The GBM-Plastics-v1.0 model (global box model for plastics, version 1.0) code is included in SI 3 as Python scripts, and in SI 2 in a Microsoft© Excel© version. It is also available via https://github.com/AlkuinKoenig/GBM-Plastics. Definitions of plastics size categories are continuously debated; here we use operational definitions of macroplastics (P, > 5 mm), large microplastics (LMP, > 0.3 mm and < 5 mm) and small microplastics (SMP, < 0.3 mm). The 0.3 mm distinction is based on the frequently used plankton net mesh size of approximately 0.3 mm. The 0.3 mm cut-off is also a reasonable starting point for the simulation of atmospheric cycling of SMP, with nearly all remote airborne SMP particles, films and 50% of fibers falling in the 1-300 μm range [5, 24]. All P, LMP, SMP reservoir sizes (i.e., inventory) and fluxes are expressed in teragrams (Tg = 10^{12} g) and Tg y^{− 1}. For some reservoirs, studies do not discern LMP or SMP, in which case we retain the generic ‘MP’ abbreviation.

LMP and SMP observations are typically expressed as MP counts per unit volume or per unit area. To estimate mass concentrations, we use, whenever reported, the full MP size distribution reported, a uniform density of 1 × 10^{− 6} μg μm^{− 3} [41], and the MP volume approximation, V = L^{3} × 0.1, where L are the reported length values of the size distribution.

We use global plastics production, 8300 Tg, and waste generation (discarded, recycled or incinerated) from Geyer et al. [3]. Produced plastics enter the ‘in-use’ pool, where they are mostly discarded within a single year due to the dominant use of single-use packaging. In 2015, 55% of non-fiber plastics are still discarded within a year, 25% incinerated and 20% recycled [3]. We assume fiber plastics to undergo similar relative discarding and incineration fates, leading to a ‘discarded P + MP’ reservoir of 4900 Tg, an incinerated pool of 800 Tg (atmospheric CO_{2}) and an in-use pool of 2600 Tg in 2015 as described by Geyer et al. [3]. Lau et al. [4] estimated the proportion of municipal solid waste that enters aquatic and terrestrial environments as primary LMP to be 14 ± 4% in 2016, which we apply here to all discarded plastics [4]. We therefore apply a primary f_{LMP} fraction of 0.14 and primary f_{P} fraction of 0.86 to estimate transfer from the in-use to discarded reservoir for the period 2050-2015. The following mass balance equations are defined for in-use and discarded pools:

$$\frac{d\left({P}_{use}\right)}{dt}={P}_{prod}-{f}_{disc}\times {P}_{waste}-{f}_{inc}\times {P}_{waste}$$

(1)

Where P_{use} is the mass of total plastic (P + LMP) in use, P_{prod} the mass of total plastics produced (Tg y^{− 1}), P_{waste} the mass of total plastic waste, and f_{disc}, and f_{inc} are the fractions of P_{use} that are discarded, incinerated and recycled.

$$\frac{d\left({P}_{disc}\right)}{dt}={f}_{disc}\times {P}_{waste}\times {f}_P-{k}_{P- river}\times {P}_{disc}-{k}_{disc P\to LMP}\times {P}_{disc}$$

(2)

Where P_{disc} is the mass of P discarded, f_{P} is the fraction of total plastic waste that are macroplastics, k_{P-river} is the transfer coefficient for P to the ocean, via river runoff.

$$\frac{d\left( LM{P}_{disc}\right)}{dt}={f}_{disc}\times {P}_{waste}\times {f}_{LMP}+{k}_{disc P\to LMP}\times {P}_{disc}-{k}_{LMP- river}\times {LMP}_{disc}-{k}_{disc LMP\to sMP}\times L{MP}_{disc}$$

(3)

Where LMP_{disc} is the mass of LMP discarded, f_{LMP} is the fraction of total plastics waste that are primary microplastics (pellets, synthetic textiles, personal care products, etc), k_{LMP-river} is the transfer coefficient for LMP to the ocean, via river runoff, and k_{LMP➔SMP} is the transfer coefficient for LMP degradation to SMP within the terrestrial ‘discarded’ pool.

$$\frac{d\left( SM{P}_{disc}\right)}{dt}={k}_{disc LMP\to SMP}\times {SMP}_{disc}-{k}_{SMP- river}\times {SMP}_{disc}-{k}_{disc- atm}\times {SMP}_{disc}$$

(4)

Where SMP_{disc} is the mass of SMP discarded, k_{SMP-river} is the transfer coefficient for SMP to the ocean, via river runoff, and k_{SMP-atm} is the transfer coefficient for SMP emission to the atmosphere from the terrestrial ‘discarded’ pool, including tire wear particles (TWP).

Transfer coefficients k_{P-river}, k_{LMP-river}, and k_{SMP-river} are calculated from 2015 plastic fluxes and inventories, e.g. k_{P-river} = P_{disc}/F_{P-river} where F stands for flux (SI 1, Table S1). The mid-point estimate for F_{P-river} of 8.5 Tg y^{− 1} [11] is used here, and subdivided into 50% P and 50% LMP [21]. The ‘discarded pool to atmosphere’ transfer coefficient, k_{disc-atm}, which theoretically equals SMP_{disc}/F_{SMP_disc-atm} is unconstrained, because the SMP_{disc} pool size, in Tg, is unknown (F_{SMP_disc-atm} is 0.18 Tg y^{− 1}, based on Brahney et al. [19], and was therefore fitted at 0.00037 y^{− 1}.

### The global ocean

Two previous box models have examined the plastics budget of the marine environment [13, 16]. In addition, a number of Lagrangian oceanic or atmospheric transport models have provided insight in marine plastics dispersal and surface ocean plastics mass balance [15, 42]. Koelmans et al. [13] used a plastics mass budget for the surface ocean to fit a marine P to LMP fragmentation rate, and a LMP sedimentation rate, under the assumption of 100% buoyant P (no settling to deep waters). To accommodate the high river plastic inputs, rapid plastic fragmentation to LMP (> 90% per year), and rapid LMP settling rates were fitted, and suggested a short plastics and LMP residence time for the surface ocean (< 3 yrs). Subsequent modeling work has investigated P and LMP beaching, resuspension in coastal waters [15, 16], marine SMP emissions [19], and P sedimentation due to loss of buyuancy [16]. Lebreton et al. [16], in their marine box model study [16], argued that observations of old plastics in the surface ocean disagree with rapid fragmentation and settling and fitted a plastics to LMP degradation rate of 3% per year, which we adopt here for the surface mixed layer (k_{Psurf-oce➔LMP} = 0.03 y^{− 1}).

Lebreton et al. [16] fitted important beaching of coastal plastics (97% per year). In the absence of a robust estimate for global beached macroplastics [43], Onink et al. [15] recently analyzed model beaching and resuspension scenarios finding at least 77% of net beaching for positively buoyant plastic debris over 5 years [15], which we adopt here in the base case as k_{P,beaching} = 0.15 y^{− 1}. Surface ocean P, LMP, and SMP equations are:

$$\frac{d\left({P}_{surf- oce}\right)}{dt}={k}_{P- river}\times {P}_{disc}-{k}_{Psurf- oce- beach}\times {P}_{oce}-{k}_{Psurf- oce\to LMP}\times {P}_{surf- oce}-{k}_{Psurf- oce\to sed}\times {P}_{surf- oce}\times {f}_{shelf}$$

(5)

$$\frac{d\left({LMP}_{surf- oce}\right)}{dt}={k}_{LMP- river}\times {LMP}_{disc}+{k}_{Psurf- oce\to LMP}\times {P}_{oce}-{k}_{LMP surf- oce\to beach}\times L{MP}_{surf- oce}-{k}_{LMP surf- oce\to shelfsed}\times {LMP}_{surf- oce}\times {f}_{shelf}-{k}_{LMP- sink}\times {LMP}_{surf- oce}\times {f}_{pelagic}-{k}_{LMP surf- oce\to SMP}\times {LMP}_{surf- oce}$$

(6)

$$\frac{d\left({SMP}_{surf- oce}\right)}{dt}={k}_{SMP- river}\times {SMP}_{disc}+{k}_{atm\to oce}\times {SMP}_{atm}+{k}_{terr\to oce}\times {SMP}_{terr}+{k}_{LMP surf- oce\to SMP}\times {LMP}_{surf- oce}-{k}_{oce\to atm}\times {SMP}_{surf- oce}-{k}_{SMP surf- oce\to sed}\times {SMP}_{surf- oce}\times {f}_{shelf}-{k}_{SMP- sink}\times {SMP}_{surf- oce}\times {f}_{pelagic}$$

(7)

$$\frac{d\left({P}_{shelf- sed}\right)}{dt}={k}_{Psurf- oce\to sed}\times {P}_{surf- oce}\times {f}_{shelf}$$

(8)

$$\frac{d\left({LMP}_{shelf- sed}\right)}{dt}={k}_{LMP surf- oce\to sed}\times {LMP}_{surf- oce}\times {f}_{shelf}$$

(9)

$$\frac{d\left( SM{P}_{shelf- sed}\right)}{dt}={k}_{SMP surf- oce\to sed}\times {SMP}_{surf- oce}\times {f}_{shelf}$$

(10)

Where f_{shelf} = 0.08, is the fraction of global continental shelf surface area, and f_{pelagic} is the fraction of open ocean surface area. Subsurface ocean equations are:

$$\frac{d\left(L{MP}_{deep- oce}\right)}{dt}={k}_{LMP- sink}\times L{MP}_{surf- oce}\times {f}_{pelagic}-{k}_{LMP\to SMP}\times {LMP}_{deep- oce}-{k}_{LMP deep\to deepsed}\times {LMP}_{deep- oce}$$

(11)

$$\frac{d\left({SMP}_{deep- oce}\right)}{dt}={k}_{SMP- sink}\times {SMP}_{surf- oce}\times {f}_{pelagic}+{k}_{LMP\to SMP}\times L{MP}_{deep- oce}-{k}_{SMP deep\to deepsed}\times {SMP}_{deep- oce}$$

(12)

$$\frac{d\left({P}_{beach}\right)}{dt}={k}_{P- beach}\times {P}_{surf- oce}-{k}_{P\to LMP}\times {P}_{beach}$$

(13)

$$\frac{d\left({LMP}_{beach}\right)}{dt}={k}_{LMP- beach}\times {LMP}_{surf- oce}+{k}_{P\to LMP}\times {P}_{beach}$$

(14)

$$\frac{d\left({LMP}_{deep- sed}\right)}{dt}={k}_{LMP- sed}\times {LMP}_{surf- oce}\times {f}_{pelagic}$$

(15)

$$\frac{d\left({SMP}_{deep- sed}\right)}{dt}={k}_{SMP- sed}\times {SMP}_{surf- oce}\times {f}_{pelagic}$$

(16)

Estimation of shelf sediment, deep sediment and beached P, and MP, based on reviews of literature data reporting MP counts per surface area and particle size statistics, is relatively straightforward. The beached MP pool is estimated at 0.5 Tg, based on the global surface of sandy beaches (2.63∙10^{5} km^{2}; [28]), a median global beach sand MP abundance of 2450 MP km^{− 2} (IQR, 613 – 2700), and median MP size of 2.0 mm (IQR, 1.1 – 3.8) [29]. Reviews of deep ocean MP and shelf sediment MP pools report numbers of MP counts per mass unit, which leads to more intricate pool mass estimates: Barrett et al. [31] reported mean deep sediment MP concentrations of 0.72 MP g^{− 1} for cored and grab sediment samples of 9 cm depth. Deep sea sedimentation rates are typically on the order of 0.1-1 cm per 1000 years, suggesting that the majority of such composite sediment samples pre-date the plastics mass production period < 1950. Yet, the measurement (0.72 MP g^{− 1}) is expressed relative to the bulk of the composite sample mass, representing on average 9 cm of deep sea sediment [31]. In this case we used the following data to estimate the global deep sea MP pool mass: depth in cm, dry sediment bulk density of 1.37 g cm^{− 3}, a water to sediment mass ratio of 3.0, the mean MP size of 0.1 mm reported [31], a MP density of 1 × 10^{− 6} μg μm^{− 3}, and an open ocean seafloor surface area of 3.36 × 10^{8} km^{2}. Similarly; the shelf sediment MP pool is estimated from subtidal sediment median MP concentrations of 100 MP kg^{− 1} (IQR, 32-120), reviewed and reported by Shim et al. [29], a corresponding median MP size of 2.0 mm (IQR, 1.1 – 3.8), a dry sediment bulk density of 1.37 g cm^{− 3}, a typical shelf sedimentation rate of 1 mm y^{− 1}, 65 years of MP accumulation (1950 – 2015), a water to sediment mass ratio of 3.0, and a shelf seafloor surface area of 3.53 × 10^{7} km^{2}. The final estimates for the deep ocean and shelf sediment MP pools are 1.5 Tg and 65 Tg (1σ, 21 to 78Tg) respectively. We acknowledge that plastic litter concentrates in given areas of the seafloor, and therefore, sediment sampling data could be biased depending on the sampling site. This is ultimately reflected in the large budget uncertainties.

### The global atmosphere

Brahney et al. [19, 24] estimated the global atmosphere to contain 0.0036 Tg of SMP. They also estimated global emissions from roads, 0.096 Tg y^{− 1}, agricultural dust, 0.069 Tg y^{− 1}, population dust, 0.018 Tg y^{− 1}, and oceans, 8.6 Tg y^{− 1}, which we adopt here. Atmospheric SMP deposition to remote terrestrial surfaces has been investigated by Allen et al. [5] in France, finding a median SMP deposition of 0.011 Mg km^{− 2} y^{− 1}, and by Brahney et al. [24]. who observed a median of 0.0012 Mg km^{− 2} y^{− 1} in the western USA. Similar sampling and analysis techniques were used, and similar SMP particle and fiber size distributions found, suggesting that the 9x difference reflects the difference in population density of both areas, 100 inhabitants per km^{2} in SW Europe vs. 16 per km^{2} in the western USA. In (sub-)urban environments in Hamburg (Germany, 240 inhabitants per km^{2}) mean SMP deposition of 0.016 ± 0.006 Tg km^{− 2} y^{− 1} was observed [44]. Precursor studies on atmospheric plastics observed mostly the LMP fiber fraction (0.3 to 5 mm) with for example 0.014 Tg LMP km^{− 2} y^{− 1} in Dongguan (China) [23], but only 0.002 Tg km^{− 2} y^{− 1} in Paris (France) [22]. For simplicity we do not include LMP emission to the atmosphere in the box model, since the short residence time of LMP likely leads to immediate deposition back to the broad terrestrial discarded LMP reservoir. We regress SMP deposition over land, from the three detailed recent studies mentioned above, as a function of population density (SI 1, Fig. S1). We then extrapolate the observed relationship globally using population density and surface area data per country for the year 2015 [45], capping SMP deposition at 0.016 Tg km^{− 2} y^{− 1} based on the Hamburg observations. Doing so leads to a global SMP deposition estimate over land of 1.1 ± 0.5 Tg y^{− 1}. SMP deposition over oceans is unconstrained by observations. We assume that global SMP emissions (8.6 Tg y^{− 1}; [19]) equal deposition, and estimate SMP deposition over oceans to be 7.5 Tg y^{− 1} (total deposition of 8.6– 1.1 Tg y^{− 1} deposition over land).

The mass inventory, emission and deposition flux estimates for 2015 serve to approximate the mass transfer coefficients associated with emission, k_{oce➔atm} and deposition, k_{atm➔oce}, k_{atm➔terr}, in the following mass balance equation:

$$\frac{d\left( SM{P}_{atm}\right)}{dt}={k}_{terr\to atm}\times {SMP}_{terr}+{k}_{disc\to atm}\times {SMP}_{disc}+{k}_{oce\to atm}\times {SMP}_{surf- oce}-{k}_{atm\to terr}\times {SMP}_{atm}-{k}_{atm\to oce}\times {SMP}_{atm}$$

(17)

We assume k_{terr➔atm} to be equal to k_{disc➔atm} which was derived from the modeled discarded SMP pool and the anthropogenic SMP emission flux of 0.18 Tg y^{− 1} (sum of road, population and agricultural SMP emission) derived from the 3D global aerosol model for SMP dispersal by Brahney et al. [19].

### Remote terrestrial pool

In the box model, agricultural and urban soils are included in the discarded plastics pool. We use a separate box for remote terrestrial surfaces, outside of the technosphere, that are solely supplied by atmospheric SMP. These include pristine soils, barren rock and land, ice sheets and remote inland waters. We estimate the approximate amount of SMP in the remote terrestrial pool by making use of the quasi-linear increase in global plastics production, discard and dispersal fluxes: global SMP deposition of 1.15 Tg y^{− 1} in 2015 suggests a mean SMP deposition flux that is about half, 0.58 Tg y^{− 1} since 1965, which multiplied by a land surface area of 1.49 10^{8} km^{2} amounts to 28 Tg of remote terrestrial SMP. SMP in this pool is mobilized by rainfall to river runoff to the surface ocean, with the same k_{SMP➔river-oce} that we derived for SMP runoff from the discarded SMP pool. The remote terrestrial pool mass balance is:

$$\frac{d\left( SM{P}_{terr}\right)}{dt}={k}_{atm\to terr}\times {SMP}_{atm}-{k}_{terr\to atm}\times {SMP}_{terr}-{k}_{SMP\to river\to oce}\times {SMP}_{terr}$$

(18)

### BAU and SCS model scenarios

Both future, 2015 – 2050, model scenarios, business as usual (BAU), and systems change scenario (SCS, from Lau et al. [4]), use the same mass transfer coefficients, k, but different production, and waste management strategies summarized in the SI 2. BAU uses exponentially increasing production, and quasi-linearly increasing incineration and recycling, and decreasing discard from Geyer et al. [3]. Lau et al. [4] developed a detailed model of plastics stocks and flows from municipal solid waste (MSW) and four sources of LMP. Their CSC scenario presents the most complete, yet feasible plastics management strategy over the period 2016 – 2040 for MSW, including a decrease in plastics production by 2040 to 220 Tg y^{− 1}. We digitized their disposal (incineration + safe landfilling), recycling and discard model output (Tg y^{− 1}), expressed these as fractions of MSW production, and extrapolated these to the year 2050 to compare to BAU. To do so, we anchored (by normalization) the SCS disposal fractions for the period 2015 – 2050 to the disposal fraction for 1950 – 2015 by Geyer et al. [3], in order to maintain a relatively smooth transition. We acknowledge that the SCS waste disposal estimates deviate to some extent from the original [4] estimates, but the overall trends are preserved: SCS disposal and recycling towards 2050 increase to 24 and 66%, while discard declines to 10%. Extrapolation of current waste disposal trends under the BAU scenario leads to surprisingly similar numbers as SCS, though the real difference lies in the plastics production numbers that reach 991 Tg y^{− 1} under BAU, and drop to 168 Tg y^{− 1} in the SCS by 2050 (SI 2).

### Budget and model uncertainty

The model assumes no temporal evolution of the mass transfer coefficients, k, implying that fragmentation, sedimentation, emission, deposition and release dynamics are considered time-invariant. While we argue that to first order these processes have remained similar through time, we acknowledge that reality is more complex. As more observational and mechanistic studies become available over the next decade, more appropriate parameterizations for plastics cycling can be tested, including the fragmentation of SMP to nanoplastics and ultimately dissolved and colloidal polymers with potential biological breakdown, i.e., as an energy source to biota.

Plastics data in the literature are predominantly reported as ‘items per mass, volume, or surface area’. We converted these data to mass numbers by taking into account, where possible, the reported particle size distribution, or the reported median (or mean) particle size. In the case of fibers, reported length and diameter were used. Studies that did not report particle size properties were not included in the budget estimates. Particles were assumed to be flake shaped [46], with volume V defined as V = L^{3}*0.1, where L is the observed effective diameter, and have a mean density of 1 g cm^{− 3}. In summary, for each particle size class, reported L was used to compute flake volumes, then multiplied by particle/fiber number, and multiplied by density to obtain particle/fiber mass. The obtained masses were summed to obtain total P, LMP or SMP mass in a sample.

Table 4 summarizes 1σ (one relative standard deviation, in %) expanded uncertainties of observed P, LMP and SMP pools (Tg) and fluxes (Tg y^{− 1}), based on reported data, or conservatively approximated as 500%. The latter corresponds to a 2σ uncertainty of 1000%, which amounts to a factor 10. In other words, we consider that a large number of plastics pools and fluxes are at the moment only known to within a factor of 10. In the future, as more observations on plastics pools, fluxes and degradation become available, we will develop a formal Monte Carlo uncertainty analysis for the model.