*2.2. Methodology*

In this study, the available groundwater level and chemistry data of 15 sample wells distributed across Ottawa city were first collected and analyzed from the Provincial Groundwater Monitoring Network (PGMN) Program of Ontario Province on the Ministry of the Environment, Conservation and Parks website [17]. Long-term qualitative data were used during a 17-year statistical period from 2002 to 2019. In this phase, the important parameters were considered to include Ca, Mg, Na, Cl, SO4, HCO3, NO3, F, pH, TDS, TH, K, EC, and alkalinity of groundwater quality.

In order to classify the water quality of groundwater and determine its type and characteristics, the GWQI index and Schoeller diagram method were used with the help of GIS software. Before that, the Schoeller diagram, a highly recommended method, was applied to investigate the quality of drinking water considering eight parameters including TDS, TH, Na, Cl, SO4, HCO3, Mg, and Ca. This diagram shows the concentration differences between the sample wells. It is drawn in six classes, including good, acceptable, average, inappropriate, completely inappropriate, and non-potable, based on several physio-chemical parameters to evaluate the quality of groundwater [8]. In the Schoeller diagram, an axis is considered separately for the parameters mentioned above, which determines drinking water quality [18]. Table 1 shows the classification of water quality using the Schoeller diagram method.

**Table 1.** The classification of water quality using the Schoeller diagram method (mg/L).


Next, The GWQI Index was utilized to determine the water quality of groundwater based on Ca, Mg, Na, Cl, SO4, HCO3, NO3, F, pH, TDS, TH, K, EC, and alkalinity parameters. After the definition of the parameters, three factors to determine the GWQI must be calculated. The values of the three factors were calculated as follow [19]:

*F1* shows the percentage of failed parameters relative to all of the measured parameters:

$$F\_1 = \left(\frac{Number\ of\ failed\ parameters}{Total\ number\ of\ parameters}\right) \times 100\tag{1}$$

*F2* demonstrates the percentage of failed tests:

$$F\_2 = \left(\frac{Number\ of\ failed\ tests}{Total\ number\ of\ parameters}\right) \times 100\tag{2}$$

*F3* indicates the value whereby failed test values did not meet their guidelines. *F3* is calculated in three steps.

Step 1. The number of times an individual's concentration exceeds the guideline is called an "excursion" and is expressed as follows. When the test value should not exceed the guideline:

$$\text{excursion}\_{i} = \left(\frac{\text{Faidel test value}\_{i}}{\text{Objective}\_{i}}\right) - 1\tag{3}$$

For cases where the test value should not be less than the guidelines:

$$\text{excursions}\_{i} = \left(\frac{Objective\_{i}}{Failed\text{ test value}\_{i}}\right) - 1\tag{4}$$

Step 2. The cumulative amount by which individual tests are out of compliance is calculated by summing the excursions of individual tests from their guidelines and dividing by the total number of tests. This parameter, called the normalized sum of excursions, or *nse*, is determined as follows:

$$nsc = \frac{\sum\_{i=1}^{n} \text{excursion}\_i}{\text{Number of tests}} \tag{5}$$

Step 3. Then, *F3* is calculated by an asymptotic function that yields the normalized sum of excursions from instructions (*nse*) to a range between 0 and 100.

$$F\_3 = \left(\frac{n\varkappa}{0.01n\varkappa + 0.01}\right) \tag{6}$$

Once the three factors have been obtained, the index itself can be calculated by summing the three factors as a vector and using the Pythagorean theorem. Therefore, the sum of squares of each factor is equal to the square of GWQI.

$$GWQI = 100 - \left(\frac{\sqrt{F\_1^2 + F\_2^2 + F\_3^2}}{1.732}\right) \tag{7}$$

A divisor of 1.732 normalizes the resulting values to a range between 0 and 100, where 0 represents the worst water quality and 100 represent the best water quality.

Computed GWQIs were classified into five categories including excellent, good, fair, marginal, and poor for human consumption in Table 2 [19]. The outcome of the index includes a number between 0 (worst water quality) and 100 (best water quality) [20,21].

Afterward, a spatial classification map for each important parameter of the Schoeller diagram and GWQI Index method was prepared as a raster layer based on the kriging interpolation technique in GIS. It should be noted that, in order to reduce the uncertainty of all the classified raster parameters, each parameter layer was fuzzified based on the linear membership function in GIS [22–24]. Then, the final interpolation layers of the two

methods (Schoeller and GWQI) were created by integrating fuzzy Raster layers as effective parameters using the fuzzy overlay tool. Finally, the classification map of the groundwater quality of the study area was generated by integrating the Schoeller and GWQI classified maps based on the overlaying method.



### **3. Results and Discussion**

In this study, the water quality parameters of sample wells in the city of Ottawa for the drinking sector were studied using the Schoeller diagram and the GWQI Index. Therefore, based on Schoeller's classification, the amounts of cations such as calcium (Ca), magnesium (Mg), sodium (Na), and anions such as chloride (Cl), sulfate (SO4), bicarbonate (HCO3), and two important parameters of total dissolved solids (TDS), and the total hardness (TH), were checked in the diagram, which is shown in Figure 2.

Regarding the discussion of limitations and practical implications in the current research, the groundwater quality in the urban area of Ottawa was explored. Using the approach implemented in this study, water quality could be analyzed concerning the environment, agriculture, and industry if more parameters were obtainable. However, due to the absence of pertinent environmental parameters such as BOD, COD, and DO, and industrial and agricultural parameters such as heavy metals including Fe, Cu, Zn, and As, and the time constraint involved in producing this article, only the drinking perspective was investigated concerning the quality of groundwater.

According to the diagrams (see Figure 2), the water quality of wells W1, W2, W4, W7, and W14 was in the good range; wells W3, W5, W6, W8, W9, W10, and W11 were in the acceptable range, and the rest of the wells were in the lower quality range. In general, it was concluded that about 71% of the parameter values were in the good range and 29% of the rest of the parameters were in other quality classes.

In the following, the values of each parameter of Schoeller's diagram were interpolated based on the six classes of Schoeller's classification in the ArcGIS software using the kriging method, and finally six classified maps were integrated with the Fuzzy Overlay tool in the form of the water quality classification map of Ottawa city (see Figure 3).

Based on to the classified map of Schoeller, the water quality in the classification for the Ottawa city area was in six categories, from good to non-potable. In the south, west, and north-west areas towards the center, the water quality was good and fair for drinking purposes, and from the central area towards the east and northeast, the water quality decreased. Based on the location of two wells, W12 and W13, it can be pointed out that saltwater infiltrated the groundwater resources of these areas, considering the high amount of Na and Cl ions and also the proximity of these two wells to the Ottawa River. According to Schoeller's classification map, some water samples may have good drinking quality, while those ones can contain other harmful and toxic substances; therefore, to solve this problem more parameters were used in the GWQI Index. Hence, those parameters such as electrical conductivity (EC), pH, alkalinity (mg/L CaCO3), Calcium (Ca), Sodium (Na), Magnesium (Mg), Potassium (K), Sulphate (SO4), Chloride (Cl), Fluoride (F), and Nitrate (NO3) were evaluated for the GWQI classification map.

**Figure 3.** Water quality classification map of Ottawa city using the Schoeller method.

Considering Equations (1)–(7), the annual average values of GWQI, considering Table 2, were calculated in the range of values 33 to 100. Therefore, the water quality in most wells for drinking purposes was rated in the range of excellent to good. The GWQI values were interpolated in the ArcGIS environment using the kriging method, shown in Figure 4. According to Figure 4, the southwest, west, and northwest regions towards the center of the study area have excellent and good drinking water quality, and from the central region toward the southeast, east, and northeast, the water quality is decreased due to the increase of NaCl ions.

**Figure 4.** Water quality classification map of Ottawa city using the GWQI Index.

Finally, after preparing Schoeller and GWQI classification maps, these two classified maps overlapped with the Fuzzy Overlay tool in ArcGIS. Additionally, the overlaid map was categorized into five classes from Excellent to Poor (see Figure 5). Furthermore, by investigating the integrated classification map, it was found that the values of groundwater quality were in the excellent and good class range for the area of Ottawa city in the south, west, and the northwest regions towards the center, and also the water quality range decreased in the east and northeast regions.

**Figure 5.** Integrated water quality classification map of Ottawa city.
