## 3 Methodology
### Designs of Feature Scores of Individual Influencing Factor Layers  
Feature scores for different influencing factor layers with the expert assessment method were prioritized and assigned according to their influences on the GWLF potential, as shown in Table 1. The higher the feature score in each influencing factor, the more significant the influence on the groundwater level fluctuation. By using the ArcGIS spatial analysis module and the extracted feature score data from 18 drilling boreholes, the spatial distribution of the feature score for each influencing factor is illustrated in Figure 11.  
Figure 10: Regolith thickness distribution of the study area. Figure 9: Depth to the water table distribution of the study area. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Influencing Factor** & **Upper Bound** & **Lower Bound** & **Feature Score** & **GWLF Potential** \\ \hline \multirow{8}{*}{Geomorphologic Factor} & \multirow{3}{*}{Slope [S] (degree)} & 90 & 60 & 1 & Low \\  & & 60 & 45 & 2 & \\  & & 45 & 30 & 3 & \(\downarrow\) \\  & & 30 & 15 & 4 & \\  & & 15 & 0 & 5 & High \\ \cline{2-6}  & \multirow{3}{*}{Drainage density [D]} & 0.083 & 0 & 1 & Low \\  & (km/km\({}^{2}\)) & 0.362 & 0.227 & 3 & \(\downarrow\) \\  & & 1.114 & 0.362 & 4 & High \\ \cline{2-6}  & \multirow{3}{*}{Land use [LU]} & \multicolumn{3}{c}{Built-up land} & 1 & Low \\  & & \multicolumn{2}{c}{Forest} & 2 & \\  & & \multicolumn{2}{c}{Exposed area} & 3 & \(\downarrow\) \\  & & \multicolumn{2}{c}{Crop land} & 4 & \\  & & \multicolumn{2}{c}{Water} & 5 & High \\ \hline \multirow{8}{*}{Geological Factor} & \multirow{3}{*}{Lithology [LT]} & Sandstone \& shale (mainly shale) & 2 & \\  & & Sandstone \& shale (mainly sandstone) & 3 & \(\downarrow\) \\  & & Slate, Phyllite, Quartzie & 4 & \\  & & Unconsidated Rock & 5 & High \\ \cline{2-6}  & & \(<\) & 10 & 1 & Low \\  & & 10 & 20 & 2 & \\  & & 20 & 30 & 3 & \(\downarrow\) \\  & & 30 & 40 & 4 & High \\  & & \(>\) & 40 & 5 & High \\ \hline \multirow{8}{*}{Hydrogeological Factor} & \multirow{3}{*}{Hydrozeological Factor} & 10 & 0 & 1 & Low \\  & & 100 & 10 & 2 & \\ \cline{1-1}  & & 1000 & 100 & 3 & \(\downarrow\) \\ \cline{1-1}  & & 10,000 & 1000 & 4 & \\ \cline{1-1}  & & \(>\) & 10,000 & 5 & High \\ \hline \multirow{8}{*}{Hydrogeological Factor} & \multirow{3}{*}{Porosity [P] (\%)} & 10 & 0 & 1 & Low \\  & & 30 & 20 & 3 & \(\downarrow\) \\ \cline{1-1}  & & 40 & 30 & 4 & High \\ \cline{1-1} \cline{2-6}  & \multirow{3}{*}{Depth to the water table [GW] (m)} & \(>\) & 40 & 1 & Low \\ \cline{1-1}  & & 30 & 40 & 2 & \\ \cline{1-1}  & & 20 & 30 & 3 & \(\downarrow\) \\ \cline{1-1}  & & 10 & 20 & 4 & \\ \cline{1-1}  & & \(<\) & 10 & 5 & High \\ \hline \hline \end{tabular} \(\downarrow\): The direction of GWLF potential from low to high.  
\end{table} 
Table 1: Assigned feature scores for different influencing factors associated with groundwater level fluctuation potential. Figure 11: _Cont._Determination of the Weightings of Individual Influencing Factors from Groundwater Level Fluctuation Data  
As stated in Section 3.1, the groundwater level fluctuation may be affected by the selected eight influential factors. Each influential factor has its weightage to control the degree of groundwater level fluctuation. While determining the weights of individual influencing factors from the feedback of groundwater level fluctuation, the following equation can be used, as shown in Figure 12.  
\[[\text{P}]_{\text{m}\times\text{n}}\times[\text{W}]_{\text{m}\times 1}=[\text{ \Delta h}]_{\text{m}\times 1} \tag{4}\]  
where [P] is the feature scores of influential factors from the groundwater monitoring wells, [W] is the estimated weighting coefficients for eight influential factors, and [\(\text{\Delta h}\)] is a specific value of groundwater level fluctuation for each groundwater monitoring well in a period. Due to the [P] matrix, which is a non-symmetric matrix in Equation (4), the weighting coefficients are estimated using the Pseudo-inverse method [31].