## 3 Results and Discussion
### Optimization of the W2 WQMP - Results and Discussion
This test provides an estimation of the number of n required in order to be able to observe a difference between rain event modalities (if there is one), with a defined threshold and a defined probability. The decision on the standard deviation, the probability and the time period for which the WQMP manager wishes to obtain the information on detecting effects of rain events must be supported by the IDSS. For instance, the decision on the standard deviation could be based on water quality classes for each observed parameter. An example would be fecal coliforms. The water quality classes provided by the Ministry of the Environment of Quebec have six classes for this parameter: \(\leq\)200 UFC/100 mL (good), 200-1000 UFC/100 mL (satisfactory), 1001-2000 UFC/100 mL (doubftul), 2001-3500 UFC/100 mL (bad), \(>\)3500 UFC/100 mL (very bad) [34]. Therefore, a standard deviation, which one would want to observe, is one where classes are changed. This is not an easy decision to make and could be considered as a biased decision, thus undermining the credibility of the WQMP. A suggested compromise would be to obtain an equal amount of samples for each modality of rain event for which differences were detected. This would result in the IDSS suggesting, as is the case here, to aim for 50% of modalities 0, 1, 2, and 4 and 50% of modality 3. The second actionable task (Table 3): Verify whether the sampling frequency was sufficient and whether a different type of sampling frequency should be adopted, leads to the application of a general linear regression with standard error test [4] for each variable at seven stations over the entire sampling period (2009-2016). \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Water Quality Parameter** & **Rain Event Modalities** & \
\begin{tabular}{c} **Number (n) of Samples** \\ **for Each Modality** \\ \end{tabular} &
\begin{tabular}{c} **Conclusions of the Kruskall –** \\ **Wallis Test** \\ \end{tabular} \\ \hline \multirow{6}{*}{Fecal coliform} & 0 - no rain for 48 h & 915 \\ \cline{2-4}  & 1- rainfall the same day & 199 \\ \cline{2-4}  & 2- rainfall 0–24 h prior to sampling & 429 \\ \cline{2-4}  & 3- rainfall 24–48 h prior to sampling & 126 & 1 and 2 and 4. \\ \cline{2-4}  & 4- rainfall 0–48 h prior to sampling & 295 \\ \hline \multirow{6}{*}{Total phosphorus} & 0 - no rain for 48 h & 918 \\ \cline{2-4}  & 1- rainfall the same day & 204 \\ \cline{2-4}  & 2- rainfall 0–24 h prior to sampling & 421 \\ \cline{2-4}  & 3- rainfall 24–48 h prior to sampling & 122 & 2 and 4. \\ \cline{2-4}  & 4- rainfall 0–48 h prior to sampling & 301 \\ \cline{2-4}  & 0 - no rain for 48 h & 840 \\ \cline{2-4}  & 1- rainfall the same day & 188 \\ \cline{2-4}  & 2- rainfall 0–24 h prior to sampling & 426 \\ \cline{2-4}  & 3- rainfall 24–48 h prior to sampling & 129 \\ \cline{2-4}  & 4- rainfall 0–48 h prior to sampling & 284 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the results of the Kruskall-Wallis test for the three water quality parameters. The results show that for all these stations and for all three water quality parameters, the sampling frequency (8 to 14 per year) should not be reduced. Stations 22 and 23 are visited more frequently than stations 1, 12, 17, and 21. An equal sampling frequency of all stations should be considered if the objective is to obtain a global picture.