## 3 Materials and Methods
### Ecosystem Services Assessment: Sediment and Nutrient Export
#### 3.5.1 Sediment Export Estimation  
The sediment export is the amount of sediment eroded in the watershed from overland sources and delivered to the stream. In principle, the SDR model is first applied to calculate the amount of annual soil loss, using the Revised Universal Soil Loss Equation (RUSLE) of [43]:  
\[A_{i}=R_{i}\cdot K_{i}\cdot LS_{i}\cdot C_{i}\cdot P_{i}, \tag{3}\]  
where \(A_{i}\) is the annual soil erosion (ton. ha\({}^{-1}\) yr\({}^{-1}\)), \(R_{i}\) is the rainfall erosivity (MJ mm ha\({}^{-1}\) h\({}^{-1}\) y\({}^{-1}\)), \(K_{i}\) is the soil erodibility (ton-ha-hr (MJ ha\(\cdot\)mm)\({}^{-1}\)), \(LS_{i}\) is the slope length-gradient factor, \(C_{i}\) is the crop-management factor, and \(P_{i}\) is a support practice factor for erosion control.  
The required input data for annual soil erosion are summarized below.  
(1) The Rainfall erosivity factor (R) was calculated based on monthly rainfall data, as suggested by [44], as:  
\[R=\sum_{i=1}^{12}1.735\times 10^{(1.5\log_{10}(\frac{P_{i}^{2}}{P})-0.08188)}, \tag{4}\]  
where \(R\) is the rainfall erosivity factor (MJ mm ha\({}^{-1}\) h\({}^{-1}\) y\({}^{-1}\)), \(P_{i}\) is the monthly rainfall (mm), and \(P\) is the annual rainfall (mm).  
We collected monthly rainfall data between 2011 and 2019 from TMD for model calibration and validation and actual sediment export estimation in 2019. Simulated rainfall data between 2020 and 2029 were collected from the National Center for Atmospheric Research (NCAR), for sediment export estimation under three scenarios.  
(2) The Soil erodibility (K) erodibility was extracted from the soil series data of LDD, whereas its value under the slope complex in the soil map was extracted from the geology unit (Table A1 in Appendix A).  
(3) The Slope length gradient factor (LS) was calculated from the DEM with a method developed by [45], as follows:  
\[LS_{i}=S_{i}\frac{\left(A_{i-\text{in}}+D^{2}\right)^{m+1}-A_{i-\text{in}}^{m+ 1}}{D^{m+2}\cdot x_{i}^{m}\cdot\left(22.13\right)^{m}}, \tag{5}\]  
where \(S_{i}\) is the slope factor for a grid cell, calculated as a function of the slope radians \(\theta\) (S = 10.8\(\cdot\)sin\(\theta\) + 0.03 where \(\theta\) < 9%, or S = 16.8\(\cdot\)sin\(\theta\) - 0.50, where \(\theta\) > 9%); \(A_{i-in}\) is the contributing area (m\({}^{2}\)) at the inlet of a grid cell, which is computed using the \(d\)-infinity flow direction method; \(D\) is the grid cell linear dimension; \(x_{i}=\left|\sin\alpha_{\text{i}}\right|\) + \(\left|\cos\alpha_{\text{i}}\right|\), where \(\alpha_{\text{i}}\) is the aspect direction for grid cell \(i\), and \(m\) is the RUSLE length exponent factor.  
(4) The crop management (C) and support practice (P) factors for erosion control, according to LULC type, are summarized in Table A2 in Appendix A.  
Then, the model calculates the sediment delivery ratio using a connectivity index (\(IC\)), threshold flow accumulation, and maximum SDR to indicate sediment retention. The SDR value was calculated, as suggested by [46], as:  
\[SDR_{i}=\frac{SDR_{max}}{1+\exp\left(\frac{IC_{0}-IC_{i}}{k}\right)}, \tag{6}\]  
where \(SDR_{max}\) is the maximum theoretical SDR, set to an average value of 0.8 [47], and \(IC_{0}\) and \(k\) are calibration parameters that define the shape of the SDR-IC relationship as a Sigmoid function.  
Finally, the sediment reaches the stream at the outlet of the Upper Ing watershed. The total sediment export was calculated from the sum of the amount of annual soil loss multiplied by the sediment delivery ratio [48]:  
\[E=\sum_{i}E_{i}, \tag{7}\]  
where \(E_{i}\) is the sediment that erodes from any LULC that reaches the stream.