## 5 Discussion
### Impact of Revision Weights  
When using the modified rating scores, the weights of Aller's common DRASTIC model result in Pearson and Spearman coefficients of 0.647 and 0.643, respectively. None  
Figure 3: Nitrate concentration changes from 1998 to 2018 and level difference maps for: (**a**) nitrate concentration changes; (**b**) level difference. of the weight vectors derived from the SPSA, CA, and LRA provide better correlation coefficients. The worst results were obtained by using the weights of the LRA calculation (Table 6). The SPSA results are better than those obtained with LRA; the Pearson and Spearman correlation coefficients are 0.646 and 0.635, respectively (Table 6). However, they are not better than the results obtained by using the rating scores of the modified DRASTIC model. When using only six parameters for CA, the best Pearson and Spearman correlation coefficients are 0.634 and 0.63, respectively (Table 6). This means that the data did not improve. Based on the correlation coefficients, these three methods are not suitable for the study area. In the following section, the rationality of the weights obtained by each method is considered. The weights for the LRA method are shown in Table 5. The \(p\)-value column shows that only the land use parameter is statistically significant and the weights are eccentric. Although the use of logistic regression for the determination of the weights is not advisable in the study area, the results obtained by using the new weights calculated by LRA and the modified rating scores are better than those obtained with Aller's common DRASTIC model. This implies that one of the key points in assessing the groundwater vulnerability in a similar hydrogeological environment is the determination of the rating scores. In other words, if the rating scores are reasonable, the results are almost acceptable, even if the weights are not appropriate. Based on SPSA, the effective weights of the D, R, A, S, T, I, C, and L factors are 3.61, 5, 1.96, 1.14, 0.7, 2.91, 2.43, and 3.46, respectively. The weight for topography is only 0.7, which implies that this parameter should be ignored. The highest weight was assigned to the recharge. The difference in the recharge in this area is the smallest (Table 4); therefore, the weights obtained by this method are not reasonable. Table 5 displays the results of the CA method. The relationship of the topography with the nitrate concentration is statistically insignificant, which implies that this parameter should be excluded from Equation (2). This phenomenon has been reported in previous studies [2]. The Pearson and Spearman correlation coefficients calculated using the seven parameters (excluding the topography parameter) and modified rating scores and weights are 0.633 and 0.624, respectively. The correlation coefficient between the net recharge and nitrate concentration is weakly negative, which can be explained with the approximately equal nitrate concentrations listed in Table 4. Therefore, it is also reasonable to exclude the net recharge parameter from Equation (2). The results of the calculation using the remaining six parameters are better than the results obtained by using seven parameters but worse than the results of the SPSA. Based on this study, it can be concluded that CA is not an effective method for weight determination. It is also worth noting that, although the results of the SPSA are currently the best, the highest weight is assigned to the recharge, which is negligible in the CA. Thus, the results of the two methods are contradictory and unreasonable. This again confirms that the SPSA and CA methods are ineffective in determining the weights of the parameters in the study area. The MC and GA methods are both data-driven but follow different theories and mechanisms. Both of these methods are used to solve Equation (7). If there is an optimal solution that is unique, the same results should be obtained from these methods. To prevent the solution from converging to a local optimum, six threads were started in sequence.