## 4 Results
### Nutrient Export Estimation Using NDR Model
#### 4.8.2 Nutrient Export Estimation of Predicted LULC under Scenario I  
The estimated total and average nitrogen and phosphorus export of predicted LULC between 2020 and 2029 and mean annual rainfall under Scenario I (Trend of LULC evolution) is presented in Table 28.  
As a result, the highest total and average nitrogen export occurred in 2029, with values of about 210,908 kg and 236.62 kg/km\({}^{2}\), respectively, while the lowest total and average nitrogen export occurred in 2020 with a value of about 197,973 kg and 222.10 kg/km\({}^{2}\), respectively. Likewise, the highest total and average phosphorus export occurred in 2029, with a value of about 47,221 kg and 52.98 kg/km\({}^{2}\), respectively, while the lowest total and average phosphorus export occurred in 2020, of about 43,358 kg and 48.64 kg/km\({}^{2}\), respectively.  
These results indicate that the changes in LULC types and areas affect parameters in the biophysical table, leading to different nitrogen and phosphorus export. In contrast, the annual rainfall, as a runoff proxy, was not observed as being sensitive to the estimated data, due to its calculation to modify the load, in order to account for runoff potential by relating the precipitation per cell to the average over the raster, as suggested by [61]. Therefore, non-linear regression analysis was considered in order to reconfirm the suggestion of [61] and the previous study of [62].  
Figure 11 shows the results of non-linear regression analysis between mean annual rainfall (mm) and average nutrient export (kg per km\({}^{2}\)). The best fit of the non-linear regression by Trend Analysis in the MS Excel software was a sixth-order polynomial equation with R\({}^{2}\) values of 0.9638 for nitrogen export and 0.9615 for phosphorus export. As a result, it was confirmed that annual rainfall, as a runoff proxy, is not sensitive to the estimated nutrient export under the NDR model.  
Furthermore, the contribution of the predicted LULC under Scenario I on nutrient export indicated that the highest total nitrogen and phosphorus export occurred on paddy fields. In contrast, the lowest total nitrogen export occurred on water bodies, and the lowest total phosphorus export occurred on miscellaneous land; however, the highest average nitrogen and phosphorus export appeared on field crops, as well as perennial trees and orchards.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Area**} & \multicolumn{2}{c}{**Nitrogen Export**} & \multicolumn{2}{c}{**Phosphorus Export**} & \multicolumn{2}{c}{**Mean Annual Rainfall**} \\ \cline{2-7}  & **km\({}^{2}\)** & **Total (kg)** & **Average (kg/km\({}^{2}\))** & **Total (kg)** & **Average (kg/km\({}^{2}\))** & **(mm)** \\ \hline
2020 & 891.35 & 197,972.93 & 222.10 & 43,358.11 & 48.64 & 1523.53 \\
2021 & 891.35 & 199,580.02 & 223.91 & 43,832.43 & 49.18 & 1508.50 \\
2022 & 891.35 & 200,858.16 & 225.34 & 44,196.29 & 49.58 & 1465.20 \\
2023 & 891.35 & 202,275.64 & 226.93 & 44,619.00 & 50.06 & 1517.76 \\
2024 & 891.35 & 203,395.90 & 228.19 & 44,951.18 & 50.43 & 1537.45 \\
2025 & 891.35 & 205,172.77 & 230.18 & 45,494.30 & 51.04 & 1544.38 \\
2026 & 891.35 & 206,743.37 & 231.94 & 45,966.11 & 51.57 & 1486.75 \\
2027 & 891.35 & 207,795.18 & 233.12 & 46,273.02 & 51.91 & 1472.48 \\
2028 & 891.35 & 209,325.14 & 234.84 & 46,740.48 & 52.44 & 1539.43 \\
2029 & 891.35 & 210,907.86 & 236.62 & 47,221.47 & 52.98 & 1498.28 \\ \hline \hline \end{tabular}
\end{table}
Table 28: Estimation of nitrogen and phosphorus export under Scenario I.  
These findings suggest that the change in LULC types associated with the biophysical table parameters affects nitrogen and phosphorus export. The LULC data of Scenario I were simulated based on the annual rate of LULC change from the transition area matrix between 2009 and 2019 using the Markov Chain model, which did not represent dramatic change under this scenario; the minor change in area also changed the load amounts and export of nutrients.