## 2 Materials and Methods
### Multivariate Analysis  
All multivariate analyses were carried out by software Pirouette ver. 4.5 (Inofmetrix, WA, USA). Several types of analyses were performed with different objectives and following the protocol of aquaphotomics data analysis [14] to ensure robustness and consistency. Hierarchical cluster analysis (HCA) was performed with the goal to examine natural groupings of water samples (clusters) according to the physico-chemical parameters measured by reference methods first, and then, second, using the NIR spectra. The clustering is based on their similarity, which is expressed by the Euclidian distance between clusters in the multidimensional space of variables chosen to describe the samples. The value of distance equal to 1 corresponds to the identical samples, whereas the value of distance equal to 0 corresponds to the most different samples. Before multivariate spectral analysis, the spectral preprocessing was applied in the form of standard normal variate transformation (SNV) [18] to correct the baseline effects, which are commonly present in the NIR spectra in order to reveal finer spectral features. To explore the magnitude of spectral changes in waters caused by the temperature perturbation, spectral subtraction was performed. The subtracted spectrum was chosen to reveal the differences in terms of pH, processing, aging and ion content. The principal component analysis (PCA) [19] was employed in order to explore the spectral data and look into the major sources of variation. In order to further explore differences in spectra of waters under temperature perturbation, discrimination analysis--soft independent modelling of class analogies (SIMCA) [20; 21]--was performed on the SNV transformed and smoothed (Savitzky-Golay, 25 pts) [22] spectra of waters, from which average of pure water (Q) at the corresponding temperatures was subtracted. The resulting interclass distance was analyzed as a function of temperature. This approach revealed different sensitivity and stability of waters to temperature change. The same analysis of interclass distance was used to explore differences between aged and freshly produced waters and processed and unprocessed waters. The objective of this analysis was to further explore differences between unprocessed and processed waters and whether processed water changes over time (2 years). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  
In order to evaluate which water absorbance bands are most affected by the change in temperature, the SIMCA analysis was performed on nine separate SNV transformed spectral datasets--one for each water under temperature perturbation. The discriminating powers for the thus developed classification models revealed the variables--i.e., wavelengths with highest ability to discriminate between classes of the same water at different temperatures. From the most influential variables that were found in the respective SIMCA models, 12 wavelengths were selected for the visualization of the absorbance spectral pattern of each water on aquagrams [14,23]. The following 12 wavelengths were selected: 1344, 1364, 1372, 1382, 1398, 1410, 1438, 1444, 1464, 1474, 1492 and 1518 nm. The aquagram type used for this purpose was \"classic\" [14], where displayed absorbance is normalized and averaged for different sample groups, and displayed on radial axes defined by the 12 selected water absorbance bands. The normalized absorbance is calculated as : \(A^{\prime}_{\lambda}=\dfrac{A_{\lambda}-\mu_{\lambda}}{\sigma_{\lambda}}\),  
where \(A_{\lambda}\)' is a normalized absorbance displayed on the aquagram, \(A_{\lambda}\) is the absorbance after SNV transformation, \(\mu_{\lambda}\) is the mean of all spectra for the examined group of samples after transformation, \(\sigma_{\lambda}\) is the standard deviation of all spectra for the examined group of samples after transformation and \(\lambda\) are the selected wavelengths.