## 3 Methodology
### Crop Information Verification Method  
To verify the accuracy of remote sensing mapping of crops in the Yuecheng Reservoir catchment area, we collected field samples of multiple crops, winter single crops, and summer single crops. Next, we superimposed these samples on high-resolution Google Earth images for artificial digitization. The overall size of the samples was consistent with the size of the field cultivated land. To ensure verification method objectivity, a mixture matrix was used to calculate the classification accuracy. User accuracy, producer  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Farmland Types** & **TN\({}_{i}\) (kg\(\cdot\)m\({}^{-2}\).yr\({}^{-1}\))** & **TP\({}_{i}\) (kg\(\cdot\)m\({}^{-2}\).yr\({}^{-1}\))** \\ \hline Winter single crops (standard farmland) & 0.009 & 0.0009 \\ Summer single crops & 0.0108 & 0.00099 \\ Multiple crops & 0.018 & 0.0012 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Coefficients of source strength of different types of farmland.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Slope (’)** & **Agrotype** & \begin{tabular}{c} **Consumption of Chemical** \\ **Fertilizers (kg\(\cdot\)m\({}^{-2}\).yr\({}^{-1}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Annual** \\ **Precipitation (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Correction** \\ **Factor** \\ \end{tabular} \\ \hline \multirow{4}{*}{Cay} & \multirow{2}{*}{Cay} & 0–100 & 0.6 \\ \cline{3-4}  & & 100–200 & 0.7 \\ \cline{2-4}  & & 0–0.0075 & 200–300 & 0.8 \\ \cline{2-4}  & & 0.0075–0.0225 & 300–400 & 0.9 \\ \hline
0–5 & Loam & 0.0225–0.0375 & 400–600 & 1.0 \\ \hline
5–15 & & 0.0375–0.045 & 600–800 & 1.1 \\ \hline
15–25 & & 0.045–0.0525 & \textgreater{}800 & 1.2 \\ \hline
25–35 & & 0.0525–0.06 & & 1.3 \\ \hline
35–50 & & \textgreater{}0.06 & & 1.4 \\ \hline \hline \end{tabular} \(>\)50  
\end{table}
Table 5: Crop growth environmental correction coefficient M.  
accuracy, overall accuracy, and the kappa coefficient were used to quantify the accuracy of the crop classification results. User accuracy represents the probability that the classifier recognizes a specific type of ground object, and its corresponding real type is also this type of ground object. Producer accuracy represents the probability that the type is a feature and is recognized as that feature by the classifier. Overall accuracy represents the proportion of all correctly classified samples in the total number of samples. The values of these three quantitative indicators are between 0 and 1, where values closer to 1 indicate higher classification accuracy. The kappa coefficient was used to evaluate whether the classification results of the classifier were consistent with the actual observations, and its value is between \(-1\) and 1, where values closer to 1 indicate higher classification model accuracy.  
To verify the remote sensing mapping of the spatial distribution difference of crop growth in the Yuecheng Reservoir catchment area, we divided the study area into its constituent counties, then fitted the yield per unit area of various crops in each county's statistical yearbook with the county's mean cultivated land quality correction coefficient. The goodness of fit \(R^{2}\) was used to measure the degree of fitting. The value range of \(R^{2}\) is between 0 and 1, where values closer to 1 indicate better fitting effect.