Statistical Analyses


Correlations and Exploratory Data Analyses


Spearman rank correlations were used to evaluate nonparametric relations among key constituents for various site groupings (mainstem, tributaries, source/finished water) using PRIMER-E, version 6 (Clarke and Gorley, 2006). Correlations were considered significant at probabilities less than 5 percent (p<0.05). To better understand patterns within the data and among groups of selected sites/samples for exploratory data analyses, multivariate analyses (principal component analysis [PCA] and non-metric dimensional scaling ordination [NMDS]) were performed using PRIMER-E. For brevity, these results are not shown.


Confidence and prediction intervals for relations between concentrations of HAA5 and FDOM_in-situ were generated using SAS (SAS Institute, Inc., 2003). The regression-line parameters (slope and intercept) for the linear relation between the FDOM_in-situ and laboratory-derived HAA5 concentrations in finished water were applied to the time‑series FDOM_in-situ values to generate a predicted time series for HAA5 concentrations.


Carbon and Disinfection By-Product Formation Potential Loads and Yields


To quantify and better understand the carbon and DBP precursor sources during each of the basin-wide synoptic samplings, instantaneous loads were calculated by multiplying DOC, TOC, and DBPFP concentrations in milligrams per liter by streamflow in cubic feet per second, then multiplying by 2.447 to convert the units to kilograms per day. The carbon and DBPFP loads were compared to those at the CRW DWTP to evaluate the contribution from a particular site to that found in source water. The instantaneous yields (in loads per day per square kilometer) were calculated by dividing the instantaneous load by the basin area, thus providing an estimate of the loading “intensity” at each of the sampling sites at one point in time. It should be stressed that this is an exploratory analysis to help identify watershed DBP precursor sources; it is not intended to convey the magnitude of DBP formation under actual treatment conditions, and may not necessarily be representative of the full range of carbon concentrations or DBP yields at a site.


Parallel Factor Analysis (PARAFAC)


PARAFAC was used to decompose the fluorescence signatures in the corrected EEMs into unique fluorescent groups and provide more information about the character of the DOM pool (Bro, 1997). PARAFAC analysis is a type of three-way PCA that resolves absorption and emission spectra of orthogonal fluorophore groups (components) and determines loadings (proportional to concentrations) of each component. The component percentages were calculated by dividing the component loading of individual components by the sum of the component loadings to reveal qualitative differences between samples (Andersson and Bro, 2000). The Stedmon and Bro (2008) PARAFAC tutorial was used to develop the model with Matlab 2009A using the N-way toolbox, version 6.1 (Bro, 1997; Andersson and Bro, 2000). Goodness of fit was determined by visual inspection of the measured, modeled, and residual (measured minus modeled) EEM spectra, as well as by good agreement between duplicates. 


PARAFAC models were validated using a combination of (1) outlier identification, (2) residual analysis, (3) component validation, and (4) replication by split-half analysis (Stedmon and Bro, 2008). The model suffered from difficulties in distinguishing weak fluorescent components from instrument noises in the low-excitation wavelengths between 240 and 250 nm, which was remedied by censoring all the EEMs at 250 nm; signals below this cut-off value were not considered. The model used a non-negative constraint to help alleviate the instrument noise and detection in samples having low fluorescence. Several model iterations were performed with different subsets of samples, mostly to examine the effects of the finished-water samples on the model results. Results indicated the finished-water samples did not contain significantly different components compared to the untreated source-water samples; thus, they were included in the model. This is consistent with a previous study that examined oxidation effects of chlorine on fluorescence (Beggs and others, 2009).


First posted February 11, 2013