Mapping Plastic and Plastic Additive Cycles in Coastal Countries: A Norwegian Case Study

The growing environmental consequences caused by plastic pollution highlight the need for a better understanding of plastic polymer cycles and their associated additives. We present a novel, comprehensive top-down method using inflow-driven dynamic probabilistic material flow analysis (DPMFA) to map the plastic cycle in coastal countries. For the first time, we covered the progressive leaching of microplastics to the environment during the use phase of products and modeled the presence of 232 plastic additives. We applied this methodology to Norway and proposed initial release pathways to different environmental compartments. 758 kt of plastics distributed among 13 different polymers was introduced to the Norwegian economy in 2020, 4.4 Mt was present in in-use stocks, and 632 kt was wasted, of which 15.2 kt (2.4%) was released to the environment with a similar share of macro- and microplastics and 4.8 kt ended up in the ocean. Our study shows tire wear rubber as a highly pollutive microplastic source, while most macroplastics originated from consumer packaging with LDPE, PP, and PET as dominant polymers. Additionally, 75 kt of plastic additives was potentially released to the environment alongside these polymers. We emphasize that upstream measures, such as consumption reduction and changes in product design, would result in the most positive impact for limiting plastic pollution.


S2 Model processes
The model proposed by Abbasi et al. 1 was adopted as a base model for plastics in the anthroposphere with slight adjustments.Fishing gear were modeled individually in this study instead of a fraction of technical textiles as assumed by Abbasi et al. 1 Additionally, processes that describe the release of plastics to the environment were added to this model.Eight additional product categories were introduced: Tires, cigarettes, as well as flushed products that contain six categories (tampons, tampon applicators, wet wipes, disposable cleaning cloths, cotton swaps, sanitary towels, and panty liners).
Table S1 shows all model processes covered in this study, while a description of the environmental sinks is given in Table S2.Material reuse, Automotive part reuse, and Textile reuse processes act as anthropogenic sinks and are not further considered in this study (i.e., the flows cannot be reintroduced to the system from one year to the next).This assumption was adopted from the base model. 1 Table S1.Processes considered in the MFA model.ASR: auto shredder residue; EEE: electrical and electronic equipment; ELB: End-of-life boats; ELV: End-of-life vehicles; HH: Household; PWT: primary water treatment; SWT: secondary water treatment; TWT: tertiary water treatment; WEEE: Waste from electrical and electronic equipment; WEEP: Waste of electrical and electronic plastic.WWTP: Wastewater treatment plant.OSSF: On-site sewage facility.CSO: Combined sewer overflow.Pant bottles refer to deposit return system.

Production and manufacturing
Consumption sectors and individual product categories

Waste collection
Recycling system

Release pathways Sinks
Recycled material

S3.1 Plastics in the anthroposphere
TCs from Abbasi et al. 1 were adopted with no further changes for LDPE, HDPE, PP, PS, PVC, EPS, and PVC.The mass distribution for PUR, PA, PC, and ABS to the different product categories were taken from Liu and Nowack, 2 with slight adjustments for the product categories naming to account for the differences, see Table S3.For tires, according to Statistics Norway (SSB), 3 86% of tires collected from households were sent to recycling, 10% to incineration, and the remaining to landfill in 2020.

S3.2.1 Initial plastic release
Plastic leakage was modeled following the methodologies presented by Kawecki and Nowack 4 and Sieber et al. 5 .The reader is referred to these studies for detailed modeling approaches.Only the adjustments to the methods to account for the release of plastics for coastal countries are discussed in the sections below.

S3.2.1.1 Macroplastics
The initial release of macroplastics is presented in this section.Figure S2 shows an overview of the release pathways.The fractions of consumer items used on the go were adjusted to be aligned with the product categories in this model.Table S4 shows the adjusted values and the assumptions taken with regards to the respective polymers with respect to the methodology presented by Kawecki and Nowack.The fraction for the loss of "Agricultural Mix" product category in this model is assumed to be the same as "Other Agricultural Plastics" in Kawecki and Nowack 4 with a value of 3.8%.

S3.2.1.1.3 Automotive
We assume that no macroplastics are lost from the "Automotive" product category.Losses are only accounted for "tires" and "mobility textiles".

S3.2.1.1.4 Dumping
Kawecki and Nowack 4 assumed that a person is 100 times more likely to discard their waste in public bins rather than dump it in Switzerland.For the Norwegian context, 125 tons of waste were collected in public bins in the city center in Trondheim in 2007 6 and the household waste can be found using Statistics Norway (SSB) data. 3The population living in the city center is 4783 and in the whole city is 207580 in 2022 (2.3% of the population lives in the city center). 7We assume that half of the waste found in public bins in the city center originate from people living in the city center (i.e., 62.5 tons).This gives us 2717.4 tons of waste found in public bins for the whole city of Trondheim.We used historical GDP to back-cast the household waste to 2007. 8ble S5 We therefore derive a rate of 0.054% of dumping in Norway, which is double rate for Switzerland derived by Kawecki and Nowack 4 .Dumping is applied to all product categories except "Automotive".We assume that the sinking of boats in the ocean has the same rate as dumping.

S3.2.1.1.5 Flushing rates
Kawecki and Nowack 4 derived flushing probabilities using various studies. 9,10Moreover, a Norwegian report 11 presented an estimate for flushing rates in 2019.the loss rate of fishing gear to the ocean range between 0.4 -4.4%.

S3.2.1.1.8 Sweeping efficiency
We applied a sweeping rate of 90% 11 to the waste littered in residential and road side areas.Littered waste in natural environments is assumed to not to be swept.

S3.2.1.1.9 Macroplastic release to the marine environment and freshwater
Here, we propose a new pathway for the release of littered macroplastics.The fraction of littered macroplastics that reach the marine environment is assumed to be proportional to the coastal population.Jambeck et al. 13 used the populations that live within 50 km from the coastlines to estimate the amount of plastics that is available to reach the marine environment.In Norway, ~92% of the population live within 50km of the coastline. 7Meijer et al., 14 estimated that 80% of littered plastics in coastal cities reach the ocean.Combining these two fractions, we therefore derive a rate of 74% of available littered plastics to be released to the ocean in Norway, while the rest is distributed to terrestrial compartments.We further assumed all macroplastics released to freshwater eventually end up in the ocean.

S3.2.1.2.1 Lifetime dependent flows
Figure S3 summarizes the release pathways for lifetime related microplastic releases.We assume 100% of cosmetic products is released to wastewater.

Figure S4. Leakage pathways for microplastic leaching outflows with all relevant processes employed in the Material Flow
Analysis (MFA) model.

S3.2.1.2.2.1 Clothes and household textiles
A shedding rate is applied on the product categories "Clothing" and "Technical Clothing", "Household Textiles", and "Household Technical Textiles".The following sections describe the derived leaching rates for washing, drying and wear: A leaching rate for shedding of microplastics during wash can be obtained by firstly deriving an annual number of washing cycles.This can be done by using the following relationship: According to various studies, 4,15-17 a textile clothing piece is washed on average between 19 and 39 times across its whole lifetime, and household textiles for 5.9 times.The annual leaching rate can then be calculated by multiplying the shedding rate of one washing cycle by the annual number of washing cycles: ℎ  = ℎ ℎ, ×  ℎ The Plastic Leak Project Report 18 presented high (134 mg/kg), average (46 mg/kg) and low (24 mg/kg) shedding rates based on an extensive literature review.Only high and low shedding rates are chosen in this study.The annual number of washing cycles discussed previously was used in the calculation of drying and wear related microplastic emissions as opposed to the total number of washing cycles used by Kawecki and Nowack 4 to derive annual leaching rates.

S3.2.1.2.2.2 Tires
During use, tires release particles due to the forces between the tire and the road surface.An average passenger car losses between 10 -30% of its tread rubber during its whole lifetime. 19,20Given that tires have a mean lifetime of 4 years, 21 the annual leaching rate per year for tires is therefore 2.5 -7.5%.The modeling of tire release follows the methodology presented by Sieber et al. 5 without any further modifications.

S3.2.1.2.2.3 Other leaching sources
The emission rates for the product categories were derived as annual rates by dividing the loss rates presented by Kawecki and Nowack 4 by the mean lifetimes used in this study without any adjustments (see Table S8), while a summary of all emission sources is presented in Table S9.
Table S8.Summary of the leaching rates modified using the loss rates presented by Kawecki and Nowack. 4ctor Product category Loss rates adopted from  According to a report by Statistics Norway, 22 there are 39,000 km of wastewater pipes in Norway, of which 7,000 km are joint pipes (wastewater and stormwater) and 32,000 km of only wastewater.Using this information, we assume that the fraction of joint pipes represents the fraction of stormwater that goes to a wastewater treatment plants (17.95%), while the rest is discharged immediately to waterbodies.We therefore assume 92% of this fraction is released into the ocean, while the rest is released to freshwater, since 92% of the population live within 50km from the coastline. 7

S3.2.1.3.2 Wastewater collection
In Norway, 87% of the population are connected to a wastewater collection system. 22We assume the remaining 13% go through on-site sewage facilities.64% of all wastewater undergo advanced treatment (primary, secondary and tertiary stages), 21% only mechanical (primary) treatment, and 2% is discharged without treatment. 222% of the collected wastewater is released to waterbodies without any treatment. 22The remaining 98% undergo treatment stages according to the method presented by Kawecki and Nowack 4 .Combined sewer overflow amounts to 1-3% in Norway. 22

S3.2.1.4 Release to outdoor and indoor air S3.2.1.4.1 Outdoor air
An estimation was done based on land cover for Norway.According to Statistics Norway, 23 6.2% of Norway consists of inland waters.We assigned this fraction for the amounts in outdoor air to be deposited to freshwater, while the rest to residential soil.

S3.2.2 Redistribution of initial releases
The redistribution of plastics after the initial release for aquatic environments was included in this model.A similar approach was applied by Schwarz et al. 24 This redistribution depends on the density of the polymer, where polymers with densities higher than water are all assumed to sink.High density polymers include PET, PVC, PS, PA, ABS, PC, CA and rubber.Low density polymers include PP, HDPE, LDPE, PUR, EPS.PET is an exception since many plastic bottles and containers are made of PET and can be airfilled if the lid is attached, increasing the floating potential 25 .Schwarz et al. 24 assumed only 89% of PET macroplastics sink, while the rest are either transported, beached, or remain afloat.Kaandorp et al. 26 estimated that 8-12% of plastics in the Mediterranean Sea remained afloat, 49-63% was beached, and 37-51% have sunk.We assume the same fractions are followed for plastics in the ocean and freshwater, except that no plastics remain afloat in freshwater.Furthermore, Hurley et al. 27 found that 70% of stored microplastics in riverbeds get flushed out to the marine environment during flooding events.We assume 70% of all plastics (micro and macro) stored in freshwater sediments are to be flushed into marine environments regardless of the polymer type.The release of plastics from terrestrial compartments to the aquatic environments is possible, especially through flooding events. 28owever, due to lack of evidence this pathway has been neglected in this model.

S4 Product lifetimes
The lifetimes of individual product categories were taken from Abbasi et al. 1 with no adjustments.For tires, a mean lifetime of 4 years is assumed. 21Flushed products are assumed to have a lifetime similar to packaging products, while cigarettes are assumed to be similar to "other plastics" product category.

S5 Combined lifetime-leaching approach
A basic, inflow-driven dynamic model relies mainly on lifetime functions.However, not all environmental releases of plastics follow this same pattern.For example, some plastic products, such as tires and textiles, exhibit a leaching behavior during their residing time in the stocks (e.g., due to wear and tear during use).This leaching can be accounted for by applying a leaching rate to the amounts residing in the stocks.
Inflow-driven dynamic models rely mainly on lifetime functions that describe the residing time of materials in stocks, which as a result establish scheduled outflows for each individual cohort distributed over a future time period.The outflow and stocks are usually described as follows (Eq.1): Where  is the time,  is the cohort,   is the inflow for cohort ,  (,) is the lifetime dependent outflows for cohort  in time ,  (,) is the mass stored in stocks for cohort  in time ,  (,) is the probability density function (for the cohort c of exiting the stock at time u), and  (,) is the survival function.
A leaching model is calculating outflows from the stock, usually using a leaching rate constant over time and cohorts (  in Eq. 3):

S16
These equations were discretized to consider time steps of one year.To account for the amounts lost due to leaching, a correction factor was applied to the lifetime dependent outflows and stocks: (,) =   × (1 −   ) − ×   ×  (,) (6)   Or   (,) =   ×  (,) (7)   Where   is the annual leaching rate,   (,) is the lifetime dependent outflows for cohort  during year ,   (,) is the leaching outflows for cohort  during year .

S6 Input data
Plastic input data were estimated using the methodology presented by Kawecki et al. 29 Trade quantities for plastic products were calculated using the harmonized system (HS) data provided by Statistics Norway (Statistisk sentralbyrå (SSB)) 30 by taking the net import for 2000 to 2020.The plastic content of LDPE, HDPE, PP, PS, PVC, EPS, and PVC were taken from Abbasi et al., 1 while the shares of PUR, PA, PC, and ABS were taken from Klotz and Haupt. 31A matrix showing the polymer content in these traded quantities for all studied polymers can be found in SI2.
The polymer composition for packaging, automotive, electrical and electronic equipment (EEE), tires, flushed products, and cigarettes were calculated separately.

S6.1 Packaging, EEE and automotive
We used data from PlasticsEurope for 2020 32 to estimate the polymer composition in traded quantities in packaging, electrical and electronic equipment (EEE) and automotive plastics, shown in Table S11.Additionally, the plastic share of packaging mass that is traded alongside goods was adjusted to 0.76% according to Kawecki et al. 29 instead of the previously used lower end share value of 0.38% in Abbasi et al. 1 Table S11.Full breakdown of plastic demand per polymer in all sectors in Europe. 32ckaging

S6.2 Tires
Tires can be imported as individual parts or alongside vehicles.For passenger cars, tires make up 3% of the total vehicle mass, and 5% of trucks. 33The net import of tires as parts and the tires in vehicles and trucks were calculated using the relevant HS codes that can be found in SI2.On average, a tire consists of 40 -60% rubber (natural and synthetic). 20,34We neglect the difference between natural and synthetic rubber in this study.

S6.3 Flushed products
Products at high risk of flushing include personal care and hygiene products.Kawecki and Nowack 4 presented a list of items using evidence from previous studies, and they estimated their polymer composition and consumption figures using a bottom-up approach in Switzerland.The derived input data for this model, which were adapted for this study.can be found in the SI2.

S6.4 Cigarettes
Cigarette filters contain cellulose acetate (CA).We assume that filters make up 35% of the cigarette total mass and contain 90% of cellulose acetate while the remaining 10% are additives.The HS codes for cigarettes can be found in SI2.

S6.5 Fishing gear
We assumed the distribution of polymers in the traded quantities according to Deshpande et al., 12 see Table S12.
Table S12.Distribution of plastic polymers in traded fishing gear.

S7 Plastic additives quantification
The mass of additive is calculated as follows (Eq 7): Where   is the total mass of additive,   is the total mass of plastic polymer, and Concentration additive is the concentration of additive in the polymer matrix.

S9. 1 S9. 2 S9. 3 S9. 6 S9. 7
Figure S1.Components of the Material Flow Analysis (MFA) model from Abbasi et al. 1 and modified for this study to include the pathways for plastic leakage to the environment.Stocks are depicted in blue.Green arrows: environmental flows.ASR: auto-shredder residues; C&D: construction and demolition; EEE: electrical and electronic equipment; ELB: end-of-life boats; ELV; end-of-life vehicles; HH: household; Ind.: industrial; WEEE: waste of electrical and electronic equipment.

Figure S3 .
Figure S3.Leakage pathways for lifetime dependent microplastic outflows with all relevant processes employed in the Material Flow Analysis (MFA) model.ASR: auto-shredder residues; CSO: combined sewer overflow; C&D: construction and demolition; OSSF: on-site sewage facilities; PWT: primary water treatment; SWT: secondary water treatment; Text.: textiles; TWT: tertiary water treatment; WEEE: waste of electrical and electronic equipment; WWTP: wastewater treatment plant.S3.2.1.2.1.1Microplastics from personal care and cosmetic products knotted fishing nets of man-made textile materials (excl.landing nets) twine, cordage, rope or cable, by the piece or metre; madeup nets, of man-made textile materials (excl.made-up fishing nets, hairnets,

Figure S6 .
Figure S6.Annual plastics entering use per A) application sector, and B) polymer type between 2000 and 2020.

Figure S7 .
Figure S7.Annual plastics in-use stocks per A) application sector, and B) polymer type between 2000 and 2020.

Figure S8 .
Figure S8.Annual plastics leaving use per A) application sector, and B) polymer type between 2000 and 2020.

Figure S10 .
Figure S10.Annual plastics A) entering use, B) in-use stocks, and C) leaving use, distinguished for the polymer type between2000 and 2020 for the agricultural sector.

Figure S12 .
Figure S12.Annual plastics A) entering use, B) in-use stocks, and C) leaving use, distinguished for the polymer type between2000 and 2020 for the automotive sector.

Figure S14 .
Figure S14.Annual plastics A) entering use, B) in-use stocks, and C) leaving use, distinguished for the polymer type between2000 and 2020 for the textiles sector.

Figure S16 .S9. 3
Figure S16.Annual plastics A) entering use, B) in-use stocks, and C) leaving use, distinguished for the polymer type between2000 and 2020 for other plastics sector.

Figure
Figure S18.A) Absolute emitted mass (kt) of microplastics in 2020 for individual product categories to the environmental sinks and B) emission factors (%).Emissions factors calculated as the total inflow into each environmental sink divided by the totaloutflow leaving the stocks for each product category.

Figure
Figure S19.A) Absolute emitted mass (kt) of macroplastics in 2020 for individual product categories to the environmental sinks and B) emission factors (%).Emissions factors calculated as the total inflow into each environmental sink divided by thetotal outflow leaving the stocks for each product category.

Figure S20 .
Figure S20.Cumulative plastic release of A) macroplastics and B) microplastics per receiving environmental compartmentbetween 2000 and 2020.

Figure S21 .
Figure S21.Cumulative plastic release of A) macroplastics and B) microplastics per polymer type between 2000 and 2020.

Figure S25 .
Figure S25.Maximum potential inflow amounts of the top 15 plastic additives per polymer type in 2020 to A) Environmental sinks, B) Recycling and reuse sinks, C) Landfill, D) Export, and E) Incineration.

Figure S26 .
Figure S26.Source of total additive amounts to A) Environment, B) Recycling and reuse, C) Landfill, D) Export, and E)Incineration.

Figure S27 .
Figure S27.Polymer types associated with the total additive amounts to A) Environment, B) Recycling and reuse, C) Landfill, D) Export, and E) Incineration.

Table S2 .
Detailed description of the environmental sinks considered in the MFA model.

Table S3 .
Assigned product categories due to the different naming between Liu and Nowack 2 and this study.

Table S4 .
Adjusted fraction of items consumed on the go per polymer with regards to the methodology presented by Kaweckiand Nowack 4 .
. Household waste generation in 2007 and 2018 in Trondheim.

Table S6 .
Derived high and low flushing probabilities per flushing product.

Table S7 .
Number of lifetime washing cycles, mean lifetime, and the derived number of washing cycles used in this study.

Table S9 .
7 summary of annual leaching rates derived and used in this study.Microplastic release to the marine environment and freshwater Since 92% of the population live within 50km from the coastline,7we assume 92% of this fraction is released into the ocean, while the rest is released to freshwater.

Table S10 .
Transfer coefficients for the redistribution in the aquatic compartments.

Table S14 .
Comparison of plastics entering use, in-use stocks, and leaving use per application sector and polymer type in 2020.

Table S15 .
39mparison of plastic flows in the anthroposphere using the results of this study and previous studies.Obtained using LDPE, HDPE, PP, PS, EPS, PET, PVC and the Norwegian population. 38*Derived using a total loss of 706 ± 161 kt and a population size of 8.19 million in 2014 in Switzerland.39 *****Equivalent to the outflows released from the stocks and excluding pre-consumer wastes.****Obtained using all 13 polymer types from this study.

Table S16 .
Comparison of plastic released to the environment using the results of this study and previous studies.Derived using a total loss of 491 ± 206 t and a population size of 8.51 million in 2018 in Switzerland. 39**Derived using a population size of 1.411 billion in 2020 in China. 42S36 *

Table S17 .
39mparison of additives emissions using the results of this study and previous studies.Derived using a population size of 1.411 billion in 2020 in China. 42*Derived using a population size of 126.26 million in 2020 in Japan. 42**Derived using a population size of 8.63 million in 2020 in Switzerland.39 *