## 3 Results
### Accuracy Verification Results  
The fitting performance of the three models is illustrated in Figures 7-9, with five detailed evaluation metrics presented in Figures 10 and 11. From Figure 7, it can be observed that the PLSR model performs better with the data from August 26 compared to January 15. Specifically, the test set R\({}^{2}\) for January 15 is 0.25, while for August 26, it increases to 0.33. This improvement may be attributed to the PLSR model's ability to better capture linear correlations, as indicated in Table 5, where the correlation on August 26 is higher than that on January 15. Figure 8 shows that the RF model demonstrates superior performance for January 15, with a test set R\({}^{2}\) of 0.55, compared to 0.36 for August 26.  
\begin{table}
\begin{tabular}{c c c} \hline DIFF1 NIR: \(-\)0.43 ** & DIFF2 NIR: \(-\)0.43 ** & SI-T:0.45 ** \\ \hline NDSI:0.44 ** & SAIO: 0.44 ** & SR: \(-\)0.43 ** \\ \hline CRSI: \(-\)0.41 ** & NDVI: \(-\)0.44 ** & EVI: \(-\)0.43 ** \\ \hline DVI: \(-\)0.43 ** & MSAVI: \(-\)0.43 ** & ARVI: \(-\)0.41 ** \\ \hline GDVI: \(-\)0.44 ** & EVI2: \(-\)0.43 ** & ENDVI: \(-\)0.42 ** \\ \hline SAVI: \(-\)0.44 ** & RVI: \(-\)0.43 & SRSI: 0.45 ** \\ \hline \end{tabular} Note: ** represents the \(p\)-value < 0.01.  
\end{table}
Table 6: Correlation between soil salinity and the feature variables on the January 15.  
\begin{table}
\begin{tabular}{c c c} \hline G: 0.45 ** & R: 0.48 ** & EXP\_G: 0.45 ** \\ \hline EXP\_R: 0.48 ** & SQRT\_R: 0.46 ** & SI\(-\)T: 0.45 ** \\ \hline NDSDI: 0.45 ** & SI1: 0.47 ** & SI3: 0.47 ** \\ \hline S3: 0.47 ** & S5: 0.45 ** & SAIO: 0.45 ** \\ \hline BRI: 0.47 ** & NDVI: \(-\)0.45 ** & SRSI: 0.45 ** \\ \hline CO: 0.43 ** & B: 0.44 ** & DIFF1R: 0.43 ** \\ \hline EXP\_CO: 0.43 ** & EXP\_B: 0.44 ** & LOGE\_R: 0.42 ** \\ \hline SQRT\_CO: 0.42 ** & SQRT\_B: 0.43 ** & SQRT\_G: 0.43 ** \\ \hline CRSI: \(-\)0.43 ** & EVI: \(-\)0.42 ** & ARVI: \(-\)0.44 ** \\ \hline GDVI: \(-\)0.44 ** & ENDVI: \(-\)0.43 ** & SAVI: \(-\)0.43 ** \\ \hline \end{tabular} Note: ** represents the \(p\)-value < 0.01.  
\end{table}
Table 7: Correlation between salinity and the feature variables on the August 26.  
Similarly, in Figure 9, the BPNN model also performs better with the January 15 data, achieving a test set R\({}^{2}\) of 0.46, compared to 0.3 for August 26. From the detailed metrics in Figure 10, the RF model for January 15 exhibits the best performance, achieving a test set R\({}^{2}\) of 0.55, RMSE of 3.4, MAE of 2.79, SD of 2.99, and MSE of 11.62, outperforming both the PLSR and BPNN models. In Figure 11, the RF model also performs the best for August 26, with a test set R\({}^{2}\) of 0.36, RMSE of 5.6, MAE of 3.92, SD of 5.6, and MSE of 31.26.  
In conclusion, the RF model for January 15 delivers the best overall performance, indicating that the data from January 15 are more suitable for salinity inversion. Furthermore, among the three models, the RF model consistently performs the best. This suggests that the random forest model can be used for soil salinity inversion in the Yellow River Delta. From Figure 10, it can be seen that both RF and BPNN performed well, with both models having an R\({}^{2}\) greater than 0.45, indicating that using original spectra, spectral indicators, and mathematical transformation variables aids in model construction.