Introduction

Scientists concerns about environmental issues, in particular about water pollution, have incremented along with an increase in urban, agricultural, and industrial activities (Baghvand et al. 2010; Gharibi et al. 2012). Evaluation of groundwater quality is accomplished using various chemical and physical parameters, among which the most common index is called the water quality index (WQI) (Kumar 2010; Gharibi et al. 2012). The quality of water resources is affected by a wide range of natural and human influences (Rui et al. 2015; Babanezhad et al. 2017) and sustainable attainment of water resources development requires having water quality conditions (Vaishali and Punita 2013). Therefore, determination of chemical conditions is a more accommodative method for the evaluation of groundwater quality (Ishaku et al. 2012). Since the chemical quality of groundwater undergoes some changes in various ways such as pollution transfer through soil, precipitation, agriculture, etc. (Babiker et al. 2007; Qaderi and Babanezhad 2017), long-term managerial decisions will be difficult to provide water for many regions (Qiao et al. 2009). This problem always has many serious managerial challenges when choosing the most optimum sources.

The chemical composition of water resources has a direct effect on human health, and thus, measurement of WQI has attracted a great deal of interest. The application of fuzzy set theory for decision-making in the assessment of groundwater quality for drinking purposes has been studied. The authors used the combination of membership functions (MFs) in the MATLAB software and GIS data to make equal ion concentration lines (Samson et al. 2010). Backman et al. (1998) presented a methodology for evaluating and mapping the degree of groundwater contamination by applying a contamination index (Cd). They hereby identified the effective parameters by incrementing the amount of contamination. Baghvand et al. (2010) conducted hydro-chemical studies of the quality of groundwater in a desert area in the central part of Iran. In this research, some qualitative parameters such as sodium, calcium, and chloride were investigated to provide drinking or irrigation water. Mir et al. (2017) conducted studies on the quality of water resources in Sistan-Baluchistan of Iran to manage a probable water shortage in dry spells. They also utilized the Schoeller diagram method to classify the water resource types. Similarity, Aksever et al. (2016) also used the Schoeller diagram method to determine the quality of water for drinking and irrigation purposes in one Turkish region. Other research which took advantage of this method was conducted by Al-Barakah et al. (2017). In this research, the chemical properties of groundwater in one part of Saudi Arabia were investigated. Many other investigations have also been carried out based on the time series without considering the space dimension (Baghvand et al. 2010; Gharibi et al. 2012; Basavarajappa and Manjunatha 2015; Al-Barakah et al. 2017; Sheikhy Narany et al. 2017; Wagh et al. 2018; Wijesiri et al. 2018).

In the past, quality assessment of water resources has been conducted in accordance with a point approach which was incapable of illustrating water quality over a district. Accordingly, utilization of continuing models has been interested in expanding the area of study. Videlicet, geographic information system (GIS) has frequently been used to assess groundwater quality around the world (Babiker et al. 2007; Yammani 2007; Nas and Berktay 2010; Yan et al. 2016). Babiker et al. (2007) investigated groundwater quality resources using GIS tools in the eastern part of India. Nas and Berktay (2010) also used GIS to access the most optimum quality of water according to data from 177 wells in the central part of Turkey. Yammani (2007) and Yan et al. (2016) conducted an investigation into the quality of drinking water by the GIS in parts of India and Japan, respectively. They managed to show the quality of water on a map using a weighting method for each qualitative indicator.

The Schoeller diagram is one of the classical procedures in the assortment of drinking water quality which distinguished various parameter concentrations on a single graph and provides the ability to compare parameters. Many investigations have been conducted according to this method (Baghvand et al. 2010; Saka et al. 2013; Kura et al. 2015). However, the results of this diagram are limited to one point which represented to the whole area (Obeidat et al. 2013; Abba 2015; Abu Bakar and Zarrouk 2016). There is no feasibility of qualitative categorization of the surrounding area, and thus the characteristics of abundant points are required in furtherance of investigating. In some previous studies, the GIS capabilities has been disregarded for developing of established procedures in water management quality (Nas and Berktay 2010; Jasrotia et al. 2013; Tian 2016; Mir et al. 2017). Accordingly, in this current work, the authors seek to present a novel method for developing Schoeller diagrams over a region through GIS information. The new method is called S-GIS, to provide classification maps of groundwater quality. According to the collected data during the 1 year studied for 105 deep and semi-deep wells that were located around of Khorramabad, the quality of groundwater was tested for drinking use. For this purpose, the concentrations of each parameter such as HCO3, SO4, CL, Mg, Ca, TDS, TH, and Na were evaluated and the final result of Schoeller diagram became recognizable for a thorough coverage of points in this area.

Materials and methods

Study area

The study area (Fig. 1) is situated in central part of Lorestan state (Khorramabad) in Iran, which is located between 48°01′ and 48°39′ longitudes and 33°17′ and 33°47′ latitudes, encompassing a geographical area of about 1966 km2 with a mean elevation of 1260 m above sea level. This location is classified as Csa (hot-summer, Mediterranean climate) by Köppen and Geiger (Kottek et al. 2006). About 488 mm of precipitation falls annually.

Fig. 1
figure 1

Study area

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Sampling

To appropriately cover the area, 105 drinking water wells were considered in the study area for sampling the groundwater which has a depth range of 25–90 m. Sampling has been conducted at the average depth. The sampling procedure consisted of water being taken from the wells, waiting for 10-min settlement, and the sampling from the supernatant. All samples have been taken daily from the wells during a month period. The physical parameters such as pH, EC, and temperature were measured in situ, and to conduct chemical analyses, samples were transported to the laboratory. All ion analyses have been conducted through HANNA instrument (HI 83200) according to the standard methods for the Examination of Water and Wastewater of APHA (American Public Health Association 2014).

GIS

The first time that a geographical information system was considered was in Canada in 1960. After that and over the years, use of GIS has expanded. The system has some features such as collecting and the saving data, analysis and simulation of information, and then updating of the results. In addition, the system can show the general function of the output to users, based on the analysis of the information. Fig. 2.

Fig. 2
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GIS performance algorithm

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Information management and access to numerous wide ranges of data are the advantages of using a GIS database. The structure of the information must be designed with a logical relationship the between data to combine spatial and descriptive data. Due to the using of a variety of sources of information, the data management algorithm should be designed with an ability to retrieve and access all information that is classified according to geographical location to complete the database. GIS can play an important role in many cases such as resource management, making an algorithm for spatial distribution of natural phenomenon, analysis of the relationship between variety of phenomenon, and classification of spatial layers.

GIS method to spread

In GIS maps, each point can be determined by a certain quantity based on user’s need. In most cases, this amount has the most similarity to the nearest adjacent points. Accordingly, it is possible to estimate the quantity of unknown point with using the known point. Approaches to estimate the unknown point are called interpolation, in which each of them implements a certain method to calculate. The data which are used as inputs in interpolation are a kind of point data which can be used to make a Raster file. Some of the most important of interpolation methods are mentioned as follows (Steinbach and Hemmerling 2012; Zheng et al. 2016; Şener et al. 2017).

Thiessen polygon method

In Thiessen polygon method, the known points connected to each other by lines, and then, the perpendicular bisector of lines are drawn; by connecting them, some polygons will be made around each known point. It is assumed that each known point represents the general condition of a polygon. Figure 3 shows a sample of division through the Thiessen polygon method (Croley and Hartmann 1985; Lock and Pouncett 2017).

Fig. 3
figure 3

Sample of division by Thiessen polygon method

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Inverse distance weighting (IDW) method

Inverse distance weighting is considered as the most important interpolation method. In this method, each unknown point has a certain weight which is calculated based on the distance between known points. These weights are controlled by a power system in which high power declines the impact of further point (related to the known point) and lower exponential distributes the weights between adjacent points, more uniformly. Equation (1) shows calculation of weights in this method:

$${\lambda _i}=\frac{{D_{i}^{{ - \alpha }}}}{{\mathop \sum \nolimits_{{i=1}}^{n} D_{i}^{{ - \alpha }}}},$$
(1)

where \({\lambda _i}\) is the weight of known point (i), D i is the distance between know points (i) and unknown point, \(\alpha\) is power weight, and n is the number of adjacent point (Huang et al. 2011; Gong et al. 2014).

Kriging method

To implement the Kriging method and to calculate the weights of the interpolation equation, the first step is to analyze the spatial structure with the aid of the semi-variogram tool defined as follows:

$$\gamma \left( h \right)=~\frac{1}{{2n(h)}}~\mathop \sum \limits_{{i=1}}^{n} {\left[ {z\left( {{x_i}} \right) - z\left( {{x_i}+h} \right)} \right]^2},$$
(2)

where \(\gamma \left( h \right)\): the value of semi-variogram for data pairs which are located in the h distance, h is the distance between x i and x j , \(n(h)\): the number of data pairs that satisfy x i  − x j  \(\cong\) h, \(z\left( {{x_i}} \right)\) the value of z in location of x i , and \(z\left( {{x_i}+h} \right)\) the value of z which located in h distance from x i (Wheater et al. 2008).

After calculating the semi-variogram, a theoretical model such as spherical (Eq. 3) or Gaussian (Eq. 4) is fitted to it:

$$\begin{array}{*{20}{l}} {\gamma \left( h \right)={c_0}+c\left( {\frac{{3h}}{{2\alpha }} - \frac{1}{2}{{\left( {\frac{h}{\alpha }} \right)}^3}} \right),}&{0<h \leqslant \alpha } \\ {\gamma \left( h \right)={c_0}+c,}&{~h>\alpha } \\ {\gamma \left( h \right)=0,}&{h=0} \end{array},~$$
(3)
$$\begin{array}{*{20}{l}} {\gamma \left( h \right)={c_0}+c\left( {1 - \exp \left( { - 3\left( {\frac{{{h^2}}}{{{\alpha ^2}}}} \right)} \right)} \right),}&{h>0} \\ {\gamma \left( h \right)=0,}&{h=0} \end{array},$$
(4)

where C is the sill (total variance), C0 is the nugget (variance of the spatially uncorrelated portion of the field), and \(\alpha\) is the range (distance over which the field is correlated) (Burkholder 1961; Wheater et al. 2008).

Implementation of these condition in kriging method leads to solve of the following matrix equation (Eq. 5):

$$AX{\text{ }}={\text{ }}B \to X~={A^{ - 1}} \cdot B,$$
(5)

where A is the C ij matrix [the quantity of semi-variogram between known points (i) and (j)], B is C oj matrix [the quantity of semi-variogram between point (i) and unknown point], and X is coefficient matrix of \({\lambda _i}\) [weight of (i) point to estimate the unknown point] (Wheater et al. 2008).

Radial basis function (RBF) method

In RBF method, a general function is used, which depends on the distance between the unknown and the unknown points. This equation is defined as follows (Eq. 6):

$$Z\left( x \right)=~\mathop \sum \limits_{{i=1}}^{m} {a_i}~{f_i}\left( x \right)+\mathop \sum \limits_{{i=1}}^{m} {b_j}~\varphi \left( {{d_j}} \right),$$
(6)

where \(\varphi \left( d \right)\) is the radial basis function, \({d_j}\) is the distance between known and unknown point, and f(x) is the trend of the Polynomial function with the power less than m (Webster and Oliver 2008).

This method is divided into five different spline categories based on the polynomial type such as completely regularized spline (CRS), spline with tension (ST), multiquadratic spline (MQ), inverse multiquadratic spline (IMQ), and thin-plate spline (TPS). The functions of each method have been mentioned in Eqs. (7)–(11):

$${\text{CRS:}}\;\;~\varphi \left( d \right)=~\ln {\left( {\frac{{cd}}{2}} \right)^2}+~{E_1}{(cd)^2}+\gamma ,$$
(7)
$${\text{ST:~}}\;\;\varphi \left( d \right)=~{\text{ln}}\left( {\frac{{cd}}{2}} \right)+~{I_0}(cd)+\gamma ,$$
(8)
$${\text{MQ:}}\;\;\varphi \left( d \right)={\left( {\sqrt {{d^2}+{c^2}} } \right)^{ - 1}}$$
(9)
$${\text{IMQ:}}\;\;\varphi \left( d \right)=\sqrt {{d^2}+{c^2}} ,$$
(10)
$${\text{TPS:}}\;\;\varphi \left( d \right)=~{c^2}{d^2}\ln (cd),$$
(11)

where c is a factor to estimate of smoothness of curvature, \({I_0}\) is Bessel functions, and \(\gamma\) Euler’s constant (Wessel and Bercovici 1998; Dobesch et al. 2007; Webster and Oliver 2008).

Assessment and selection of the appropriate interpolation method

Choosing the appropriate interpolation method is depending on the nature of the variable and its spatial variations. Therefore, it is very difficult to provide a straightforward policy to choose a method. However, Thiessen polygon is one of the practical, simplest, and most popular methods (Dobesch et al. 2007; Lock and Pouncett 2017). On the other side, the other methods such as kriging, radial basis function, or inverse distance weighting need a large number of known points in area (Dobesch et al. 2007; Gong et al. 2014). This condition also can restrict the user. In addition, it seems that analysis based on these methods needs a long time for running the process. Therefore, it will not appropriate to make multiple maps’ project.

S-GIS approach

The Schoeller diagram (Schoeller 1965) allows the major ions of many samples to be represented on a single graph, in which samples with similar patterns can be easily distinguished. In the present study, the CSD method contains major cations (Na+, Ca2+, and Mg2+) and major anions (SO42−, HCO3−, and Cl−), along with total hardness (TH) and total dissolved solids (TDS). Six quality categories of groundwater for drinking use have been determined to related characteristics (Table 1).

Table 1 Schoeller assortment for assessment of groundwater quality for drinking use
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However, this classification is very difficult and impossible to do if it needs to describe water resources over a wide area. For this reason, there are two ways to deal with this situation: first, take samples from a large number of wells in a wide area, and second, estimate the quality of resources according to a fewer number of wells and generalize to other areas with a high level of error.

The combined use of GIS and Schoeller diagrams provides a new tool to investigate the quality of water in an extensive area. Therefore, the groundwater resources in Khorramabad plain in the western part of Iran were studied. In this area, the qualitative information from 105 wells was collected. Then the data in an excel file were given to ArcGIS software version 10.3 as input data. The UTM coordinate system and concentration of each parameters based on the Schoeller diagram existed in each set of information. After locating the UTM coordinates of each wells on the map, the study area was determined to be 1966 km2. After that, separate shape files were created for all of eight measured parameters. Then, raster files were created by converting the shape files to tin files. In this case, two types of information can be extracted: first, the relative classification of each parameter in the region and then identify upper and lower concentrations; second, classification of parameters based on the Schoeller diagram limitations. Finally, using vector files and quality of water can be determined by combining all Schoeller diagram parameters. As a result, by selecting any arbitrary point in the study area, it is possible to show the output based on the Schoeller diagram.

Results

According to the analysis that was done by GIS, relative concentrations for each parameter as well as the condition of the qualitative parameters based on the Schoeller diagrams were determined in an integrated approach over the study area. The results are shown in Fig. 3.

CSD method

To make CSD of the aquifer, an average of each quality parameter was calculated, and then, the related diagram was drawn (Fig. 4). The results indicate that all parameters placed in the Good category except calcium and magnesium. This evaluation provides an overall view of the aquifer, since there are some points that have unsuitable or moderately suitable quality. However, remember that the CSD method does not predict water quality for other extractable points in the region.

Fig. 4
figure 4

Schoeller diagrams according to average and maximum of ions concentrations

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Assessment of groundwater quality

One of the most important features of S-GIS map is to increase the accuracy of the determination of water quality. According to Fig. 5, the total area of study region was estimated about 1966 km2. If testing the quality of water uses the CSD approach, the total number of wells, i.e., the measured points, will be 105 spots. Therefore, regarding the total area, it can be said that, for every about 19 km2, there will be one unique quality. According to basic definitions, raster data are a type of digital imagery consist of an array of same-sized cells. If a large cell size is selected, the imagery is too coarse to display the detailed information or smaller features. The smaller cell sizes lead to higher quality of the raster data but require larger space for storage and take longer to access and process (Tian 2016). Therefore, a balanced approach implemented to ensure good data quality and system performance. Whereas, it has been reported that varying the model cell sizes (in normal ranges) has no significant effect on simulation of groundwater quality (Oladeji 2011). In the present study, all vector data were converted into raster format with a cell size (pixel) of 245 × 245 m. At this case, the number of evaluation spots in S-GIS approach was increased from 105 to 32,374 (total area of the study region divided by the cell size), which led us to have one unique quality for each 60,000 m2 (0.06 km2). As a result of this comparison, the accuracy of the determination of water quality had 317 times increase. In addition, due to this capability of the S-GIS mapping, it is possible to increase this accuracy by using a smaller areal zone.

Fig. 5
figure 5

showing the tested point in two approach

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Figure 6 shows the determination of water quality in two different approaches: first, the relative quality of water resource for each parameter, and second, quality of water according to the Schoeller diagram.

Fig. 6
figure 6

Two plots were presented for each parameter: first, the relative concentration of Ca (a), Mg (c), Na (e), TDS (g), hardness (i), Cl (k), SO4 (m), and HCO3 (o) from high to low; second, Schoeller classification of aquifer for Ca (b), Mg (d), Na (f), TDS (h), hardness (j), Cl (l), SO4 (n), and HCO3 (p) using six levels,

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One of the most important matters is the slight quality change in S-GIS maps. For example, concentration of some parameters such as Na, TDS, and Cl was in the GOOD range at all points. In addition, the other parameters except Mg had a little change in quality. However, in contrast, the investigation of the relative quality of the parameters shows a wide change in water sources. This is important during decision-making and it can be helpful to make the best decision based on the quality of water. On the other hand, determining the quality of the parameters at each point makes it be possible to choose the less expensive spot according to treatment cost.

In accordance with World Health Organization (WHO) standards, aquifer quality has been evaluated for the study area and is presented in Table 2. According to the listed data, the number of wells that the concentrations of Ca, Mg, Na, TDS, TH, CL, and SO4 were lower than “Allowable limit” was 13, 19, 105, 103, 2, 104, and 96, respectively. In addition, there are only four wells that were higher than Ca permissible limit and seven wells higher than SO4 permissible limit, and the others were lower than the permissible limit. This information has showed in the “WHO standards for aquifer quality” part in Table 2. ALP and PLP are two indexes showing this information in percentage.

Table 2 Comparison of observed values with standard specifications for groundwater as per WHO and assortment of aquifer quality according to the derived Schoeller scale
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All ions have been assessed within different quality categories except Na, TDS, and Cl which were entirely located within the “Good” range. This matter is important between CSD and S-GIS approach, because CSD considers just one category for the study area. For example, Mg located in “Moderately Suitable” area; it means all 1966 km2 is moderately suitable, while, according to S-GIS approach, 57% (1120 km2) is located in “Moderately Suitable”, and 4% (79 km2) and 39% (767 km2) are located in “Good” and “Permissible” categories, respectively. Following this method, the mean percentage difference between CSD and S-GIS approach was calculated about 30% (Table 2). For instance, CSD method judgment for Ca is Permissible category, whereas the portion of this category for Ca is 85%. Therefore, the difference between these two methods will be 15%. This difference shows that, for judgment of aquifer quality, the S-GIS has detail and more reliable result, but CSD only gives a rough quality for all part of aquifer area.

S-GIS results

Parameters values can be saved as a Shapefile layer to develop CSD upon the district, and then through the Payton tool in GIS, the Schoeller diagram is accessible for each point on maps. Therefore, by clicking on each point in the GIS environment (Shapefile layer), a table consisting of groundwater quality parameters would be available, as shown in Fig. 7.

Fig. 7
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S-GIS data of groundwater quality for specified point

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Development plans of classical water quality assessments methods should include the capability for water resource management. In this research, a classic Schoeller diagram has been converted to pixel-based S-GIS maps to provide a tool for better water resource management. For instance, Table 3 shows the effect of concentration decrease of Mg and TH in four levels (0, 10, 30, and 50%) on areas of water quality assessment in the study, whereas this evaluation has never been practicable by classical Schoeller diagram that it is shown in the second part of Table 3. In the CSD part, the quality of each situation is located only in one certain level and it is not obvious whether the other levels have any quota in water quality or not.

Table 3 Impact of Mg and TH concentration changes on the result of water quality assessment
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Conclusion

The primary objective of the presented study was the development of CSD upon a study area through use of GIS information in order to provide a tool for better water resource management. Although there are various methods to investigate the quality of water resources, most of them do not consider the space dimension. Despite the fact that, in this approach, they have spread based on space dimension, users will be able to investigate both known and unknown points in the area. It is more practical in making decision process while to avoid the managers to squander time or money and also it will help them to have a more accurate decision.

The findings of the present study may sum up as follows:

  1. 1.

    The aquifer quality for CSD is in the Good category, whereas in the S-GIS approach, it is located within the categories of “Good” (55%), “Permissible” (36%), and “Moderately suitable” (8%).

  2. 2.

    S-GIS increases the feasibility of making a CSD for each point in a district.

  3. 3.

    S-GIS is an enhancement of aquifer quality assessment which leads to more accurate management of water resources.