## 2 Research Methodology
### Testing Methodology-CCME WQI  
The CCME Water Quality Index (CCME WQI) offers a practical way to summarize complex water quality data and communicate them effectively to a general audience. This index includes three key components: Scope--indicating the number of parameters that do not meet water quality guidelines; Frequency--showing how often these guidelines are not met; and Amplitude--reflecting the degree to which the guidelines are exceeded. The index generates a score between 0 (worst water quality) and 100 (best water quality), which is categorized into five descriptive levels for easier interpretation. The specific parameters, guidelines, and timeframes used in the CCME WQI can vary depending on regional conditions, the purpose of the index, and local water quality issues. Endorsed in 2001, the CCME WQI has since been widely utilized in Canada and internationally to report on water quality status. Extensive testing and evaluations of the CCME WQI have been conducted over the years. The User's Manual integrates the original development work with additional insights gained since 2001, updating the 2001 Technical Report and User's Manual. In our analysis, we adhered to CCME guidelines to calculate the water quality index for all twelve samples, considering data from the pre-monsoon, monsoon, and post-monsoon seasons. We calculated three variance measures from the selected water quality objectives: Scope, Frequency, and Amplitude. 'Scope (F\({}_{1}\))' denotes the extent of non-compliance with water quality guidelines over the specified period; 'Frequency (F\({}_{2}\))' represents the percentage of individual tests failing to meet the objectives; and 'Amplitude (F\({}_{3}\))' reflects the magnitude by which the failed tests deviate from their objectives. These factors are combined to produce a score between 0 and 100, representing the overall water quality. The WQI calculation follows the methodology outlined in the Canadian Water Quality Index 1.0 Technical Report (CCME 2001), where Scope is represented by F\({}_{1}\), indicating the level of non-compliance with water quality guidelines over the relevant timeframe. \[\text{F}_{1}=\left(\frac{Number\ of\ failed\ variables}{Total\ number\ of\ variables}\right)\times 100 \tag{1}\]  
where the number of failed variables means the number of parameters that have failed and the total number of variables is the total number of parameters tested, which in our case is 14. The measure for Frequency is F\({}_{2}\). This will represent the percentage of individual tests that do not meet objectives (referred to as 'failed tests'). \[\text{F}_{2}=\left(\frac{Number\ of\ failed\ tests}{Total\ number\ of\ tests}\right)\times 100 \tag{2}\]  
where the number of failed tests means the number of tests across all the data points that have failed and the total number of tests is the total number of tests, which in our case is 42 (14 \(\times\) 3, as we have considered three seasons). The measure for Amplitude is denoted as F\({}_{3}\), representing the extent to which failed values deviate from their objectives. This is determined through a three-step process:  
_Step 1--Calculation of Excursion_  
Excursion refers to the number of times an individual concentration exceeds (or falls below) the objective, particularly when the objective is set as a minimum threshold. When the test value is required to stay below the objective, excursions are calculated based on instances where the concentration surpasses this limit. \[\text{Excursion}_{\text{i}}=\left(\frac{Failed\ Tests\ Value_{\text{i}}}{ Objectives_{j}}\right)-1 \tag{3}\]  
_Step 2--Calculation of Normalized Sum of Excursions_  
The normalized sum of excursions, referred to as 'nse', quantifies the overall extent of non-compliance across individual tests. It is calculated by summing the excursions of individual tests from their respective objectives and then dividing this total by the number of tests, which includes both those meeting the objectives and those failing to meet them.