## 3 Methodology
### Pollution Source Intensity Calculation Method  
After obtaining the crop distribution map using 10-m-resolution Sentinel-2 images, we calculated NSP intensity. To facilitate the zoning management of farmland, the Yuecheng Reservoir catchment area was divided into 1 km \(\times\) 1 km grids to calculate NSP intensity. First, we calculated the areas of all kinds of cultivated land using the following formula:  
\[A_{i}=\sum_{n=1}^{q}n\times p^{2} \tag{6}\]  
where \(A_{i}\) is the planting area of cultivated land type \(i\) in the grid, \(n\) is the number of pixels, \(p\) is the spatial resolution of the pixel (10 m in this study), and \(q\) is the number of pixels identified as cultivated land type \(i\).  
To calculate the spatial distribution characteristics of the emission potential of total nitrogen (TN) and total phosphorus (TP) in farmland, we improved the calculation formula of farmland NSP intensity proposed by [PERSON] et al. [1] and added the farmland quality correction factor. The specific calculation method is as follows:  
\[\text{Q}_{\text{TN}}=\sum_{i}^{n}\text{A}_{i}\times\text{TN}_{i}\times 1/ \varepsilon_{i}\times\text{M} \tag{7}\]  
\[\text{Q}_{\text{TP}}=\sum_{i}^{n}\text{A}_{i}\times\text{TP}_{i}\times 1/ \varepsilon_{i}\times\text{M} \tag{8}\]  
\[\text{M}=\text{S}\times\text{A}\times\text{F}\times\text{P} \tag{9}\]  
where \(\text{Q}_{\text{TN}}\) and \(\text{Q}_{\text{TP}}\) are the TN and TP emissions from agricultural production, respectively; \(i\) is the type of cultivated land and \(n\) is the total number of farmland types, including multiple crops, winter single crops, and summer single crops. \(\text{TN}_{i}\) and \(\text{TP}_{i}\) are the NSP intensity coefficients of pollutants TN and TP of the \(i\)th crop, respectively; the specific values are listed in Table 4. \(\varepsilon_{i}\) is the cultivated land quality correction coefficient of the \(i\)th crop, which can be obtained using Equation (5). \(M\) is the total environmental correction coefficient; S, A, F, and P are the correction coefficients for slope, soil type, fertilizer amount, and annual precipitation, respectively (Table 5). The above correction coefficients TN\({}_{i}\), TP\({}_{i}\), and M are determined in accordance with the requirements of \"The Technical Guide for National Water Environmental Capacity Verification\" [60] issued by the State Environmental Protection Administration of China. The \"National Technical Guide for the Verification of Water Environment Capacity\" provides the source intensity coefficient of winter wheat, which is commonly used to represent all crop types in traditional methods. We determined the source intensity coefficients of multiple crops and summer single crops by consulting the literature [61; 62; 63] and combining factors, such as the amount of fertilizer applied and the amount of crop absorption. In our study area, we focused on three common crop types. In practical application, more cultivation modes (e.g., more than single-year crops) would require the determination of source intensity coefficients from empirical values or field experiments [60].  
For the correction of crop growth factor, the \"National Technical Guide for Verification of Water Environment Capacity\" provides the environmental conditions of standard farmland when determining the source intensity coefficient. It clearly indicates the approximate range of each correction coefficient for specific environmental conditions. On this basis, we stratified the correction coefficient more carefully to facilitate accurate source intensity calculation. The crop growth correction is an additional step in the existing process. Because we were focused on calculating the NSP source intensity of a large-scale catchment, spatial differences in crop growth could not be ignored. For different crops, crop quality was corrected by GPP.