Model approach

Our global model computes plastic load inputs from 40,760 watersheds worldwide21 into the ocean using geospatial data on population density18,19 and MPW production per inhabitant and per day in 182 individual countries5,20. Waste is considered mismanaged when it is littered or inadequately disposed. MPW corresponds to the fraction of plastic found in mismanaged waste material on land. This definition was applied in a previous estimate of global plastic waste inputs into the ocean from coastal population worldwide5. MPW production rates are integrated inside catchments. The resulting mass is accumulated following natural drainage patterns derived from local topography, and taking into account the presence of artificial barriers (for example, dams and weirs) acting as sinks. The seasonality of inputs at the outfall location is derived from monthly average catchment runoff. An empirical relation using integrated MPW mass production upstream of river mouths and seasonal runoff is formulated and calibrated using a set of field observations (Fig. 4).

Figure 4: Model framework. Plastic mass production per river catchment (M mpw ; n=40,760 rivers) is computed from data on MPW production rates per country, population density, topographic elevation and location of artificial barriers. Seasonality of inputs is derived from monthly averaged runoff (R). A parametric equation with parameters k and a is used to fit model predictions (M out ) against results from observational studies. For our mid-point estimate, best fit was found for k=1.85 10−3 and a=1.52 (r2=0.93, n=30). Full size image

Model formulation

To estimate daily plastic mass input from individual watersheds, we used the following parametric equation:

where M out is the plastic mass release at the outflow in kilogram per day, M mpw , the mass of MPW produced inside the catchment downstream of artificial barriers and R, monthly averaged catchment runoff. k and a are the regression parameters. We find a strong coefficient of determination (r2=0.93) for k=1.85 10–3 and a=1.52 (midpoint estimate, Fig. 2) using n=30 records from 13 different rivers, where data on plastic contamination in surface waters were reported in the literature.

We considered only peer-reviewed studies that provided reliable estimates of plastic concentrations (number and/or mass of plastic particles per volume and/or area of river water) using surface net devices. For plastic concentrations reported in number of particles per unit area of river surface, we used the depth of the trawling devices to convert reported surface areas (km2) into volume of water sampled (m3). The bibliographic review and selection criteria described above led to the consideration of seven studies in our model calibration exercise. These studies reported river plastic concentrations in 13 rivers, at 30 sampling events that occurred in different time periods (Table 2). Our approach is conservative because we neglected the contribution of buoyant plastic that may occur below the sampled depth due to water turbulence13. Furthermore, this approach does not account for the contribution of non-buoyant plastics that, once introduced in rivers, may slowly make its way to the oceans due to turbulent transport, accumulating in deep sea river canyons38. Around 48% of the plastic produced yearly is made of polymers lighter than seawater (Polyethylene and Polypropylene;1), this number is likely higher due to existence of objects made of polymers heavier than seawater that can float due to air entrapment (for example, PET bottles and foamed Polystyrene).

Not all studies considered here reported micro- and macro-plastic concentrations at surface waters of rivers. As such, for our midpoint estimate, we homogenized our data set using the mean ratio micro- to macro-plastic numerical concentration from studies reporting both types (mean ratio equals to 0.04). For comparison, a study compiling thousands of samples at sea found a relatively similar mean ratio of 0.07 (ref. 29). When only numerical concentrations were reported, we estimated the mass concentrations using the average mass of micro- and macro-plastic particles sampled at sea: 0.003 and 0.17 g, respectively29. The results of the standardization exercise are presented in Table 3.

We acknowledge however, that the extrapolations described above are a limitation of the calibration exercise presented here, as the average mass of river plastic particles, as well as the ratio between micro- and macro-plastic concentrations may vary across catchments due to local differences in in-situ fragmentation rates, plastic transport processes and levels of primary micro-plastic emissions (for example, pre-production pellets, microbeads from cosmetics and hygienic products, laundry powders, paint and coating flakes). A sensitivity analysis was conducted by varying the mean ratio micro- to macro-plastic numerical concentration (range: 0.01–0.12) and the average mass of particles (range: 0.002–0.004 g and 0.04–0.33 g for micro- and macro-plastic, respectively) using range values found at sea29. We determined an upper and lower input estimate using equation (1) with respectively k=1.07 10–3, a=1.61 (r2=0.93, n=30) and k=4.46 10−3, a=1.42 (r2=0.91, n=30). Further details on the sensitivity analysis are provided in Supplementary Table 1.

Correction for surface waters

Some studies8,9 directly provide an estimate of daily or yearly plastic mass input rate. For the other studies, we computed the daily releases of plastic from rivers into the ocean by multiplying the estimated mass concentrations from observations by the volume of water flowing at the surface layer per day. For each river, the surface layer thickness was taken at the sampling depth reported by the study, therefore the contribution of any particles suspended below the sampled depth was neglected. We derived the surface layer flow from the river depth and the total monthly averaged discharge predicted by our hydrological model using the month corresponding to the surveyed time period. When the river depth was not reported by the study, we used the following relationship in equation (2) between channel form and discharge39:

where Q is the river discharge, D is the river depth, c and f are parameters. A good coefficient of determination (r2=0.75) was found for c=0.349 and f=0.341, when comparing discharge and bed form of 674 rivers in Canada and USA40. When studies reported surveys directly from estuaries, the depth was estimated using nautical charts.

Estimating MPW mass in catchments worldwide

We combined data on waste generation in kilograms per inhabitant and per day for 182 individual countries5,20 with gridded population densities in inhabitants per km2 (refs 18, 19) to estimate inland MPW production rates per year. An exception was made for Sri Lanka, where we replaced the World Bank statistics with values reported in more detailed regional assessments41,42. We computed a global ¼ degree resolution grid of estimated mass of MPW generation on land in tonnes per year. In this model, we assumed that inland plastic is accumulated by following natural drainage patterns, derived from the space borne elevation data22. The global landmass surface area was divided in river catchments from the U.S. Geological Survey Agency that are used by the Global Land Data Assimilation System (GLDAS, ref. 21). We used the flow accumulation toolset from ESRI’s ArcGIS software to compute the total mass of inland MPW upstream of the outflow location. The outflow is the most downstream position in a river catchment and determines the input source point into the ocean. Input from catchments with an outflow not connected to the ocean (for example, specifically arid inland areas) were discarded. The model takes into account the presence of artificial barriers and treats them as accumulation sinks, where plastic at the surface is intercepted. As a result, the predicted plastic concentration at the river mouth is representative of the accumulation of inland MPW (in tonnes per year) in the catchment area downstream of artificial dams.

The consideration of dams in our numerical model was motivated by a better correlation found with measurements (Table 4) than when including MPW production rates upstream of dams. Artificial barriers in rivers may retain 65% of the global input into freshwater, as we calculated an annual 2.13–4.46 million tonnes of plastic introduced upstream of dams that are not accounted as input into the oceans by our model. These results were calculated using the parametric equation determined when considering MPW downstream of dams as model proxy. Including MPW production upstream of dams, when assessing the linear regression would result in different model parameters k and a in equation (1). While determining regression coefficients based on MPW quantities upstream of dams, our model predicted a global input of 0.76–1.55 million tonnes per year (midpoint at 0.91 million tonnes per year) which remains in the same order of magnitude than the initial scenario. The decrease in predicted global input from the current model may be explained by the number of dams present in the large rivers covered by the observational studies. In the Yangtze River and Danube River catchments particularly, respectively 68% and 78% of MPW production occurs upstream of a dam. Therefore, relative MPW mass have less weight on the overall prediction result which ultimately leads in a decrease of our global estimate.

Table 4 Pearson’s product moment correlations of total mass concentration measurements with watershed characteristics. Full size table

Dam locations were derived from the United Nation Food and Agriculture Organization’s AquaStat dam database23, consisting of 8,800 dams worldwide with a minimum height of 15 m or a reservoir capacity of >3 million m3. The Global Rivers and Dam Database (GRanD database; ref. 24) was used for South America as the AquaStat database was incomplete for this continent. The catchments containing the largest number of dams were the basins of the Mississippi River (718 dams), Yangtze River (342 dams) and Danube River (184 dams). As the analysis is based on natural drainage patterns, the model limitations are that man-made channels are not taken into account and that plastic load accumulates in the main arms of rivers at deltas, introducing uncertainties at local scales. These limitations however do not affect the global inputs estimate. An example for the island of Java in Indonesia illustrating the different datasets involved in this framework is provided in Fig. 5.

Figure 5: Modelled data flow illustration for Western Java, Indonesia. (a) Estimated MPW production rates in t yr−1. (b) Accumulated MPW production in rivers and location of artificial barriers. (c) Predicted plastic mass input into the ocean at river mouths in t d−1. Full size image

Estimating monthly averaged catchment runoff

In our model, surface runoff is included as a model parameter to account for (1) the introduction of MPW in riverine system during episodes of heavy rainfall10 and (2) the remobilization of deposited plastic particles during flood events31. Monthly averaged catchment runoff in millimetres per day was calculated using GLDAS driving the NOAH Land Surface Model21. This land surface modelling system integrates data from advanced ground and space-based observation systems. The model contains land surface parameters for vegetation, soil, elevation and slope. The forcing data in the model are near-real-time satellite-derived precipitation and evaporation data (wind, radiation, temperature, humidity and surface pressure). The model computes the daily surface and subsurface runoff globally on ¼ degree resolution, by solving terrestrial water and energy budgets21. Subsurface runoff consists of water that infiltrates into the soil and flows to a water body by groundwater flow. Surface runoff occurs either when the rainfall exceeds the infiltration capacity of the soil or when the soil is saturated with groundwater. Monthly and yearly averages are calculated over the period 2005–2015. The surface and subsurface runoff are summed and subsequently averaged per catchment area22. A better correlation was found with estimated flux inputs from observational studies when considering monthly averaged runoff instead of the yearly average (Table 4). Therefore, monthly averaged catchment runoff corresponding to sampling event month was considered while calibrating our model to account for temporal variations and seasonality of inputs.

The main motivation behind using runoff data from GLDAS is the provision of land surface processes including runoff estimates at a global level. Nonetheless, it is important to notice that comparisons between river discharge predictions from GLDAS and observations in 66 basins worldwide43 demonstrated that predictions are somewhat dryer than observations. The authors of this validation study attributed the differences to uncertainties in precipitation rates. As our framework relies on intra-annual variability, the NOAH land surface model predictions, forced with GLDAS, were still in good agreement with seasonal variations measurements with a predicted date of maximum discharge within 20 days of observed annual discharge peak date for most rivers covered in the GLDAS validation study.

Data availability

The authors declare that the main data supporting the findings of this study are available within the article and its Supplementary Information. Global model inputs and outputs for lower, midpoint and upper estimates and for the 40,760 catchments considered in this study have been deposited in geospatial vector data format for geographic information system (GIS) software on figshare with the identifier doi:10.6084/m9.figshare.4725541.