## 3 Results  
### Model Development and Sensitivity Analyses  
Table 1 shows that the models based on samples with larger sizes had slightly better performance than those based on smaller sizes. Both MAE and R decreased with increasing sample size. MAE was stable when half of training samples was used. The results of validation also showed that the performance was improved as more samples were used to develop the model, and it was quite stable when the size of samples was more than 100,000. Figure 2 provided a detailed insight into the final selection of the SIF models. The curves in Figure 2a suggest that the models based on larger sample sizes had lower errors at low SIF values (e.g., 0-0.3 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\)) but larger errors at high SIF values (e.g., \(>\)0.5 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\)) than those based on smaller sample sizes. Since the majority of the  
test set had relatively lower SIF values (Figure 2b: 89.1% was <0.3 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\) and 78.8% was <0.2 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\)), the models based on more samples had lower accumulated errors (Figure 2c). The model based on half of the training samples had nearly the same performance as that based on all the training samples (two lines are almost completely coincident in Figure 2c), and therefore we used half of the training samples to develop the model for both low computation demand and high accuracy. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**With Land Cover Type**} \\ \hline  & \multicolumn{2}{c}{**Fitting**} & \multicolumn{2}{c}{**Validation**} \\ \hline
**Size** & **MAE** & **RE** & **R** & **R\({}^{2}\)** & **RMSE** \\ \hline
10,000 & 0.09 & 0.34 & 0.93 & 0.77 & 0.08 \\ \hline
100,000 & 0.08 & 0.39 & 0.91 & 0.80 & 0.07 \\ \hline
250,000 & 0.08 & 0.42 & 0.89 & 0.81 & 0.07 \\ \hline
500,000 & 0.07 & 0.42 & 0.89 & 0.80 & 0.07 \\ \hline Half & 0.05 & 0.45 & 0.89 & 0.80 & 0.07 \\ \hline All & 0.05 & 0.44 & 0.89 & 0.80 & 0.07 \\ \hline \multicolumn{4}{c}{**Without Land Cover Type**} \\ \hline  & \multicolumn{2}{c}{**Fitting**} & \multicolumn{2}{c}{**Validation**} \\ \hline
**Size** & **MAE** & **RE** & **R** & **R\({}^{2}\)** & **RMSE** \\ \hline
10,000 & 0.09 & 0.35 & 0.92 & 0.76 & 0.09 \\ \hline
100,000 & 0.08 & 0.40 & 0.90 & 0.79 & 0.07 \\ \hline
250,000 & 0.08 & 0.42 & 0.89 & 0.79 & 0.07 \\ \hline
500,000 & 0.07 & 0.42 & 0.89 & 0.79 & 0.07 \\ \hline Half & 0.05 & 0.45 & 0.89 & 0.79 & 0.07 \\ \hline All & 0.05 & 0.45 & 0.89 & 0.79 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The statistical measures for model development and validation. All the models were developed with training samples in 2015 and 2016 and validated with testing data in 2017. MAE, RE, and R represent mean absolute error, relative error, and correlation coefficient, respectively. R\({}^{2}\) and RMSE represent the coefficient of determination and root mean squared error, respectively. MAE, RE, and R are used for fitting, while R\({}^{2}\) and RMSE are used for validation. Figure 2: The RMSE between observed SIF and predicted SIF in each 0.05\({}^{\circ}\) SIF interval by different models (**a**). The percentage of each 0.05\({}^{\circ}\) SIF interval relative to all the observed SIF in the test set (**b**). (**c**) showed that the accumulated errors of predicted SIF by different models decreased with increasing sample size. Table 1 also shows that the models without land cover type had almost identical statistical measures and thus comparable performance to those with land cover type. This difference was better visualized in Figure 3 (only the results for 250,000 training samples and half of training samples are provided here). The models with land cover type had slightly lower accumulated errors than those without land cover type when observed SIF was over 0.3 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\).