## 4 Results
### Land Requirement Estimation and LULC Prediction under Scenario II  
The land requirement estimation under Scenario II (Maximization of ecosystem service values), which was estimated based on the annual rate change between classified LULC data in 2019 and allocated LULC data in 2029 after maximization of ecosystem services according to the objective function (see Equation (1)) and constraining decision variables (see Table A5 in Appendix B) using LP through the Simplex method, is reported in Table 15.  
As a result, the increased LULC classes under this scenario were urban and built-up area, para rubber, perennial trees and orchards, and wetland, with increasing annual rates of 0.38, 0.87, 1.95, and 1.34 km\({}^{2}\), respectively. In contrast, the decreased LULC classes in 2029 were paddy fields, forest land, rangeland, and miscellaneous land, with annual rates of decrease of 0.99, 2.06, 1.36, and 0.14 km\({}^{2}\), respectively. Meanwhile, field crops and water bodies were unchanged. The results of LULC prediction data between 2020 and 2029 under Scenario II, which were simultaneously allocated based on elasticity values and the conversion matrix of LULC change (Tables 9 and 11), the land requirements (Table 15), and driving factors of LULC change for specific LULC type location preference (Table 8), are presented in Table 16 and Figure 5. Meanwhile, the deviation between the estimated land requirements and predicted LULC data in 2029 under Scenario II is reported in Table A6 in Appendix B.  
Figure 4: Spatial distribution of LULC data under Scenario I: (**a**) in 2020 and (**b**) in 2029. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**LULC Types**} & \multicolumn{8}{c}{**Area (in km\({}^{2}\))**} \\ \cline{2-11}  & **2020** & **2021** & **2022** & **2023** & **2024** & **2025** & **2026** & **2027** & **2028** & **2029** \\ \hline Urban and built-up area & 33.36 & 33.84 & 34.22 & 34.60 & 34.99 & 35.39 & 35.42 & 36.17 & 36.47 & 36.94 \\ Paddy field & 219.74 & 218.73 & 217.75 & 216.77 & 215.78 & 214.77 & 213.82 & 212.74 & 211.81 & 210.78 \\ Field crop & 21.85 & 21.82 & 21.81 & 21.81 & 21.86 & 21.85 & 21.84 & 21.86 & 21.80 \\ Para rubber & 20.67 & 21.50 & 22.37 & 23.23 & 24.09 & 24.98 & 25.87 & 26.74 & 27.56 & 28.46 \\ Perennial trees and orchards & 81.16 & 83.12 & 85.05 & 87.01 & 88.96 & 90.81 & 92.90 & 94.81 & 96.70 & 98.68 \\ Forest land & 434.86 & 432.77 & 430.71 & 428.65 & 426.61 & 424.52 & 422.49 & 420.45 & 418.34 & 416.34 \\ Water body & 33.57 & 33.57 & 33.57 & 33.57 & 33.57 & 33.70 & 33.70 & 33.70 & 33.70 & 33.70 \\ Rangeland & 25.87 & 24.51 & 23.16 & 21.78 & 20.43 & 19.14 & 17.72 & 16.35 & 14.97 & 13.57 \\ Wetland & 17.72 & 19.07 & 20.42 & 21.76 & 23.10 & 24.27 & 25.82 & 26.93 & 28.44 & 29.72 \\ Miscellaneous land & 2.56 & 2.42 & 2.29 & 2.15 & 2.02 & 1.89 & 1.77 & 1.62 & 1.48 & 1.36 \\ \hline
**Total** & **891.35** & **891.35** & **891.35** & **891.35** & **891.35** & **891.35** & **891.35** & **891.35** & **891.35** & **891.35** \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Area of predicted LULC between 2020 and 2029 under Scenario II. Figure 5: Spatial distribution of LULC data under Scenario II: (**a**) in 2020 and (**b**) in 2029.