Predicting Fe and Mn concentrations from optical measurements using PLSR
We used PLSR to compute predictions of total and soluble Fe and Mn concentrations based on the correlation between absorbance spectra and sampling data. Data analysis and QA/QC was performed in the R programming environment (R.v.4.2.1). Model building was conducted using the pls package (Mevik et al. 2020; R Core Team 2022), as described in Supplementary Information 1.1.
Separate PLSR models were developed for each variable (total Fe, soluble Fe, total Mn, and soluble Mn) and deployment. Based on the distinctly different chemical and biological characteristics between layers of the reservoir (i.e., epilimnion and hypolimnion), we found that the best fit was obtained when we used different models for the two layers. In stratified reservoirs such as FCR, Fe and Mn concentrations are much higher in the hypolimnion than the epilimnion. Therefore, we had an epilimnion model which included data from 0.1, 1.6, and 3.8 m and a hypolimnion model which included data from 6.2, 8.0, and 9.0 m (Table 1). Although we also collected data from 5.0 m, we did not include them in our analyses since this is at the transition between the two layers (metalimnion; see McClure et al. 2018) and thus not applicable to either layer. We developed separate models for the Turnover Deployment and the Oxygen On Deployment. In the end, we had four separate models for each of the four variables (total and soluble Fe and Mn), resulting in 16 different models.
To assess the uncertainty of the predictions made using PLSR, we calculated nonparametric bootstrap predictive intervals following methods described by Denham (1997) and reported in Supplementary Information 1.2. Model skill was assessed using the coefficient of determination (R2) from the linear regression between predicted and observed values, as well as the root mean squared error of prediction (RMSEP) for each model (following Wold et al. 2001 and Mevik et al. 2020).
All observational data, including the spectrophotometer data, are published in the Environmental Data Initiative repository (Carey et al. 2022a, Carey et al. 2022b, Carey et al. 2022c, Schreiber et al. 2022, and Hammond et al. 2022). All code used to analyze the spectrophotometer data with PLSR and generate the figures is available in the Zenodo repository (Hammond 2022).
3. Results
3.1 Routine Fe and Mn sampling trends
Weekly sampling at FCR showed levels of Fe and Mn in exceedance of the EPA standards during the 2020 and 2021 stratified periods, with maximum total Fe and Mn concentrations of 18.5 mg/L and 2.2 mg/L, respectively (Figure 2). Hypolimnetic concentrations of both metals generally increased throughout the summer stratified period of each year, until reservoir fall turnover (Figure 2). Following reservoir turnover, concentrations of both metals remained low (< 1 mg/L) until the following spring. HOx activation from 11 June until 02 December in 2020 resulted in substantially lower hypolimnetic total Fe but not total Mn concentrations (Figure 2).
3.2 PLSR Model Performance
A comparison of skill metrics among the 16 models revealed that PLSR performed best for models calibrated with higher Fe and Mn concentrations that exhibited a larger standard deviation (Tables 1, S1; Figure S10). Model skill was also sensitive to the number of components included in each model. For the Turnover Deployment, the number of components included in the PLSR models ranged from 3-5 (9-14% of n). For the Oxygen On Deployment, 4 components were used for all PLSR models (8-9% of n) (Table 1). Sample size was negatively correlated with R2, but positively correlated with RMSEP (Figure S10).
Turnover Deployment models explained a high proportion of the variability in total and soluble Fe and Mn concentrations, excluding hypolimnetic soluble Fe which had a poor model fit (R2= 0.06), due to extremely low concentrations (median = 0.02 mg/L) during this time period (Table 1; Figure 3). In comparison, Oxygen On Deployment models explained a lower proportion of the variability in total and soluble Fe and Mn concentrations, despite having larger sample sizes for calibration (Table 1). In particular, PLSR model performance for total and soluble Mn was notably lower for the Oxygen On Deployment than for the Turnover Deployment (Tables 1, S1). PLSR model performance also varied between the hypolimnion and epilimnion. For most models, the epilimnetic PLSR model had a higher R2 value than the corresponding hypolimnetic PLSR model (Table 1).
In most cases, PLSR predictions were within the range of concentration values in the calibration dataset (Figures 3, S11-12), but they did not capture some of the high-magnitude fluctuations in the sampling data. Analysis of the Fe and Mn time series (Figures 4D-E and 5D-E) and calibration (Figures S11-12) suggests that inaccuracy in the models was largely attributed to high calibration error for observations far from the mean concentration of the calibration data (i.e., outliers). Additionally, when predicting variables with relatively low concentrations (< 1 mg/L), especially with the epilimnion models, some predictions were in the negative range (Figures 4D-E; 5D-E).
3.3 Reservoir Turnover Deployment