## 3 Results  
### Influence of Empirical Parameters on SIF Retrievals  
The range of retrieval RMSE when different values were set for a parameter stands for the necessity of optimizing this parameter. In this study, we selected the median value of each parameter in Table 4 as a default value. Then, for each parameter, the RMSE of different values were recorded when other parameters were fixed as their default value in order to clarify the influence of different parameters on retrieval accuracy (Figure 3). The fitting window of SIF retrieval (represented by \(\lambda_{1}\) and \(\lambda_{2}\)) notably affected the accuracy of SIF retrieval, both in the far-red and red fitting windows. Improper setting of the fitting window greatly increased the RMSE to 1.48 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) and 8.79 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) for far-red and red SIF retrieval, respectively. However, an RMSE of 0.59 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) and 0.87 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) could be achieved when the optimal fitting window was selected. The changing range of RMSE can be 104.51% and 295.52% of the average RMSE in different far-red and red fitting windows, respectively. The polynomial order (n\({}_{\text{P}}\)) and the feature vectors (n\({}_{\text{SV}}\)) also have a great influence on the retrieval. For far-red SIF retrieval, the RMSE changed within 0.57-1.09 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) with different n\({}_{\text{P}}\) (66.67% of the average RMSE), and when a different n\({}_{\text{SV}}\) was set, the RMSE varied between 0.57 and 0.96 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) (47.56% of the average RMSE). For red SIF retrieval, the influence of n\({}_{\text{P}}\) and n\({}_{\text{SV}}\) was greater. An RMSE within 0.76-3.27 mW m\({}^{-2}\) sr\({}^{-1}\) nm \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Description** & **Range** & **Step** \\ \hline \(\lambda_{1}\) (nm) & Starting wavelength of far-red fitting window & [715; 745] & 5 \\ \(\lambda_{2}\) (nm) & Ending wavelength of red fitting window & [685; 697] & 2 \\ n\({}_{\text{P}}\) & Polynomial order & [1; 5] & 1 \\ n\({}_{\text{SV}}\) & Number of feature vectors & [2; 20] & 1 \\ \(\mu_{\text{h1}}\) (nm) & The central wavelength of h\({}_{\text{r}}\) at the far-red band & [735; 745] & 1 \\ \(\sigma_{\text{h1}}\) (nm) & The standard deviation of h\({}_{\text{f}}\) at the far-red band & [20; 40] & 1 \\ \(\mu_{\text{h2}}\) (nm) & The central wavelength of h\({}_{\text{f}}\) at the red band & [683; 693] & 1 \\ \(\sigma_{\text{h2}}\) (nm) & The standard deviation of h\({}_{\text{f}}\) at the red band & [9; 11] & 0.5 \\ \hline \end{tabular}
\end{table} 
Table 4: The parameters involved in SIF retrieval using the data-driven algorithm. Figure 3: The root mean square error (RMSE) of SIF retrieval when different values for each parameter were set. The influence of each parameter was investigated when other parameters were set as their default values, i.e., uh1 = 740 nm, \(\sigma_{\text{h1}}\) = 30 nm, \(\mu_{\text{h2}}\) = 688 nm, \(\sigma_{\text{h2}}\) = 10 nm, n\({}_{\text{P}}\) = 3, n\({}_{\text{SV}}\) = 11, \(\lambda_{1}\) = 730 nm, and \(\lambda_{2}\) = 691 nm (SNR = 322). The horizontal bar in blue represents the median, diamonds in red represent the average, and the box bar covers 50% of the RMSE values. RMSE values that do not fall within the upper and lower limits of the boxplot are excluded as outliers. (138.67% of the average RMSE) and 1.02-3.36 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) (121.62% of the average RMSE) can be obtained when selecting different \(\mathrm{n_{p}}\) and \(\mathrm{n_{SV}}\), respectively. On the contrary, the impact of \(\mathrm{\mu_{h}}\) and \(\mathrm{\sigma_{h}}\) was negligible, and the changing ranges of RMSE using different \(\mathrm{\mu_{h}}\) and \(\mathrm{\sigma_{h}}\) were no more than 5% of the average RMSE value for both far-red and red SIF retrieval. Thus, the fluorescence function was fixed according to the study of [PERSON] et al. [18], i.e.