## 4 Results and Discussion
### Urban LULC Prediction
#### 4.3.2 Transition Probability Analysis  
To simulate the future LULC and urban expansion, this study considered a sophisticated method to estimate the rate of land transition in each specific time using the conventional scheme of the MC and application of the projected population to calculate the transition probabilities from statistical extrapolation and SD approach. The details of this analysis are discussed in two separate sections. * Transition probability calculation from the MC  
The MC was used to quantify the change between a pair of LULC maps. It created a transition probability matrix for each LULC category to be converted to any other categories (Table 5). The contingency matrix, which displays the relative frequencies of change in a certain time step, was utilized to calculate the transition probability. The resulted matrices were then used with the transition potential map in the next step of the change prediction. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Year** & **Factor** & **Overall V** & **A** & **W** & **U** & **F** & **M** \\ \hline \multirow{6}{*}{2011} & Distance to agriculture & 0.4496 & 0.5449 & 0.9966 & 0.1789 & 0.9238 & 0.1283 \\  & Distance to BTS and MRT & 0.2466 & 0.5991 & 0.5356 & 0.0902 & 0.5253 & 0.0696 \\  & Distance to built-up area & 0.4723 & 0.7801 & 0.9306 & 0.3010 & 1.0000 & 0.0656 \\  & Distance to center of city & 0.1734 & 0.7794 & 0.3712 & 0.1161 & 0.3462 & 0.0753 \\  & Distance to forest & 0.2027 & 0.4043 & 0.2934 & 0.1734 & 0.2912 & 0.2918 \\  & Distance to miscellaneous & 0.2338 & 0.4055 & 0.3398 & 0.0567 & 0.2914 & 0.0384 \\  & Distance to road & 0.1651 & 0.0109 & 0.3463 & 0.0751 & 0.3564 & 0.0322 \\ \hline \multirow{6}{*}{2011} & Distance to water & 0.3646 & 0.5748 & 0.2449 & 0.7866 & 0.1878 & 0.0899 \\  & Economic growth rate & 0.1801 & 0.0298 & 0.3674 & 0.1104 & 0.3495 & 0.1172 \\  & Elevation & 0.2585 & 0.6823 & 0.1397 & 0.5676 & 0.1075 & 0.0219 \\  & Housing density & 0.2404 & 0.5694 & 0.5053 & 0.1330 & 0.4951 & 0.0776 \\  & Housing growth rate & 0.2322 & 0.2842 & 0.4554 & 0.1634 & 0.4384 & 0.1609 \\  & Population density & 0.2370 & 0.4840 & 0.5058 & 0.1209 & 0.4909 & 0.0648 \\  & Population growth rate & 0.2136 & 0.7338 & 0.4244 & 0.1551 & 0.4086 & 0.1311 \\  & Slope & 0.0661 & 0.1697 & 0.0284 & 0.1447 & 0.0260 & 0.0137 \\ \hline \multirow{6}{*}{2014} & Distance to agriculture & 0.4491 & 0.6516 & 0.9981 & 0.1619 & 0.9456 & 0.1127 \\  & Distance to BTS and MRT & 0.2272 & 0.3075 & 0.4932 & 0.0771 & 0.4896 & 0.0627 \\  & Distance to built-up area & 0.4559 & 0.7176 & 0.9484 & 0.2107 & 0.4552 & 0.0821 \\  & Distance to center of city & 0.1681 & 0.4045 & 0.3639 & 0.0916 & 0.3325 & 0.0939 \\  & Distance to forest & 0.2069 & 0.6778 & 0.2977 & 0.1547 & 0.3009 & 0.3128 \\  & Distance to miscellaneous & 0.2781 & 0.4165 & 0.0854 & 0.2331 & 0.1068 & 0.0794 \\  & Distance to road & 0.1545 & 0.2389 & 0.3302 & 0.5810 & 0.3345 & 0.0318 \\
2014 & Distance to water & 0.2663 & 0.4229 & 0.1508 & 0.0660 & 0.0980 & 0.0786 \\  & Economic growth rate & 0.1700 & 0.1255 & 0.3366 & 0.0718 & 0.3415 & 0.1443 \\  & Elevation & 0.2764 & 0.0618 & 0.1358 & 0.6100 & 0.1003 & 0.0275 \\  & Housing density & 0.2251 & 0.2134 & 0.4769 & 0.0991 & 0.4732 & 0.1076 \\  & Housing growth rate & 0.1847 & 0.1065 & 0.3495 & 0.1267 & 0.3514 & 0.1670 \\  & Population density & 0.2218 & 0.2052 & 0.4712 & 0.0880 & 0.4671 & 0.1105 \\  & Population growth rate & 0.2075 & 0.3831 & 0.4078 & 0.1104 & 0.3978 & 0.1905 \\  & Slope & 0.0814 & 0.0361 & 0.0595 & 0.1719 & 0.0431 & 0.0182 \\ \hline \hline \end{tabular} Note: A = agriculture; W = water; U = Urban; F = forest; M = miscellaneous.  
\end{table} 
Table 4: _Cont._* Integration of the future population and economic demand for the transition probability of urban expansion in 2014 and 2035  
To quantify the future LULC in 2014, this study considered the existing population data collected by DOPA, Ministry of Interior. Based on the population growth calculation between 2011 and 2014, the annual growth rate of population was observed as 0.01 per year.