## 2 Material and Methods
### Statistical Methods  
Basic descriptive statistics, such as minimum, maximum, mean, and standard deviation, were firstly computed. Additionally, the relative standard deviation (or coefficient of variation) was computed. The Shapiro-Wilk test of normality was applied to determine which variables adjusted to a normal distribution, to properly select further statistical methods. Based on the results of the test of normality, we adopted the non-parametric Spearman rank correlation test for the quantification of the correlation among the variables. Different spatial statistics were computed in order to assess the spatial distribution of the water characteristics. Spatial analysis was done with GeoDa software (Center for Spatial Data Sciences at The University of Chicago, Chicago, IL, USA; URL: [[https://geodacenter.github.io/](https://geodacenter.github.io/)]([https://geodacenter.github.io/](https://geodacenter.github.io/)), accessed on 30 September 2021). Firstly, a non-parametric spatial correlogram was computed as a measure of global spatial autocorrelation. This procedure does not imply the specification of a spatial weight matrix. It is based on a local regression fitted to the covariances or correlations computed for all pairs of observations, as a function of the distance between them [27]. Standardized variables (\(z\)) were employed, and the correlogram was computed as a local regression [28]:  
\[z_{i}\cdot z_{j}=f\big{(}d_{ij}\big{)}+u \tag{1}\]  
where \(d_{ij}\) is the distance between a pair of locations \(i\)-\(j\), \(u\) is an error term, and \(f\) is the non-parametric function to be determined from the data. Spatial correlograms allowed the identification of the (first) distance at which spatial autocorrelation ceased. This distance was specific for each parameter analyzed, and was then employed for their respective spatial weight's matrix for further analysis. This strategy, of computing a global statistic to assess the distance threshold, and then employing this information for further local spatial statistics, was successfully applied by [PERSON] et al. [29]. The second stage of the spatial analysis was the computation of the Moran's I statistic [30; 31]. It is computed as a cross-product between a variable and its spatial lag, with the variable expressed in deviations from its mean [28]. For an observation at location \(i\), this is expressed as:  
\[z_{i}=x_{i}-\overline{x} \tag{2}\]  
where \(\overline{x}\) is the mean of variable \(x\). The computation of Moran's I statistic is done with the following expression  
\[I=\frac{\sum_{i}\sum_{j}w_{ij}z_{i}\cdot z_{j}/S_{0}}{\sum_{i}z_{i}^{2}/n} \tag{3}\]  
with \(w_{ij}\) as the elements of the spatial weights' matrix, \(S_{0}=\sum\limits_{i}\sum\limits_{j}w_{ij}\) as the sum of all the weights, and \(n\) as the number of observations. Moran's I provided a measure of global spatial autocorrelation within the distance threshold specified for each water quality parameter by the respective spatial weights matrix. Values may range from \(-1\) (perfectly sparse values) to \(1\) (the largest spatial autocorrelation). A value equal to zero indicates a random pattern. Finally, a point pattern analysis was done by computing the Getis-Ord \((G_{i}^{*})\) statistic [32]. It compares the values for a given location, respecting the values at neighboring locations. The distance threshold is determined by the previously defined spatial weightsmatrix. The row standardized \(G_{i}^{*}\) statistic was computed according to the following expression [28]:  
\[G_{i}^{*}=\frac{\sum_{j}w_{ij}x_{j}}{\sum_{j}x_{j}} \tag{4}\]  
This statistic was employed to detect local focus of spatial dependence for each water quality parameter. The interpretation of the results is that, for a value larger than the mean, the \(G_{i}^{*}\) statistic suggests a high-high cluster or hotspot, while a value smaller than the mean indicates a low-low cluster or cold spot. Clusters resulting from the Getis-Ord statistic were employed for an additional statistical analysis.