## 2 Materials and Methods
### Data-Driven SIF Prediction Model Using the Random Forest Algorithm  
#### 2.3.1 Explanatory Variable Selection for SIF Prediction Model  
According to [PERSON] et al. [(32)], the SIF can be calculated as:  
\[\mathit{SIF}=\mathit{PAR}\text{:}\varepsilon\alpha_{gm}\text{:}\Phi_{\mathit{SIF}} \tag{2}\]  
where \(\varepsilon\) is the canopy escape probability of SIF photons, \(\alpha_{gm}\) is the fraction of PAR absorbed by green leaves, and \(\Phi_{\mathit{SIF}}\) is the fluorescence quantum yield. This formula can be divided into three terms: \(\mathit{PAR}\), \(\varepsilon\alpha_{gm}\) (the SIF variation related to the canopy structure) and \(\Phi_{\mathit{SIF}}\) (the SIF variation related to plant physiological factors). Since the incoming PAR of instantaneous SIF differs according to the location, the SIF normalized by PAR has been widely used to describe the global photosynthetic capability [(46; 47)]. For satellite SIF observations, which are available only under clear-sky conditions, the PAR can be assumed to be linearly correlated with the cosine value of the solar zenith angle at the transit time of the satellite [(8; 11; 48)]. \(\mathit{SIF}_{\mathit{normalized}}\) is the SIF normalized to a fixed transit time, based on the central latitude and longitude of each grid cell (Equation (3)):  
\[\mathit{SIF}_{\mathit{normalized}}=\frac{\mathit{SIF}}{\mathit{PAR}}=\frac{ \mathit{SIF}}{\mathit{cos}(\mathit{SZA})} \tag{3}\]  
where \(\mathit{cos}\) (\(\mathit{SZA}\)) is the cosine of the solar zenith angle at the satellite transit time. Then Equation (2) can be written as:  
\[\mathit{SIF}_{\mathit{normalized}}=\varepsilon\alpha_{gm}\text{:}\Phi_{ \mathit{SIF}} \tag{4}\]  
At the far-red band, \(\varepsilon\), the canopy escape probability of the \(\mathit{SIF}\), is dominated by the canopy bi-directional reflectance (BRF) [(49; 50; 51; 25)]. \(\alpha_{gm}\), the FAPAR for green leaves, has been widely estimated \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ecosystem Type** & **Site Name** & **ID** & **Latitude** & **Longitude** & **Height** \\ \hline \multirow{3}{*}{Cropland} & Huailai & HL & 40.35\({}^{\circ}\)N & 115.79\({}^{\circ}\)E & 4 m H \\  & Daman & DM & 38.86\({}^{\circ}\)N & 100.37\({}^{\circ}\)E & 25 m H \\  & Aurora & - & 42.72\({}^{\circ}\)N & 76.66\({}^{\circ}\)W & 7 m H \\ Forest & Niwot Ridge & NR & 40.03\({}^{\circ}\)N & 105.55\({}^{\circ}\)W & 26 m H \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the Eddy Covariance (EC) flux sites. using combinations of BRFs [52; 53; 54]. The second term in Equation (2) depends on the reflectance and vegetation indices (VIs), which are directly related to plant structure. Additionally, since the selected TanSat SIF was acquired nadir mode, it was reasonable to assume that \(\varepsilon\alpha_{gm}\), which is the contribution of the structural information to SIF, could be modeled using BRDF-corrected reflectance and VIs. \(\Phi_{SIF}\), which accounts for the contribution of plant physiological factors to SIF, can be determined using chlorophyll fluorescence parameters, which, in turn, can be obtained by pulse-amplitude-modulated (PAM) fluorometry [32]. Since, in this case, the value of PSI SIF was low and stable, PSI was not taken into consideration when calculating \(\Phi_{SIF}\)[32; 33; 55];  
\[\Phi_{SIF}=\frac{1-\Phi_{PSIImax}}{(1+k_{DF})[(1+NPQ)(1-\Phi_{PSIImax})+q_{L} \Phi_{PSIImax}]} \tag{5}\]  
where \(k_{DF}\) is the ratio of thermal dissipation (\(k_{D}\)) to fluorescence emission (\(k_{F}\)), \(NPQ\) is the adjustable heat dissipation, \(q_{L}\) is the fraction of photosynthesis system II (PSII) reaction centers, and \(\Phi_{PSIImax}\) is the maximum photochemical quantum yield of PSII. In Equation (5), \(k_{DF}\) is always assumed to be constant as \(k_{D}\) and \(k_{F}\) are considered to be intrinsic physical properties of the chlorophyll molecule. \(\Phi_{PSIImax}\) typically ranges from 0.8 to 0.83 and varies slightly under environmental stress [56].