Modeling Temporal Trends of Oceanic Plastic

We modeled OSL temporal trends in plastic abundance and distribution with the above datasets corrected for wind and basin over time. Although there are many examples of global and regional plastic abundance and distribution estimates at a single point in time, temporal trends proved more challenging to produce.
Here, we used a model that removed the effects of site-bias and non-detects from the observed concentrations. We corrected for non-detects by treating zeros in the data as censored observations, in which the actual observation is below the detection level (1/volume of water sampled), instead of being considered a true zero value. We estimated the likely values of the zero records with the cenros function in the NADA package [25 ]; this function is a regression on ordered statistics that fits a model to the observed data and their quantiles to extrapolate the left-censored values. After correcting for non-detects with the cenros function, we estimated the actual values of the zeros to include in the model (S1 Fig). Plotting log-transformed observed concentration and expected concentration from an oceanographic transport model revealed an ocean-basin and concentration bias (quantile–quantile (qq) plot) (S2 Fig). To correct the collinear effect of expected concentration, we first fit a generalized additive model (GAM) model (gamma distribution) between log-transformed observed concentration and expected concentration from the van Sebille model [9 (link)]. We fit the model (concentration = expected concentration + basin) to the observed concentrations to get the residuals. Here the predicted density has no temporal component, only a spatial one, so the residuals from this relationship give a measure of how much an observation diverges from the relative concentration across space that we would expect. We then explored support for a time trend by modeling the residuals from the model above using a smooth function on time in a generalized additive model (S3 Fig). This approach is similar to adding all variables to a single model but allows us to interpret more precisely the effect of time by itself without influence from the other variables due to collinearity. We then estimated the average concentration change through time by multiplying the mean concentration observed by the reverse log-transformed residual fit. This approach allowed us to predict global plastic quantity weighted by observed mean plastic concentrations without influence from spatial effects.
Modeled results of floating microplastic item count (trillion of particles) and mass (millions of tonnes) globally for each year were calculated by averaging daily model results. Daily model results for particle counts were calculated by multiplying model results (particles km^-2) x 361,900,000 km² (ocean surface-area). Daily model results for mass were calculated by multiplying 1.36 x 10⁻² g (average particle mass and weight from [21 (link)] x the number of particles.