## 3 Results
### Empirical Algorithm
\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** & \multicolumn{2}{c}{**Formula**} & \multirow{2}{*}{**R-Squared**} \\ \cline{4-5}
**Number** & & & & **Parameters** & **Coefficient** & \\ \hline \multirow{4}{*}{NO.1} & & & & Intercept & \(4.73\times 10^{2}\) & \\  & & & & Rrs655 & \(-3.55\times 10^{4}\) & 0.6291 \\  & & & & Rrs443 & \(2.08\times 10^{4}\) & \\ \hline \multirow{4}{*}{NO.4} & \multirow{4}{*}{
\begin{tabular}{c} Stepwise \\ regression \\ \end{tabular} } & & & & Intercept & \(4.05\times 10^{2}\) & \\  & & & & Rrs655 & \(-6.87\times 10^{4}\) & \\  & & & & Rrs655/ & Rrs483 & \(-1.72\times 10^{7}\) & \\  & & & & Rrs443 & \(-1.28\times 10^{5}\) & \\  & & & & Rrs443/ & Rrs561 & \(-4.30\times 10^{6}\) & \\  & & & & Rrs561 & \(-8.54\times 10^{4}\) & 0.8641 \\  & & & & Rrs561/ & Rrs655 & \(7.94\times 10^{6}\) & \\  & & & & Rrs483 & \(2.57\times 10^{5}\) & \\  & & & & Rrs483/ & Rrs443 & \(2.97\times 10^{6}\) & \\  & & & & Rrs655/ & Rrs443 & \(1.17\times 10^{7}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The optimal models of stepwise regression correspond to two groups of spectral variables and their related details. Group 1 represents the spectral variables that use a single band or band combination. Group 2 represents the spectral variables that use band combination and band ratio arrangement. The experiment number corresponds to Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment Number** & **Model** & \begin{tabular}{c} **Training Dataset** \\ **(Time Window)** \\ \end{tabular}  & **Spectral Group** \\ \hline NO.1 & Stepwise regression & 1-day & Group 1 \\ NO.2 & Stepwise regression & 3-day & Group 1 \\ NO.3 & Stepwise regression & 7-day & Group 1 \\ NO.4 & Stepwise regression & 1-day & Group 2 \\ NO.5 & Stepwise regression & 3-day & Group 2 \\ NO.6 & Stepwise regression & 7-day & Group 2 \\ NO.7 & Multi-layer perception & 1-day & Group 1 \\ NO.8 & Multi-layer perception & 3-day & Group 1 \\ NO.9 & Multi-layer perception & 7-day & Group 1 \\ NO.10 & Multi-layer perception & 1-day & Group 2 \\ NO.11 & Multi  
The models with the highest R-squared, which are optimal solutions for different sets of spectral variables, are plotted in Figure 4. As shown in Figure 4, both machine-learning models have some scatter that deviates from the fitted line in the figure. In general, the MLP model has a scatter distribution that is closer to the fitted line, whereas the scatter distribution of the different sets of spectral variables for MLP was not significant. Further, there was no significant difference between the scatter distribution of different spectral variable groups of the MLP, where the SVM using a single band or a combination of bands (blue dots) had a larger deviation value compared to the spectral variable group using a combination of bands and a combination of band proportions (orange dots). Similar to the empirical algorithm model, the use of spectral variable groups with band combinations and band proportional combinations (orange points) reduces the bias of the SVM model, whereas the MLP model using different spectral variable groups does not produce significant differences. Therefore, the MLP model using a 1-day time window training dataset was the best machine-learning model for estimating regional lake SD. Experiments were conducted to evaluate the performance of machine-learning models with spectral datasets shorter or longer than their training data, in which the MLP and SVM models using spectral variable group 2 were selected and trained with 1-day and 7-day time window training datasets, respectively. As shown in Table 6, the prediction accuracy of the MLP model decreased substantially and was particularly low when interpreting data beyond its own training dataset; however, it performs well for a shorter time window dataset.