## 4 Discussion
### Algorithm Comparison  
Several studies have demonstrated that the accuracy of empirical algorithms applied to the inversion of lake SD could be improved by using band and band ratio combinations; however, the accuracy of empirical algorithms also has certain limitations [18, 37, 51, 52]. For example, [PERSON] et al. collected the R-squared values (range: 0.6-0.98) of 13 previously published non-machine-learning empirical algorithms, including single-band, band-logarithm, multi-band, and inter-band-ratio algorithms, and found that the R-squared values were 0.6 (\(n\) = 120), 0.93 (\(n\) = 374), and 0.85 (\(n\) = 15,615) in 2021 [19]. Additionally, [PERSON] et al. established a stepwise regression model with Landsat 8 OLI to explore the relationship between all bands (or band ratio) and SD in Minnesota Lake in 2016 [32]. The model yielded R-squared values in the range of 0.6-0.83, which was similar to the R-squared values reported by [PERSON] et al. [19]. [PERSON] et al. applied 17 combinations of the highest \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{
\begin{tabular}{c} **Testing Dataset** \\ **(Time Window)** \\ \end{tabular} } & \multirow{2}{*}{**Spectral Group**} & \multicolumn{2}{c}{**Training Dataset**} & \multirow{2}{*}{**Statistic**} & \multirow{2}{*}{\(p\)**-Value**} \\ \cline{3-4} \cline{6-6}  & & & **Sample1** & & **Sample2** \\ \hline \multirow{6}{*}{Stepwise regression} & Group 1 & 3-day & 0.9482 & 0.3441 \\  & Group 1 & 7-day & 0.3431 & 0.7318 \\  & Group 1 & 1- to 3-day & 0.6366 & 0.525 \\  & Group 1 & 1- to 7-day & 0.3412 & 0.7332 \\  & Group 1 & 3- to 7-day & 0.6184 & 0.5369 \\  & Group 2 & 3-day & 0.3879 & 0.6984 \\  & Group 2 & 7-day & 0.2418 & 0.8092 \\  & Group 2 & 1- to 3-day & 0.2995 & 0.7648 \\  & Group 2 & 1- to 7-day & \(-\)0.0424 & 0.9662 \\  & Group 2 & 3- to 7-day & 0.2993 & 0.765 \\ \hline \multirow{6}{*}{Multi-layer perceptron} & Group 1 & 3-day & \(-\)0.1351 & 0.8926 \\  & Group 1 & 7-day & 0.1541 & 0.8776 \\  & Group 1 & 1- to 3-day & 0.022 & 0.9825 \\  & Group 1 & 1- to 7-day & \(-\)0.5074 & 0.6124 \\  & Group 1 & 3- to 7-day & \(-\)0.3291 & 0.7424 \\  & Group 2 & 3-day & 0.0783 & 0.9377 \\  & Group 2 & 7-day & \(-\)0.0545 & 0.9566 \\  & Group 2 & 1- to 3-day & \(-\)0.693 & 0.489 \\  & Group 2 & 1- to 7-day & \(-\)0.3651 & 0.7154 \\  & Group 2 & 3- to 7-day & 0.2928 & 0.77 \\ \hline \multirow{6}{*}{Support vector machines} & Group 1 & 3-day & 0.3482 & 0.728 \\  & Group 1 & 7-day & 0.5229 & 0.6016 \\  & Group 1 & 1- to 3-day & 1.5386 & 0.1253 \\  & Group 1 & 1- to 7-day & 0.358 & 0.7207 \\  & Group 1 & 3- to 7-day & 0.7433 & 0.4581 \\  & Group 2 & 3-day & 0.1303 & 0.8964 \\  & Group 2 & 7-day & \(-\)0.773 & 0.4403 \\  & Group 2 & 1- to 3-day & \(-\)1.3009 & 0.1946 \\  & Group 2 & 1- to 7-day & \(-\)1.2284 & 0.2206 \\  & Group 2 & 3- to 7-day & 0.1303 & 0.8964 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Difference in prediction results between models trained with a 1-day time window dataset and models trained with other time window training datasets (using 1-day time window data as a testing dataset). Group 1 represents the spectral variables that used a single band or band combination. Group 2 represents the spectral variables that used a band combination and band ratio arrangement. The 1- to 3-day, 1- to 7-day, and 3- to 7-day time windows of the training dataset were obtained by subtracting the 1-, 3-, and 7-day time windows of the dataset. The \(p\)-value is a scale used by the \(t\)-test to detect the effect, and a \(p\)-value less than 0.05 represents a significant difference. correlation band/band ratios to estimate the SD, and the highest R-squared obtained was 0.866 in 2016 [53]. [PERSON] et al. verified the relationship between landsat8 blue/red bands and SD in Canada using an empirical algorithm with a maximum R-squared value of 0.65 in 2021 [16]. [PERSON] et al. applied partial band ratios for SD prediction in the Baltic Sea and inland waters of Northern Europe with an accuracy of 0.66-0.73 in 2017 [24].