New Regression Model for Estimating Irrigation Water Quality Index

Water quality plays an important role in the general health of human life and the quality of agricultural production. That is why there are a great interesting in finding ways and tools to improve water quality and make it suitable for drinking and irrigation. In general, most of the water resources are exposed to pollution resulting from the various bad use of civic, agricultural, and industrial activities. Groundwater is one of the important water sources that are most exposed to pollution as a result of these activities. Therefore, determination and investigation of the groundwater quality are continuously conducted in many regions in the world for different purposes [1]. The quality of groundwater can be affected by the geological actions and different types of activities induced by human, which result from industrial wastes, agricultural processes, municipal and residential activities [2]. The evaluation of groundwater quality requires conducting of continuous measurements and observation [3]. Assessment of the groundwater quality depends on its physical, chemical, and biological properties. The suitability of a groundwater for irrigation purposes is founded by the amount and kind of salts that the groundwater contains [4].

The most common tool for assessing groundwater and surface water quality is so-called Water Quality Index (WQI), which has been widely used in conducting many studies in this field. WQI is defined as a mathematical tool for expressing a variety of physical and chemical variables polluting water in the form of a single variable representing the assessment of water quality in a given area and time [5, 6]. For irrigation, the WQI is abbreviated as IWQI, which is calculated by different methods and models. One of the common models is called the Brazilian’s model developed by Meireles et al. [7]. This model is found to be suitable and efficient to evaluate the water quality for irrigation purposes by many researchers, e.g. [8-12]. The parameters that mainly required to determine the IWQI are concentration of salinity (Electrical Conductivity) (EC), Sodium Absorption Ratio (SAR), sodium (Na⁺¹), chloride (Cl^-1), and bicarbonate (HCO₃^-1).

Omran [13] derived a new weighted value of the parameters of Meireles model and used this model to assess the groundwater quality for irrigation purposes in the Darb El-Arbaein region, Southwestern Desert, Egypt. Omran’s results showed that most of the groundwater samples were unsuitable for irrigation. Al-Mohammed and Mutasher [14] conducted a study using a WQI techniques to evaluate the quality of groundwater for drinking purpose in Dibdiba aquifer, Kerbala city, Iraq. They found that the groundwater was unsuitable for drinking purposes for all studied wells. According to IWQI values; Siswoyo et al. [15] found that the quality of groundwater was between no restriction and moderate restriction for irrigation purposes in Jombang Regency, East Java, Indonesia. Gidey [16] developed an IWQI model based on parameters proposed by the University of California Committee of Consultants (UCCC) and the criteria established by Ayres and Westcott [17], with the same procedure that adopted by; Meireles et al. [7] and Omran et al. [18]. Gidey used his model to assess the groundwater quality in Elala catchment, Northern Ethiopia. The model results showed that the quality of groundwater included all the categories of classification with different percentages. Depending on Meireles model, Al-Kubaisi et al. [19] used a GIS technique to draw maps of the groundwater quality Index for irrigation in the Dibdibba aquifer at Karbala - Najaf plateau, central of Iraq. The spatial distribution of IWQI shown on these maps indicted that the groundwater quality in Dibdibba aquifer is generally within moderate category of quality. Nwankwoala & Amachree [20] used the weighted arithmetic index method adopted by Duckad et al. [21] for determination of WQI to evaluate the groundwater quality in contaminated areas in the Niger Delta. Their results for the Water Quality Index (WQI) ranged from 53.55 to 112.92, indicating that the quality of this water fell into the water quality categories; Poor; (WQI: 50-75), Very poor; (WQI: 75 -100), and Unsuitable; (WQI ˃100). Therefore, the quality of the groundwater was inappropriate for human consumption as a drinking water. This study recommended that treatment plants should be installed in the pumping system of groundwater before using for drinking and other purposes.

Al-Hadithi et al. [22] presented a study based on the complementarity of the Brazilian model developed by Meireles et al. [7] with ArcGIS technology in order to assess the appropriateness of groundwater quality for irrigation. The study was conducted to generate maps showing IWQI values for twelve groundwater wells at different locations in Baghdad, the capital of Iraq. The maps results showed that 25% of the groundwater wells can be classified within the low Restriction (LR) categories; IWQI: 70-85, this means that they are suitable for irrigation with low restrictions, and 46% of these wells are classified under the category of Moderate Restriction (MR) categories; IWQI: 55-70, which indicates that they are suitable to irrigate moderately salts tolerant plants, and can be used only in soils with a high permeability, requiring moderate leaching of salts. The map results also showed that 26% of the studied wells should be avoided and not used for irrigation under normal conditions because they fall within the Severe Restriction (SR) categories; IWQI: 0-40. The former type of water can be used to irrigate only highly salt tolerant plants and only if the soil permeability is high, and the excess of water is applied to avoid the accumulation of salt.

Al Maliki et al. [23] presented a study to assess the groundwater suitability for irrigation in an agricultural area. Their findings showed that the IWQI index together with GIS can prepared the final water quality maps using spatial distribution tools. These maps can help the decision makers in the assessment and management of groundwater quality. The results confirms that all groundwater samples over the study area are suitable for agriculture.

In the present study, the quality of groundwater was assessed for seventy-eight outlet wells in the Dibdaba Basin between Karbala and Najaf governorates in Iraq. The IWQI of Merieles’s model [7], was applied to assess the groundwater quality for irrigation purposes. A new non-linear regression model of IWQI was developed by using the SPSS software program depending on the results of the Merieles’s model. Moreover, this new model was verified by using other observed data. The novelty of this study is to find a new model that is easy to use and efficient in estimating the irrigation water quality index and predicting of the groundwater quality in the study area for future studies instead of other methods.

3.1 Collected data

Data were collected for the physical and chemical parameters investigations of the water quality of seventy-eight wells as an annual average for the year 2018. Table 1 shows the geographical coordinates of these wells. Figure 1 shows the Google Earth map of wells location. All these wells are constructed in unconfined aquifer of the study area. The physical and chemical parameters are electrical conductivity (EC), sodium (Na⁺¹), chloride (Cl^-1), calcium (Ca⁺²), magnesium (Mg⁺²), and bicarbonate (HCO₃^-1). It should be noted that measurements were carried out in the Central Water Laboratory of the Karbala Agriculture Directorate, according to the standard specification adapted from American Public Health Association [29].

3.2 Determination of the irrigation water quality index (IWQI)

The IWQI was determined depending on the Meireles’s model [7], as follows:

(1) The collected parameters mentioned above were selected because they are the most effective variables in the water quality used for irrigation purposes.

(2) The quality measurement of the irrigation water, qi, for each parameter were computed by using Eq. (1) [7], based on the measured water quality data and the criteria of limits of tolerance shown in Table 2.

Table 1. Geographical coordinates of wells location in the study area

Table 2. Values of the parameter's limits used for quality measurement (qi) computation [7]

Table 3. Weight values of the IWQI parameters [7]

$\mathrm{qi}=\mathrm{qi}_{\max }-\left[\frac{ \left.\left(\mathrm{Xij}-\mathrm{X}_{\mathrm{inf}}\right) * \mathrm{qi}_{\mathrm{amp}}\right)}{\mathrm{X}_{\mathrm{amp}}}\right]$  (1)

where,

qi_max = the maximum value of the qi,

xij = the observed value of the quality parameter,

x_inf = the lower limit of the quality parameter,

qi_amp = the category amplitude of qi,

x_amp = the category amplitude of the quality parameter.

The x_amp of the last category of each parameter is determined by considering that the upper limit of this category is the highest measured value.

(3) The IWQI is computed as follows [7]:

$\mathrm{IWQI}=\sum_{i=1}^{\mathrm{n}}$ qi wi  (2)

where,

• wi is the weighting value of the ith water quality parameter shown in Table 3. This value was established by Merieles’s model depending on the importance and effectiveness of each parameter on the overall quality of irrigation water.
• IWQI is a dimensionless number ranged from 0 to 100 and divided by five categories indicating the restrictions use of the irrigation water in agriculture as shown in Table 4 [7, 12].

(4) The sodium adsorption ratio (SAR) that depends on the ions concentration of calcium, magnesium, and sodium is calculated as follows:

$\operatorname{SAR}=\frac{\mathrm{Na}^{+1}}{\sqrt{\frac{\left\{\left(\mathrm{Mg}^{+2}\right)+\left(\mathrm{Ca}^{+2}\right)\right\}}{2}}}$  (3)

where, Na⁺¹, Mg⁺², and Ca⁺² are in meq/l. Because of continuously dissolving the calcium by the water leaching inside the soil like the rainfall water and the irrigation water, its concentration changes in the soil water. Therefore, Eq. (3) had been modified to process this change by using the concentration of equilibrated calcium (Caeq⁺²) instead of the concentration of calcium. Thus, the SAR in Eq. (3) is changed to the adjusted SAR with a symbol of SARadj [4]. The details of the procedure to compute the concentration of equilibrated calcium were explained by Lesch and Suarez [30].

Table 4. Classification of irrigation water quality index (IWQI) [7]

3.3 Development of a non-linear regression model of IWQI

The software package–IMB Statistics Product and Service Solution (SPSS) version 25 was used to establish a non-linear model of IWQI. First, the irrigation water quality parameters; EC, SAR_adj, Na⁺¹, Cl^-1, and HCO₃^-1 for seventy-eight wells were divided into two parts; the first part consisted of data of sixty-nine wells was used to calibrate the proposed model, and the second part contained data of nine wells was used to verify the validity stage. Second, the regression relation between IWQI calculated by Eq. (2), and each one of the mentioned parameters was determined by using curve fitting estimation analysis, which gives eleven model description of relations for each regression between IWQI and each one of these parameters. For these eleven relations, the relation of best fit, the highest value of the coefficient of determination (R²) was selected. Thus, five relations were obtained, and each of them represents the relation of IWQI with one of the quality parameters. Third, these five relations were combined in one equation with unknown coefficients and then used nonlinear regression analysis to find a non-linear model of IWQI with the quality parameters. Fourth, the calibration for the proposed model was performed depending on the value of R². Finally, the validity of the new non-linear model was verified through testing the coefficient of determination between the values of IWQI estimated by the proposed model and the IWQI values calculated by Eq. (2).