## 6 Conclusions  
The results of numerical modeling of the possible pathways and fate of floating HDPE microplastic particles released at the Kara Sea shelf are presented. Two different sizes of microplastic particles were considered, 0.01 and 0.5 mm in diameter. The Lagrangian transport of the particles was determined using the Arctic Ocean current and ice drift fields for the period of 2016 to 2020, obtained from numerical simulations based on the three-dimensional ocean and sea ice model SibCIOM. A model of microplastic biofouling in the seawater, based on the study by [PERSON] et al., 2017 [42], including both biofilm growth and degradation processes, was combined with the Lagrangian transport of the particles. For this model, daily fields of temperature, salinity, seawater density, sea ice thickness, and concentration calculated using the SibCIOM model were used to provide the spatial and temporal variability of the Arctic water and sea ice. The sea surface chlorophyll concentration was obtained from satellite observations [55; 56]. A series of constants for the model were chosen according to in situ measurements in polar waters [54; 58; 59]. To simulate microplastic biofouling in sea ice, a parameterization based on the results of a modeling study analyzing the seasonal variability of algal biomass in Arctic ice by [PERSON] et al., 2017 [51] was used. The present study shows that modeling biofilm growth and degradation on the microplastic particles caused an oscillatory behavior of the particles in the vertical direction. The oscillations resulted from the repeated processes of sinking of the biofilm-coated microplastic particles and their ascent to the sea surface as the biofilm degraded. The depth of submergence and the frequency of vertical oscillations varied considerably between particles of different sizes. Smaller particles of 0.01 mm tended to sink earlier but rose very slowly when their biofilm disappeared. In contrast, larger particles of 0.5 m, being free of biofilm, rose to the surface layer within several days, so they quickly entered an environment that was favorable for further biofilm accumulation. The model results show that the characteristics of the water environment influence the biofouling of particles, their immersion depth, and their oscillation intensity. Using the parameterization of biofilm degradation processes based on the [PERSON] et al., 2017 [42] model, the majority of microplastic particles do not sink deeper than 75 m in polar waters unless they have reached the region of relatively warm Atlantic waters. The depth of submergence of the particles affects their trajectory. The differences in the Arctic system of currents and sea ice drift contribute to the transport of particles released in the Kara Sea to different regions of the Arctic Ocean. For 0.01 mm particles that remain in the aquatic environment for a long time, the most notable features are their presence on the Kara Sea shelf and their subsequent export beyond the shelf, followed in a cyclonic direction along the continental slope of the Eurasian basin. Particles with a diameter of 0.5 mm, which oscillate most frequently in summer and rise to the ocean surface, are incorporated into the ice drift system in winter and are subsequently transported to the Barents and Greenland Seas. This study was based on a mathematical formulation of the problem, including some assumptions about the rates and scales of change of certain Arctic environmental parameters, which are highly relevant for accurate modeling of microplastic biofouling. In order to further develop the model and refine, and test the parameterization of physical and biological processes concerning the subject under study, it is of the highest importance to obtain observational data and the results of investigations involving field experiments.