Influence of Barotropic Tidal Currents on Transport and Accumulation of Floating Microplastics in the Global Open Ocean

Abstract Floating plastic debris is an increasing source of pollution in the world's oceans. Numerical simulations using models of ocean currents give insight into the transport and distribution of microplastics in the oceans, but most simulations do not account for the oscillating flow caused by global barotropic tides. Here, we investigate the influence of barotropic tidal currents on the transport and accumulation of floating microplastics, by numerically simulating the advection of virtual plastic particles released all over the world's oceans and tracking these for 13 years. We use geostrophic and surface Ekman currents from GlobCurrent and the currents caused by the four main tidal constituents (M 2, S 2, K 1, and O 1) from the FES model. We analyze the differences between the simulations with and without the barotropic tidal currents included, focusing on the open ocean. In each of the simulations, we see that microplastic accumulates in regions in the subtropical gyres, which is in agreement with observations. The formation and location of these accumulation regions remain unaffected by the barotropic tidal currents. However, there are a number of coastal regions where we see differences when the barotropic tidal currents are included. Due to uncertainties of the model in coastal regions, further investigation is required in order to draw conclusions in these areas. Our results suggest that, in the global open ocean, barotropic tidal currents have little impact on the transport and accumulation of floating microplastic and can thus be neglected in simulations aimed at studying microplastic transport in the open ocean.

1.Text S1.Calculation of the main tidal currents in Parcels 2. Figures S1 to S5

Text S1. Calculation of the main tidal currents in Parcels
There exist a great number of tidal constituents; Doodson (1921) distinguished as many as 388 different constituents (Casotto & Biscani, 2004).In the Kernel developed for Parcels at https://github.com/OceanParcels/TidesGlobalOceanPlastic, we compute the tidal currents using harmonic analysis of the four largest tidal constituents, for any location and time.The strongest tidal constituent is the M 2 tide, or semidiurnal lunar tide.It is caused by forcing due to the Moon and its angular frequency is ω M 2 = 28.9841042• /hour, which corresponds to a period of half a lunar day (12 h 25 m).Likewise, the S 2 tide, or semi-diurnal solar tide, is the result of forcing by the Sun; it has angular frequency ω S 2 = 30.0000000• /hour, and period half a solar day (12 h) (Schureman, 1958). 1 Two other important constituents are the K 1 tide, or diurnal luni-January 13, 2020, 3:23pm X -2 : solar tide, and the O 1 tide, or diurnal lunar tide.These tides are related to the inclinations of the Earth's axis and the Moon's orbit.Their frequencies are ω K 1 = 15.0410686• /hour and ω O 1 = 13.9430356• /hour, respectively (Schureman, 1958).Since the Moon causes the strongest tidal force,the M 2 constituent has the largest amplitude of all tidal constituents.
The K 1 tide has the second-largest amplitude, which is 58.4% of the M 2 amplitude.The S 2 and O 1 tide follow in third and fourth place, respectively, with 46.6% and 41.5% of the M 2 amplitude.
Because these are the main tidal constituents, as a first approximation only the M 2 , S 2 , K 1 and O 1 constituents are taken into account here for the computation of tidal velocity fields.Data for the amplitudes and phase shifts of the main tidal currents are obtained from the FES2014 data set.The astronomical argument correction and nodal modulation amplitude and phase corrections can be calculated from a number of astronomical variables (Foreman, 1977): T (t), solar angle relative to Greenwich; h(t), longitude of the Sun; s(t), longitude of the Moon; N (t), longitude of the Moon's ascending node.
For our calculations, we take the origin of time t 0 to be January 1, 1900, 00:00:00 UTC.
For each time t, let τ = t − t 0 be the time that has passed since t 0 , expressed in number of Julian centuries (36,525 days).Then the astronomical variables defined above can be January 13, 2020, 3:23pm : X -3 calculated as These constants are taken from the code accompanying the FES2014 data set.They can also be found in (Doodson, 1921), where some of the values are slightly different from those in the FES2014 code (differences occurring in the third decimal); since the FES2014 code is more recent, it is assumed that the values used there are the results of more precise measurements, so these values are used for the calculations.
From these numbers, we can calculate the values of V (t), u(t) and f (t) for each of the main tidal constituents.The formulas for these calculations are listed in Table S1.
All these formulas are taken from (Schureman, 1958).For further background and discussion on these formulas, we refer to (Godin, 1972) and (Schureman, 1958).The total eastward and northward currents due to the four main tidal constituents can now be January 13, 2020, 3:23pm X -4 : calculated for every location and every time, using observational data for the tidal current amplitudes and phase shifts from the FES2014 data set, and with V , u and f calculated as in Table S1.

Figure S5 .
Figure S5.The average microplastic particle density for four different years of the simulation