## 2 Materials and Methods
### Methods  
#### 2.4.1 Methods for Correlation Analysis between SIF and NPP  
SIF shows potential for estimating vegetation productivity and monitoring drought stress on crops, yet there is currently no research establishing the potential correlation between SIF and NPP. Given the close relationship between GPP and NPP, there is an opportunity to explore the association between SIF and NPP [47; 48]:  
\[NPP=GPP-R_{a} \tag{1}\]  
where \(R_{a}\) is the assimilation product consumed by the autotroph's respiration.  
Taking reference from current studies on the linear relationship between SIF and GPP [49; 50; 51], the derived equation and relationship between SIF and GPP are as follows:  
\[GPP=PAR*fPAR*LUE_{P} \tag{2}\]  
where \(PAR\) is the value of the photosynthetically effective radiation received, \(fPAR\) is the fractional absorption rate of the radiation, and \(LUE_{P}\) is the value of the absorbed photosynthetically effective radiation used for photosynthetic efficiency.  
SIF can be similarly expressed as follows:  
\[SIF(\lambda)=PAR*fPAR*LUE_{F}(\lambda)*f_{esc}(\lambda) \tag{3}\]  
where \(\lambda\) is the spectral wavelength, \(LUE_{F}(\lambda)\) is the light utilization efficiency of the SIF, and \(f_{esc}(\lambda)\) is used to account for the SIF escaping from the canopy into space.  
Based on these two equations, the relationship between GPP and SIF can be expressed as follows:  
\[GPP\approx SIF(\lambda)*\frac{LUE_{P}}{LUE_{F}(\lambda)} \tag{4}\]  
This relational equation quantifies the linear relationship between SIF and GPP and has been consistently confirmed in recent studies.  
According to the above equation, we can deduce that there is a theoretical relationship between SIF and NPP. Since we cannot confirm whether the temporal and spatial relationship between SIF, NPP, and related environmental factors is a linear relationship, we used the Spearman analysis method to conduct pixel-by-pixel correlation analysis on  
Figure 2: Flow chart of the research method.  
the temporal data, calculating the correlation coefficient between the data and verifying the significance. The formula for the Spearman method is as follows:  
\[corr(X,Y)=\frac{\frac{1}{n}\sum(x_{i,j}-\overline{x})*\sum(y_{i,j}-\overline{y} )}{\sqrt{\left(\frac{1}{n}\sum(x_{i,j}-\overline{x})^{2}\right)*\sqrt{\left( \frac{1}{n}\sum(y_{i,j}-\overline{y})^{2}\right)}}} \tag{5}\]  
where \(corr(X,Y)\) is the Spearman correlation coefficient, \(x_{i,j}\), \(y_{i,j}\) are the two variables at coordinates (\(i\),\(j\)) of the pixels, and \(\overline{x}\) and \(\overline{y}\) represent the time series of the two variables at the coordinates with mean values of (\(i\),\(j\)).  
The Spearman correlation coefficient ranged from [\(-1\), \(1\)]. If the calculated result tends to \(1\), then it means that the spatial-temporal changes in the two variables are highly synchronized; if the calculated result tends to \(-1\), then it means that the two variables have opposite variability; and if the calculated result tends to \(0\), then it means that the changes in the two variables are not correlated.  
Furthermore, the analysis of the relationship between SIF and environmental factors also employs the [PERSON]'s rank correlation method.