Darb El-Arbaein, a historic desert track running between Sudan and Egypt and passing El-Kharga Oasis to Assuit, is geographically located between 30°21′56.7″–31°27′4.1″ E and 24°40′28.5″–23°40′31.6″ N, in Southwestern Desert, Egypt. Arid climatic conditions are dominant and rainfall is rare. The area is considered one of the horizontal extensions for settlement developments in the Western Desert, which aims at establishing a link between the South Valley Project and Al-Kharga Oasis. The current project aims at reclamation 4654 ha and digging 85 wells of 150–500 m depth.

The project “Development of Trans-Sahara camel route between the Sudan and Egypt (Darb El-Arbaein)” is intended to: (a) reduce camel mortality due to inadequacy of water and services on a 1500 km long route to markets; (b) promote regional camel trade and improve the economies of the region; and (c) motivate desert nomads to become more interested in camel breeding and marketing [21]. Groundwater is the only available source of water in the area. The assessment of agricultural potentiality in the Darb El-Arbaein area requires water resource evaluation. The general geology and geomorphology of the area studied are outlined in the geology of Egypt [22] which is a desertic plateau with vast flat expansions of rocky deep closed in depressions (Figure 1). The greatest altitude is attained in the extreme southwestern corner where the general plateau character is disturbed by the great mountain Gebel Uweinat. The study area (Figure 1), which consists of four villages 1–4, encompasses around 5723.18 ha. The area of villages 1,2 is equal to 1933.45 ha, however; villages 3,4 have an area equal to 3789.73 ha.

The methodology adopted for groundwater quality mapping using water quality data in the GIS environment is shown in Figure 2. The study was carried out with the help of four major components: input from remote sensing data, topographic sheets, groundwater quality data and data collected during field visits. In order to evaluate the quality of groundwater for irrigation in the Darb El-Arbaein area, 36 surveyed wells (13 in villages 1,2 and 23 in villages 3,4) with GPS (Garmin eTrex Venture HC) data were used to produce the evaluation map. The water samples were collected after 30 min of pumping to avoid stagnant and contaminated water. White plastic containers of 1 L capacity were rinsed out three to four times with sampling water. Then the containers were filled up to the brim and immediately sealed to avoid exposure to air [23]. The containers were labeled for identification and brought to the laboratory. The groundwater samples were analyzed for (pH, EC, Na⁺, Ca⁺⁺, Mg⁺⁺, B, Cl⁻ and HCO₃^-) irrigation purposes. Sodium Adsorption Ratio (SAR), Soluble Sodium Percentage (SSP) and Residual Sodium Carbonate (RSC) were calculated on some standard equations basis. These equations are as follows:

The concentrations of the heavy metals (Co, Fe, Pb, Ni, Cd, Zn and Cu) were determined using atomic absorption spectrophotometer. Area elevation and depth to water were also measured. Water quality maps were generated for different water properties and surfaces were interpolated using Kriging interpolation technique. A salinity hazard map was prepared and delineated into three classes: unsuitable, moderate, and suitable. Thus the final groundwater quality map for irrigation purposes was prepared by overlying the above-mentioned grid data. Finally the study area was delineated.

The water quality evaluation model proposed in this study was developed in three steps. In the first step, principle component and factor model were developed. Parameters that contribute to most variability in irrigation water quality were identified using Principal Components and Factor Analysis (PC/FA) as described in SPSS (v.13). Factor analysis provides a useful tool to draw information from multivariate data by exploring the covariance structure among observable variables in terms of a smaller number of unobservable variables. In exploratory factor analysis, the model is usually estimated by the maximum likelihood method with the use of efficient algorithms and then a rotation technique, such as the Varimax method, is utilized to find a meaningful relationship between the observable variables and the common factors. A rotation method gets factors that are as different from each other as possible and helps you interpret the factors by putting each variable primarily on one of the factors. In other words, rotation of factors helps to define which underlying factor a set of items is most strongly associated with.

Indexes based on statistical techniques favor the recognition of the most characteristic indicators of the water under study. Factorial analysis allows the reduction of a great number of data obtained upon monitoring and permits an interpretation of the various constituents separately [24], making it possible to find a better selection of the relevant parameters for water quality classification [25,26]. The correlation matrix was calculated based on the normalized data of the 13 parameters, evaluated for the sampling sites throughout the Darb El-Arbaein. A preliminary analysis of the representative parameters of water quality was performed upon correlation matrix. According to [27] only values above 0.5 should be considered; this rationale was used in this study. In order to identify the most significant interrelation of water quality parameters in the Darb El-Arbaein area with each resulting factor of PC, a matrix rotation procedure was adopted using the Varimax method. This method minimizes the contribution of parameters with a lower significance to the factor such that the parameters will present loads close to one or zero, eliminating the intermediate values, which makes interpretation more difficult.

In a second step, a water quality index WQI model was proposed. A definition of quality measurement values (Qi) and aggregation weights (Wi) was established. Values of (Qi) were estimated based on each parameter value shown in Table 1.

Water quality parameters were represented by a non-dimensional number: the higher the value, the better the water quality. Values of Qi were calculated using the following equation, based on the tolerance limits shown in Table 1 and water quality results determined in the laboratory:

where qi_max is the maximum value of Qi for the class; x_ij is the observed value for the parameter; x_inf is the value corresponding to the lower limit of the class to which the parameter belongs; qi_amp is the class amplitude; x_amp is the class amplitude to which the parameter belongs.

In order to evaluate xamp of the last class of each parameter, the upper limit was considered to be the highest value determined in the physical-chemical and chemical analysis of the water samples, then Wi values were normalized such that their sum equaled one.

where Wi is the weight of the parameter for the WQI; F = component 1 autovalue; A_ij is the explainability of parameter i by factor j; i is the number of physical- chemical and chemical parameters selected by the model, ranging from 1 to n; j is the number of factors selected in the model, varying from 1 to k.

The water quality index was calculated by summation of Qi, and Wi values as:

where WQI is a dimensionless parameter ranging from 0 to 100; Qi is the quality of the ith parameter, a number from 0 to 100, a function of its concentration or measurement; Wi is the normalized weight of the ith parameter, a function of its importance in explaining the global variability in water quality.

Division in classes based on the proposed water quality index, which was based on existent water quality indexes, and classes were defined considering the risk of salinity problems, soil water infiltration reduction, as well as toxicity to plants as observed in the classifications presented by [29]. Restrictions to water use classes were characterized as shown in Table 2.

In a third step, the water quality data (attribute) was linked to the sampling location (spatial) in ArcGIS and maps showing spatial distribution were prepared to identify the variation in concentrations of the groundwater parameters at various locations of the study area. Different water quality maps were produced using point data like pH, EC, SAR, Cl, and B by ArcMap GIS software. Geostatistical analyses were performed using the Geostatistical analyst extension available in ESRI ArcMap (v. 10) [30]. Kriging differs from other methods (such as IDW), in which the weight function is no longer arbitrary, being calculated from the parameters of the fitted semivariogram model under the conditions of unbiasedness and minimized estimation variance for the interpolation. Thus, Kriging is regarded as best linear unbiased estimation (BLUE). A more detailed explanation of the method is given by [31,32,33,34,35]. Of the different Kriging techniques, the ordinary Kriging (OK) method was used in the present study because of its simplicity and prediction accuracy in comparison to other Kriging methods [31].

Geostatistical analysis was the first to fully explore the data in which the histogram, normality, trend of data, semivariogram cloud and cross covariance cloud of the raw data were observed [36]. Kriging methods work best if the data is approximately normally distributed [37]. Transformations were used to make the data normally distributed and satisfy the assumption of equal variability for the data. In ArcGIS Geostatistial Analyst, the histogram and normal QQPlots were used to see what transformations were needed to make the data more normally distributed. For each water quality parameter, an analysis trend was made. Directional influences (anisotropy) are critical to the accurate estimation of water quality surface. The directional search tool was used to remove the directional influences from the groundwater quality data. In this study, the semivariogram models were tested for each parameter data set. Prediction performances were assessed by cross validation. Cross validation allows determination of which model provides the best predictions. For a model that provides accurate predictions, the standardized mean error should be close to 0, the root-mean-square error and average standard error should be as small as possible (useful when comparing models), and the root-mean square standardized error should be close to 1 [37]. Finally, to produce a simple (salinity and WQI) hazard map, simple classes were used. The suitability map obtained from the computed index value was evaluated according to three categories: unsuitable (0–40), moderate (40–70), and suitable (70–100). Also the salinity hazard map was assessed based on three categories: unsuitable (˃1500 μScm⁻¹), moderate (1500–750 μScm⁻¹), and suitable (˂750 μScm⁻¹). The area with WQI value of less than 40 was considered to be poor quality irrigation water not suitable for irrigating agricultural fields. Such water could impair soil quality and result in yield loss. As a rule of thumb, water extraction from such areas should be avoided.

Table 3 shows the summary of the statistical evaluation of the laboratory analyses conducted on the samples. 15 of 20 parameters were used in the analysis at this stage because the remaining five parameters were used in the calculation of SAR and RSC parameters. The pH of the water samples was within a range of 7–8. The overall EC values varied between 642 and 2686 μScm⁻¹. EC was lowest for a sample collected from Village 1 (Sample 3) while the highest occurred in a sample from Village 4 (Sample 32). The chloride concentration of the water samples was within a wide range of 124.1–570.9 ppm. The concentration of chloride in most of the areas was high with the maximum of 570.86 ppm in Village 2 (Sample 9). The range of SAR values in the water samples was 1.83–8.47, where the highest SAR value related to Village 4 (Sample 32) and the lowest value related to Village 1 (Sample 3). Based on the RSC criterion, all water samples were −7.1 to −1.86 (Table 3). Water samples analyses revealed that heavy metal pollution of groundwater was low. The variations in the distribution of the investigated heavy metals (Cu, Fe, Pb, Mn, Ni and Zn) in the study area were small. Except for Cd whose concentration in the water samples was detected to be abnormally high (0.013 ppm) and above the standard value (0.01ppm) for irrigation [38,39], all other heavy metals were within the maximum permissible range (Table 3).

The only abnormal and interesting result of a higher Cd amount than the standard value in groundwater at the depth varied between 214 and 530 m. The reason for the existence of Cd in Darb El-Arbaein is that cadmium can be present in groundwater through contact with soluble rocks and minerals. The primary mineral associations of cadmium are with otavite (CdCO₃), greenockite (CdS). Soil weathering can lead to the release of the Cd²⁺ ions, which are generally soluble and mobile in water. Other sources of cadmium in groundwater include mining (sulfide ores of zinc), industrial operations, burning of fossil fuels, and fertilizer application. An important source of cadmium is the production of phosphate. Phosphate deposits were recorded at a depth of 600m in the Darb El Arbaein area [40]. Substitution of cadmium with natural apatite has also been documented [41] and may be a more common route for partitioning to phosphate minerals at concentrations undersaturated with respect to precipitation of cadmium phosphate. Cadmium is known to form solid solutions with calcium carbonate (calcite) [42,43,44].

Table 4 shows the correlation matrix for the analyzed parameters. High correlations (above 0.9) were observed between EC and SAR and Cl. Kaiser-Meyer-Olkin (KMO) adequacy test for coefficient magnitude comparison indicated an optimum value of 0.82, indicating that the factorial model may be applied without restrictions. A similar result was found by [45] in the water quality evaluation in tropical lake systems, with a KMO value of 0.85, considered adequate for the study.

Table 5 shows the principal component analysis application to describe the dispersion of original parameters which implies a four component model, explaining 77.393% of total variance, diluted in fifteen dimensions. This result is in agreement with the works of [25,27,46] in which the two to three first generated components explain a great part of the variation of original data (60% to 90%). In many cases the use of these components allows the description of the entire data system without significant loss of information. Selection of this four-component model used the criterion described by [47] considering only those components with a variance that had an auto-value above one. Any component must explain a variance above that presented by a single variable. This criterion is observed by [48] upon water quality evaluation in the Guadalquivir river in the south of Spain, where through PC three hydrochemical factors were identified with variances above unity and explaining 79.1% of total variance of the data.

Table 5 presents factorial loads for the chemical and calculated parameters. A matrix rotation was performed and data for factorial loads and communalities after transformation are presented in Table 5. The first Factor explains 43.371% of total variance in the data, whereas the second and third factors explain 15.366% and 11.510%, respectively. In the first Factor/Component, parameters such as elevation, depth to well, EC, SAR, Cl, B and Mn present a load above 0.70, indicating the most common composition of the observed parameters. In the second Factor/Component, parameters Zn and Ni show high factorial loads of 0.774 and 0.625 respectively. The fourth Factor/Component showed Cd as the element with the load (0.644).

In order to develop the proposed WQI, EC, Cl, Na, HCO3 and SAR parameters were used. These carry the major factorial load (above 0.82 in Table 5), that is, they best define water quality [46,47,48]. Only these parameters have reference, weight, and hazard ranges, however the other parameters are missing from in the literature. Henceforth, the weight of each parameter was based on the variance of the first factor (Table 6), associated with the explainability of each parameter, in relation to this factor. The normalized weights (Wi), computed through Equation (2), are listed in Table 6. The suitability index, which wascalculated based on Equation 3, is shown in Table 7.

Table 7 shows the suitability index map calculated. The suitability index is calculated to determine the suitability of water for irrigation purposes. Suitability index values revealed that the groundwater in the study area is of “suitable” quality with the suitability index ranging from 85 to 100 (two wells are of excellent water quality) and therefore can be used for irrigation usage. Most of the samples are very poor (25 wells) with a suitability index range from 40 to 55. One sample (well No. 32) is of “unsuitable” quality and cannot be used for irrigation purposes. Five wells are of good quality and three wells of poor quality. Overall, most of Village 1 wells are of good quality and can be used for irrigation with low restrictions, except for well No. 1 which is of very poor quality. Village 2 wells are of very poor quality with high restrictions for irrigation except for wells No. 7,11 that are of excellent quality and can be used for irrigation with no restriction. The wells of villages 3,4 are of very poor quality and can be used for irrigation only with high restrictions.

Overall, the results in Table 7 indicate that villages 1,2 generally have good water quality, however villages 3,4 have a very poor water quality. Restrictions for using this water in irrigation at long term are required especially because the soil texture is heavy and the climate is hot.

Water samples were taken from 36 wells in the study area. The data was checked by a histogram tool and normal QQPlots to see if it showed a normal distribution pattern. Normal QQPlots provide an indication of univariate normality. If the data is asymmetric (i.e., far from normal), the points will deviate from the line. Histogram and normal QQPlot analysis were applied for each water quality parameter. It was determined that electrical conductivity, chloride, Mn, Cd, Pb, Ni and SAR concentrations showed normal distributions, however, only the pH, B, and Zn parameters did not show normal distributions. For these parameters, a log transformation was applied to make the distribution closer to normal. For each water quality parameter, an analysis trend was made and it was determined that there was no global trend for all parameters. In this study, the semivariogram models (circular, spherical, tetraspherical, pentaspherical, exponential, gaussian, rational quadratic, hole effect, K-Bessel, J-Bessel, and stable) were tested for each parameter data set. Prediction performances were assessed by cross validation, which examines the accuracy of the generated surfaces.

Figure 3 and Table 8 list cross validation results of the examined validity of the fitting models and parameters of semivariograms for EC and Cl parameters. All of the water quality parameters were assessed by cross validation and given EC and Cl parameters as an example. For the EC sample, the standardized mean range is from 0.006153 to −0.000346 and the RMSS range is from 0.9642 to 0.9788. In this case, for the EC parameter the best fit is the J-Bessel model (SME −0.000346) and Circular model for Cl with a 0.005528 standardized mean error. It is closest to zero, and the 0.9788 RMSS value is closest to 1. When the average estimated prediction standard errors are close to the root-mean-square prediction errors from cross-validation, then you can be confident that the prediction standard errors are appropriate [37].

After applying different models for each water quality parameter examined in this study, the error was calculated using cross validation and models giving best results were determined. Table 9 shows the most suitable models and their prediction error values for each parameter. Table 9 also shows that for different parameters different models may give better results. For water quality parameters, RMSS range from 0.945 to 1.2452.

Table 10 shows parameters of water quality variograms. The ratio of nugget to sill variances, expressed as percentage, can be regarded as a criterion to classify the Spatial Dependency (Sp.D) of parameters. If the ratio is less than 0.25, the variance has strong spatial dependency and if the ratio ranges between 0.25 and 0.75, the variance has moderate spatial dependency. All parameters of water quality have a strong spatial structure except Cl (0.67). Also the effective ranges of most parameters are close together, within the range of 600 to 850 m.

Figure 4 shows the spatial distribution of different parameters (e.g., EC, pH, SAR, Cl…) in the study area and some selected parameters (e.g., Cd, Mn, and water depth), which have F1 and F4 factorial loads. The groundwater quality prediction maps show the concentration distribution generated from the surface map developed from the cross validation process.

The groundwater quality maps for agricultural purposes are shown in Figure 5.

The whole area is divided into three classes on the basis of EC. The water quality for irrigation purposes depends on the salinity classified into suitable, moderate, and unsuitable. Also, the map of WQI is presented. When the computed index value is bigger than 70, the area is considered to have minimum problems with respect to irrigation quality. Therefore, a well drilled in this zone is considered to represent ideal conditions for irrigation water quality. When the computed index value is between 40 and 70, the water demonstrates moderate suitability for irrigation purposes. On the other hand, values below 40 indicate water that should only be used with caution and better be avoided, particularly for sensitive crops. Three of the groundwater samples fall into the moderate WQI. Most of the samples (26) fall into the unsuitable WQI category. Seven samples fall into the suitable WQI category. Groundwater samples that fall into the low salinity hazard class and high WQI can be used in irrigation for most crops and the majority of soils.

The map of villages 3,4 (Figure 5) shows that 382.35 ha (10.09%) of area fall into the moderate category, however, much of the area (3407.38 ha) has unsuitable water quality. For the villages 1,2, the corresponding area of suitable category is 266.66 ha (13.79%), however, the moderate category is 1666.79 ha. The observed low suitability index of the groundwater quality is due to the desert location and the deficiency of water and rainfall, which leads to the need to dig deep and semi-deep wells. Since the map shows the spatial distribution of irrigation water quality in the area as index values, it is now much easier for a decision maker to assess the quality of water for irrigation purposes and further locate the most suitable site for drilling wells to extract irrigation water.

Groundwater resource degradation is an issue of significant societal and environmental concern in the Darb El-Arbaein area. In order to prevent groundwater pollution and avoid the future need for costly remediation efforts, GIS can be used to assess groundwater pollution. It is also helpful for the public to understand that the quality of water is a useful tool in many ways in the field of water quality management [49].