## 2 Materials and Methods
### The Data-Driven SIF Retrieval Algorithm
The results showed that retrievals using a fitting window containing oxygen absorption lines (755-778 nm and 747-780 nm) or merely water vapor absorption lines (724-747 nm and 715-748 nm) are not as good as using a fitting window that combines water vapor absorption lines and the atmospheric window (735-758 nm and 720-758 nm), which is also true for the fitting windows of the same width (735-758 nm, 724-747 nm and 755-778 nm). Exp. 6-14 showed that with the adjustment of \(n_{\rm p}\) and \(n_{\rm SV}\), reasonable retrievals (with RMSE less than 1 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\)) could be achieved when \(n_{\rm p}\) was between 1-5 and \(n_{\rm SV}\) was less than 20. Through the optimization, the RMSE of SIF retrieval can be reduced from 1.18 mW m\({}^{-2}\) nm\({}^{-1}\) sr\({}^{-1}\) to 0.63 mW m\({}^{-2}\) nm\({}^{-1}\) sr\({}^{-1}\) at the far-red band and reduced from 0.62 mW m\({}^{-2}\) nm\({}^{-1}\) sr\({}^{-1}\) to 0.53 mW m\({}^{-2}\) nm\({}^{-1}\) sr\({}^{-1}\) at the red band. Based on the analysis above, we designed the list of parameter values shown in Table 4. The fitting windows for far-red SIF retrieval were selected to cover the weak water vapor absorption lines and Fraunhofer lines between 712 and 758 nm; 758 nm was taken as the final wavelength, only the starting wavelength (\(\lambda_{1}\)) of the fitting window was changed, and the width of the window was then determined. The fitting windows for red SIF retrieval were selected between 682 and 697 nm to cover the oxygen absorption lines. Then, 682 nm was taken as the starting wavelength, and the fitting window was determined by the ending wavelength (\(\lambda_{2}\)). We took the intensity of SIF at a specific wavelength (depending on \(\mu_{\rm h}\)) simulated by SCOPE as the true values, which were compared to the SIF retrievals. The root mean square error (RMSE) was used to evaluate the influence of the parameters, and the optimized parameters were determined for these settings with the smallest RMSE. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Exp.** & \(\mathbf{w_{1}}\) & \(\mathbf{w_{2}}\) & \(\mathbf{n_{p}}\) & \(\mathbf{n_{SV}}\) & **RMSE *** & **bias *** & **r** & **slope** & **Intercept *** \\ \hline
1 & 755 & 778 & 2 & 7 & 1.18 & \(-\)0.34 & 0.77 & 0.87 & \(-\)0.03 \\
2 & 747 & 780 & 4 & 7 & 0.86 & 0.01 & 0.87 & 0.99 & 0.03 \\
3 & 724 & 747 & 2 & 10 & 0.80 & 0.33 & 0.91 & 1.01 & 0.29 \\
4 & 715 & 748 & 3 & 9 & 0.69 & 0.14 & 0.93 & 0.95 & 0.25 \\
5 & 720 & 758 & 3 & 11 & 0.61 & 0.24 & 0.96 & 0.98 & 0.29 \\
6 & 735 & 758 & 2 & 4 & 0.63 & \(-\)0.03 & 0.93 & 1.00 & \(-\)0.01 \\
7 & 735 & 758 & 4 & 4 & 0.78 & 0.25 & 0.91 & 1.04 & 0.16 \\
8 & 735 & 758 & 2 & 15 & 0.84 & \(-\)0.01 & 0.88 & 1.03 & \(-\)0.07 \\
9 & 735 & 758 & 2 & 20 & 0.92 & \(-\)0.01 & 0.87 & 1.03 & \(-\)0.09 \\
10 & 682 & 697 & 2 & 5 & 0.60 & 0.19 & 0.57 & 1.24 & 0.06 \\
11 & 682 & 697 & 2 & 7 & 0.53 & 0.11 & 0.60 & 1.08 & \(-\)0.14 \\
12 & 682 & 697 & 2 & 10 & 0.62 & 0.26 & 0.53 & 1.10 & 0.20 \\
13 & 682 & 697 & 5 & 4 & 0.53 & 0.01 & 0.57 & 1.13 & \(-\)0.03 \\
14 & 682 & 697 & 1 & 15 & 0.56 & \(-\)0.18 & 0.51 & 0.98 & \(-\)0.17 \\ \hline \end{tabular}
\end{table} 
Table 3: Comparisons of retrieved SIF (SIFretrieved) and true SIF (SIFtrue) simulated using SCOPE model in different experiments. A certain number of feature vectors (\(n_{\rm SV}\)) and polynomial order (\(n_{\rm p}\)) were used within the fitting window from the starting wavelength \(n_{1}\) to the ending wavelength \(w_{2}\). The statistical results included the root mean square error (RMSE), the mean difference (bias) between SIFretrieved and the SIFtrue, the correlation coefficient (r), as well as the slope and intercept of the linear fitting (SIFretrieved = slope * SIFtrue + intercept). The radiance units (denoted by *) are mW m\({}^{-2}\) nm\({}^{-1}\) sr\({}^{-1}\).