## 2 Materials and Methods
### Methods  
#### 2.3.1 Estimation of GPP Based on SIF Data  
GPP is mainly determined by two variables: absorbed photosynthetically active radiation of vegetation canopy (\(APAR\)) and light use efficiency (LUE, \(\varepsilon\)). The calculation equation is as follows:  
\[GPP=APAR\times\varepsilon_{P} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c} \hline
**sc\_PDSI** & **Wet/Dry Grade** & **sc\_PDSI** & **Wet/Dry Grade** \\ \hline \(\leq\)\(-\)4.00 & Extreme Drought & 0.50–0.99 & Initial wetness \\ \(-\)3.00\(-\)\(-\)3.99 & Severe Drought & 1.00–1.99 & Slight wetness \\ \(-\)2.00\(-\)\(-\)2.99 & Moderate drought & 2.00–2.99 & Moderate wetness \\ \(-\)1.00\(-\)\(-\)1.99 & Slight drought & 3.00–3.99 & Severe wetness \\ \(-\)0.50\(-\)\(-\)0.99 & Initial drought & \(\geq\)4.00 & Extreme wetness \\
0.49\(-\)\(-\)0.49 & Normal & & \\ \hline \end{tabular}
\end{table}
Table 1: sc_PDSI Dry and wet grades.  
where \(APAR\) represents the photosynthetically active radiation absorbed by the canopy (MJ\(\cdot\)m\({}^{-2}\)) and \(\varepsilon_{P}\) denotes the actual light use efficiency of vegetation photosynthesis (gC\(\cdot\)MJ\({}^{-1}\)), which is the efficiency of photosynthetically active radiation absorbed by the canopy to be converted into organic carbon.  
SIF contains information on light use efficiency (\(\epsilon\)) and absorbed photosynthetically active radiation of canopy (\(APAR\)) (see Equation (2)):  
\[SIF(\lambda)=APAR\times\varepsilon_{F}(\lambda)\times f_{esc}(\lambda) \tag{2}\]  
where \(\lambda\) is the spectral wavelength, \(\varepsilon_{F}\) is the fluorescence quantum yield (i.e., the ratio of fluorescence emitted by the plant after absorbing photosynthetically active radiation), and \(f_{esc}(\lambda)\) is the proportion of fluorescence emitted by chloroplasts that can escape from the canopy. Combining Equations (2) and (3) can be obtained as follows.  
\[GPP=SIF(\lambda)\times\frac{\varepsilon_{P}}{\varepsilon_{F}(\lambda)}\times \frac{1}{f_{esc}(\lambda)} \tag{3}\]  
When the vegetation area covered by the satellite repeat does not change in canopy structure within a certain time, \(f_{esc}(\lambda)\) can be assumed to be a constant value and will be defaulted to 1. The relationship between \(GPP\) and \(SIF\) is determined by the ratio of the two light energy utilization rates:  
\[\frac{GPP}{SIF}=\frac{APAR\times\varepsilon_{P}}{APAR\times\varepsilon_{F}( \lambda)\times f_{esc}(\lambda)} \tag{4}\]  
\[GPP=SIF\times\frac{\varepsilon_{P}}{\varepsilon_{F}(\lambda)}=SIF\times S_{i} \tag{5}\]  
In addition, [PERSON] et al. [24] showed that the product of \(NIR_{T}\) and \(NDVI\) can effectively separate the signal from the vegetation, thus eliminating the problems caused by the non-vegetation component of the pixels. By multiplying \(NDVI\) by \(NIR_{T}\), the effect of canopy structure on the observed \(SIF\) can be effectively reduced.  
\[NIR_{V}=NIR_{T}\times NDVI \tag{6}\]  
\[GPP=\frac{SIF}{NIR_{\gamma}}\times S=SIF_{TOTAL}\times S_{i} \tag{7}\]  
where \(SIF_{TOTAL}\) is the \(SIF\) of the total canopy obtained after eliminating the effect of canopy structure, and \(S_{i}\) is the fit coefficient between the \(GPP\) observations and \(SIF\) for different vegetation types that we presented in Section 2.2.3.