## 4 Results
### Optimization of the DRASTIC Model with Respect to the Vulnerability to Nitrate
#### 4.2.2 Revision of the Weights  
To obtain better results, the weights of the parameters must be modified. The modification process and results are as follows.  
1. Using single-parameter sensitivity analysis  
Based on the SPSA, the effective weights of the D, R, A, S, T, I, C, and L factors are 0.17, 0.24, 0.09, 0.05, 0.03, 0.14, 0.11, and 0.16, respectively. Based on the use of Equation (9) to scale the values to the range of 1 to 5, the equivalent weights are 3.61, 5, 1.96, 1.14, 0.7, 2.91, 2.43, and 3.46, respectively. The Pearson and Spearman correlation coefficients calculated using both the modified rating scores and weights are 0.646 and 0.635, respectively.
2. Using correlation analysis  
Table 5 lists the results of the correlation analysis, which includes the Spearman \(\rho\) and Kendall \(\tau\) correlation coefficients between the nitrate concentration and rating scores for different parameters. The \(sp\) and \(kp\) columns present the \(p\)-values of the two correlation coefficients, respectively. Based on the statistical significance, the Pearson and Spearman correlation coefficients were calculated using seven parameters (excluding topography parameters) and six parameters (excluding topography and recharge parameters) based on the modified scores and weights, respectively. The results of the two calculations  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Depth to the Water Table (D)** & \multicolumn{4}{c}{**Net Recharge (R)**} & \multicolumn{4}{c}{**Aquifer Thickness (A)**} \\ \hline
**Range (m)** & \(\mathbf{NO_{3}}^{-}\) **(mg/L)** & **Score** & **Range (mm)** & \(\mathbf{NO_{3}}^{-}\) **(mg/L)** & **Score** & **Range (m)** & \(\mathbf{NO_{3}}^{-}\) **(mg/L)** & **Score** \\ \hline
0–30.5 & 47.37 & 10 & 0–102 & 29.64 & 9.87 & 0–45 & 55.64 & 10 \\ \(>\)30.5 & 20.45 & 4.32 & \(>\)102 & 30.02 & 10 & \(>\)45 & 25.67 & 4.61 \\ Infiltration coefficient (S) & \multicolumn{4}{c}{Hydraulic Conductivity (C)} & \multicolumn{4}{c}{Land use (L)} \\ \hline Range & \(\mathbf{NO_{3}}^{-}\) (mg/L) & Score & Range (m/d) & \(\mathbf{NO_{3}}^{-}\) (mg/L) & Score & Types & \(\mathbf{NO_{3}}^{-}\) (mg/L) & Score \\ \hline
\begin{tabular}{c} \(\mathbf{NO_{3}}^{-}\) \\ (mg/L) \\ \end{tabular} & Score & \\ \hline
0–2 & 22.66 & 4.31 & River belts & 12.06 & 2.19 & \\
2–6 & 32.61 & 6.2 & Alluvial and flood plains & 13.21 & 2.4 & \\
6–12 & 25.06 & 4.76 & Lakes and depressions & 21.12 & 3.84 & \\ \(>\)12 & 52.59 & 10 & Alluvial-proluvial fans & 44.44 & 8.08 & \\  & & & & 55.03 & 10 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Modified rating scores for the DRASTIC model parameters.  
are 0.633 and 0.634 and 0.624 and 0.63, respectively, corresponding to the Pearson and Spearman coefficients.  
(3) Using logistic regression  
The threshold for the conversion of nitrate concentration into a binary variable is 50 mg/L because it has a conventional meaning, that is, a pottable limit. Table 5 shows the b coefficients, \(p\)-value, and weights. The Pearson and Spearman coefficients based on the new weights were calculated by LRA and the modified rating scores are 0.591 and 0.593, respectively.  
(4) Using data-driven methods  
The MC method and GA were used to calculate the weights. For a fair comparison with CA, the calculation for weighting was performed three times: (1) using eight parameters, (2) using seven parameters (excluding topography), and (3) using six parameters (excluding both topography and net recharge). The results, which were also used for comparison with SPSA and LRA, are shown in Table 5.  
To make the results clearer and easier to compare, Table 6 lists the correlation coefficients for vulnerability and nitrate concentration calculated by different methods.  
Figure 2c,d shows the results of the evaluation using MC and GA. The results are similar.  
\begin{table}
\begin{tabular}