## 4 Discussion  
### Uncertainty of SD Remote Sensing  
The uncertainty of SD remote sensing was mainly induced by two factors, the dataset for model training and the algorithms themselves. The uncertainty induced by the dataset was primarily due to the mismatch between the in situ data and satellite data. [PERSON] et al. found that when the in situ data were collected within \(\pm 1\) day of satellite imaging, the highest fitting degree of the empirical algorithm could be obtained, and when the data were collected within \(\pm 7\) days, although the model accuracy was reduced, it was still at a high level in 2002 [36]. [PERSON] et al. verified the relationship between the accuracy of the empirical model and the time window and concluded that there is a negative correlation between them, although a time window of 12 days can still maintain high accuracy in 2021 [37]. Our results are consistent with these findings in that an increase in the training time window reduces the accuracy of the model (Tables S1 and S2). However, this condition was effectively mitigated by using band combinations and band ratio combinations, and there were even cases in the SVM model where the model accuracy did not change substantially as the time window increased (Figure 3). We believe that this phenomenon occurred because machine-learning models explain the relationship between band combinations, band ratio combinations, and SD more effectively. Moreover, to verify whether the predictions of models trained by different time windows differ from each other, we conducted a double-sample \(t\)-test on the 1-day time window prediction results of each model. The results (Table 7) showed that there was no significant difference between the prediction results of the models trained with the 1-day and 7-day time window datasets. These results clearly show that it is reasonable to use a 7-day time window dataset for training without significantly affecting the accuracy of the model. The uncertainty of the algorithm arises from the random assignment of data to the training and test sets and parameters [49; 50]. Random selection of the training and test sets can improve the generalization ability of the model, but it may also cause uncertainty in the training results [50]. It was difficult to obtain the same results with different training sets, despite the conditions remaining consistent. Moreover, different parameters (threshold of the stepwise regression model, number of hidden layers of the MLP, number of neurons per layer, penalty coefficients of the SVM, etc.) may result in different results for the same training set. A feasible strategy for improving the generalization ability and prediction accuracy of the model is to increase the number of tests. However, this strategy may also have certain uncertainties; for instance, we cannot exhaust all tests to determine whether the model is optimal. In this study, the MLP model with certain parameters (details are provided in Section 2.4. Algorithm implementation) and the spectral variable group 2 and 3-day time window training dataset was the best model obtained; however, as per our \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment** & **Model** & \
\begin{tabular}{c} **Training Dataset** \\ **(Time Window)** \\ \end{tabular} & **Spectral Group** &
\begin{tabular}{c} **Testing Dataset** \\ **(Time Window)** \\ \end{tabular} & **R-Squared** \\ \hline NO.10 & & 1-day & Group 2 & 1-day & 0.988 \\ NO.10 & Multi-layer perceptron & 1-day & Group 2 & 7-day & 0.5731 \\ NO.12 & & 7-day & Group 2 & 1-day & 0.9812 \\ NO.12 & & 7-day & Group 2 & 7-day & 0.9721 \\ \hline NO.16 & & 1-day & Group 2 & 1-day & 0.865 \\ NO.16 & & 1-day & Group 2 & 7-day & 0.7671 \\ NO.18 & & 7-day & Group 2 & 1-day & 0.8686 \\ NO.18 & & 7-day & Group 2 & 7-day & 0.869 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Influence of the time window of the training set on the prediction results of the machine-learning model (in the case of spectral variable group 2).