## 3 Results
### Influence of Empirical Parameters on SIF Retrievals
#### 3.1.2 Influence of Polynomial Order and the Number of Feature Vectors on SIF Retrievals  
The influence of the polynomial order is clarified in the optimal fitting window selected in Section 3.1.1 (Figure 6). As can be seen, the RMSE decreased first and then increased with the increase in the polynomial order. The second-order polynomial was a better choice in both far-red and red fitting windows, with an RMSE of 0.82 \(\pm\) 0.36 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) and 0.71 \(\pm\) 0.16 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\) for far-red and red SIF retrieval, respectively. Figure 5: The RMSE of SIF retrieval in different (**a**) far-red and (**b**) red fitting windows (\(\lambda_{1}\)—758 nm at far-red band and 682—\(\lambda_{2}\) nm at red band) when the other parameters in Table 4 arbitrarily change (SNR = 322). The horizontal bar in blue represents the median, diamonds in red represent the average, 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. Figure 6: The RMSE of SIF retrieval in the optimal (**a**) far-red (735–758 nm) and (**b**) red fitting windows (682–697 nm) with different polynomial orders when the other parameters in Table 4 arbitrarily change. The horizontal bar in blue represents the median, diamonds in red represent the average. The case where n\({}_{\text{p}}\) is 5 in the far-red fitting window is excluded for the abnormal RMSE value with an average of 17.14 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\). The RMSEs of different numbers of feature vectors were evaluated (Figure 7). The accuracy of SIF retrieval decreased first and then increased with the increase in \(\mathrm{n_{SV}}\) in both the far-red and red fitting windows as too many feature vectors over-fit the random noise of the sensor. For far-red SIF retrieval, \(\mathrm{n_{SV}}\) was set as 4 with a minimal RMSE of 0.63 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\), while for red SIF retrieval, \(\mathrm{n_{SV}}\) was set as 7 with a minimal RMSE of 0.53 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\). Except for the analysis above, we also investigated whether different fitting windows and SNR affected the optimal setting of \(\mathrm{n_{P}}\) and \(\mathrm{n_{SV}}\) (Figure 8). Figure 8: The optimal polynomial order (**a**,**c**) and number of feature vectors (**b**,**d**) of SIF retrieval in different far-red (**a**,**b**) and red (**c**,**d**) fitting windows (\(\lambda_{1}\)—758 nm at far-red band and 682—\(\lambda_{2}\) nm at red band). The influence of the SNR is also shown by the number of scattered points in the same fitting window. The optimal parameters were selected with the smallest RMSE. Figure 7: The RMSE of SIF retrieval in (**a**) far-red and (**b**) red fitting windows using different numbers of feature vectors. The order of the polynomial is 2 and the fitting windows are 735–758 nm and 682–697 nm for the far-red and red band, respectively. Our results showed that in far-red fitting windows, there was an obvious positive linear correlation between window width and the optimal \(\mathrm{n_{p}}\) and \(\mathrm{n_{SV}}\), with an \(\mathrm{R^{2}}\) of 0.71 and 0.46 respectively, which means that a larger number of feature vectors and polynomial orders are preferable in wider fitting windows. In the red band, the SIF signal was weaker and more affectable by the random noise. Thus, for red SIF retrieval, although the optimal \(\mathrm{n_{p}}\) and \(\mathrm{n_{SV}}\) still had a positive linear correlation with the width of fitting windows, the correlation between \(\lambda_{2}\) and the optimal \(\mathrm{n_{p}}\) or \(\mathrm{n_{SV}}\) was lower than that of far-red fitting windows with the \(\mathrm{R^{2}}\) of 0.24 and 0.38 for the relationship between \(\lambda_{2}\) and the optimal \(\mathrm{n_{p}}\) and the optimal \(\mathrm{n_{SV}}\), respectively.