Introduction

Due to the increasing population growth and water requirements, the use of freshwater sources, such as groundwater resources, has become very important. On the other hand, human activities, such as agriculture, urbanization, and industry, have reduced groundwater quality (Kazakis and Voudouris 2015). The groundwater flow is very slow, and, if contaminated, it will take a lot of time to remove contamination. Therefore, prevention measures are the most appropriate strategy to combat groundwater contamination. One of the important tools for the management and protection of groundwater is the provision of groundwater vulnerability maps (Patrikaki et al. 2012). So far, various definitions have been presented for the aquifer vulnerability and its concept in hydrogeology. Among them can be pointed to the definition of the National Committee of the United States in 1993 (Stigter et al. 2006). According to the definition of this committee, groundwater vulnerability is the possibility of infiltration and diffusion of pollution to reach the groundwater system from the ground surface (Almasri 2008). The vulnerability of groundwater is divided into two types of intrinsic and specific vulnerability. Intrinsic vulnerability depends on the characteristics of geology, hydrology, and hydrogeology of the region and human activities, while it is independent on the nature of pollution (Hamza et al. 2007). Specific vulnerability indicates groundwater vulnerability to particular pollution or a group of pollution caused by human activities; in fact, it depends on the inherent sensitivity, location, and type of the contaminant source (Gogu and Dassargues 2000). There are various approaches to assess intrinsic vulnerability, for example, DRASTIC ((Aller et al. 1987)), AVI (Van Stempvroot et al. 1993), GOD (Foster 1987), SINTACS (Civita 1994), and Time-Input (Kralik and Keimel 2003). The most common method to assess the groundwater vulnerability is the DRASTIC which was presented by the US Environmental Protection Agency (USEPA) for the first time (Aller et al. 1987). The effective parameters in the DRASTIC method are the depth of groundwater, net recharge, aquifer media, soil media, impact of the vadose zone, topographic slope, and hydraulic conductivity being provided in seven layers in the GIS software environment. Through ranking and assigning weights to the aforementioned input layers, the DRASTIC index is calculated. Different hydrological, hydrogeological, and geological characteristics for different areas can lead to optimizing the DRASTIC method. Also, due to the fact that the rates and weights in the DRASTIC method are somewhat dependent on the expert’s decision, therefore, reducing the subjectivity is necessary to provide a reliable vulnerability map. So far, different methods have been used to optimize the DRASTIC method. A number of these methods are presented in Table 1.

Table 1 A number of methods to optimize the DRASTIC method
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In this paper, the optimized methods, such as genetic algorithm (GA), and ant colony optimization (ACO), as a new methodology, were used to optimize the weights. Also, Wilcoxon rank-sum test (WRST) was used to modify the rates of the DRASTIC approach. Accordingly, the various DRASTIC models, including typical DRASTIC, ACO-DRASTIC, GA-DRASTIC, WRST-DRASTIC, WRST-ACO-DRASTIC, and WRST-GA-DRASTIC, were generated. These models were employed to evaluate the groundwater vulnerability of the Shabestar plain, NW Iran, as a case study. The main objective of this study is to compare the performance of the mentioned optimization models in assessing the vulnerability of the study area.

Material and methods

Study areas

Shabestar plain with an area of 350 km2 and geographical coordinates, x = 540500 to x = 587500 eastern longitude and y = 4215000 to y = 4239550 northern latitude, is situated in East Azarbaijan province in NW Iran. The plain is bordered to the north by the Marand Zilberchay basin, to the east by the Tabriz plain, to the south by the Urmia Lake, and to the west by the Tasuj Basin. The slope of the ground surface in the northern parts is high, and, to the south of the plain, the amount of slope is reduced and the ground becomes almost flat. The DEM (digital elevation model) of the study area is shown in Fig. 1. The average annual rainfall in the region is 325 mm (Asghari Moghaddam et al. 2017). The highest and lowest rainfall occurred in May and August, respectively. The climate of the area is semi-arid. The most important rivers in the plain are the Daryan-Chay, Payam-Chay, Shanehjan-Chay, and Sis-Chay which flow approximately northeast–southwest (Asghari Moghaddam et al. 2017).

Fig. 1
figure 1

Digital elevation model (DEM) of the Shabestar basin, NW Iran

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Geologically, the oldest deposit in the area, in the southern part of Mishoo and the northern plain of Shabestar, is the Kahar Formation, which includes micaceous shale with fine sandstone, schist, and a little dolomitic stromatolite with layers of chert and dark limestone. On the southern slopes, there is the Barut Formation that includes sandstone and dolomite. In the Mishoo Mountain, the Dorood and Rute Formations are composed of dark and red limestone recovered by shale. Cretaceous sediments in the area include massive limestone (the eastern part of the region) and sedimentary flesh (the middle section of the region). Cenozoic rocks are dominated by a condensed conglomerate, silt, marl, clay (west and center of the region), and red marl with layers of the conglomerate (northern part of Khamene and northeastern part of Shabestar). The expansion of Quaternary deposits in the region is high, such as conglomerates, long alluvial terraces, old alluvial, alluvial plains, and young alluvial terraces, which are exposed (Asghari Moghaddam et al. 2017).

The Shabestar plain aquifer is single-layered and unconfined. However, in the southern parts of the plain, there is a confined aquifer, but the water table falls below the impermeable layer indicating hydrogeologically that the aquifer is not merely a confined aquifer but also acts as an unconfined aquifer. Based on the pumping test data, the amount of transmissivity in the middle of the plain is estimated to be about 1000 to 1500 m2/day, which decreases towards the south of the plain with a value of 100 m2/day. The storage coefficient of the aquifer ranged between 2 and 8%.

DRASTIC method

The DRASTIC method (Aller et al. 1987) is based on the seven hydrological, hydrogeological, and geological parameters, including groundwater depth (D), net recharge (R), aquifer media (A), soil media (S), topography (T), impact of vadose zone (I), and hydraulic conductivity (C). Relative weight is allocated to each of the aforementioned parameters with respect to their importance in the transmission of pollution to the groundwater system. The weight ranged between 1 and 5, which is the least and most important parameters, respectively. The rate of the parameters varied from 1 to 10 based on the characteristics of the region, in which 1 means the lowest and 10 means the most dangerous for groundwater contamination (Panagopoulos et al. 2006). Table 2 shows the rates of DRASTIC index parameters.

Table 2 The rates of DRASTIC index parameters (Aller et al. 1987)
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To calculate the aquifer vulnerability index, the parameters used are introduced into a simple linear equation as follows:

$$ DI={D}_r{D}_w+{R}_r{R}_w+{A}_r{A}_w+{S}_r{S}_w+{T}_r{T}_w+{I}_r{I}_w+{C}_r{C}_w $$
(1)

In the above-mentioned relationship, DI is a vulnerability index. The capital letters represent the seven parameters, r is the rate of value (rank), and w is the weight assigned to each parameter. The larger the index, the greater the potential for contamination.

Sensitivity analysis

Sensitivity analysis provides useful information about ratings and weights assigned to each parameter (Gogu and Dassargues 2000). The effect of each of the used seven DRASTIC parameters can be determined on the vulnerability of the study area. For this purpose, the sensitivity analysis was used as the variation index. The VARi is calculated as follows (Sadat-Noori and Ebrahimi 2016):

$$ {VAR}_i=\left(\frac{v_i-{v}_{xi}}{v_i}\right)\times 100 $$
(2)

where VARi is the variation index of the removal parameter and vi and vxi are vulnerability index calculated using Eq. (1) on the ith subarea and vulnerability index of the ith subarea removing one map layer, respectively.

Nitrate concentration data

Nitrate as one of the most common groundwater pollutants has different origins, such as domestic, municipal, and industrial wastewater, chemical fertilizers, and animal wastes. In this study, nitrate was used as an indicator to validate vulnerability assessment, because of the fact that nitrate, produced by human activities, is reached into the groundwater from the ground surface and also is considered as indicator of groundwater quality degradation (US EPA 1996). Therefore, nitrate concentration collected from 66 water wells was used to validate the DRASTIC method. The concentration of nitrate is varied between 0.2 and 70 mg/L with an average of 16.4 mg/L. Figure 2 shows the distribution map of nitrate concentration in groundwater of Shabestar plain.

Fig. 2
figure 2

The spatial distribution of the nitrate concentration of Shabestar plain

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Ant colony optimization

Ant colony algorithm was first introduced in 1992 by Marco Dorigo in his Ph.D. thesis. This algorithm is based on the actual behavior of the ants, in which the ants can find the shortest route to find food using their simple communication mechanisms. As they move on their path, a chemical material called pheromone remains on the earth which guides the ants to the target. Ants choose their own pathway, which has the greatest effect of pheromone. Due to the fact that pheromone is evaporated with time, the path that more ants cross it has more pheromone and encourages other ants to cross that. As shown in Fig. 3, the mechanism of finding food from the shortest path by ants includes the following three steps:

  1. 1)

    The ant by walking a route finds a food source and returns to the nest by placing the effect of the pheromone.

  2. 2)

    Ants follow one of the four possible paths, but the gradual increase in the amount of pheromone in the shortest path increases the tendency of ants to path this route.

  3. 3)

    Ants follow the shortest route that has the highest amount of pheromones to reach the food (Dreo 2006).

Fig. 3
figure 3

The mechanism of finding food from the shortest path by ants (Dreo 2006)

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A simple ant colony optimization composed of two nodes of vs (representing nest of ant) and vd (representing a source of food). e1 and e2 are between vs and vd. Lengths of l1 and l2 are allocated to e1 and e2, respectively. l1 and l2 indicate short and long paths between vs and vd, respectively. An artificial pheromone value ti is considered for each of the two links ei = i = 1, 2. This shows the strength of pheromone trail on the path. Finally, na artificial ants are introduced. The behavior of each ant is as follows (Blum 2005):

$$ {p}_i=\frac{t_i}{t_1+{t}_2}\kern1.3em i=1,2 $$
(3)

If t1 > t2, it means a trail of pheromone in the path e1 is a strength. Then, the probability of choosing a path e1 is higher and vice versa. An ant uses the same path as it chose to reach vd. For returning from vd to vs, the ant changes the value of artificial pheromone as follows (Blum 2005):

$$ {t}_i\leftarrow {t}_i+\frac{Q}{l_i} $$
(4)

where Q is a positive constant parameter of the model. The above-mentioned equation shows artificial pheromone value that is added depending on the chosen path. In other words, the shortest path has a high pheromone value. In nature, pheromone deposits evaporate over time. Simulation of this pheromone is as follows (Blum 2005):

$$ {t}_i\leftarrow \left(1-p\right).{t}_i,\kern0.5em \mathrm{i}=1,2. $$
(5)

The parameter p ϵ (0, 1] regulates the evaporation of pheromone.

Genetic algorithm

A genetic algorithm was introduced by Holland in 1975 (Holland 1975). GA is a randomized optimization method that mimics the same biological concepts. In the GA, a population is initially formed, and, then, the individuals develop from one generation to the next with a repetitive process of evolution. Each evolutionary stage is called a generation. Each person of this generation is judged by the suitability function. The evolutionary routine consists of choice, combination, and mutation. An evolutionary algorithm generally determines the initial population randomly and measures the suitability of each individual based on their fitness value in the environment. In this way, more qualified people will be selected several times to participate in the new population and thus have a greater chance of reproduction.

In this method, each optimization problem has three basic and fundamental components, including the objective function, the decision variables or parameters, and constraints (Jafari and Nikoo 2016). For each optimization problem, the population of the probable solutions chosen becomes the best possible solution. Each solution can be modified based on its compatibility with the selection, crossover, and mutation operators (Jafari and Nikoo 2016) (Fig. 4).

Fig. 4
figure 4

Flowchart of the genetic algorithm methodology (Chen and Lin 2006)

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Wilcoxon rank-sum test

The Wilcoxon rank-sum test (WRST) (Wilcoxon 1945) is a non-parametric statistical test that is used to evaluate the similarity of two samples dependent on a rating scale. In addition to considering the differences in symptoms, this test also takes into account the difference between them. So, since it uses more information, it has a more accurate answer (Ahmadi et al. 2013).

Modeling procedure

For arranging seven layers of the DRASTIC method, relevant information was inserted into the GIS environment and the layers were prepared as the raster layers. The groundwater depth parameter represents the depth that the pollutant needs to pass through it to reach the water table. In order to provide the groundwater depth layer, the 24-piezometer water table information in the study area for the year 2016–2017 was entered into the GIS software environment and interpolated with the IDW method. Afterwards, they were classified using the ratings shown in Table 2. The average depth to groundwater ranged between 2.5 and 86.6 m in the study area. Therefore, rates between 1 and 9 are assigned to this parameter (Fig. 5a). To calculate the net recharge, Piscopo’s (2001) method was employed. For this method, three layers, including precipitation, slope, and soil maps, are needed. To prepare the slope map, a digital elevation model (DEM) of the area was obtained and then the percent slope of the ground surface was extracted and ranked according to the standards in Table 3. In order to prepare the soil map, considering the type of soil layer in 2 m above the logs of the observation wells, the soil map was classified into five classes and interpolated by the Kriging method. Afterward, a rate was assigned to each class based on soil permeability according to Table 3. As regards the fact that the amount of precipitation for the area is less than 500 mm per year, rank 1 was considered for the precipitation layer. Three raster maps were prepared according to Eq. (6) and superimposed. Then, the net recharge layer was reclassified and rated (Fig. 5b). The ratings of net recharge ranged between 1 and 3 in this study.

$$ \mathrm{Net}\ \mathrm{recharge}=\mathrm{soil}\ \mathrm{permeability}+\mathrm{rainfall}+\mathrm{gradient} $$
(6)
Fig. 5
figure 5

Input layer maps in the DRASTIC method

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Table 3 Ranking of net recharge based on Piscopo (2001)
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To prepare the aquifer media, soil media, and vadose zone layers, 35 available well logs in the area were considered. Materials of these logs consist of gravel, sand, mud, clay, and silt. To prepare the aquifer media layer, based on the aquifer materials, the ratings between 3 and 7 were given according to Table 2 and interpolated (Fig. 5c). For the soil layer, the upper part of the unsaturated zone or the surface layer (upper 2 m of the well logs in the area) is considered. The ratings between 2 and 5 were assigned according to Table 2 and transformed into a raster layer by the Kriging method (Fig. 5d). The percent slope of the ground surface was calculated in the GIS and classified based on Aller et al. (1987). Then, the rating values were assigned for each class and raster topography map was generated (Fig. 5e). Ratings between 1 and 10 were assigned to topography layer. For the impact of the vadose zone, the material of this zone was considered, and the ratings between 3 and 5 were assigned according to Aller et al. (1987) (Fig. 5f). Hydraulic conductivity refers to the ability of the aquifer-forming material to convey water, depending on the percentage of void spaces associated with the saturated layer. By dividing amounts of transmissivity (obtained from 52 observation wells), saturation thickness amounts of hydraulic conductivity in the study area are ranged between 0.1 and 38.2 m/day. Then, conductivity ratings are ranged between 1 and 6 (Fig. 5g).

In this study, in order to optimize the weights of the DRASTIC method, ACO and GA methods were used. WRST method was also employed to modify the rates.

In the WRST method, the rates of parameters (e.g., D, R, A, S, T, I, C) were rescaled based on the mean nitrate concentration in each class for each layer, then the highest rate of each parameter was assigned to the class with the highest mean of nitrate concentration, and other rates were modified linearly according to this relation. Table 4 shows the modified rates based on the Wilcoxon’s method.

Table 4 The typical and modified rates based on mean nitrate concentration in the Wilcoxon’s method
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The ACO is generally expressed as P = (S, f), in which the limited set of objects S and fitness function f: S → R are given that attributes a fitness value to every s ∈ S. The aim is to search for an object of minimum fitness value. Knowing that there are n input data xi and an output data y, the estimation error is calculated as follows:

$$ e=y-t\left({x}_1,{x}_2\dots {X}_n\right) $$
(7)

where t is the output of linear model written as follows:

$$ t\left({x}_1,{x}_2,\dots {X}_2\right)={a}_1{x}_1+{a}_2{x}_2+\dots .{a}_n{x}_n+{a}_n+1 $$
(8)

where a1, a2, …an are weighting coefficients of the input parameters (Kadkhodaie 2015). Seven parameters of the DRASTIC were considered as the inputs of the ACO. The output of the ACO is calculated using the following equation:

$$ y=\frac{vul_{\mathrm{max}}}{{\left({No}_3\right)}_{\mathrm{max}}}{\times}_{{\left({No}_3\right)}_i} $$
(9)

In the above-mentioned equation, y is the adjusted vulnerability index, vulmax is the maximum DRASTIC index, (No3)max is the maximum nitrate concentration, and (No3)i is the nitrate concentration. The MSE (mean squared error) of adjusted vulnerability index was employed as the objective function to be minimized by ACO as follows (Kadkhodaie 2015):

$$ \mathrm{MSE}=\frac{1}{m}{\sum}_{j=1}^m{\left({y}_j-t\left({x}_{ij}\right)\right)}^2\kern0.5em i=1,2,\dots, n $$
(10)

where m and n are the number of estimated points and input parameters for prediction of adjusted vulnerability index, respectively.

For developing the ACO, the number of initial ants of 500, epoch of 20, and 1 < a < 5 were set. Finally, the optimized weights were obtained when a minimum MSE for the objective function was reached. Table 5 represents the optimized weight values of the DRASTIC method obtained by the ACO method.

Table 5 Main weighting and modified weighting coefficients using the ant colony algorithm
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For GA-based optimization of the DRASTIC method, seven parameters of the DRASTIC as the variables were considered. The minimum and maximum values between 1 and 5 were defined as constraints for the weights of the variables. The objective function for the GA method was the correlation coefficient between the nitrate concentration and DRASTIC index. The objective function used to optimize the DRASTIC through the GA is presented as follows (Jafari and Nikoo 2016):

$$ \mathit{\operatorname{Max}}\;F= Corr\left(x,y\right) $$
(11)
$$ F=\frac{\sum_{j=1}^n\left(\left({x}_j-\overline{x}\right)-\left({y}_j-\overline{y}\right)\right)}{\sqrt{\sum_{j=1}^n{\left({x}_j-\overline{x}\right)}^2}\sqrt{\sum_{j=1}^n{\left({y}_j-\overline{y}\right)}^2}}\kern0.5em Constrain:1\le {W}_i\le 5\kern1em j=1,2,\dots, $$
(12)

where F represents an objective function, n denotes the number of wells, yj is contaminant concentration, \( \overline{y} \) represents the mean concentration of contaminant, xj is vulnerability index, \( \overline{x} \)is mean vulnerability index, and Wi is the weight of the DRASTIC parameters. Finally, with the purpose of maximizing the function, optimized weights were obtained. The results of the GA-based optimization for DRASTIC are presented in Table 6. Considering the optimized rates using the WRST method, weights of the DRASTIC method were optimized by the GA and ACO. The results of the optimization of the rate and weight of the DRASTIC method are presented in Table 7.

Table 6 Original and optimized weights of DRASTIC using GA method
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Table 7 Typical and modified weighting coefficients based on WRST-GA and WRST-ACO models
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Validation of models

In order to validate the various vulnerability maps, the correlation coefficient (r) was calculated as follows:

$$ r=\frac{\sum_{i=1}^n\left( Vu{l}_i-\overline{Vul}\right)\left({N}_i-\overline{N}\right)}{\sqrt{\sum_{i=1}^n{\left( Vu{l}_i-\overline{Vul}\right)}^2\sqrt{\sum_{i=1}^n{\left({N}_i-\overline{N}\right)}^2}}} $$
(13)

where r is the correlation coefficient, Vuli is the vulnerability index, \( \overline{Vul} \) is the mean of a vulnerability index, Ni represents the nitrate concentration, and \( \overline{N} \) is the mean of nitrate concentration.

Results and discussion

By overlapping the seven effective layers (e.g., D, R, A, S, T, I, C) in the DRASTIC approach and using Eq. (1), intrinsic vulnerability index was calculated from 53.3 to 118.3 in the study area. The vulnerability index was categorized into five categories, according to geometrical interval classification suggested by Huan et al. (2012), including very low, low, moderate, high, and very high vulnerability. The DRASTIC-based vulnerability map of the Shabestar plain is shown in Fig. 6. Based on the typical DRASTIC vulnerability map, very low and very high vulnerable areas are located in the west and south-west of the plain, respectively. Distribution of the class area shows that areas with very low, moderate, high, and very high vulnerability covered 6.79, 39.11, 47.45, 6.02, and 0.6% of the study area, respectively. The amount of r between the DRASTIC index and the concentration of nitrate was calculated as 0.38 indicating an adaptation of the vulnerability map to the distribution of nitrate concentration data does not show much correlation. In other words, zones with a high vulnerability index do not show high nitrate concentration. Accordingly, the typical DRASTIC index cannot be precise enough to evaluate the vulnerability of Shabestar plain aquifer. On the other hand, the typical DRASTIC map is a general model and the weight assigned to each parameter should be modified based on the hydrogeological characteristics of each specific area. Sensitivity analysis by variation index method was performed to determine the effect of ratings and weights assigned to each parameter. By removing one parameter of the typical DRASTIC method and using Eq. (2), the statistical results of the sensitivity analysis were calculated (Table 8). The results show that the effect of the vadose zone and aquifer media has the greatest impact on the vulnerability of the area, while hydraulic conductivity and soil media have the least effect. On the other hand, the sensitivity of each of the parameters in addition to the weight is influenced by the rates. Therefore, it can be stated that both weights and rates of the DRASTIC method need to be optimized. Accordingly, in this study, the GA and ACO were used to optimize weights, and WRST was employed to modify the rates. Afterward, various optimized models were developed to assess the vulnerability of Shabestar plain aquifer (Fig. 6). Validation of the models also was calculated by r between the nitrate concentration and optimized DRASTIC index. The validation results of optimized models are shown in Table 9. It can be concluded that all optimized models elevated the r compared to the typical DRASTIC model. Using ACO and GA methods to optimize weights, r increased to 0.47 and 0.52 compared to the typical DRASTIC model, respectively. The WRST method was used to optimize the ratings of increased r to 0.6 compared to the typical DRASTIC model. By applying ACO and GA based on the WRST-DRASTIC model, r increased to 0.62 and 0.63, respectively. These results indicate that the WRST-GA-DRASTIC model with higher r outperforms the other optimized models in assessing the vulnerability of the Shabestar plain aquifer. Based on this model, zones with very low, low, moderate, high, and very high vulnerability cover 8.08, 37.32, 46.17, 7.82, and 0.58% of the total area, respectively. Various optimized models showed different percentages for different vulnerability categories (Fig. 7). Based on ACO-DRASTIC model, zones with very low vulnerability index are located in north and northwest (28.57% of total area) while zones with very high vulnerability index are situated in south and southeast (11.91% of total area). According to the GA-DRASTIC model, zones with very low and very high vulnerability indices are located in the west (1.6% of total area) and parts of the east and southeast (3.5% of total area), respectively. Based on the WRST-DRASTIC model, zones with very low and very high vulnerability indices are located in western and southern parts, respectively, which cover 3.72 and 5.64% of the total area, respectively. Based on the WRST-ACO-DRASTIC model, zones with very low and very high vulnerability indices are located in the western parts (2.84% of total area) and a small part of the southeast (0.52% of total area).

Fig. 6
figure 6

Typical and optimized DRASTIC vulnerability maps for the Shabestar aquifer

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Table 8 Statistical results of the map removal sensitivity analysis for typical DRASTIC model
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Table 9 Validation results of the various DRASTIC models
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Fig. 7
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Distribution of the class areas (%) according to each applied method

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Conclusion

DRASTIC vulnerability index was calculated from 53.3 to 118.3 in the Shabestar plain. In this model, the areas with very low, moderate, high, and very high vulnerability cover 6.79, 39.11, 47.45, 6.02, and 0.6% of the study area, respectively, while the zones with very low and very high vulnerability indices are located in the west and south-west of the study area, respectively. Nitrate concentration data were used for validation of the DRASTIC model. The r value of 0.38 between the DRASTIC indices and nitrate concentrations was calculated, which indicates a low correlation. Results of sensitivity analysis show that the vadose zone and aquifer media with mean variation index of 27.55 and 17.93%, respectively, have the greatest impact on the vulnerability of the area while hydraulic conductivity and soil media with mean variation index of 8.09 and 9.55%, respectively, are less effective on vulnerability. WRST was used to modify the rates, while ACO and GA were used to optimize the weights. Afterward, various optimized frameworks were developed to assess the vulnerability of the plain. By applying ACO and GA methods to optimize weights, the r value was increased to 0.47 and 0.52 compared to the typical DRASTIC approach, respectively. The WRST method used to optimize the rates increased the r value to 0.6 compared to the typical DRASTIC method. By applying ACO and GA based on the WRST-DRASTIC framework, the r increased to 0.62 and 0.63, respectively. These results indicate that the WRST-GA-DRASTIC framework with higher r value outperforms the other optimized models in evaluating the vulnerability of the Shabestar plain aquifer. Based on the proposed model, zones with very low, low, moderate, high, and very high vulnerability index cover 8.08, 37.32, 46.17, 7.82, and 0.58% of the total area, respectively. Based on the model, new industrial units should be constructed in the western part of the study area with very low vulnerability.