## 2 Materials and Methods
### Biofuling Model
Although the value of the nutrient-limited growth rate \(\mu^{\prime}\) is not explicitly stated in the paper [42], it is assumed that nutrients are sufficiently available for the algae. Therefore, we suppose that \(\mu^{\prime}=1\) (1/day). The vertical \(Chl\;a\) profiles are parameterized based on a modification of the Gaussian equation [53]:  
\[BT=\frac{f_{ice}}{\rho_{b}}\cdot 10^{-6} \tag{4}\]1  
where empirical parameters \(C_{b}\), \(s\), \(C_{max}\), \(Z_{max}\), and \(\Delta z\) are taken from reference [54], which provided several sets of values for the Arctic, varying with ocean depth, season, and surface chlorophyll-a concentration (the used set is presented in the Supplementary Materials, Tables S1 and S2). The averaged monthly data of the MODIS spectroradiometer installed on the AQUA and TERRA satellites [55; 56] are used as the surface concentration of chlorophyll-a \(Chl\;a(0)\). In our study, the average concentration of the vertical profile, \(\overline{Chl\;a_{Z_{\text{laser}}}}\), is determined for each grid point in a way that the formula (12) ensures the surface concentrations of chlorophyll-a at \(z=0\):  
\[BT=\frac{f_{ice}}{\rho_{b}}\cdot 10^{-6} \tag{4}\]2  
For the deep Arctic (\(>50\) m), the resulting vertical profile is bounded by a depth \(H_{\text{{{chl}}}}\) that is a solution to the minimization problem:  
\[BT=\frac{f_{ice}}{\rho_{b}}\cdot 10^{-6} \tag{4}\]3  
The depth \(H_{\text{{{chl}}}}\) cannot be deeper than the ocean depth in the corresponding water column \(H_{\text{{{oct}}}}\). Below depth \(H_{\text{{{chl}}}}\), the chlorophyll-a concentration is equal to zero. The shelf (\(\leq\)50 m) vertical profile (Formula (12)) is considered for the normalized depth coordinate:  
\[BT=\frac{f_{ice}}{\rho_{b}}\cdot 10^{-6} \tag{4}\]4  
thus, it is defined from the surface to the bottom. The authors of the biofouling model [42] relied on the existing aggregation theory for the formation of marine algal flocs in their description of the collision process. The attachment of algae cells to microplastic particles occurs during the processes of Brownian motion, differential settling, and advective shear. Consequently, the collision rate \(\beta_{A}\) is calculated as the sum of the rates of these processes. The growth rate of the attached algae \(\mu_{A}\) is limited by the intensity of light and the water temperature. It is defined as the reproduction rate under optimal temperature conditions for a certain light intensity \(I_{z}\), multiplied by a temperature influence coefficient that depends on the minimum, maximum, and optimum temperatures for sustaining algae growth. A significant portion of the daily photosynthetic productivity in algae is lost at night as a result of respiration [57]. Another mechanism that regulates the accumulated biomass is the mortality of algae. The Kooi model is based on the assumption of constant respiratory and mortality rates. The collision rate, respiration process, and light intensity at depth \(z\) are modeled identically to the Kooi model [42], including the values of all the parameters needed for their calculation. However, in order to take into account the characteristics of the investigated region, we use spatially and temporally variable ocean fields (temperature, salinity, density, light intensity at the ocean surface), in contrast to a column with constant characteristics, as in the aforementioned work. Additionally, we take different values for some constants that are specific to the polar region. Thus, we set the mortality rate \(m_{A}=0.16\) day\({}^{-1}\)[58]. The growth rate of the attached algae \(\mu_{A}(T,I_{z})\) is also modeled similarly to [42], but different values are used for the maximum, minimum, and optimum temperatures to sustain algae growth (averaged according to Table 1 in [59]), namely 10, \(-1.5\), and 6 \({}^{\circ}\)C, respectively. In contrast to the approach in ref.