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Edited by: Matteo Baini, University of Siena, Italy

Reviewed by: Carlo Brandini, CNR, Italy; Shiye Zhao, Japan Agency for Marine-Earth Science and Technology (JAMSTEC) Japan

*Correspondence: Claudio M. Pierard,

This article was submitted to Marine Pollution, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Most marine plastic pollution originates on land. However, once plastic is at sea, it is difficult to determine its origin. Here we present a Bayesian inference framework to compute the probability that a piece of plastic found at sea came from a particular source. This framework combines information about plastic emitted by rivers with a Lagrangian simulation, and yields maps indicating the probability that a particle sampled somewhere in the ocean originates from a particular river source. We showcase the framework for floating river-sourced plastic released into the South Atlantic Ocean. We computed the probability as a function of the particle age at three locations, showing how probabilities vary according to the location and age. We computed the source probability of beached particles, showing that plastic found at a given latitude is most likely to come from the closest river source. This framework lays the basis for source attribution of marine plastic.

Floating plastic items have been found in all of the world’s oceans (

Here, we use numerical simulations to compute the pathways of virtual plastic particles that float on the surface of the ocean (

Such a probabilistic approach has been used before to locate objects lost at sea, like the submarine Scorpio (

As an illustration of this probabilistic framework for attribution of likely plastic sources, we apply it to plastic emitted by rivers around the South Atlantic Ocean, as rivers are considered the principal pathway for mismanaged plastic waste (MPW) into the ocean (

Bayesian inference uses Bayes’ Theorem to estimate the conditional probability of an event happening under certain conditions by combining prior knowledge about the problem with data obtained through an experiment. In particular, our objective is to estimate the probability that a particle sampled at sea would come from a certain source. This can be written as the conditional probability _{i}
_{loc}
_{loc}
_{i}
_{i}
_{loc}

where _{i}
_{loc}
_{loc}
_{i}
_{i}
_{i}
_{loc}
_{i}
_{loc}
_{loc}
_{i}
_{i}
_{i}
_{i}
_{loc}
_{i}
_{loc}
_{i}
_{loc}

In eq. (1), computing the normalizing constant _{loc}
_{loc}
_{loc}

where the sum is defined for the _{i}
_{loc}

and by factorizing and solving for _{loc}

we obtain a normalizing constant that only considers the sum of all our hypotheses (i.e. products of prior and likelihoods). Finally, by substituting _{loc}

which is an alternative form of Bayes’ theorem (

Our prior is based on the annual amount of riverine plastic estimated by

We then clustered the rivers in 10 groups that contained the top polluting rivers and their neighboring rivers. These clusters are 2° by 2° square regions centered around ten locations that coincide with important cities or river estuaries. They contain the river mouth locations of the rivers within their limits and we used these locations as release locations. The 10 clusters (

Map of the top plastic-emitting rivers (red dots) in the South Atlantic from

We defined the prior distribution _{i}

Prior probability _{i})_{i}

Sources (_{i} |
_{i} |
---|---|

Congo | 0.016 |

Cape Town | 0.042 |

Rio de la Plata | 0.098 |

Porto Alegre | 0.080 |

Santos | 0.039 |

Paraibá | 0.025 |

Itajaí | 0.070 |

Rio de Janeiro | 0.270 |

Salvador | 0.063 |

Recife | 0.107 |

Unclustered America | 0.181 |

Unclustered Africa | 0.010 |

The prior represents the proportion of the total annual plastic released to the South Atlantic by each of the clusters.

To compute the likelihood _{loc}
_{i}
_{i}

We performed one simulation per cluster, with 100,000 particles each, using a fourth-order Runge-Kutta integration time step of 1 h. For each simulation, we released the particles from the river mouth locations within the cluster. The number of particles released at each river mouth was proportional to the emission of each of the rivers within the cluster. In the simulations for the unclustered rivers, we released the particles from the river mouth locations outside the clusters. The number of particles released was proportional to the plastic emissions of each unclustered river. We released the particles continuously. The date of release of the particles was randomly selected from a uniform distribution over a time interval of one year. On average, the particles were released 10 km from the coast, or at the centers of the closest cell next to the river. We stored the particles’ positions every 24 h, for a total of 1,234 points per trajectory (3.4 years).

The domain of the simulation was the South Atlantic Ocean, from 70°W to 25°E and between 50°S to the Equator. We stopped tracking the particles if they exited the domain. In total, 16.2% of the particles exited the domain: 12.8% across the Equator and 3.4% into the Indian Ocean. We used hydrodynamic data from 1 April 2016 to 31 August 2020, releasing particles in the first year only and then tracking them for another 3.4 years. We selected these periods because the main objective of this study is to demonstrate the method with computationally feasible time scales, although they are small compared to plastic degradation time scales.

In the simulations, we implemented a stochastic parametrization for beaching of buoyant particles as described in _{b}
_{b}
_{b}
_{r}
_{r}
_{r}
_{r}

To parametrise unresolved turbulence that acts on the floating plastic (^{2}s^{–1}, similar to

We computed the likelihood _{loc}
_{i}
_{loc}
_{i}
_{loc}
_{i}
_{i}

The likelihood was computed based on the positions of the particles according to their age. The particle age represents the transit time of particles between the source _{i}
_{loc}
_{loc}

We computed the posterior probability _{i}
_{loc}

Since we use a stochastic parametrization for simulating the beaching of particles near the coast, we can also map the probability of a beached particle coming from a specific cluster. To compute this, we built two cumulative latitudinal histograms of the particles that were beached at a specific time step: one for the American coast and the other for the African coast. The cumulative latitudinal histogram is formed by counting the particles that are beached in latitudinal bins of 1°, disregarding the longitude of those particles, and by classifying them into particles that beached either at the American or the African coast. With the counts per latitude, we computed the average at each bin for the duration of the whole simulation and normalized by the sum of all average counts per bin. As for the posterior probability maps, we computed the beached posterior probability _{i}
_{lat}
_{lat}

_{i}
^{–4}, as they represent the proportion of particles (in relation to the total number of particles from a cluster in the domain) that cross a grid cell. Each cluster has 100,000 particles, minus the particles that exited the domain at a certain time step, so if in one bin there are 100 particles, the likelihood would be in the order of 10^{–4}.

Likelihood maps of the spatially binned _{loc}|R_{i})

In general, the dark blue areas represent regions where almost no particles were found from a specific cluster, while the yellow regions represent locations where it was more likely to find particles from that cluster. Specifically, for the South American clusters, the likelihood of finding particles from Recife, Santos, and Salvador is almost zero in the open ocean between 20°S to 40°S, that is, where the subtropical gyre is located. The particles released from those clusters tend to stay close to shore and beach because of the effect of Stokes drift that pushes them towards the coast.

The major contributors to the subtropical gyre plastic content (between 20°S to 40°S) are Itajaí, Paraíba, Porto Alegre, Rio de Janeiro, Rio de la Plata, and Unclustered-America, with likelihoods ranging from 1 x 10^{–4} to 10^{–4}. From these clusters, Porto Alegre is the largest contributor. Closer to the South American coast, the likelihood is above 3 x 10^{–4} for all these clusters. North of the gyre, from 20°S and further north, the likelihood of finding particles from the American coast is near-zero.

For the African clusters, shown on

_{i}
_{loc}

Posterior probability maps, averaged over 3.4 years, showing _{i}|S_{loc}),

Regarding the individual panels in

The posterior age distributions yield the probable sources of a particle of a certain age, sampled at a certain location.

Local posterior age distributions at three different locations for the posterior probability. The map on the top right marks the locations _{i}|S_{loc}

The panel for sampling location A in

The posterior age distributions for location B (32.37°S, 5.80°E) in

_{i}
_{lat}
_{i}
_{lat}
_{lat}

Horizontal bar plot for the posterior probabilities of beached particles (

In the right panel of

We introduced a Bayesian probabilistic framework that estimates _{i}
_{loc}

The framework supports different types of analyses and can be used, for example, to compute spatial probabilities, compute the local probability as a function of particle age, or analyse the probabilities once a physical process (e.g. beaching) alters the particles’ state. We applied this method to the use case of plastic emitted at river mouths in the South Atlantic. This application ignores other types of sources that also contribute to marine plastic pollution, such as fisheries, cities, or plastic from outside the domain; and thus make it difficult to validate these results with direct observations. Nevertheless, the framework could in principle be extended to other types of sources.

The time average window used for computing the likelihood _{loc}
_{i}

As we showed in _{i}
_{loc}

The local posterior age distributions, shown in

The latitudinal beached posterior probabilities, shown in

In our use case on floating plastic emitted from rivers in the South Atlantic, we ignore plastic entering the domain from the Indian Ocean leakage (

One major advantage of the Bayesian nature of our framework is that it allows updating the results when better estimates of plastic emissions are available without having to redo the (computationally expensive) Lagrangian simulations. For instance, it can be expanded by including a prior that accounts for seasonal variations in river-borne plastic inputs, or by taking into account different types of land-based or sea-based sources. Also, the forward simulation releases the same amount of particles per cluster or source, which makes small emitting sources have equal spatial representation compared to larger and more dominant sources.

The original contributions presented in the study are publicly available. This data can be found here:

CP, DB, and ES contributed to the conceptualization and design of this study. CP performed the simulations and the analysis, and wrote the original draft. BD, FM, ES contributed to the editing of the original draft. All authors contributed to manuscript revision, read, and approved the submitted version.

This project was supported by NWO through grant OCENW.GROOT.2019.043. EvS was partly supported through funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 715386).

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.

The Supplementary Material for this article can be found online at