## 3 Experimental Design  
The output of the 3D coupled ocean and sea ice model SibCIOM [61; 62; 63] is used to describe the spatio-temporal variability of the Arctic Ocean state. The SibCIOM model solves the Reynolds-averaged primitive equations in the Boussinesq and hydrostatic approximations in combination with the ice thermodynamics and transport model (CICE, version 3 [64; 65; 66]). The SibCIOM is forced by NCEP/NCAR atmospheric reanalysis data [67] (wind speed, surface air temperature, precipitation, longwave and shortwave radiation). The modeling domain includes the Arctic Ocean and the Atlantic Ocean, bounded by 20\({}^{\circ}\) S. Previous publications [68; 69; 70; 71] demonstrate that the SibCIOM results for the Arctic Ocean are in agreement with observational data.  
The daily three-dimensional fields of ocean state (current velocity, temperature, salinity, density) and two-dimensional fields of ice state (drift velocity, volume, concentration, freezing and melting rates) calculated by SibCIOM are used in the Lagrangian particle transport and biofouling models. The light intensity at the ocean surface is obtained from NCEP/NCAR reanalysis data [67].  
We consider spherical floating high-density polyethylene particles (HDPE, \(\rho=955\) kg/m\({}^{3}\)) that are biofilm-free when they initially enter the ocean. The time behavior and propagation trajectories of particles of two sizes (\(d=0.5\) mm and \(d=0.01\) mm) are analyzed.  
The initial experiment was carried out to determine the characteristics of the movement of microplastic particles due to their size. Furthermore, it was interesting to see how the trajectories of these particles differed depending on the season when they entered the shelf waters. Two particles of selected sizes were released once a month during 2016 at the same location on the Kara Sea shelf. The particles were tracked until the end of 2020. In this experiment, it was crucial to establish identical conditions for particles released at the same moment. Accordingly, the probability-based approach proposed in [45] for the parameterization of particle embedding in ice was not feasible. The experiment assumed that the particles would automatically enter the ice when the ice concentration reached 50%. Thus, the variability of particle incorporation into the ice cover was excluded. The variation in particle release during ice melting was also excluded: it occurred when the ice concentration became less than 50%. The objective of this experiment was to analyze the behavior of the particles in a vertical direction and to identify any differences in their trajectory as a result of their location in the various water layers or in the ice.  
The second experiment was focused on analyzing the distribution of microplastics entering the shelf of the Kara Sea with the waters of the Ob and Yenisey rivers. The motivation for choosing these rivers as a source of MPs has been described in detail in our previous study [45], where we performed a similar calculation with a simpler biofouling model. The particles entered the oceanic area with the river waters during the entire period of 2016-2020. The daily mass of incoming pollution was estimated according to the annual river load of microplastics (795.55 t/year for the Ob and 117.85 t/year for the Yenisey [72]) and monthly river discharge [73]. A particle was initiated in the area for every 5 tons of microplastics that entered.  
In contrast to the initial experiment, the second simulation employed an experimental design that was identical to that described in [45], whereby the incorporation of particles into the ice was defined in accordance with the descriptions provided in Section 2.1.