## 3 Results and Discussion
### Evaluation of the Machine Learning Models  
Five input scenarios were produced by combining all 13 inputs, and the models now need to be trained on these. After being randomly assigned to the training and testing phases, the input scenarios were fed into the models. The models were put into practice, and the MBE, MAPE, and MARE criteria were used to assess the estimations of the models (Table 5). While there are clear distinctions between the models, there are also significant parallels concerning certain situations. The closer the MAPE, MBE, and MARE are to one, the better the model performance. The models demonstrate good performance in GWFP estimation as the greatest MAPE value of 120.97 was attained under RF and Sc3, while the lowest value of \(-\)8.30 was noted under the SVR model and Sc3. The finest MBE under RF and Sc3 was 5.14 m\({}^{3}\) ton\({}^{-1}\), the highest reported MBE under RF-SVR was 5.05 m3 ton\({}^{-1}\), and the lowest MBE under RF-SVR and Sc1 was 0.03. Table 5 shows that the maximum MARE values for RF and XGB with Sc3 were 59.23 and 57.82, respectively, while the lowest values were \(-\)4.05 and \(-\)3.99 for SVR with Sc2 and Sc1, respectively. The relationship between the actual and predicted GWFP values is represented in Table 6 with a coefficient of determination (R\({}^{2}\)) and the best-fitting equation for the relationship. Among the various equations tested, the linear equation yielded the highest R\({}^{2}\) value compared to exponential and logarithmic equations. The analysis revealed that the lowest R\({}^{2}\) values were observed for Sc3, which represented remote sensing indices (EVI, NDVI, SAVI, and NDWI), across all single and hybrid ML models. Conversely, the highest R\({}^{2}\) values were obtained for Sc1 (all parameters), Sc2 (climatic parameters), and Sc4 (Pe, Tmax, Tmin, and SA). Notably, the SVR model consistently achieved the highest R\({}^{2}\) values across all scenarios. Interestingly, the R\({}^{2}\) values for double hybrid models were higher than those for triple hybrid models, and the SVR model outperformed both double and triple hybrid models. The lowest R\({}^{2}\) value of 0.232 was observed for XGB and Sc3, while the highest R\({}^{2}\) value of 0.9846 was achieved for SVR and Sc4. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Vegetation Index**} & \multirow{2}{*}{**Classes**} & \multicolumn{6}{c}{**Area**} \\ \cline{3-10}  & & \multicolumn{2}{c}{**(2000–2005)**} & \multicolumn{2}{c}{**(2006–2010)**} & \multicolumn{2}{c}{**(2011–2015)**} & \multicolumn{2}{c}{**(2016–2020)**} \\ \cline{3-10}  & & **(km\({}^{2}\))** & **(\%)** & **(km\({}^{2}\))** & **(\%)** & **(km\({}^{2}\))** & **(\%)** & **(km\({}^{2}\))** & **(\%)** \\ \hline \multirow{3}{*}{NDVI} & No Veg. & 816.46 & 2.04 & 837.64 & 2.10 & 851.378 & 2.13 & 761.27 & 816.46 \\  & Low & 37,199.34 & 93.09 & 33,347.96 & 83.46 & 34,352.1 & 85.97 & 32,210.81 & 37,199.34 \\  & Moderate & 1942.90 & 4.86 & 5773.10 & 14.45 & 4755.19 & 11.90 & 6986.57 & 1942.90 \\ \hline \multirow{3}{*}{SAVI} & No Veg. & 702.94 & 1.76 & 760.40 & 1.90 & 730.998 & 1.83 & 622.38 & 702.94 \\  & Low & 38,933.90 & 97.44 & 38,606.98 & 96.62 & 38,572.5 & 96.53 & 38,885.99 & 38,933.90 \\  & Moderate & 321.76 & 0.81 & 591.32 & 1.48 & 655.174 & 1.64 & 497.22 & 321.76 \\ \hline \multirow{3}{*}{NDWI} & No Veg. & 39,11.52 & 97.88 & 34,207.52 & 85.61 & 34,056.7 & 85.23 & 33,498.87 & 39,111.52 \\  & Low & 320.63 & 0.80 & 5374.52 & 13.45 & 4874.58 & 12.20 & 6382.57 & 320.63 \\ \cline{1-1}  & Moderate & 32.06 & 0.08 & 372.66 & 0.93 & 678.6 & 1.70 & 77.26 & 32.06 \\ \hline \multirow{3}{*}{EVI} & No Veg. & 921.86 & 2.31 & 960.04 & 2.40 & 952.29 & 2.38 & 885.93 & 921.86 \\ \cline{1-1}  & Low & 37,911.68 & 94.88 & 37,515.68 & 93.89 & 37,648.95 & 94.22 & 34,761.71 & 37,911.68 \\ \cline{1-1}  & Moderate & 544.5 & 1.36 & 902.07 & 2.26 & 776.80 & 1.94 & 3730.40 & 544.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The changes in areas occur through periodic intervals for each vegetation index.