## 2 Materials and Methods
### Wet Deposition  
Detailed methods are described by [PERSON] et al. (2017). Briefly, weekly composited precipitation samples are collected and analyzed using modifications of U.S. Environmental Protection Agency (U.S.EPA) Methods 1669 ([PERSON] et al., 2018) and 1631 ([PERSON] et al., 2018). Precipitation samples were analyzed for total mercury concentration (Hg\({}_{\text{precip}}\)) at Frontier Global Sciences in Seattle, Washington. Data included herein met the NADP's acceptance criteria, ([PERSON] et al., 2018; [PERSON] et al., 2018) although some further screening of apparent outlier Hg\({}_{\text{precip}}\) values was done as described below. Inspection of weekly MDN data revealed a limited number of outliers in the weekly data, some of which were suspected as extreme outliers, i.e. unusually high or low, and which may impart an artefact into the calculations of annual wet Hg deposition rate and precipitation-weighted mean concentrations. We used the following approach to identify extreme outliers prior to wet deposition calculations:  
Weekly data for the study sites were downloaded from the NADP/MDN website. Weekly Hg\({}_{\text{precip}}\) and precipitation volumes were analyzed using a multiple-regression \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Lake Name** & **Lake Area** & **W.A.** & **\% Wet-** & **Lake** & **Maximum** & **Mean** & **Mean** & **AUC** & **TOC** & **Transparency** \\
**Name** & **(ha)** & **(ha)** & **lands** & **(10\% m\({}^{3}\))** & **Depth (m)** & **Depth (m)** & **pH** & **Time (yr)** & **(\(\mu\)e\({}_{\text{a}}\) L\({}^{-1}\))** & **(mg L\({}^{-1}\))** & **Depth (m)** \\ \hline Brown & 30.8 & 158.9 & 9.9 & 1.3 & 8.2 & 4.2 & 7.0 & 0.8 & 129 & 9.4 & 2.7 \\ Peary & 45.3 & 734.6 & 19.8 & 1.2 & 4.6 & 2.6 & 7.2 & 0.6 & 195 & 10.1 & 2.4 \\ Ryan & 14.2 & 86.9 & 6.4 & 0.3 & 3.7 & 2.1 & 6.9 & 1.2 & 130 & 12.7 & 2.8 \\ Shoepack & 123.8 & 1735 & 25.8 & 3.6 & 7.3 & 2.9 & 6.5 & 0.7 & 114 & 15.5 & 1.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected lake characteristics ([PERSON] et al., 2018; [PERSON] et al., 2018); and selected water-column measurements from the approximate centroid of each lake ([PERSON] et al., 2018). [W.A., watershed area; % Wetlands, wetlands as a percentage of watershed area; Renewal time = mean hydraulic residence time, in years; ANC, acid-neutralizing capacity; \(\mu\)e\({}_{\text{q}}\) L\({}^{-1}\), microequivalents per liter; TOC, total organic carbon; mg L\({}^{-1}\), milligrams per liter]. Figure 1: Location of four study lakes within Voyage National Park, and nearby National Atmospheric Deposition Program precipitation-monitoring sites MN16 and MN18. approach developed previously [31], using the REG procedure in SAS software (v. 9.4. SAS Institute, Carey, NC, USA). Hg\({}_{\text{precip}}\) and precipitation depth data were log-transformed to remove skewness and heteroscedasticity of residuals. A regression model was developed to account for the exogenous effects of weekly precipitation depth; season (Fourier terms); and time (T, in years) (Equation (1)). \[\log[\text{Hg}_{\text{precip}}]=\beta_{0}+\beta_{1}\log(\text{Precip})+\beta_{2} \,\sin(2\pi\text{T})+\beta_{3}\,\cos(2\pi\text{T})+\beta_{4}\,\text{T}+\varepsilon \tag{1}\]  
where Hg\({}_{\text{precip}}\) is mercury concentration in weekly precipitation samples in ng L\({}^{-1}\); Precip is the precipitation depth in mm; sin and cos are the sine and cosine functions; T is time in decimal years. Additional Fourier terms (sine and cosine of 4\(\pi\)T) were significant at many MDN sites across North America [31], but were not significant for the current study sites, thus were not included in the analysis herein. The residual, \(\varepsilon\), is the unexplained variation in log[Hg\({}_{\text{precip}}\)], accounting for exogenous effects of precipitation amount, seasonality, and time. Inspection of the data indicated the presence of outliers. Therefore, two passes of the regression analysis were performed.