iron and steel use and corresponding lifetimes for different iron and steel products: 40% construction (lifetime 75 years), 25% transport (lifetime 20 years), 25% machinery and appliances (lifetime 30 years), 10% others (lifetime 15 years). Based on this information, we calculate a weighted mean lifetime of 44 ± 22 years. Average lifetime for iron and steel remain constant for the whole period. A significant fraction of steel is used in combination with concrete (reinforced concrete). This is reflected in the overlap of the average lifetime of the two stock groups. For the MCS we used ± 15% on the mean lifetimes, similar to previous studies (Müller et al., 2011; Pauliuk et al., 2013). Our assumptions on the development of recycling rates of iron and steel is based on information from previous studies and two data points: For 2014, we assume a recycling rate of 83% (75–91% for the MCS) for iron and steel (Pauliuk et al., 2013), and a recycling rate of 74% in 1955 (Pounds, 1959). We linearly interpolate recycling rates from these two data points for the whole time period, which means that recycling rates for iron and steel increase from 65% in 1900 to 83% in 2010, from which on they are held constant until 2014. Copper: According to the ew-MFA database (Krausmann et al., 2009a) the global average ore grade of copper ores declined from 4% in 1900 to 1.1% in 2010; manufacturing and construction losses were estimated at 2.7% (Glöser et al., 2013). From a more detailed study on global socioeconomic copper cycles (Glöser et al., 2013), we derived average lifetimes of copper products of 19 years in 1989 and 23 years in 2010, the last year of this study. We held lifetimes constant at the level of 1989 prior to 1989 and from 2010 also constant until 2014. For the MCS we used ± 15% on the mean lifetimes. End-of-life recycling rates for copper for the period 1910 to 2010 are derived from the same study. We assume an increase from 10% in 1900–1910 to around 43% (39–47% for the MCS) in 2010, with most of this increase occurring between 1940 and 1950 (Glöser et al., 2013), from which on recycling rates are held constant until 2014. SI -5

Aluminum: According to the ew-MFA database (Krausmann et al., 2009a) the global average aluminum content of Bauxite fluctuates between 20% and 16%; manufacturing losses were estimated at 9.6% (Cullen and Allwood, 2013). Based on the average of sector specific lifetimes of aluminum products provided in a study on the development of global in-use aluminum stocks (Liu and Müller, 2013), we calculated the average lifetimes of aluminum to increase from 19 to 23 years during the time period 1950 to 2010, from which on they are held constant. For the MCS we used ± 15% on the mean lifetimes. For the period 1900 to 1949, average lifetime was held constant at the level of 1950 (22 years). Recycling rates for 1950 to 2010 were calculated from data of the World Aluminium Institute on total available scrap and recovered scrap (World Aluminium, 2015), resulting in recycling rates increasing from 2% to 62% (57–67% for the MCS) during this time period, from which on they are held constant until 2014. Prior to 1950 aluminum was used in small quantities only and recycling was assumed to be negligible and therefore set to zero. Other metals and minerals: According to the ew-MFA database (Krausmann et al., 2009a) the global average grade of other metal ores and minerals fluctuated between 9% and 3%; for manufacturing and construction losses we used the average of iron, copper and aluminum (9.2%). This heterogeneous group of mostly metals and some industrial minerals is a small flow (roughly 5% of all metal and industrial mineral inflows). The largest amount of the metals in this group (e.g. manganese, molybdenum, titanium, nickel) is used in alloys with iron, copper and other metals. We therefore applied the average of the lifetimes assumed for iron and steel, aluminum and copper, which is 30 years. For the MCS we used ± 15% on the mean lifetimes. Recycling rates for this material group was estimated to lie at 30% (Graedel et al., 2011). For the MCS we used ± 30% on the recycling rate, yielding a range of 29 – 35%. Plastics: Manufacturing and construction losses were assumed at 10%, based on a substance flow analysis study for Austria (Van Eygen et al., 2016). From studies on the use of plastic materials in Europe and the USA (Patel et al., 1998; PlasticsEurope, 2013; Shen and Worrell, 2014; US EPA, 2015), India (Mutha et al., 2006) and China (Zhang et al., 2010, 2007) we conclude that a third of annual plastics use is packaging and other short-lived applications which are discarded mostly within a year. Approximately a quarter of global production enters long-lived products such as cable coatings, pipes and tubes or insulations, while the remainder are medium-lived applications such as consumer electronics or furniture. Based on this information we assume a weighted lifetime distribution of 6 ± 2 years globally and for all regions. For the MCS we used ± 30% on the mean lifetimes. Based on several studies on plastic flows (Mutha et al., 2006, 2006; Nandy et al., 2015; PlasticsEurope, 2012; Shen and Worrell, 2014; US EPA, 2015; Zhang et al., 2007) we assume that re- and down-cycling of plastic waste (excluding incineration and energy recovery) began in the 1970s and linearly increased to today’s levels of approximately 20% of end-of-life outflows. For the industrial countries, where most plastics are incinerated, we arrive at a recycling rate of 20% for 2010 (PlasticsEurope, 2013; US EPA, SI -6

2015) and for China of 21% (Zhang et al., 2007). With the exception of India, where some authors report recycling rates of up to 60% (Mutha et al., 2006; Nandy et al., 2015), no further information for other countries was found. We generally assumed ± 30% uncertainty of the recycling rates in the MCS, yielding a range of 14 – 26%. Glass: We discern between flat glass and container glass. Global glass production was estimated on the basis of data provided in UNSD (2010) and industry statistics (Glass Alliance Europe, 2017; Mahrenholtz and Ommer, 2011; NSG Group and others, 2011). Raw material demand for glass production was estimated on the basis of data for the global glass production and an assumed demand of 730 kg of silica sand per t of glass (Ruth and Dell’Anno, 1997). Other raw materials used in glass production (e.g., soda ash, limestone) were assumed to be included in the reported data on global production of other mining and quarrying products (e.g. soda ash) (Table S1). We assumed that the average lifetime of container glass declined from of 5 to 4 years between 1900 and 2014 and that of flat glass from 50 to 39 years. Flat glass is generally not recycled, for container glass we assumed that global average recycling rate increased to 38% in 2014 based on data reported in (Butler and Hooper, 2011; EPA, 2016; OECD, 2001). Asphalt (road pavement): Manufacturing and construction losses (wastage) were assumed at 4%, based on construction manuals and construction waste studies (Bossink and Brouwers, 1996; Buchan et al., 2012; Cochran and Townsend, 2010; Poon et al., 2004; Tam et al., 2007). Most bitumen is used in asphalt pavements, only a very small fraction is utilized for roofing or water insulation. Asphalt layers are usually replaced approximately every 15–30 years (Birgisdottir et al., 2006; Cochran and Townsend, 2010; Huang et al., 2009; Miatto et al., 2016; Steger, 2012; US EPA, 2015), depending on technical standards and physical wear of the specific road section, the priority of the road and the economic situation of the country. In particular, low priority rural roads with little heavy traffic might be in use considerably longer before maintenance is required. We assume a global average lifetime distribution for the asphalt layers of roads of 25 (18-33) years. For the MCS we used ± 15% on the mean lifetimes. Recycling of asphalt pavements is feasible and widely practiced; however the remaining end-of-life wastes from stocks are often down-cycled (Miliutenko et al., 2013; Silva et al., 2012; Tojo and Fischer, 2011). For 1996 the Environmental Protection Agency of the USA reports that of 91 million tons of asphalt pavement debris generated, 72% were recycled into pavements, 8% were down-cycled into basecourses and the remainder, 20%, were landfilled (Mundt et al., 2009a, 2009b). Based on this information and data for Europe (Wiedenhofer et al., 2015), we assume that in the industrial countries recycling of end-of-life asphalt outputs began in 1960, with a linear increase of the recycling rate up to 80% in 2010. For non-industrial countries no information on asphalt recycling could be found. We assumed a global average recycling rate for asphalt of 27% in 2010 (14–39% for the MCS), which we held constant until 2014. For assumptions on down-cycling see below. SI -7

Concrete (buildings and infrastructures): Processing losses for limestone (CO2 emissions due to the calcination of limestone for cement production) were assumed at 44%; manufacturing and construction losses (wastage) were assumed at 4%, based on construction manuals (Avery, 1980; Bossink and Brouwers, 1996; Cochran and Townsend, 2010; Poon et al., 2004; Tam et al., 2007). Estimates of the lifetimes of different types of buildings and infrastructures differ along world-regions. For industrial countries we found estimates ranging from 20 to 90 years with a clustering around 50 years (Aktas and Bilec, 2012; Hashimoto et al., 2007; Kapur et al., 2008; Rincón et al., 2013). Lifetimes of buildings in China are reported to be shorter at 20 to 40 years (Cai et al., 2015; Hu et al., 2010; Huang et al., 2013; Shi et al., 2012). Based on this literature we assume a global average lifetime of concrete stocks of 50 ± 45 years. For the MCS we used ± 30% on the mean lifetimes. While recycling of concrete is technically feasible, in industrial countries most of the concrete which is recovered from construction and demolition waste is down-cycled. In industrial countries approximately 40% of concrete is recovered after demolition (Kapur et al., 2009, 2008; Tojo and Fischer, 2011; US EPA, 2015). In China the overwhelming majority of all construction and demolition waste is being landfilled or often dumped in uncontrolled sites, but recycling into concrete is increasing (Cai et al., 2015; Duan et al., 2015; Huang et al., 2013). For other parts of the world qualitative information suggests that there is hardly any recycling and very little technical down-cycling, therefore most construction and demolition waste is landfilled or, more realistically, left in place or dumped into uncontrolled sites (Agrawal et al., 2014; Rao et al., 2006). Based on this literature review we assume a global average recycling rate for concrete of 7% in 2010, with a linear increase from 0% in 1970. For the MCS we used ± 45% of the recycling rates, yielding a range of 3-9%. For the assumptions on down-cycling see below. Down-cycling of asphalt and concrete: A large fraction of construction and demolition waste is crushed and used to substitute for natural aggregates (mostly in sub-base layers of built structures or base-course layers of roads), which we define as down-cycling. Down-cycling rates refer to the amount of waste material remaining after recycling has been deducted. We assume that down-cycling rates of asphalt and concrete are similar. For the industrial countries, where construction and demolition waste became a topic much earlier, we assume down-cycling rates of 10% for the period 1900–1970. We assume that after 1970, with growing amounts of construction and demolition wastes accruing and landfilling becoming more expensive, down-cycling gained significance and linearly increases to 30% in 2010. For China we assume a linear increase of the down-cycling rate from 0% in 1980 to 30% in 2010. For the RoW we assume a linear increase from 1980 onwards to 10% in 2010. For the global average we then arrive at 3% until 1980 and a linear increase to 23% in 2010, which are held constant until 2014. For the MCS a ± 45% uncertainty range for all down-cycling rates across time is assumed. Bricks (buildings): Processing losses (mainly due to changes in moisture content of clay in brick production) were assumed at 26% (Krausmann et al., 2009a); manufacturing and construction losses SI -8

(wastage) were assumed at 4%, based on construction manuals and construction waste studies (Bossink and Brouwers, 1996; Cochran and Townsend, 2010; Poon et al., 2004; Tam et al., 2007). Bricks are mainly used in buildings. Based on the average lifetimes of buildings (see concrete) we assume a global mean lifetime of bricks of 40 (4-76) years. For the MCS we used ± 30% of the mean lifetimes. Recycling of bricks is usually only possible via direct re-use, which is labor-intensive and requires careful deconstruction. We assume that the beginning of the period (1900 to 1930) 15% of discarded bricks were recycled and that this rate linearly decreased to zero from 1930 to 1960 where it remained until 2010. Down-cycling of bricks is more significant. We assume a rate of 35% for 1900 to 1930 and a linear decrease to zero in 1970, when it began to increase again to 23% in 2010, continuing until 2014. For the MCS we assumed a ± 60% uncertainty range of the respective parameter until 1970, after which the assumed uncertainty range decreases to ± 45% in 1980, from which it remains constant. Sand and gravel used as sub-base layer for buildings and in base-course layers of roads: A considerable amount of sand and gravel is used to build sub-base layers for buildings and base-courses for roads and other infrastructures. Often these materials remain in place and are not recovered when a new building is constructed and roads are refurbished. We therefore assume that the lifetime of these material stocks is considerably longer than that of roads and buildings. For aggregates used in basecourse and sub-base layers of roads and buildings (see section 1.5) we assume a lifetime of 80 (8-152) years for all regions and the global average. For the MCS we assumed ± 30% uncertainty of the mean lifetime. Most of these materials are directly re-used or recycled on site and we assume a constant recycling rate of 60% and globally. For the MCS we assumed ± 60% of the recycling rate.

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Table S4: Summary of the applied global average values of MISO model parameters for 1900 and 2014: material input uncertainties, lifetime distributions and uncertainties as well as end-of-life (EoL) recycling and down-cycling rates and their uncertainty ranges. All uncertainty ranges are expressed as relative variation of the respective parameter (in %) and contain three standard deviations. The ranges shown for the normal (Gaussian) lifetime distributions contain three standard deviations, which means that 99.7% of the stock reaches the end of its service lifetime between these two values, with the shown mean lifetime. For detailed documentation, sources and regional parameterization see section 2.4.

Stock type

Material input uncertainty (±)

Lifetime distribution parameters Lifetimes, mean µ (years) 1900 2014

µ ± 3σ (years, rounded, 99.7% of cases) 1900

2014

Recycling parameters

Mean lifetime uncertainty (±)

Recycling rates (% of EoL outflow) 1900

Uncertainty (±)

2014

Down-cycling parameters Down-cycling rates Uncertainty (% of EoL outflow (±) after recycling) 1900 2014

Solidwood

15%

30

30

8 – 53

8 – 53

30%

-

-

-

-

-

-

Paper

15%

2

2

1–4

1–4

30%

15%

32%

15%

-

-

-

Iron and steel

15%

44

44

22 - 66

22 – 66

15%

65%

83%

15%

-

-

-

Copper

15%

19

23

9 – 29

11 – 35

15%

10%

43%

45%

-

-

-

Aluminum Other metals and minerals Plastics

15%

22

23

11 – 33

11 – 34

15%

-

62%

15%

-

-

-

15%

28

30

14 - 43

15 - 45

15%

30%

30%

45%

-

-

-

15%

-

6

-

4–8

30%

-

20%

45%

-

-

-

Flat glass

15%

50

39

15 – 65

12 – 51

15%

-

-

-

-

-

-

Container glass Asphalts (roads) Concrete (buildings, infrastructure) Bricks (buildings) Aggregate (primary) Aggregate (down-cycled)

15%

5

4

2-7

1–6

15%

-

36%

30%

-

-

-

15%

25

25

18–33

18 – 33

15%

-

27%

45%

-

23%

45%

15%

50

50

5–95

5–95

30%

-

6%

45%

3%

23%

45%

45%

40

40

4–76

4 – 76

30%

15%

-

45%

35%

23%

45%

60%

80

80

8–152

8 – 152

30%

60%

60%

45%

-

-

-

60%

80

80

8–152

8 – 152

30%

60%

60%

45%

-

-

-

SI -10

Choosing appropriate lifetime distributions Currently normal (Gaussian) lifetime distributions are employed, with the exception of the materials category “paper”, where a simple leaching model (1 / LT) is employed. The effect of using different functional forms of lifetime distributions L(t,t’), or even only specific lifetimes (termed ‘delayed model’ (van der Voet et al., 2002)), as well as various distributions such as Gaussian, Weibull, gamma and lognormal have been investigated previously (Kapur et al., 2008; Miatto et al., 2017). Using specific lifetimes in a delayed model assumes perfect knowledge of the exact lifetime and directly transfers fluctuations in the inflow data to outflows, which makes it inappropriate for the purpose of the MISO model. It has been shown, that different functional forms for lifetime distributions yield reasonably similar results for stocks (Kapur et al., 2008; Miatto et al., 2017; Müller et al., 2014). Which form to use then depends either on the availability of statistical data for estimating specific survival rates and finding the best fitting functional form (Johnstone, 2001; Miatto et al., 2017; Müller et al., 2014; Rincón et al., 2013). In case of lacking information the commonly applied Gaussian normal distribution can be used (Hu et al., 2010; Müller, 2006; Shi et al., 2012). The MISO model can be easily adapted to any other lifetime distribution, but because the model covers all infrastructures and buildings, the empirical basis for the specification of more complex functional forms is limited. Specific parameter values for the lifetime distributions (mean and standard deviation) were sourced from an extensive literature review summarized above.

Uncertainty – specifying the Monte-Carlo Simulations module We incorporate a systematic quantification of uncertainty for our modeling results, using Monte-Carlo Simulations (MCS) (Džubur et al., 2016; Laner et al., 2014; Morgan, 2006). The dynamic MISO model can be seen as a stochastic system, where each input parameter is understood to be the mean µ of a normal (Gaussian) distribution with an uncertainty parameter σ. In each model run, input parameters are then randomly drawn from a distribution 𝑋 ~ 𝒩(𝜇, 𝜎). For the following parameters errors are propagated through all modelling runs in each MCS (Table S1). Table S2: Parameters and error ranges covered by the Monte-Carlo Simulations (MCS) Input Parameter

Vintage v

Material m

Region r

Time t

Material inflow

Yes

Yes

Yes

Yes

Loss factor

No

All metals

No

Yes

Lifetimes µ

Yes

Yes

No

Yes

Shape of lifetime distribution σ

No

No

No

No

Base course multiplier for roads

No

Asphalt

No

Yes

Sub-base layer multiplier for buildings

No

Concrete, bricks

No

Yes

Recycling rates r

No

Yes

Yes

Yes

Downcycling rates dcycl_r

No

Concrete, asphalt and bricks

Yes

Yes

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Only for some parameters and points in time uncertainty ranges could be directly taken from the literature (see SI). For most parameters generalized assumptions on the underlying reliability of different types of data and sources had to be used. These assumptions were made on the basis of in-depth knowledge of data sources, information from data compilation methods available from technical documentations and from expert judgements. For example, data in material flow accounts has been subject to quality control and cross checks and is generally deemed to be quite reliable; it has been shown that different estimates of aggregate material use for countries and regions differ by only 10-20% (Fischer-Kowalski et al., 2011). Only for clay and natural aggregates used in concrete, asphalt and base layers we assumed higher uncertainties of ± 40% (Fehler! Verweisquelle konnte nicht gefunden werden.Fehler! Verweisquelle konnte nicht gefunden werden.). Assumptions for model parameters such as lifetime distributions or recycling and downcycling rates are derived from scattered evidence from the literature and are considered less reliable and therefore assigned higher uncertainty ranges. From the Monte-Carlo simulations we can then derive confidence intervals for all modelled results on material stocks and flows. When using MCS, the number of required simulations to achieve ‘stable’ model outputs arises, for which we used the standard error of the mean calculated for increasing numbers of MCS for each material and visually check if model outputs on stocks and end-of-life waste reach sufficiently ‘stable’ estimates (Groen et al., 2014). Because the standard error of the mean decreases with increasing sample size, a slight decrease will necessarily occur when running more MCS. For our case, we would argue that a certain stabilization already occurs between 1,000 – 2,000 MCS and above 5,000 MCS all further reductions are probably only due to increasing sample size alone (Figure S1).

Figure S1: Testing for the stabilization of modelling results on in-use of materials and subsequent end-of-life waste with increasing numbers Monte-Carlo Simulations.

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Model Output Data The model provides results for material in-use stocks by vintage, material, functional stock type, region, and each Monte-Carlo Simulations. For each time step losses from stock accumulation, end-of-life outputs from stocks, recycled as well as waste amounts are estimated, again by material, region and each MCS. Over all MCS mean estimates standard deviations are calculated to describe the resulting distributions.

Evaluation Model results are evaluated and calibrated against the available, usually substance specific or spatially confined literature using bottom-up and top-down methods to estimate in-use stocks. Additionally, we assess and attribute uncertainty in model outputs to the respective model inputs and perform various tests for local model sensitivities (see sections below).

Detailed model description In the generalized MISO model the total stock of any material at a certain time t is estimated from the remaining in-use stock from t-1 (model driven), minus end-of-life wastes from stocks in t (model driven), plus gross additions to stock in t (data and model driven). The annual additions to stock at the time t of material m in region r and Monte-Carlo Simulation mc is handled as its own vintage v = t of 𝑚𝑐 in-use stock 𝑆 𝑣,𝑚,𝑟 (𝑡) (Eq. 1). 𝑚𝑐 𝑚𝑐 𝑚𝑐 𝑆𝑡𝑜𝑐𝑘 𝑚𝑐 𝑣,𝑚,𝑟 (𝑡) = 𝑆𝑡𝑜𝑐𝑘𝑣,𝑚,𝑟 (𝑡 − 1) − 𝐸𝑜𝐿_𝑤𝑎𝑠𝑡𝑒𝑣,𝑚,𝑟 (𝑡) + 𝐺𝑟𝑜𝑠𝑠 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑡𝑜 𝑠𝑡𝑜𝑐𝑘𝑠𝑣=𝑡,𝑚,𝑟 (𝑡)

Equation 1 The average vintage 𝑣̅ of in-use stock 𝑆̅ at the time t is then defined as the mean over all vintages v of material m and region r in the Monte-Carlo Simulations mc at the time t (Eq. 2). 𝑆𝑣̅̅,𝑚,𝑟 (𝑡) =

1 𝑛

𝑚𝑐 ∑𝑛𝑖=𝑚𝑐 𝑆𝑣,𝑚,𝑟 (𝑡)

Equation 2

The total in-use stock of material m is then calculated as the sum over the average vintages 𝑣̅ of material m, in region r at the time t. Uncertainty ranges are calculated similarly, where the standard deviations are calculated via error propagation for independent means (Sachs, 2004) across each Monte-Carlo run mc (Eq. 3). ̅ (𝑡) = ∑𝑣 𝑆𝑣,𝑚,𝑟 ̅ (𝑡) 𝑆𝑚,𝑟

Equation 3

The annual gross additions to stock (GAS) of material m, at the time t in region r of Monte-Carlo Simulation mc are handled as specific vintages v (v = t). The gross additions to stocks include primary materials GAS_primary (data driven), and secondary processed materials (model driven), which SI -13

includes material flows of recycled and down-cycled materials, where GAS_secondary = GAS_recycled + GAS_downcycled (Eq. 4). A factor on 𝑚𝑎𝑛𝑢𝑓_𝑐𝑜𝑛𝑠𝑡𝑟_𝑤𝑎𝑠𝑡𝑒 represents that re-manufacturing & construction waste occur during stock-building activities, which covers primary and secondary stockbuilding materials (see Figure 2, main article). The waste occurring in these processes are assumed to not be recyclable. 𝑚𝑐 𝑚𝑐 𝑚𝑐 𝑆 𝑚𝑐 𝑣=𝑡,𝑚,𝑟 (𝑡) = 𝐺𝐴𝑆𝑚,𝑟 (𝑡) = [𝐺𝐴𝑆𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑚,𝑟 (𝑡) + 𝐺𝐴𝑆𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑚,𝑟 (𝑡)] = 𝑚𝑐 = [𝑆𝑡𝑜𝑐𝑘_𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔_𝑖𝑛𝑝𝑢𝑡𝑠𝑚,𝑟 (𝑡) ∗ ( 1 − 𝑚𝑎𝑛𝑢𝑓_𝑐𝑜𝑛𝑠𝑡𝑟_𝑤𝑎𝑠𝑡𝑒 𝑚𝑐 𝑚,𝑟 (𝑡) )

Equation 4 The end-of-life wastes from stocks at the time t is defined as the end-of-life waste over all vintages v, by material m, in region r and Monte-Carlo Simulation mc, determined via vintage-, material-, region′ and time-specific lifetime distributions 𝐿𝑚𝑐 𝑣,𝑚,𝑟 (𝑡, 𝑡 ) (Eq. 5). 𝑚𝑐 𝑚𝑐 ′ 𝐸𝑜𝐿_𝑤𝑎𝑠𝑡𝑒_𝑠𝑡𝑜𝑐𝑘𝑣,𝑚,𝑟 (𝑡) = 𝑆𝑣,𝑚,𝑟 (𝑡) ∗ 𝐿𝑚𝑐 𝑣,𝑚,𝑟 (𝑡, 𝑡 )

Following (Müller, 2006), we utilize normal lifetime distributions,

Equation 5 L(t,t’), which represent the

probability that the stock of vintage v of material m, in region r and Monte-Carlo Simulation mc from time t’ < t reaches its useful service lifetime at time t, assuming that these lifetimes follow a normal distribution with a mean lifetime 𝜇 and a standard deviation 𝜕 (Eq. 6). 𝐿𝑚𝑐 𝑣,𝑚,𝑟

(𝑡, 𝑡

′)

=(1− Φ) =

1 √2𝜋∗ 𝜇 𝑚𝑐 𝑣,𝑚,𝑟

∗ 𝑒𝑥𝑝

− (𝑡−𝑡′ − 𝜏𝑚𝑐 𝑣,𝑚,𝑟 )² 2∗ 𝜇 𝑚𝑐 𝑣,𝑚,𝑟 ²

Equation 6

The function is normalized that the integral over time equals 1 for any combinations of 𝜏 and 𝜕. As the lifetime conceptually cannot be negative (t > t’), a fraction of the curve is effectively cut-off, which can result in integrals smaller than one in this predefined positive area. This opens up the possibility that some vintages never entirely turn into end-of-life wastes. However, this cut-off remains marginal when 2𝜕 ≤ 𝜏 (Müller, 2006). The modelled end-of-life waste from stocks are subjected to waste management activities and some of them are re-used and recycled Recycl, i.e. materials that re-enter the original processed material flow (e.g. steel is recycled into steel products), while some flows are only downcycled Dcycl, i.e. a material that effectively turns into another additions to stock flow (e.g. cement and bricks are crushed and used as aggregates). All materials that are not recycled or downcycled during waste management, are treated as final wastes and count as processed outputs to nature. Recycling is calculated on the basis of material, time- and region- specific recycling rates 𝑟𝑒𝑐𝑦_𝑟𝑎𝑡𝑒, for each Monte-Carlo Simulation mc (Eq. 7). 𝑚𝑐 (𝑡) 𝑚𝑐 (𝑡) (𝑡) 𝑅𝑒𝑐𝑦𝑐𝑙𝑚,𝑟 = [∑𝑐 𝐸𝑜𝐿_𝑤𝑎𝑠𝑡𝑒_𝑠𝑡𝑜𝑐𝑘𝑠𝑣,𝑚,𝑟 ] ∗ 𝑟𝑒𝑐𝑦𝑟𝑎𝑡𝑒 𝑚𝑐 𝑚,𝑟

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Equation 7

Downcycling is estimated using material-, time- and region- specific down-cycling rate dcycl_r for each Monte-Carlo Simulation mc to quantify the amounts based on the remaining sum of end-of-life waste from stocks after recycling has been deducted (Eq 7), for each material m in region r and Monte-Carlo Simulation mc of recycled materials recycl (Eq 8). 𝑚𝑐 (𝑡) 𝑚𝑐 (𝑡) 𝑚𝑐 (𝑡)] 𝑚𝑐 𝐷𝑐𝑦𝑐𝑙𝑚,𝑟 = [∑𝑣 𝐸𝑜𝐿_𝑤𝑎𝑠𝑡𝑒_𝑠𝑡𝑜𝑐𝑘𝑠𝑣,𝑚,𝑟 − 𝑅𝑒𝑐𝑦𝑐𝑙𝑚,𝑟 ∗ 𝑑𝑐𝑦𝑐𝑙_𝑟𝑚,𝑟 (𝑡)

Equation 8

Final waste from stock-building is then defined as the amount of end-of-life wastes from stocks remaining after recycling and downcycling.

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Validating MISO results: systematic comparison with the literature

Figure S2: Comparison of MISO estimates with results from studies on specific substances and materials for A)

steel (Pauliuk et al., 2013), C) aluminum (Liu and Müller, 2013) and D) copper (Glöser et al., 2013). Each study includes stock results based on high, median and low lifetime assumptions. Uncertainty ranges for MISO results are shown in the same way as in the main text (with 3 standard deviations which cover 99.7% of the 10 3 MonteCarlo Simulations). Overall, MISO-modeling results agree well with this literature.

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Figure S3: Comparison of MISO concrete stock estimates with results A) for cement (Müller et al., 2013) and B)

also for cement (Cao et al., 2017). Please note that the results for both studies on cement were re-calculated into the material concrete, which is a factor 6 larger to account for the additional sand, gravel and aggregate required for concrete. Uncertainty ranges for the MISO results are shown in the same way as in the main text, with 3 standard deviations which cover 99.7% of the 103 Monte-Carlo Simulations. Overall, MISO-modeling results agree well with this literature.

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Figure S4: Comparison of MISO stock estimates with results from materials specific for A) wood products (Lauk et

al., 2012) compared with solidwood and paper results from MISO, and B) bitumen stocks (Lauk et al., 2012). Please note that asphalt consists of 5% bitumen and 95% sand and gravel, where for the purpose of comparison, the MISO results were re-calculated to only show bitumen content in the asphalt modeling. Uncertainty ranges for the MISO results are shown in the same way as in the main text, with 3 standard deviations which cover 99.7% of the 103 Monte-Carlo Simulations. Overall, MISO-modeling results agree quite well with this literature.

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Figure S5: Comparison of MISO stock estimates for plastics with materials specific studies by A) (Geyer et al.,

2017), and B) (Lauk et al., 2012). Uncertainty ranges for the MISO results are shown in the same way as in the main text, with 3 standard deviations which cover 99.7% of the 103 Monte-Carlo Simulations. Overall, MISOmodeling results agree well with this literature, although the recent estimate by (Geyer et al., 2017) is 19% lower than the MISO results.

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Figure S6: MISO stock estimates for aluminum in comparison with results from a large range of studies (Gerst and

Graedel, 2008; Liu and Müller, 2013; Rauch, 2009; Rauch and Pacyna, 2009). Uncertainty ranges for the MISO results are shown in the same way as in the main text, with 3 standard deviations which cover 99.7% of the 10 3 Monte-Carlo Simulations. Overall, MISO-modeling results agree well with this literature.

Figure S7: Comparison of MISO copper stock estimates with results from other studies (Gerst and Graedel, 2008;

Glöser et al., 2013; Rauch, 2009; Rauch and Graedel, 2007; Rauch and Pacyna, 2009). Uncertainty ranges for the MISO results are shown in the same way as in the main text, with 3 standard deviations which cover 99.7% of the 103 Monte-Carlo Simulations. Overall, MISO-modeling results agree well with this literature.

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Uncertainty attribution to model input parameters The dynamic MISO model is implemented in a stochastic manner, where each exogenous model input parameter is understood to be the mean µ of a normal (Gaussian) distribution with an uncertainty parameter σ. In each model run, input parameters are then randomly drawn from a distribution 𝑋 ~ 𝒩(𝜇, 𝜎). The 6 exogenous model input parameters (Table S2) are expected to have different influences on the endogenous model results and their uncertainty, depending on the relations between specific exogenous variables and endogenous variables, so-called first-order effects. Additionally, interactions between variables can also lead to higher-order effects (Borgonovo and Plischke, 2016; Džubur et al., 2016; Norton, 2015; Plischke et al., 2013). However, due to the data limitations for empirically specified probability density uncertainty functions for all exogenous parameters, a relatively simple approach for attributing first-order uncertainty has been deemed more appropriate than more sophisticated methods. Here we document our method and show detailed findings, while the main results for the attribution of uncertainty are shown in the main manuscript. We used the method of normalized squares of Spearman’s rank-correlation coefficients as a Global Sensitivity Analysis approach to attributing first-order effects (Borgonovo and Plischke, 2016; Saltelli and Sobol, 1995). This means quantifying the relative influence of each exogenous variable’s uncertainty on the uncertainty of the endogenous model results for in-use stocks and end-of-life waste from stocks. For each endogenous variable EN (14 materials as in-use stocks and as end-of-life waste), Spearman’s rank-correlation coefficient 𝑟ℎ𝑜 was calculated, using the 10,000 Monte Carlo Simulations as sample. The rank-correlation Rho was calculated for each exogenous model input parameter EX, against the endogenous model results EN and tested against the null hypothesis of no significant correlation at the confidence level of p = 0.05.

𝑟ℎ𝑜𝐸𝑁,𝐸𝑋,𝑡 = 1 −

6 ∑𝑛 𝑀𝐶=1(𝑟𝑎𝑛𝑘 𝐸𝑁𝑀𝐶,𝑡 −𝑟𝑎𝑛𝑘 𝐸𝑋𝑀𝐶,𝑡 ) 𝑛(𝑛2 −1)

2

Equation 9

Where 𝑟𝑎𝑛𝑘 𝐸𝑁𝑀𝐶,𝑡 and 𝑟𝑎𝑛𝑘 𝐸𝑋𝑀𝐶,𝑡 are the ordinal rankings of the 𝑛 Monte Carlo results of the endogenous variable 𝐸𝑁 and exogenous variable 𝐸𝑋, respectively, at model time step 𝑡, and 𝑛 = 10,000 Monte Carlo model runs. The resulting statistically significant 6 𝑟ℎ𝑜 values for each endogenous variable are then normalized in the following fashion:

𝐶𝐸𝑁,𝐸𝑋,𝑡 =

(𝜌𝐸𝑁,𝐸𝑋,𝑡 )

2

6

∑

(𝜌𝐸𝑁,𝐸𝑋,𝑡 )

𝐸𝑋=1

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2

Equation 10

Where 𝐶𝐸𝑁,𝐸𝑋,𝑡 is the normalized square of Spearman’s rank-correlation coefficients, which allow comparisons and attribution of uncertainty in the exogenous variables to the uncertainty of the endogenous variable (Borgonovo and Plischke, 2016; Saltelli and Sobol, 1995). The sum of 𝐶𝐸𝑁,𝐸𝑋,𝑡 for any given endogenous variable 𝐸𝑁 at model time step 𝑡 is equal to 1.

Figure S8: Attributing sources of uncertainty for global in-use stock estimates to model input parameters, using normalized Spearman’s rank correlation coefficients (Borgonovo and Plischke, 2016; Saltelli and Sobol, 1995), over 10^5 Monte-Carlo Simulations.

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Figure S9: Attributing sources of uncertainty in end-of-life waste from stocks to model input parameters, using normalized Spearman’s rank correlation coefficients (Borgonovo and Plischke, 2016; Saltelli and Sobol, 1995), over 10^5 Monte-Carlo Simulations.

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Testing for local model sensitivity Additionally to the Global Sensitivity Approach shown above, it is quite useful to also explore the sensitivity of the model results to changes in key exogenous parameters (Norton, 2015; Pianosi et al., 2016). From the GSA above it is clear that variation in lifetime distributions across the MCS are a key factor for the overall variation in in-use stock estimates. Because lifetime distributions rely on broad literature-based assumptions, it makes sense to also test for systematic errors in these assumed values for mean lifetimes and the standard deviation of the lifetime distribution applied. Seven different sensitivity tests of the MISO model against the parameters mean lifetimes and standard deviation of the resulting lifetime distribution were modeled, starting from the main parameters summarized in Table S2: 1) All lifetimes were decreased by –1/3, 2) All lifetimes were increased by +1/3, 3) All lifetimes were increased by +50%. 4) All standard deviations of the lifetime distributions were decreased by -2/3 5) All standard deviations were increased by +1/3. 6) All lifetimes were increased by +1/3 while the standard deviations were decreased by -2/3 7) All lifetimes were decreased by -1/3 while standard deviations were decreased by -2/3. The results shown in Figure S10 indicate that the results of the global stock estimate are relatively robust against systematic under/overestimation of mean lifetimes and standard deviations. Assuming 50% longer lifetimes yields only a 15% larger stock in 1950 and a 9% larger stock in 2014. The sensitivity test with significantly shorter lifetimes (-1/3) yields –11% lower global stocks for 2014. Interestingly, reducing the standard deviations of the lifetime distributions by -2/3 yields a larger stock of +6% in 2014, compared to the main results. The sensitivity tests for interactions between lifetimes and standard deviations however yielded quite similar results. Increasing lifetimes (+1/3) while reducing standard deviations (-2/3) yields a 12% larger stock in 2014. However, reducing lifetimes by 1/3 and standard deviations by -2/3, yields a -3% smaller stock in 2014. Note that the low and asymmetric impact of changes in lifetime is strongly influenced by the dynamics of inputs to stocks over time (Figure S10 B). Inputs to stocks rapidly increased after World War II and a large fraction of all inputs occurred only after 1980, resulting in non-linear and asymmetric impacts of changes to the lifetimes.

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Figure S10: Results of the sensitivity analysis of global in-use stock estimates to systematic changes in the lifetime

distributions. LT stands for mean lifetimes, LTdev for standard deviations around the lifetime. Comparison of global stock estimates resulting from the standard MISO model run with uncertainty ranges derived from MonteCarlo Simulations and seven different sensitivity tests with different assumptions on average lifetimes and standard deviations.

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As a final step, we visualize the sensitivity of global in-use stock estimates for each material against the relevant exogenous model input parameters, to check for non-uniform and unexpected model behaviour. We conclude that there seem to be no locally specific nor unexpected sensitivities of the model outputs to certain parameter spaces (Figure S7).

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Figure S11: In-use stock estimates for 2014 derived from 10^4 Monte-Carlo Simulations, plotted against the respective variations of each model input parameter to check for non-linear or otherwise unexpected model behavior. Uniform distributions indicate low model sensitivity to the respective parameter, while non-linear patterns would indicate high sensitivity to certain parameter spaces. Stock estimates are in Gigatons, while primary and secondary material inputs are in Megatons. The factor for manufacturing and construction waste is implemented from 0 to 1, where a value of 1 indicates no construction wastes. Overall, no unexpected or specifically non-linear relationships between model input parameters and in-use stock results can be observed.

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