## 1 Introduction  
Groundwater is an important natural resource that is used as a drinking water supply and for industrial and agricultural production, especially in areas with scarce surface water resources. Because of significant agricultural production activities and population growth, the vulnerability of groundwater is constantly increasing. Generally, groundwater vulnerability assessment is an effective and feasible tool for groundwater pollution prevention and control. Groundwater vulnerability mapping can be used to evaluate the groundwater sensitivity to contamination by distinguishing vulnerability extents and regions. The assessment results will help managers in developing sound plans for socioeconomic activities. They also provide recommendations for the mitigation or control of pollution in combination with vulnerability control factors [1; 2; 3; 4; 5]. Existing vulnerability assessment methods can be divided into three categories: (1) process-based methods, (2) statistical models, and (3) overlay and index methods. In process-based methods, the groundwater flow and contaminant transport are numerically solved to calculate the vulnerability distribution. Based on the requirement of large datasets and their complexity, these methods are primarily applicable to small areas. Statistical models use either simple statistics of the concentration of special contaminants or sophisticated regression analyses simultaneously incorporating the effects of several explanatory variables. They generally assume the probability of the occurrence of a pollution event [6]. The user will then use the probability to interpret the results. Overlay and index methods are based on the superposition of several indexes for different hydrogeological parameters to calculate composite indexes reflecting the degree of vulnerability. They are widely used for vulnerability assessment because of their ease of use, minimum data requirements, and explanation of groundwater vulnerability and reliability [7; 8; 9]. The DRASTIC model is one of the most widely used overlay and index methods [10; 11]. The DRASTIC model is composed of seven hydrogeological parameters: depth to water table (D), net recharge (R), aquifer media (A), soil media (S), topography (T), impact of the vadose zone (I), and hydraulic conductivity (C). Each of the parameters is divided into ranges with a rating score (1-10) and assigned a weight (1-5) according to its relative importance [11]. Subsequently, the DRASTIC index is computed using Equation (1):  
\[DI=D_{\rm r}\times D_{\rm w}+R_{\rm r}\times R_{\rm w}+A_{\rm r}\times A_{\rm w }+S_{\rm r}\times S_{\rm w}+T_{\rm r}\times T_{\rm w}+I_{\rm r}\times I_{\rm w }+C_{\rm r}\times C_{\rm w}, \tag{1}\]  
where \(DI\) is the DRASTIC index, \(D\), \(R\), \(A\), \(S\), \(T\), \(I\), and \(C\) are the hydrogeological parameters, and the subscripts \(\rm r\) and \(\rm w\) represent the rating score and weight of each parameter, respectively. The higher the DRASTIC index is, the greater is the vulnerability. The DRASTIC model is designed for two cases, that is, common and pesticide cases. The former is used for intrinsic vulnerability and the latter is used for specific vulnerability. The pesticide DRASTIC assigns higher weights to the soil media and topography to account for the natural attenuation of contaminants. Despite its popularity, the application of the DRASTIC method has been questioned. Arguments focus on parameter selection and the judgment of expertise in determining the weights and rating scores for the parameters. In some studies, depending on the specific hydrogeological setting of the study area, the DRASTIC method has been improved by subtracting factors [12; 13; 14] or including additional factors [15; 16; 17; 18; 19] and by employing the Analytic Hierarchy Process [20; 21] or statistical techniques [22; 23; 24; 25] to determine the weights and rating scores. The improvement of the DRASTIC model mainly focuses on overcoming the subjectivity in the judgment of expertise.