As a prerequisite to integrate the plastic-related elementary flows into LCIA, a convention for defining plastic emission types is proposed (cf. “Sect. 2.1”). Then, FFs are calculated per plastic emission type based on the following elements:
The FF of a plastic emission (characterized by a particular polymer type, size, and shape and initially released into a particular environmental compartment) is determined by the final compartment share after a possible redistribution and the expected degradation times in those compartments compared to a reference degradation time, which is set to 1 year in our methodology. We chose this reference time since plastics degrade at different rates in different environmental compartments. Moreover, by choosing a reference time we avoid uncertainties related to the measurement of the degradation of a certain plastic. The resulting FF is expressed as kg plastic pollution equivalent (PPe) per kg plastic emitted. The FF allows for a comparison of various plastic emissions and enables assessing emissions to different compartments by considering the different degradation rates.
Since degradation rates vary in different compartments, ideally, various environmental compartments should be considered, such as the marine environment (eulitoral, pelagic, benthic), freshwater systems, marine and river sediment, soils, and air. However, since the knowledge about the transfer rates and degradation rates of plastic items in different compartments is currently very limited, we propose to consider plastic emissions exclusively into the initial compartments fresh or marine water, soil, and air, and redistribution only to the final compartments marine water, marine and river sediment, and soil, as a first step.
The requirements regarding the definition of elementary flows and initial compartments and the materials these requirements are based upon are outlined in “Sect. 2.1.” “Sect. 2.2” explains the patterns underlying plastic redistribution in the ecosphere based on polymer-specific and generic research regarding transport processes in the environment. The calculation of the residence time is dependent on polymer and compartment specific degradation rates extracted from a comprehensive literature review and equations developed by the authors to describe the persistence of plastic emissions in the environment. Details regarding the materials used and the formulas derived can be found in “Sect. 2.3.” “Sect. 2.4” explains how specific surface degradation rates are calculated based on the degradation model. Finally, “Sect. 2.5” illustrates the data quality assessment applied to the literature-based data and its implications for further use.
Defining elementary flows and initial compartments
Elementary flows are used to describe a plastic flow from the technosphere into an environmental compartment of the ecosphere. For each elementary flow, it is necessary to quantify the initial release rate of the corresponding plastic. Following the definition of Edelen et al. (2017), the initial release is the quantity of plastic emissions that leaves the technosphere and enters the ecosphere. Examples of plastic losses that directly enter the ecosphere are lost fishing nets in the sea, the burying of mulch films, or other plastic applications in an open environment, such as geotextiles which are not removed. However, the challenge is that the boundaries between the technosphere (e.g., streets or sewage systems) and the ecosphere (e.g., soil or freshwater) are often unclear (Maga et al. 2020). In this paper, we differentiate between technical flows like microbeads in wastewater, environmental flows addressing the initial release, such as microplastics directly emitted to agricultural soil, and redistribution flows which occur between different environmental compartments. Figure 1 presents the distinction between these three flow types and the boundaries between the technosphere and the ecosphere made in this paper. It is visualized with a simplified model that shows the possible pathways of plastic emission from the point of loss to sinks. Redistribution flows that are assumed to have a higher probability are displayed in bold, those with a smaller likelihood are thinner.
The initial compartment is the environmental compartment where a plastic item is first emitted from the technosphere. For example, during a picnic in the park, plastic cutlery might be emitted onto urban soil. Another example is the emission of plastic microbeads, which can be found in some cosmetics. They most likely reach a wastewater treatment plant as part of the wastewater, where they are either retained and later partially emitted onto agricultural soil as part of sewage sludge or pass the treatment process and are emitted to freshwater. Since degradation speed and transport processes between environmental compartments are country-specific, e.g., dependent on soil and water temperatures or the ratio of water to land, region-specific elementary flows should be defined and characterized, where possible.
Besides the initial compartment, the polymer type, shape, and size of plastic emissions influence transport characteristics and degradation speed. Therefore, these attributes need to be included in the definition of elementary flows. The size, shape, and material type are crucial parameters concerning potential effects (de Ruijter et al. 2020). Regarding the shape, the emission can be characterized as a film, a fiber, or a nearly spherical pellet or particle. To simplify, larger plastic items such as bags or cutlery are considered formed film in this publication. The characteristic length refers to the emission’s diameter (fiber, particle) or thickness (film). As shown in “Sect. 2.3,” the shape and characteristic length of an emission and the environmental compartment to which the emission is finally redistributed strongly influence its degradation time. Therefore, these attributes should be part of the definition of the elementary flow. Ogonowski et al. (2016) have shown for Daphnia magna that plastic items’ shape is relevant for exposure and potential impacts. Likewise, Ziajahromi et al. (2017) found differences in effects on the water flea Ceriodaphnia dubia between beads and fibers. Although the knowledge about the influence of the shape of plastic emissions on adverse impacts in organisms is limited to date, the shape might also be relevant to address the potential effects of plastic emissions more in detail in the future.
The naming of the elementary flow, therefore, should include first the region, second the material type (including specification, e.g., rigid vs. foam), third the shape of the plastic emission (film, fiber, or particle), fourth the characteristic length of the emitted plastic item. Fifth, according to Edelen et al. (2018), the initial environmental compartment into which the plastic is emitted should be part of the definition.
In order to cover the majority of possible plastic emissions, we propose to differentiate between the following three ranges of characteristic lengths as a proxy: < 0.1 mm, 0.1–1 mm, and > 1 mm. These size classes address the range of the characteristic length of films, fibers, and particles which are typically released to the environment either as microplastic or as macroplastic emissions. As a conservative assumption, to not overestimate the degradation rate, each residence time (cf. “Sect. 3”) is calculated using the maximum characteristic length of the respective class. For the class of the largest emissions, a characteristic length of 10 mm is used. When calculating a specific well-known plastic emission’s FF, the exact characteristic length should be used instead (cf. “Sect. 2.3”).
Some frequently used LCA processes, such as a transport process via truck, result in various plastic emissions such as tire wear and abrasion of road markings. These plastic emissions should be treated as different flows. Besides, if a plastic emission consists of various polymers on a single-particle level (e.g., tire wear consists of natural rubber and synthetic rubber), it should be treated as one flow. In this case, degradation data should be used that reflects the degradation behavior of this specific emission type. If degradation rates are unavailable for this specific emission type, the degradation rate of the slowest degrading polymer type of the complex should be used as a conservative estimation.
Various approaches to estimate the initial release of macro- and microplastics exist (Maga et al. 2020), e.g., Kawecki and Nowack (2019) for Switzerland and Peano et al. (2020) and Boucher et al. (2020) for other countries.
Estimation of redistribution between environmental compartments
In order to estimate the redistribution of an emission between different environmental compartments, as presented in Fig. 1, several research papers addressing the fate of plastics were analyzed. For some plastic emissions, specific data could be extracted. For instance, according to the research conducted by Unice et al. (2019) about the Seine watershed (France), tire wear particles initially accumulate on the road and are washed off by rain equally into the road runoff (water) and onto the surrounding soil. Considering the sewage system and partial re-emittance of tire wear particles as part of the sludge, only 24% of the particles are accurately managed. The rest is emitted to and redistributed in the environment with a final compartment share of 56% on soil, 13–16% in river sediment, 2–5% in the ocean, and 2% in air. However, we assume that the 2% emitted to air do not remain in air but are redistributed to soil and water, as presented in Table 1.
Table 1 Redistribution of plastic emissions to final compartments after initial release into the ecosphere For other plastic emissions, data concerning redistribution and compartment shares are unavailable. In these cases, assumptions are made based on parameters suggested in the literature, which affect the behavior of plastic emissions in the environment, such as:
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Environmental compartment initially emitted to (e.g., Kawecki and Nowack 2019);
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Density of the plastic (e.g., Kowalski et al. 2016; Nizzetto et al. 2016; Horton and Dixon 2018);
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The emission’s size and shapes (e.g., Chubarenko et al. 2016; Fazey and Ryan 2016; Kowalski et al. 2016).
Regarding the environmental compartment the plastic is initially emitted to, there is a chance that plastic items (mostly macroplastics) emitted to terrestrial environments are transported to water on the surface, e.g., by wind and rain-based erosion (Jambeck et al. 2015). The amount of plastic transferred from land into water bodies, which in most cases finally ends up in the ocean, highly depends on local conditions such as the local waste management system, climate conditions, and the proximity of the plastic waste emission to water bodies. According to the model of Jambeck et al. (2015), macroplastics initially emitted onto soil as mismanaged waste are partly redistributed to the ocean via inland waterways, wastewater outflows, wind, or tides if the plastic is emitted within 50 km of a coast. Accordingly, macroplastics emitted further away from the coast do not end up in the ocean. Although this rough estimation was only made for macroplastics, we assume the same for microplastics. No indication for other redistribution mechanisms (e.g., subsurface redistribution) from soil to other compartments could be found. Hurley and Nizzetto (2018) concluded that soil systems could store microplastics. Likewise, Fauser et al. (1999) found little downward movement for tire wear particles initially emitted onto soil, as most particles were found in the upper 1 cm of the soil, and 30 times less, only 2 cm further into the ground. This suggests that there is a very small probability of microplastics reaching groundwater through vertical movement. Bioturbation, the physical displacement of solutes and solids in soils caused by the activities of organisms, particularly by burrowing activities of earthworms, can technically lead to a downward transport in soil (Huerta Lwanga et al. 2016). However, since no quantifiable and reliable data are available for transfer rates from soil to groundwater, we neglect these mechanisms and only assume an average redistribution rate from soil to marine water of 27.5% (Jambeck et al. 2015 suggested a range of 15–40%), applied to the respective coastal population share of the analyzed region. Furthermore, we assume that once plastic items reach the ocean, the same redistribution patterns apply to plastics directly emitted into the sea.
Although the shape and characteristic length of the emission might play a role in the redistribution from soil to other compartments, there is no universal information about their influence. Therefore, soil redistribution rates to different compartments are assumed to be independent of the shape, characteristic length, emission material type, and density.
On the other hand, in water bodies, the plastic emission’s density plays a more prominent role, especially concerning the vertical movement of the emission and its proneness to sediment (Chubarenko et al. 2016; Kowalski et al. 2016). Depending on the density of the plastic ρp compared to the density of the water ρw, the plastic item might float (ρp < ρw), stay in the water column (ρp \(\approx\) ρw), or sink to the sediment (ρp > ρw). When Sanchez-Vidal et al. (2018) analyzed 29 sediment samples collected from southern European seas, most fibers found were polymers with higher densities, such as polyester, acrylic, and polyamide. We assume that plastic emissions with a density greater than or equal to that of water ultimately sink and become part of the respective water body’s sediment (river or marine sediment). Emissions with a density smaller than that of water float and therefore remain in the water. We assume that initial plastic emissions to freshwater bodies, such as rivers, with a density below that of freshwater, are transported on the water surface and ultimately reach the sea. Therefore, we do not consider freshwater as a final compartment. Although it might be possible for plastic items with a density below that of freshwater, which are emitted into a water body without connection to a flowing water body, to remain in that freshwater body, we assume this neglectable when determining generic distribution rates.
Although, polymers with lower densities than water can also sink and, ultimately, sediment, for example, through turbulence, (bio-)fouling, or heteroaggregation with suspended solids (Besseling et al. 2017), we neglect these mechanisms, because defouling might occur, which might resuspend the emission, creating a loop of sinking and suspending over time (Ye and Andrady 1991).
According to Fazey and Ryan (2016) and Chubarenko et al. (2016), smaller plastic emissions and those with a high surface area tend to sink faster as they are more susceptible to biofouling due to their surface area-to-mass ratio. On the other hand, water turbulence, e.g., by wind or currents, increases the vertical movement, especially of microplastics in the water (Kooi et al. 2016; Lebreton et al. 2018). Since clear assignments are impossible, the redistribution rates from fresh and marine water to the river or marine sediment do not consider the emissions’ size and shape.
Like Kawecki and Nowack (2019) and Peano et al. (2020), we assume that all plastics emitted to air are deposited onto soil or water, with compartment shares dependent on the water to land surface ratio. They are further redistributed in the same way as plastics directly emitted into these compartments.
Since we assume that transport velocities between the compartments are relatively high compared to the degradation times (especially transport by air and in running waters), any degradation occurring during the redistribution is not considered. For example, water within the river Rhine only takes a few weeks to travel from its source at Tomasee (Switzerland) to its delta at Hoek van Holland in the Netherlands. Due to a lack of available data, a possible recollection from environmental compartments into the technosphere, e.g., by beach cleanups, is not considered. Most assumptions presented in “Sect. 2.3” are generic and can be applied in the same way globally and to specific countries. The redistribution of items emitted to soil and air, however, is country-specific because the water to land surface ratio differs per country. The FF presented in SM3 are given for Germany as an example. They may be adapted to suit other regions.
Calculation of degradation rates, total lifetimes, and residence times
In order to determine the degradation rates of different polymers, a comprehensive literature review was conducted. As presented in Fig. 2, 146 research papers were identified from peer-reviewed journals accessible via the search engines Web of Science, ScienceDirect, and Google Scholar based on keywords such as “plastic,” “fate,” “degradation,” “depolymerization,” “mineralization,” “mass loss,” and “impact.” Following a snowball sampling approach, research papers quoted in the identified publications were also considered. For polymers for which no sufficient data could be obtained via the described method, research papers were searched applying the same approach, adding into the search term that specific polymer.
Research papers that did not disclose all necessary information, e.g., regarding the shape and characteristic length of the investigated plastic item, were excluded. Besides, only studies were taken into account where degradation measurements were based on either weight loss, biochemical oxygen demand, or the amount of CO2 formed during the degradation. Studies examining material property changes, such as tensile strength or crystallinity, were left out as there is no available correlation to material loss. Only for polymers for which no data are available concerning the described measurement methods, studies were taken into account that measured viscosity at higher temperatures and relied on Arrhenius projection to deduct degradation speed at temperatures found in nature. The few degradation studies focusing on other environmental compartments and pure laboratory studies under artificial conditions were ruled out.
The data found pertain to many different polymer types, including both fossil-based and biobased polymers. Some fossil-based polymer types are commonly assumed not to be biodegradable (ASTM D7611 standard codes 01–06) and are referred to in this study as conventional fossil-based polymers. Nevertheless, as explained further below, we do assume a slow degradation of these polymers. We refer to polymer types of ASTM D7611 code 07 (other) as either biodegradable fossil-based polymers or biobased polymers, depending on their source of material.
For some polymers and compartments, several data sets from one or more publications were available. If any of these data sets did not indicate any degradation, but others for the same polymer and compartment did, those without degradation measurements were excluded, which was considered a measurement error or an insufficient accuracy of the measurement device. For the same reason, data sets that did not indicate any degradation, but were the only data sets available for the respective polymer and compartment, were set to an SSDR of 0.001 µm per year, as further calculations would be impossible with an SSDR of 0 µm per year. The chosen value is slightly lower than the lowest SSDR measured that was unequal to zero to not overestimate degradation for those polymers and compartments.
Since data availability for various environmental compartments is limited, we only differentiate between degradation in soil, river and marine sediment, as well as marine water at this stage of work. As investigated by Lott et al. (2020, 2021) for polyhydroxyalkanoate copolymer (PHA) in eulitoral, pelagic, and benthic habitats of the Mediterranean Sea and Southeast Asia (Pulau, Bangkam Sulawesi), there are relevant differences in degradation rates. Degradation was observed to be faster in the benthic zone compared to the pelagic zone. The region, however, had the greatest influence on the degradation time. Degradation rates of PHA films in SE Asia were observed to be higher than in the Mediterranean Sea. While degradation rates for different regions are generally not available yet, we distinguish between the marine water body and marine and river sediment.
The extracted data sets contain information regarding the investigated plastics (polymers, additives), the shape and characteristic length of the research subject, the degradation test compartment, whether the degradation conditions could be considered natural, measured degradation, and the time span of the experiment. Data extracted from research papers that did not indicate having examined plastics with additional additives to enhance biodegradation were marked as “no enhancing additives.” Nevertheless, it can be assumed that these plastics include typical additives such as plasticizers, antistatic agents, flame-retardants, or UV stabilizers that are indifferent to or even reduce the degradability. However, the knowledge about types and quantities of additives might be relevant for future integration of more realistic degradation rates and additional ecotoxicity impact assessments.
As a result, 38 studies concerning 172 data sets for various polymer types and the environmental compartments marine water, marine sediment, river sediment, and soil under natural or near-natural conditions and without additional additives to influence degradation were used for calculating degradation rates. Data for degradation in soil include values measured during experiments with compost under near-natural conditions. Many studies, especially concerning conventional fossil-based polymers, did not last long enough to reach a significant degradation. In these cases, the value at the last measuring point is taken. In cases where experiments lasted long enough to reach a degradation of more than 50%, the value at the measuring point closest to 50% degradation is taken.
As mentioned before, the residence times depend on (1) the polymer type, (2) the shape of the plastic item, (3) the initial size of the investigated item, and (4) the environmental compartment where the degradation takes place. Following Chamas et al. (2020), three assumptions are made:
-
(a)
The degradation mainly happens in the top layer at the surface of the emitted item (Fig. 3) (cf. Ohtake et al. 1998).
-
(b)
A specific surface degradation rate (SSDR) vd can be defined that depends on the type of plastic and the environmental compartment the degradation takes place.
-
(c)
vd is assumed to be constant during the entire time of degradation.
Naturally, these assumptions are simplifications: some polymers will show degradation in the bulk material or might be eroded in part by mechanical influences. However, also following Chamas et al. (2020), we assume that surface degradation is the factor that ultimately determines the amount of time needed for a plastic emission to vanish.
The initial plastic item is eroded from the overall outer surface. Therefore, the characteristic length dt reduces over time t by twice the degradation rate vd, irrespective of the item’s shape (Fig. 3). Only for hollow items (e.g., closed bottles), this might not be true initially. However, it can be assumed that these items fracture quickly.
Films are considered to degrade at the main surfaces A (from both sides) only, fibers are considered to be cylinders whose length L does not reduce significantly over time, and particles are regarded as spheres. As illustrated in Fig. 4 and Eq. (2), the characteristic length dt at a point in time t refers to the film’s thickness or the fiber or particle’s diameter, respectively.
$${d}_{t}={d}_{0}-2{v}_{d}t$$
(2)
From this equation, the total lifetime \({\tau }_{L}\) of the emission until the polymer is completely degraded can directly be calculated by setting dt = 0:
$${\tau }_{L}=\frac{{d}_{0}}{2{v}_{d}}$$
(3)
The total lifetime only depends on the initial size and the specific surface degradation rate and is independent of the shape of the emission due to our degradation model chosen. Nevertheless, the persistence of a specific plastic emission depends not only on this total lifetime but also on the temporal degradation behavior. This temporal degradation behavior depends on the shape because even with a constant SSDR, the velocity of mass degradation varies over time due to a change of the surface-to-volume ratio. Hence, we introduce the residence time \({\tau }_{R}\) as measure for the persistence of plastic emissions in the environment (see below). The degrading volume Vt of a particular plastic emission at time t is calculated depending on its shape:
$$\begin{array}{c}\;\;\;{{V}_{t}}_{film}=A{d}_{t}^{1}\\\;\;\;\; {{V}_{t}}_{fiber}=\frac{\pi L}{4}{d}_{t}^{2}\\ {{V}_{t}}_{particle}=\frac{\pi }{6}{d}_{t}^{3}\end{array}$$
(4)
Here \(A\) is the surface area of the foil and \(L\) the length of the fiber. In general, the volume can be calculated by a constant and the characteristic length to the power of a:
$${V}_{t}=const. {d}_{t}^{a}$$
(5)
where a equals 1 for infinite films, 2 for fibers, and 3 for particles, respectively. Particles are idealized as spheres. However, assuming particles as cubes would lead to the same result. Nevertheless, irregular shapes of three-dimensional items may be approximately reflected by using a different constant or power in Eq. (5). As long as the constant and power a in Eq. (5) stay approximately constant during the item’s degradation, they cancel out in the following calculation. Combining Eqs. (2) and (5) leads to the emission’s remaining volume Vt at a particular time concerning the initial volume \({V}_{0}\).
$$\frac{{V}_{t}}{{V}_{0}}={\left(\frac{{d}_{t}}{{d}_{0}}\right)}^{a}={\left(1-\frac{2{v}_{d}t}{{d}_{0}}\right)}^{a}={\left(1-\frac{t}{{\tau }_{L}}\right)}^{a}$$
(6)
Assuming a constant density, the same relation holds for the masses of the emission (cf. Fig. 5):
$$\frac{{m}_{t}}{{m}_{0}}={\left(\frac{{d}_{t}}{{d}_{0}}\right)}^{a}={\left(1-\frac{2{v}_{d}t}{{d}_{0}}\right)}^{a}={\left(1-\frac{t}{{\tau }_{L}}\right)}^{a}$$
(7)
The environmental impact according to our approach can be calculated by integrating the curve function of the actual dimensionless fraction of the remaining mass: the dimension of this quantity is time and it will be called residence time \({\tau }_{R}\) (explanation see below):
$${\tau }_{R}={\int }_{0}^{{\tau }_{L}}{\left(1-\frac{t}{{\tau }_{L}}\right)}^{a}dt=\frac{1}{a+1}{\tau }_{L}$$
(8)
Hence, the residence time \({\tau }_{R}\) of a film, fiber, or particle is:
$$\begin{array}{c}{\tau }_{R}=\frac{1}{2}{\tau }_{L},\;\mathrm{ for\; film}\\\; {\tau }_{R}=\frac{1}{3}{\tau }_{L},\;\mathrm{ for \;fiber}\\\;\;\;\;\;\; {\tau }_{R}=\frac{1}{4}{\tau }_{L},\;\mathrm{ for\; particle}\end{array}$$
(9)
As shown in Fig. 5, the velocity of mass degradation of films is constant, resulting in a linear reduction of mass, while for fibers and particles, the degradation is faster in the beginning and slower at the end. This results in a higher residence time \({\tau }_{R}\) for films than for particles at similar life time Eq. (9).
Figure 6 shows the residence time \({\tau }_{R}\) of a particle. In this case, the residence time is 75 years. In contrast, the point in time at which 50% of the mass is degraded (half-lifetime) of the particle would be slightly lower with 61.9 years. The name residence time was chosen, because during the total degeneration process mass will continuously vanish and the average age of this leaving mass is equal to the residence time introduced. Furthermore, the residence time can be interpreted as that time a non-degradable emission would have to stay in the environment to give the same impact: in Fig. 6, the gray box has the same area as the integral below the degradation curve.
The consideration of time horizons \({\tau }_{H}\) is a common practice in LCIA (Hauschild and Huijbregts 2015). When calculating FFs (“Sect. 3.3” and supplementary material), time horizons of 100, 500, and 1000 years are applied. Both a 100- and 500-year time horizon are commonly used for other environmental impact assessments, e.g., global warming potential. The longer time horizons allow for greater differentiation between hardly degradable polymers. By selecting a short time horizon, e.g., 100 years, FFs will only differ when emissions degrade faster than 100 years while polymers with life times of, e.g., 500 years, 10,000 years, or 50,000 years will all obtain an residence time close to 100 years. This might encourage politicians and the industry to focus on fast degradable polymers if resulting emissions into the environment are hardly avoidable. When applying a time horizon, the integration is performed until the time horizon is reached and Eq. (8) becomes:
$${\tau }_{R,{\tau }_{H}}={\int }_{0}^{{\tau }_{H}}{\left(1-\frac{1}{{\tau }_{L}}\right)}^{a}dt=\frac{{\tau }_{L}}{a+1}\left(1-{\left(1-\frac{{\tau }_{H}}{{\tau }_{L}}\right)}^{a+1}\right)\mathrm{ for }{\tau }_{L}>{\tau }_{H}$$
(10)
This means, as illustrated in Fig. 7, by applying a time horizon, only the area inside the time horizon is considered (blue area), while everything after the time horizon is omitted (gray area).
The ratio of \(\tau\) R and \(\tau\) H ranges between 0 and 1 and measures the “occupation” of the time horizon. However, the results need to be interpreted cautiously: the residence time in a time horizon is always smaller than the residence time without a time horizon. Especially durable polymers like PVC with residence times greater than 1000 years without considering a time horizon might appear more favorable than they are when interpreting the residence time with a short time horizon (e.g., 100 years). Consequently, the residence time must always be interpreted relative to the time horizon considered. If the value of the residence time is close to the value of the time horizon, very little degradation occurs during this time horizon. The equations obtained (8 and 10) hold for the degradation models chosen. However, the approach can be easily adapted to other degradation mechanisms (e.g., Junker et al. 2016) as long as the degradation curves are known.
Another derivation of the residence time and the FF as measure of the environmental impact is shown in Fig. 8. Assuming a constant yearly flow \(\dot{m}\) there is only a partly degeneration in the first year. After 1 year, the remaining amount is transferred to the second year and a fresh inflow will appear (and so on). The curve will have the same shape as in the calculations before. When summing up all yearly amounts by integrating the curve Eq. (9), the hold-up M, i.e., the total mass accumulated in the environment due to this emission, is calculated. The degeneration of this hold-up balances the emission flow in the steady state case. Dividing this hold-up by the emission flow a residence time is calculated, which is equal to the residence time before.
$${\tau }_{R}=\frac{M}{\dot{m}}$$
(11)
This shows vividly the equivalence of mass-flow and residence time as stated before. One unit of an emission A with a specific residence time results in the same hold-up as an emission of two units of an equally sized emission B with half the residence time of emission A. This holds for diluted, widely spreaded emissions. It is not suitable to calculate effects of local or temporal concentration hot spots.
With the residence time approach, it is straightforward to calculate the fate of an emission that is divided and transferred to different final environmental compartments. The mass of the initial release is distributed according to the transfer factors \({T}_{i,j}\) and for each environmental compartment, residence times are calculated separately. The transfer factors are the fractions of an emission i transferred to compartments j. The overall residence time is calculated as a weighted sum of the individual ones.
$${FF}_{i,tot}={\textstyle\sum_{j=1}^n}\left[T_{i,j}\frac{\tau_{R,i,j}}{\tau_{R,ref}}\right]=\sum\nolimits_{j=1}^n\left[T_{i,j}{FF}_{i,j}\right]\;\;\mathrm{with}\;{\textstyle\sum_{j=1}^n}\left(T_{i,j}\right)=1$$
(12)
In Fig. 9, an emission is divided into two compartments (30/70%) with total lifetimes of 200 and 100 years, respectively. The residence time of the entire emission is the weighted sum of the individual ones (50 and 25 years, respectively). From the residence time (32.5 years), a total lifetime of 130 years of the emission in a hypothetical compartment can be calculated by Eq. (9).
Calculation of specific surface degradation rates
The degradation model described is used to evaluate experimental results in the literature.
Experimental studies on degradation usually report the loss of mass Δm relative to the initial mass m0 during a period. In order to calculate the specific surface degradation rate vd (SSDR) of a plastic emission, Eq. (7) can be rearranged:
$${v}_{d}=\frac{1}{2}\frac{{d}_{0}}{t}\left(1-\sqrt[a]{1-\frac{\Delta m}{{m}_{0}}}\right)$$
(13)
This yields the SSDR of the experimental mass loss Δm/m0 during a period t and the given initial characteristic length d0 and shape (to determine the power a). SSDRs are calculated for each polymer type and each compartment. The SSDR values displayed in the supplementing material are based on experimental data extracted from the research papers analyzed, as explained at the beginning of this section. For polymers for which data are insufficient to calculate SSDRs, values are estimated according to the following assumptions, which have to be confirmed or improved in the future:
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Where data for only one of the environmental compartments are available, degradation is assumed to be comparable in the other three, and the same value is utilized for all four compartments.
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Where data are available for river or marine sediment but not the other type of sediment, the same value is utilized for both types.
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Where data are available for marine water and soil, but not river and marine sediment, the lower degradation rate of the two compartments, marine water and soil, is used for both sediment types as a conservative estimate not to overestimate the sediment’s degradation.
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For polystyrene (PS) and polyvinyl chloride (PVC), no data are available to calculate SSDR in any compartment. SSDR of PS and PVC are estimated to aim towards 0 (cf. Chamas et al. 2020 based on information published by Otake et al. 1995, obtained by a measurement method otherwise irrelevant to our research: through observation by phase contrast microscope and scanning electron microscopy or mere estimation). For further calculations, the SSDR for these polymers is set to 0.001 µm per year.
Data quality and uncertainty analysis
The procedure to select data for calculating FFs is based on a data quality assessment. For example, for some polymer types and environmental compartments, several studies with different degradation rates were available. The assessment of the data quality enabled the decision for the most accurate degradation rate to be used. In order to indicate the quality of the data provided in this paper, we adapted the pedigree matrix approach, which was first introduced by Funtowicz and Ravetz (1990) and was adapted by Weidema and Wesnæs (1996) for life cycle inventory data, and applied it to our input data. The pedigree matrix approach allows to assess data quality and translation to uncertainty values although a small sample size for most of the SSDRs is given. If the number of SSDRs increases or uncertainty values for SSDR measurements are provided, these values should be used instead. Since no pedigree matrix exists for degradation rates and transfer coefficients between environmental compartments, we altered the initial categories to suit the research purpose. Like Laner et al. (2016), we distinguish between experimental data and expert judgments. Scores indicate good data quality (data quality indicator score (DQIS) = 1) up to low data quality (DQIS = 4).
The quality of experimental data is affected by its reliability, completeness, temporal and geographical correlation as well as the measurement method used. For the geographical correlation, Germany is set as a reference, to match the country of the redistribution patterns, as described in “Sect. 2.3.” The quality of expert judgments depends on the foundation of the judgment, for example, on an (empirical) database, the experts’ qualification, and the transparency of the procedure by which the judgment was obtained (Laner et al. 2016).
Based on these DQIS, uncertainty scores are calculated for each input data set: transfer coefficients and degradation rates as explained in SM1. The modeler sets the size and shape of a plastic emission for each elementary flow; therefore, these parameters are assumed not to induce additional uncertainty. However, this could be the case in terms of measurement uncertainties. Nonetheless, the uncertainty induced by size and shape is assumed to be small compared to the uncertainty induced by transfer coefficients and degradation rates. For transfer coefficients, expert judgment is used to apply relevant information from existing publications to our research case and Germany’s environmental conditions. For degradation rates, where more than one data set per polymer and compartment were found, the data set with the lower uncertainty score is used for further calculations. The geometric average of SSDRs is used when more than one data set had the same lower uncertainty score. The uncertainty calculation of the FFs is done using Monte Carlo simulation based on the geometric standard deviation (GSD) and median, taking log-normal distributions for the estimates of SSDR and redistribution (Limpert et al. 2001).
In order to calculate the confidence interval of 68%, the FFs need to be multiplied by the GSD for the upper limit and divided by it for the lower limit. To calculate the confidence interval of 98%, multiply or divide the given FFs by GSD2. The Python script for the FFs’ uncertainty calculation is given in SM4 for reproducibility and traceability reasons.