Plastic contamination of the environment, particularly the oceans, has become a major global concern in recent years. This concern has arisen, in part, due to the longevity of many types of plastic material which has resulted in accumulation and an apparent ubiquity of plastic at sea (Welden, 2020). Evidence of plastic debris has been found in every major ocean basin (Barnes et al., 2009). The potentially harmful effects of plastic on wildlife include physical entanglement, reduced stomach capacity, intestinal blockage and internal injury following ingestion (Oehlmann et al., 2009; Eriksen et al., 2014; Sigler, 2014). It has also been suggested that plastics can enhance exposure to toxic hydrophobic organic compounds which sorb to plastic particles (Teuten et al., 2007; Chua et al., 2014) although this notion has recently been challenged (e.g., Gouin et al., 2011; Koelmans et al., 2017). In any case, the fact that plastic pollution negatively affects environmental aesthetics is uncontroversial (Sheavly and Register, 2007).

Although rivers have been recognised as major sources for marine plastic debris (Jambeck et al., 2015; Lebreton et al., 2017; Schmidt et al., 2017; Meijer et al., 2021), their exact contribution remains highly uncertain. To identify the most polluting rivers and to prioritise mitigation efforts, accurate estimates of global riverine plastic emissions are required. So far, three modelling studies have estimated this emission: Lebreton et al. (2017), Schmidt et al. (2017), and Meijer et al. (2021). In all three cases, global plastic flux was estimated from the sum of fluxes from individual catchments predicted using models which were calibrated against observations of riverine plastic flux reported in the literature. Lebreton et al. (2017) and Schmidt et al. (2017) used similar approaches to estimate catchment flux, based on river discharge and mismanaged plastic waste (MMPW) generation. They estimated the global flux range to be 1.15–2.41 Mt yr⁻¹ and 0.41–4 Mt yr⁻¹, respectively. Meijer et al. (2021) used a different approach to estimate catchment flux, based on MMPW generation, the probability of debris entering the river network, and the probability of debris transfer to the ocean. These probabilities were derived from physical factors believed to drive MMPW transfer to the coast (precipitation, wind, land use, distance to river, stream order, river discharge and distance to river mouth). This resulted in an estimated flux in the range 0.8–2.7 Mt yr⁻¹. Although similar in magnitude, the large difference between the upper and lower estimates of plastic flux in these studies reflect considerable uncertainty in model predictions. Additionally, the spatial distribution of plastic inputs was different in each study, particularly in the study of Meijer et al. (2021). They suggest over 1,000 rivers are accountable for 80% of global riverine plastic emission, compared to 47 and 5 rivers in Lebreton et al. (2017) and Schmidt et al. (2017), respectively.

Given that modelled estimates of plastic flux have been generated using some form of calibration based on field measurements, the quality of these estimates are directly affected by the quality of these field measurements. Field measurements, however, are scarce, not standardised, spatially and temporally variable and are biassed by the higher frequency of studies in North American and European rivers (González-Fernandez and Hanke, 2017; van Emmerik et al., 2018, 2019a,b; González-Fernandez et al., 2021). Research is ongoing to improve field measurements of plastic concentration (e.g., van Emmerik et al., 2018). However, relatively little is known about how plastic debris is displaced in fluvial systems and research is urgently needed. In particular, dominant modes of transport, residence times, accumulation processes (temporary and permanent) and storage zones in different reach types and under different flow regimes remain uncertain (see Figure 1, which summarises the main processes affecting macroplastic displacement in rivers). One recent study which contributes to closing these knowledge gaps is that reported by Tramoy et al. (2020), who used GPS trackers to understand the transfer dynamics of macroplastic in the River Seine and its estuary. They found that macroplastic debris moved intermittently and its residence time was much longer than the transit time of water.

The mechanisms promoting macroplastic debris displacement in rivers are analogous to those which transport sediment—suspension, saltation and traction (see Charlton, 2008). However, unlike sediment, many plastic materials are buoyant. This means they can be transported on the surface by the current and by wind (Ivar do Sul et al., 2014; Kooi et al., 2018). Displacement is likely to be controlled by a combination of factors including the specific characteristics of each river reach (hydraulic geometry, discharge, and velocity) and plastic properties (e.g., density, buoyancy, shape and size). Plastic properties may be altered by fragmentation, biofouling and other degradation mechanisms (Ryan, 2015; Kooi et al., 2018).

The transport of plastic debris can be conceptualised over a series of discrete “step” (the movement phase) and “rest” (the stationary phase) periods between sites of temporary storage (or “trapping points”). This is the same conceptualisation as for sediment transport (see Hassan et al., 1991). Trapping points can be broadly categorised as either hydraulic (trapping by flow separation structures) or physical (trapping by physical obstacles). Flow separation generates recirculation eddies, turbulence and “dead zones” of weak reverse flow (Ferguson et al., 2003), within which macroplastic debris can potentially become trapped. This often occurs where there are topographic irregularities at the channel boundary, which include undulations caused by erosion and the slumping of bank material, channel obstructions (e.g., channel bars) and meander bends (Ferguson et al., 2003; Kean and Smith, 2006). Physical traps include aquatic (instream), riparian (bankside), and overhanging vegetation, morphological features (e.g., channel bars, rough banks, and exposed boulders) and infrastructure (e.g., dams, weirs, bridges, fords, culverts, and flow deflectors). Vegetation is a potentially significant trap of macroplastic debris. In a study on the Saigon River, Vietnam, Schreyer et al. (2021) found that plastic transport was strongly linked to the presence of water hyacinths in the river, which act as accumulation zones of plastic debris. Similarly, Ivar do Sul et al. (2014) demonstrated that plastic debris can be retained by mangrove forest patches for long periods of time (months-years). Clearly, hydraulic and physical traps interact with one another: flow separation can cause macroplastic debris to become trapped in physical traps; and physical traps can promote flow separation. Thus, individual traps may be the result of a combination of hydraulic processes and the presence of barriers.

In this study, we present a “proof of concept” macroplastic tracer experiment, in which plastic tracers were introduced at the upstream boundary of a lowland river reach and displacement and trapping of these tracers were characterised. We also developed a general framework for modelling macroplastic debris transport in rivers, which was informed by the experiment. The model is intended to be used to: (1) estimate a travel distance distribution for plastic debris; (2) identify sites of temporary storage and; (3) estimate the residence time distribution of plastic debris at plastic accumulation zones. It should be noted that this study focusses on the macroplastic size fraction (items larger than 5 mm). The transport of microplastic particles (<5 mm) is also an important issue, but their fate and behaviour differs markedly from that of macroplastic and is, thus, beyond the scope of this study.

Plastic pollution is a significant and growing global threat. The potential issues in marine systems are now widely recognised. However, despite the fact that rivers are potentially significant contributors to ocean plastic pollution, the transport of macroplastic debris in rivers remains poorly understood. In addition, plastic pollution can result in direct deleterious impacts within riverine ecosystems (Blettler and Wantzen, 2019). Here, we present the results from a “proof of concept” macroplastic tracer experiment, which was used to characterise the displacement and trapping of macroplastic debris in rivers. In the experiment, PET bottle tracers were introduced at the upstream boundary of an experimental reach of a lowland river and their locations were recorded after 24 h. A similar approach was employed by Ivar do Sul et al. (2014) in mangrove forests. As reported by Ivar do Sul et al. (2014), we also found that travel distances were low, highly variable and mediated by the location of discrete “trapping points” (particularly, in our case, overhanging trees and meander bends). In most cases, stranding appeared to be independent of other plastic debris—i.e., bottles were trapped individually or were lodged individually but in clusters behind overhanging branches or in emergent vegetation. However, there were some occasions when trapped bottles may have disrupted the movement of others and enhanced their potential to strand. We attempted to reduce such interactions by introducing the bottles individually and believe that the overall interactive effect was minimal. Since macroplastic debris appears to be captured and retained relatively easily, it is likely that many items of debris never make it to the ocean, or do so only after very long periods of time.

We also present the results from a new probabilistic model of fluvial plastic transport, which was calibrated using data from the tracer experiment. The model is based on the probability of trapping, which is constructed from the probabilities of trapping along meander bends, in overhanging vegetation and along channel banks. These probabilities were described by hypothetical relationships with reach and vegetation characteristics. The calibrated model was able to match the observed distribution of macroplastic storage reasonably well. However, model performance with respect to independent data (validation) was inferior to that during calibration. This may, in part, reflect the stochastic nature of macroplastic transport itself (as illustrated by differences in observed bottle distributions between replicate runs: Figure 3). The generation of larger measured and simulated datasets is needed to fully assess the extent to which the model is statistically robust. Nevertheless, the fact that the broad spatial pattern of plastic accumulation appears to have been captured by the model, even during validation, suggests that there is wider potential to utilise the same approach to model macroplastic transfer in rivers more generally—possibly up to the catchment scale. The explicit recognition that most riverine macroplastic resides in stores with variable residence times, and that plastic transport between these stores is intermittent needs to be more explicitly recognised in models of terrestrial to ocean flux. For example, the model of Meijer et al. (2021) employs an estimated bulk probability of plastic transport in river channels to the ocean which is based on stream order, discharge and distance to the sea, but this does not explicitly recognise the number and nature of plastic traps which will exist in all channel networks. Experimental and modelling work along the lines described in this paper may allow riverine plastic transfer efficiencies between sources and the sea to be better quantified and potentially disaggregate the bulk parameters estimated in catchment scale models, such as that of Meijer et al. (2021).

The predictive quality of our model is currently limited by (inter alia): (1) an imperfect understanding of what controls plastic transport in rivers; (2) a poor understanding of the relationships between reach characteristics and the probability of trapping and (3) the limited size of the calibration dataset. To improve the fundamental understanding of the processes controlling plastic displacement (and, therefore, the quality of the model), additional tracer experiments should be conducted on reaches of varying characteristics (e.g., straight, wide or sparsely vegetated). These experiments should also be conducted with other types of litter (e.g., plastic carrier bags, snack packets and straws), made from different plastic materials and under different flow conditions to understand how plastic properties (e.g., buoyancy, shape, and size) and river stage/discharge affect plastic transport. Our experiments focused on buoyant (air filled) particles. However, many non-air filled particles (including PET) have densities similar to or greater than that of water and will, therefore, be suspended within the water column or even travel by saltation along the bed. Furthermore, weathering (e.g., from exposure to ultraviolet light or physical abrasion) and biofouling (the development of a microbial film on the surface of the particle) are known to alter fundamental properties of the original item (such as particle size, shape and density) which can change transport behaviours. For example, Kowalski et al. (2016) showed that plastic sinking rates were affected by particle shape as well as by density and size. Kowalski et al. (2016) also showed that abrasion in turbulent sedimentary systems (such as rivers or the surf zone) can result in the incorporation of quartz grains, which can also potentially influence the behaviour of the particle. The development of biofilms on plastic particles can increase their density and enhance settling rates (Chubarenko et al., 2016; Semcesen and Wells, 2021). Future work should also consider these effects by comparing the behaviour of virgin and weathered/fouled debris.

In principle, the model is able to make estimates of real-world plastic retention and flux. However, more information on the residence time of plastic debris in different trap types and accurate estimates of the location, frequency and volume of plastic emission to channels are required. The residence time of plastic debris in rivers is of primary importance because it directly controls riverine plastic flux and can be used to quantify q(i). Again, this can be determined with additional tracer experiments, but across longer temporal scales. For practicality, these types of experiment could usefully employ GPS trackers (see Tramoy et al., 2020). These have the added advantage of providing high temporal resolution data on the location of plastic tracers. This information can be used to understand the movement of plastic during shorter periods than the 24 h monitoring period employed in our study. Data we collected from pilot studies (not shown here) suggest that some stranded bottles are remobilised (and almost always re-trapped) over shorter periods. Trackers could also be used to understand the behaviour of macroplastic debris over longer periods. Although our model was calibrated for a 24 h sampling period, this type of information could be used to incorporate better probabilistic descriptions of trap and release dynamics in the model, which could make it more generally applicable, without calibration. Disadvantages of GPS trackers include inter alia their relatively high procurement and running costs and limited accuracy. Other research is emerging to predict the amount and volume of plastic entering river channels. For example, Melink et al. (2021) have developed a modelling concept to predict plastic transport on land, but this research is at a very early stage. Additional experimental and modelling work should consider the effects of emission location characteristics on the initiation of plastic displacement (i.e., considering more realistic release scenarios). Initiation of motion could be affected by, for example, the type and density of riparian and in-channel vegetation, the presence of physical obstacles (e.g., bridge piers, lock gates and weirs) and the presence of other (plastic) debris.

The model also has the potential to be scaled up to the catchment scale. For large catchments, it would probably not be practical to estimate p(T) at 10 m resolution. Instead, a representative value of p(T) could be applied to longer reach segments based on aggregate characteristics. These values could be determined empirically from experiments conducted along different study reaches (as above) with model parameters derived from statistical relationships. To assist with scaling up the model, reach characteristics could be automatically calculated in a geographical information system from existing channel network datasets (e.g., the WWF's HydroSHEDS data; see Lehner et al., 2008). Channel width could be estimated from bankfull discharge (Q_bf) using hydraulic geometry (see Leopold and Maddock, 1953). Q_bf itself can be estimated from the discharge with a recurrence interval of 1.5 years using readily available gauged flow data, if available; see Benson and Thomas, 1966). If gauged flow data are not available (as is the case in many parts of the world), mean annual discharge could be estimated from a combination of modelled runoff fields (e.g., from water balance calculations; see Fekete et al., 1999) and accumulated area. A large number of long-term and refined experiments are likely to be needed to get a good quantitative understanding of the different controls on macroplastic transport and release. This represents a significant challenge going forward, which needs to be met in order to scale up the model. Nevertheless, the approach presented here has significant potential to investigate and model macroplastic debris transfer in rivers and potentially improve estimates of riverine plastic flux at river-basin scale.

Perhaps the most important finding of the study reported here is that travel distances for macroplastic debris in rivers are short and variable. This is consistent with the finding of Tramoy et al. (2020) in the Seine and implies that some previous estimates of the terrestrial to marine macroplastic flux may not be accurate. Of course, fluxes are likely to vary with river stage but may not necessarily be higher as discharge increases. For example, at very high stage, rivers often flow overbank. In these situations, plastic debris may also leave the channel and be deposited on floodplains or in oxbow lakes when water levels subside. Further work is needed to investigate the potential sink effect of this phenomenon which, along with other long-term plastic sinks in river channel and riparian zone networks, may go some way to explaining the missing plastic question (the disparity between estimated emissions of plastics to the environment and the estimated stock of plastic which in the world's oceans: e.g., Cózar et al., 2014; Owens and Kamil, 2020; Weiss et al., 2021). Our work broadly supports the general conclusion of Weiss et al. (2021) that previous estimates of riverine plastic flux to the oceans may have been over-estimated.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

This study was conceived by RAN, DMP, and MJW. Fieldwork and data analysis were conducted pre-dominantly by RAN with contributions by DMP and MJW. The model was developed by RAN and MJW. The paper was written by RAN with inputs from DMP and MJW. All authors contributed to the article and approved the submitted version.

This work was funded via a University of Leicester bursary to RAN.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.