## 3 Results
### Evaluation and Regression Results of Models  
Figure 4 depicts the loss variation during the training process of the multilayer denoising autoencoder. It can be observed that as the number of training epochs increases, the loss gradually decreases. Figure 5 illustrates the difference in retrieval performance between the model trained with data processed by the multilayer denoising autoencoder and the model trained with raw data. It is evident that the water quality inversion performance of the model has significantly improved after being processed by the multilayer denoising autoencoder. Specifically, the R\({}^{2}\) of linear regression increased from 0.27 to 0.42, the R\({}^{2}\) of the bagging model increased from 0.62 to 0.9, the R\({}^{2}\) of random forest increased from 0.55 to 0.78, and the R\({}^{2}\) of decision tree increased from 0.45 to 0.71. These experimental results indicate that after denoising processing by the multilayer denoising autoencoder, the noise in the remote sensing spectral data is reduced, retaining effective spectral information.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Spectral Characteristics** & **Correlation Coefficient** \\ \hline B5 & 0.501 \\ B7/B9 & 0.493 \\ (B7 \(-\) B9)/(B7 + B9) & 0.492 \\ B6/B10 & 0.487 \\ B7/B10 & 0.484 \\ (B6 \(-\) B10)/(B6 + B10) & 0.462 \\ (B7 \(-\) B10)/(B7 + B10) & 0.460 \\ B6/B9 & 0.458 \\ (B6 \(-\) B9)/(B6 + B9) & 0.455 \\ B8/B10 & 0.428 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The selected spectral features and their correlation coefficients with total phosphorus.  
Figure 3: Correlation heat map of each spectral feature and TP concentration.  
Consequently, subsequent models can learn useful information, thereby improving the water quality inversion performance of the models.  
Figure 6 depicts the difference in retrieval performance of total phosphorus among different models trained with processed data, and the specific values of each evaluation metric can be found in Table 4. It is evident that the bagging model achieves the best inversion performance, followed by the random forest model, while the linear regression model performs the worst. Except for the linear regression model, all other models have an R\({}^{2}\) greater than 0.7, indicating good inversion performance. Specifically, the bagging model achieves an R\({}^{2}\) of 0.9, MSE of 0.00031, and MAE of 0.014 on the test set. In contrast, the R\({}^{2}\) of the linear regression model is only 0.42, significantly lower than that of the bagging model. Figure 7 displays the scatter plot between in situ total phosphorus observation data and the total phosphorus estimated values retrieved by different models. It can be seen that the bagging model has the smallest errors in predicting total phosphorus concentration, showing high consistency with the real results. Conversely, the linear regression model exhibits larger discrepancies between predicted and real results, especially for data points with higher total phosphorus concentrations. This indicates that the linear regression model performs poorly in handling extreme values and fails to capture the nonlinear relationships  
Figure 4: Graph of the loss change during the training of the multilayer denoising autoencoder.  
Figure 5: Comparison of the inversion performance of each model before and after denoising autoencoder processing.  
between variables. Overall, the proposed bagging model effectively captures the nonlinear relationships between spectral features and water quality indicators, yielding relatively accurate inversion results. This suggests that the model performs well in addressing complex water quality monitoring tasks.  
Figure 6: Comparison of the performance of models trained on denoised data.  
Figure 7: Plots of the observed versus retrieved total phosphorus concentrations when applying the different models to the testing dataset: (**a**) linear model, (**b**) bagging model, (**c**) random forest model, and (**d**) decision tree model.