## 5 Results  
The decision trees constructed using the two algorithms were applied to each grid cell of the study area. For GPP mapping, predictors as factors and the probability (\(p\)-value) in the leaf node can be considered as the GPP. After the tree-construction process, leaf nodes were calculated. Then, the probability in the leaf node was considered as the groundwater productivity potential index (GPPI). To obtain a GPP map, the GPPI values were reclassified into different productivity potential classes. The index was classified into three classes based on area for easy visual interpretation: high, medium, and low index ranges considering distribution area, respectively. GPP maps made using the GPPI are shown in Figure 5. The classification is useful for estimating GPP in each class and for visually delineating predicted GPP areas. Figure 4: Architecture of the decision-tree model. A decision tree consists of the following three elements: node, condition, and production (p-value). Moreover, there are three types of node, the root (A), internal (B), and terminal nodes (C). A GPP map should effectively predict GPP areas and can be validated by incorporating data from new GPP-likely datasets as they occur. Here, the result of the GPP analysis was validated using a test GPP-likely dataset (50% of the total GPP-likely dataset) that was not used for the analysis. To validate the GPP map, the calculated GPP values of all cells were sorted in descending order. Then, the ordered cell values were divided into 100 classes at 1% cumulative intervals. The above procedure was also adapted for the GPP-likely dataset cells by comparing the 100 classes obtained with the distribution in the study area. Then, a graph was made by connecting the two classified values. For example, in the case of the CHAID algorithm, the 90%-100% (10%) class of the Boryeong city where  
Figure 5: Groundwater productivity potential map created using decision-tree model. The index was classified into three classes based on area for easy and visual interpretation: high, medium, and low index ranges of the study area, respectively. (**a**) CHAID algorithm for Boryeong city; (**b**) QUEST algorithm for Pohang city; (**c**) CHAID algorithm for Boryeong city; and (**d**) QUEST algorithm for Pohang city. the GPPI had a higher rank could explain 51% of the entire productivity potential. Furthermore, the 80%-100% (20%) class of the study area where the GPPI had a higher rank could explain 68% of the productivity potential. To compare the results quantitatively, the areas under the curve (AUC) were re-calculated as the total area [36,37]. Hence, the area under a curve can be used to assess the prediction accuracy qualitatively. From the validation of the GPP maps, the decision tree (CHAID and QUEST algorithms) approaches produced AUC values of 83.31 and 79.47, respectively, meaning that the GPP maps had accuracies of 83.31% (CHAID) and 79.47% (QUEST) (Figure 6) in the case of Boryeong city. In the case of Pohang city, the decision tree (CHAID and QUEST algorithms) approaches produced AUC values of 86.18 and 80.00, respectively, meaning that the GPP maps had accuracies of 86.18% (CHAID) and 80.00% (QUEST) (Figure 6). The other validation is performed by comparing the GPP map with borehole SPC data. The 72 wells in Boryeong city and 44 wells in Pohang city were used to validate the accuracy of the predicted map. The actual SPC value in each wells were compared with GPP maps and the Agreement/Disagreement between the expected/actual SPC data are shown in Table 3. The values which are greater than 4.55 m\({}^{3}\)/day/m in Boryeong city and are greater than 6.25 m\({}^{3}\)/day/m in Pohang city were used as actually high SPC value. So, the Equation (2) was used to calculate to accuracy. Figure 6: Cumulative frequency diagram showing the groundwater-productivity-potential (GPP) index rank (x axis) occurring in the cumulative percent of well (SPC\(>\)4.55 m\({}^{3}\)/day/m (Boryeong) and 6.25 m\({}^{3}\)/day/m (Pohang)) (y axis).