**4. Water quality index calculation**

Though, a lot of water quality parameters are used for water assessment, some of the parameters seem to have a common similarity as they have their basis of comparing water quality parameters with their respective regulatory standards with interpretation of the results as good or bad [33].The parameters involved in the weighted arithmetic water index method water quality uses:

i. Degree of purity which is obtained from the most commonly measured water quality variables: temperature, biochemical oxygen demand, fecal coliform, pH, dissolved oxygen, total phosphates, turbidity, nitrates and total solids.

*Application of Water Quality Index for the Assessment of Water from Different Sources… DOI: http://dx.doi.org/10.5772/intechopen.98696*


The WQI is calculated by averaging the individual index values of some or all of the parameters within five water quality parameter categories that depicts the pollution level or status of the water:


The numerical value of the quality rating (*qi*) is obtained from the water quality data then multiplied by a weighting factor that is relative to the significance of the test to water quality. The formula below is used to obtain *qi*:

$$q\_i = \frac{c\_i}{s\_i} \propto 100\tag{1}$$

where,

*qi*, = quality rating scale. *ci*, = concentration of *i* parameter. *si* = WHO standard value of *i* parameter. Relative weight (*wi*) is calculated by

$$w = \frac{1}{s\_i} \tag{2}$$

The standard value of the *i* parameter is inversely proportional to the relative weight. The relative weight (*wi*) is calculated by

$$w\_i = \frac{w\_i}{\sum\_{1}^{n} w\_i} \tag{3}$$

Finally, overall WQI was calculated according to the following expression:

$$WQI = \frac{\sum\_{i}^{n} Q\_{iW\_{i}}}{\sum W\_{i}} \tag{4}$$

The sub-index Si and WQI are computed using the relationship in Eqs. (3) and (4), respectively

$$\text{SI} = w\_i \propto q\_i \tag{5}$$

$$WQI = \sum \text{SI} \tag{6}$$

where *SIi* is the sub-index of the *ith* parameter and *qi* is the rating based on the concentration of the *ith* parameter.

Ranking of WQI Values.

The Global Environmental Monitoring Systems [34] adopted the Water Quality Index (WQI) developed by the Canadian Council of Ministers of Environment (CCME) and based its development on the combination of three factors into one index. The detailed formulation of the WQI, as documented by CCME [17] and Amir *et al.,* [35] comprises three factors which include:

*Scope,* **F1** - the number of variables whose objectives are not met and calculated as

$$F\_1 = \frac{Number\ of\ failed\ Variables}{Total\ Number\ of\ Variables} \ge 100\tag{7}$$

*Frequency,* **F2,** � the frequency with which the objectives are not met.

$$F\_2 = \frac{Number\ of\ failed\ Tets}{Total\ Number\ of\ Tets} \ge 100\tag{8}$$

*Amplitude***, F3,** � the amount by which the objectives are not met. F3 is calculated in three steps:


$$\text{Exclusive}\_{i} = \frac{\text{Faidel test values}\_{i}}{\text{Objective}\_{i}} - 1 \tag{9}$$

For cases in which the test value must not exceed the objective:

$$Exclusion\_i = \frac{Objective\_i}{Exclusive\_iObject\_i} - 1\tag{10}$$

c. The collective amount by which individual tests is out of compliance is calculated by summing the excursions of individual tests from their objectives and dividing by the total number of tests (both those meeting objectives and those not meeting objectives). This variable, referred to as the normalized sum of excursions (*nse*), is calculated as:

$$mse = \sum\_{i=1}^{n} \frac{excurs\_i}{Number\ of\ tets} \tag{11}$$

d. F3 was thereafter calculated by an asymptotic function that scales the normalized sum of the excursions from objectives (*nse*) to yield a range between 0 and 100 as given in Equation

$$F\_3 = \frac{nse}{0.01nse + 0.01} \tag{12}$$

*Application of Water Quality Index for the Assessment of Water from Different Sources… DOI: http://dx.doi.org/10.5772/intechopen.98696*

The CCME WQI is determined using equation below:

$$\text{WQI} = \mathbf{100} - \frac{\sqrt{F\_{1+}^2 F\_{2+}^2 F\_3^2}}{1.732} \tag{13}$$

The calculation produces a score value that ranges between 0 and100. The higher the score the better the quality of water. The CCME WQI values ranges between 0 which depicts a worst water quality and 100, the best water quality [36]. The interpretation is that a water body with WQI scores that range between 71 and 100 are very suitable for the expected use, meet the required expectations for water quality and are of lowest concern, scores that ranges between 51 and 70 indicate marginal concern while a water body with WQI values with scores below 50 do not meet expectation and are of highest concern.

The CCME places the WQI values into five categories with the following interpretations [22]:


A number of indices have been developed to summarize water quality data in an easily expressible and easily understood format. The scores are then ranked into one of the five categories described below (**Table 3**) [34, 37]:


**Table 3.** *Ratings of water quality indices.*
