## 2 Materials and Methods
### Wet Deposition
After the first pass, Hg\({}_{\text{precip}}\) in weekly samples was set to missing if deemed an outlier according to the following rules:  
Rule 1: absolute value of studentized residual from multiple-regression analysis (Equation (1)) greater than 4, regardless of precipitation amount. This removed extreme outliers for weekly samples with less than 10 mm of precipitation; low-volume events tend to be noisier. From this analysis, four outlier results were removed for MN16 and three for MN18. Rule 2: for samples with precipitation volume >10 mm, values were set to missing if the absolute value of studentized residual from multiple-regression analysis (Equation (1)) was greater than 3. Using this rule, one Hg\({}_{\text{precip}}\) result was set to missing for MN16 and two for MN18. Mercury concentrations for the screened samples were deemed extreme outliers for the precipitation amount of the event and were likely an artefact rather than a realistic representation of Hg\({}_{\text{precip}}\) in precipitation. One outlier in particular had an abnormally high Hg\({}_{\text{precip}}\) for a relatively large precipitation event and occurred late in the study period (site MN18; 5 July 2017; reported Hg\({}_{\text{precip}}\) = 89.59 ng L\({}^{-1}\); Precip = 27.686 mm). The resultant calculated weekly Hg deposition was 2.48 ug m\({}^{-2}\), which is about 25 percent of the annual wet deposition reported by NADP/MDN at this site and would have influenced the trend analysis were it not removed. A table of removed outliers is provided (Supplementary Materials, Table S1). The above-described screening process retained weekly observations (with precipitation volume retained), but outlier values of Hg\({}_{\text{precip}}\) were set to missing. After removal of outliers, regression analysis was applied (again using Equation (1)), and missing log[Hg\({}_{\text{precip}}\)] values were predicted by the regression. Predicted Hg\({}_{\text{precip}}\) was calculated by exponentiating regression-predicted log[Hg\({}_{\text{precip}}\)] values, and multiplying by the mean of the exponentiated residuals to correct for back-transformation bias (Duan smearing estimator, as described in [PERSON] et al., pp. 256-257 [32]). Weekly Hg\({}_{\text{precip}}\) values, then, consisted of MDN-reported values in nearly all cases, but regression-predicted values where weekly Hg\({}_{\text{precip}}\) was missing (including observations where outliers were screened as described above). Annual wet Hg deposition was then calculated as the sum of weekly deposition rates (concentration times precipitation depth); and precipitation-weighted mean Hg\({}_{\text{precip}}\) were calculated as annual deposition rate divided by annual precipitation depth. This methodology differs from NADP/MDN network methodology. NADP/MDN effectively estimates missing Hg\({}_{\text{precip}}\) as the precipitation-weighted annual mean concentration, whereas our methodology estimates missing Hg\({}_{\text{precip}}\) using regression-based predictions based on the precipitation volume and season associated with each weekly sample. For the purposes of this paper, regression-based estimates were preferred because, given the dependence of Hg\({}_{\text{precip}}\) concentrations on precipitation depth, precipitation-weighted mean concentrations may underestimate concentrations for small events and overestimate concentrations for large events (which are more important in determining annual loads). Owing to modest nonlinearity in the time trends, trends in the annual wet Hg deposition rate and in precipitation-weighted annual mean Hg concentration were determined by locally weighted regression, after dealing with extreme outlier Hg concentrations as described above. Locally weighted regression used the LOESS procedure in SAS software, allowing the procedure to select the smoothing parameter by Akaike information criterion algorithm.