## 3 Results and Discussion
### SERS Characteristic Peaks Model Analysis  
Based on the above analysis, 994, 1028, 1370, 1436, and 1636 cm\({}^{-1}\) were preliminarily selected as characteristic peaks of soil water-soluble nitrogen. The selected characteristic peaks were modeled and analyzed by PLS, whose model performances are shown in Table 3. Also, the calibration set and the prediction set was divided according to the ratio of 2:1 using the SPXY method.  
The PLS models predicted by five characteristic peaks together achieved good results (\(R_{p}^{2}=0.87\), RMSE\({}_{p}=11.03\) mg/L, \(RPD=2.56\)), which indicated that 994, 1028, 1370, 1436, and 1636 cm\({}^{-1}\) could be integrated together to predict soil water-soluble nitrogen content accurately. However, the \(R_{p}^{2}\) of single characteristic peaks was lower than the five characteristic peaks combined. The maximal \(R_{p}^{2}\) was 0.86 using 1370 cm\({}^{-1}\), and the corresponding RMSE\({}_{p}\) and \(RPD\) were 10.41 mg/L and 2.52 respectively. Meanwhile, the prediction result (\(R_{p}^{2}=0.77\), RMSE\({}_{p}=13.07\) mg/L, \(RPD=1.73\)) was poor when modeled with the characteristic peak 994 cm\({}^{-1}\), which was consistent with the relationship between the SERS absorption peak intensity and water-soluble nitrogen content. Moreover, the \(R_{p}^{2}\) and \(RPD\) at 1028, 1436, and 1636 cm\({}^{-1}\) all reached more than 0.80 and 2 respectively. Thus, 1028, 1370, 1436, and 1636 cm\({}^{-1}\) could be selected as characteristic peaks of soil water-soluble nitrogen in further studies.  
Based on the analysis, the regression equation between the characteristic peaks (1028, 1370, 1436, and 1636 cm\({}^{-1}\)) and the soil water-soluble nitrogen concentration was established. The fifteen point in each figure was the average SERS of fifteen different soil water-soluble nitrogen concentrations, the abscissa was the soil water-soluble nitrogen concentration, and the ordinate was the SERS intensity. The regression results are shown in Figure 7.  
Figure 7a-d display the linear regression relation at 1028, 1370, 1436, and 1636 cm\({}^{-1}\) respectively, where the coefficient of determination (\(R^{2}=0.94\)) at 1370 cm\({}^{-1}\) was the highest and the regression equation was \(y=93.491x+1771.5\), which was related to the SRES peaks intensity in different Raman peak positions. The coefficient \(a\) of \(x\) was from 57.862 to 93.791, the constants \(b\) ranged from 1017.8 to 1771.5, and the standard error was from 378.94 to 539.41. The \(R^{2}\) of all linear regression equations was higher than 0.9, which indicated that the soil water-soluble nitrogen could be detected by those SERS characteristic peak intensities.  
Given the division standard of soil water-soluble nitrogen in China [35] and the combination with the soil water-soluble nitrogen concentration in this experiment, the soil water-soluble nitrogen concentration was divided into low concentration (22.7-63.7 mg/L) and high concentration (70.5-118.3 mg/L) to analyze. PCA was used to cluster the samples, and LS-SVM was applied for classification based on two principal components and four characteristics peaks. The total number of samples was 120, and the ratio between the calibration set and the prediction set was 5:3 using SPXY.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Calibration Set**} & \multicolumn{3}{c}{**Prediction Set**} & \\ \hline \(R_{c}^{2}\) & **RMSE\({}_{c}\) (mg/L)** & \(R_{p}^{2}\) & **RMSE\({}_{p}\) (mg/L)** & **RPD** & **Wavenumber (cm\({}^{-1}\))** \\ \hline
0.84 & 12.27 & 0.87 & 11.03 & 2.56 & 994, 1028, 1370, 1436, \\
0.78 & 13.57 & 0.77 & 13.07 & 1.73 & 994 \\
0.81 & 13.42 & 0.81 & 12.61 & 2.16 & 1028 \\
0.88 & 10.82 & 0.86 & 10.41 & 2.52 & 1370 \\
0.86 & 12.11 & 0.86 & 11.50 & 2.51 & 1436 \\
0.87 & 11.21 & 0.85 & 11.54 & 2.44 & 1636 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model performance of five characteristic peaks.