## 3 Materials and Methods
### Ecosystem Services Assessment: Sediment and Nutrient Export
#### 3.5.2 Nutrient Export Estimation  
Under the NDR model, the nutrient loads are first defined based on the LULC map and associated loading rates. Then, the model calculates LULC-based loads and the runoff potential index to approximate modified loads, which are divided into sediment-bound (surface flow) and dissolved parts (subsurface flow). After that, nutrient delivery is computed for surface NDR and subsurface NDR based on the properties of pixels belonging to the same flow path (particularly the slope and retention efficiency of the land use) [48]. The NDR model requires specific factors and parameters to run the model. Some factors in this model are the same as those in the SDR model, including DEM, LULC, TFA, and \(K_{b}\). Other parameters, including nitrogen and phosphorus loads, nutrient runoff proxy, maximum retention efficiency, and critical length, were added. The specific required factors of the NDR models are summarized below. (1) The nutrient runoff proxy (RP) is used to calculate the runoff potential index. The runoff proxy was interpolated, based on annual rainfall, using the inverse distance weighted (IDW) method. (2) Land-use and land-cover (LULC) data represent the influence of the nutrient delivery to the stream. LULC data were used as input data to assign the nutrient loading for each LULC class (loads), as summarized in Table 4.  
(3) The maximum retention efficiency (eff) indicates the proportion of nutrient retention by vegetation. The value for each LULC class varies between zero and one (see Table 4). (4) The critical length (crit_len) is the distance that a patch of LULC retains nutrients in its maximum capacity. The critical length ranges from 10 to 300 m [49; 50]. In this study, the value was first set to the pixel resolution, with a value of 30 m (see Table 4). (5) The subsurface proportion (proportion_subsurface) value is the proportion of dissolved nutrients that travels by surface and subsurface flow. We set its value to zero, which indicates that all nutrients are delivered by surface flow (see Table 4). After that, the NDR model was computed to transport nutrients by surface flow. The surface nutrient delivery ratio is the product of a delivery factor, representing the ability of downstream pixels to transport nutrients without retention, and was calculated using Equation (8) [48]:  
\[NDR_{i}=\frac{NDR_{0,i}}{1+\exp\left(\frac{\textit{IC}_{i}-\textit{IC}_{o}}{k }\right)}, \tag{8}\]  
where \(NDR_{0,i}\) is the proportion of a nutrient that is not retained by downstream pixels (which is based on the maximum retention efficiency of the land between a pixel and the stream), \(\textit{IC}_{i}\) is a topographic index, and \(\textit{IC}_{0}\) and \(k\) are calibration parameters that define the shape of the NDR-IC relationship. Finally, the total nutrient export at the outlet of the watershed is estimated, from the sum of the product of the load and the NDR [48], as:  
\[x_{\exp_{\textit{tot}}}=\sum_{i}x_{\exp_{i}}, \tag{9}\]  
where \(x_{\exp_{i}}\) is the nutrient export from any LULC, as the product of the load and the NDR. \begin{table}
\begin{tabular}{c} **Proportion** \\ **subsurface** \\ \end{tabular} \\ \hline
1 & Urban & 7.75 & 0.05 & 30 & 0 & 1.3 & 0.05 & 30 & 0 \\
2 & Paddy field & 11 & 0.25 & 30 & 0 & 3 & 0.25 & 30 & 0 \\
3 & Field crop & 11 & 0.25 & 30 & 0 & 3 & 0.25 & 30 & 0 \\
4 & Para rubber & 10 & 0.45 & 30 & 0 & 3 & 0.45 & 30 & 0 \\
5 & Perennial trees and orchards & 10 & 0.45 & 30 & 0 & 3 & 0.45 & 30 & 0 \\
6 & Forest area & 1.8 & 0.7 & 30 & 0 & 0.011 & 0.7 & 30 & 0 \\
7 & Waterbody & 0.001 & 0.05 & 30 & 0 & 0.001 & 0.05 & 30 & 0 \\
8 & Rangeland & 2 & 0.5 & 30 & 0 & 0.011 & 0.5 & 30 & 0 \\
9 & Wetland & 2 & 0.8 & 30 & 0 & 0.05 & 0.8 & 30 & 0 \\
10 & Miscellaneous land & 4 & 0.05 & 30 & 0 & 0.001 & 0.05 & 30 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Data related to nitrogen, phosphorus, and related variables corresponding to each LULC class.