## 3 Materials and Methods
### Land Demand Estimation of Three Different Scenarios  
The land requirements under three different scenarios for LULC prediction between 2020 and 2029 were estimated based on their characteristics, as follows:  
**(1) Scenario I (Trend of LULC evolution):** The land requirements were calculated based on the annual change rate of LULC between 2009 and 2019 from the transition area matrix using the Markov Chain model.  
**(2) Scenario II (Maximization of ecosystem service values):** The land requirements were calculated based on LULC allocation for maximizing ESV using Linear Programming (LP) with the Simplex method. The objective function and constraints were solved to maximize ecosystem service values using Equation (1), based on the coefficient values for the ESs of each LULC type (Table 3).  
\[\begin{split} Z_{max}=[12.7(X_{1})+1032.3(X_{2})+1032.3(X_{3})+194 9.0(X_{4})+1949.0(X_{5})+1949.0(X_{6})+6873.7(X_{7})+808.6(X_{8})+\\ 9368.7(X_{9})+96.3(X_{10})],\end{split} \tag{1}\]  
where \(Z_{max}\) is the objective function of scenario II for ESV maximization, \(X_{1}\) is the urban and built-up area (UR), \(X_{2}\) is paddy field (PD), \(X_{3}\) is field crop (FC), \(X_{4}\) is para rubber (RP),  
\begin{table}
\begin{tabular}{c l l l l} \hline \hline \multirow{2}{*}{**No**} & \multirow{2}{*}{**LULC Classification for SVM**} & \multirow{2}{*}{**LULC Classification for ESV 1**} & \multicolumn{2}{c}{**Coefficient Values**} \\  & & & **(USD/ha/Year) 1** & **Land-Use Classification 2** \\ \hline
1 & Urban and built-up area (UR) & Construction land & 12.7 & Urban and built-up area \\ \hline
2 & Paddy field (PD) & Cultivated land & 1032.3 & Paddy field \\ \hline
3 & Field crop (FC) & Cultivated land & 1032.3 & Cassava, sugarcane, and maize \\ \hline
4 & Para rubber (RB) & Forest land & 1949.0 & Rubber plantation \\ \hline
5 & \
\begin{tabular}{l} perennial trees and orchards \\ (PO) \\ \end{tabular} & Forest land & 1949.0 &
\begin{tabular}{l} Mixed perennial trees and orchards \\ which exclude para rubber \\ \end{tabular} \\ \hline
6 & Forest land (FO) & Forest land & 1949.0 & Natural forest and man-made forest \\ \hline
7 & Water body (WB) & Water body & 6873.7 &
\begin{tabular}{l} River, canal, natural water resource, \\ reservoir, pond, irrigation canal \\ \end{tabular} \\ \hline
8 & Rangeland (RL) & Rangeland & 808.6 & Scrub, grass, and pasture \\ \hline
9 & Wetland (WL) & Wetland & 9368.7 & Marsh and swamp \\ \hline
10 & Miscellaneous land (ML) & Unused land & 96.3 &
\begin{tabular}{l} Bush fallow, mine, laterite pit, soil pit, \\ garbage dump, landfill, rock outcrop \\ \end{tabular} \\ \hline \hline \end{tabular} Note: 1[36], 2[23].  
\end{table}
Table 3: Description of LULC classification system.  
\(X_{5}\) is perennial trees and orchards (PO), \(X_{6}\) is forest land (FO), \(X_{7}\) is water body (WB), \(X_{8}\) is rangeland (RL), \(X_{9}\) is wetland (WL), and \(X_{10}\) is miscellaneous land.  
**(3) Scenario III (Economic crop zonation):** The suitable zonation of four economic crops (paddy field, field crop, para rubber, and perennial trees and orchards) of LDD in 2018 was updated using the existing LULC data for 2019 in order to estimate the land requirements.