## 2 Data and Methods
### Research Methods
#### 2.4.3 Method for GPP/SIF Verification  
To verify the changes in light distribution-sensitive diagnostic indicators (GPP/SIF) under different weather conditions, the Clear Sky Index (CI) method proposed by [PERSON] et al. [52] was used to calculate the weather index of the study area in 2020. Subsequently, the weather conditions were comprehensively classified using the weather condition classification standard proposed by [PERSON] et al. [53] (Table 4). Finally, the GPP/SIF method derived by [PERSON] et al. [54] was used to calculate the light distribution-sensitive diagnostic values. We set the suitability of SIF satellite products for arid regions when the GPP/SIF ratio in each ecosystem shows fluctuations around the 1:1 line without major abrupt changes. The parameter calculation formula is as follows:  
\[CI=R_{s}/R_{0} \tag{9}\]  
\[R_{0}=R_{sc}(1+0.33\cos(360d/365))\sin\beta \tag{10}\]  
\[\sin\beta=\sin\phi\cdot\sin\delta+\cos\phi\cdot\cos\delta\cdot\cos\omega \tag{11}\]  
where \(R_{sc}\) is the solar constant, \(\beta\) is the solar zenith angle, \(\varphi\) is the latitude of the study area, \(\delta\) is the solar declination angle, and \(\omega\) is the hourly angle.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Weather Conditions** & **Criteria for Division** & \begin{tabular}{c} **Kelameili Station** \\ **Cultivated and Farmland Area** \\ \end{tabular} & \
\begin{tabular}{c} **Ulastai Station** \\ **Pasture Grassland Area** \\ \end{tabular} &
\begin{tabular}{c} **Ulan Usu Station** \\ **Desert Vegetation Area** \\ \end{tabular} \\ \hline Sunny Day & 0.6 \(\leq\) CI \(<\) 1 & 191 d & 177 d & 178 d \\ Cloudy Day & 0 \(<\) CI \(<\) 0.3 & 75 d & 69 d & 96 d \\ Overcast Day & 0.3 \(\leq\) CI \(<\) 0.6 & 100 d & 120 d & 92 d \\ \hline \hline \end{tabular}
\end{table}
Table 4: Study area weather division results.  
2.4.4. Method for SIF Precision Improvement  
To further explore the optimal accuracy of SIF data in three typical ecosystems in arid regions, we employed two methods to improve the precision of RTSIF satellite products, and then repeated the linear regression fitting analysis process.  
Method 1: Accuracy improvement method based on canopy. This method decomposes the incident sunlight into three parts as follows: zero-order canopy transmittance (denoted as \(t_{0}\)), canopy interception rate (denoted as \(i_{0}\)), and escape probability (denoted as _fesc_). Among them, a portion of the sunlight intercepted by the canopy is absorbed (denoted as _a_) and a portion is scattered (denoted as _s_). When scattering occurs, collisions occur between the canopies, resulting in a recollision rate (denoted as _p_). Based on the relationships between these factors and incorporating other parameters (Table 3), the accuracy of SIF data is improved using the following formula:  
\[a+s+t_{0}=1 \tag{12}\]  
\[P=n-1/n\;\times\;\omega \tag{13}\]  
\[R_{obs}=\pi\;\times\;L/(E\;\times\;\cos\theta_{S}) \tag{14}\]  
\[Le=LAI\;\times\;CI \tag{15}\]  
\[i_{0}=1-\text{EXP}(-G(\theta))\;\times\;Le\;\times\;\pi\;\times\;L/\cos\theta _{s} \tag{16}\]  
\[f_{esc}=R_{obs}/i_{0}\times\omega\;\times\;\lambda \tag{17}\]  
\[\text{SIF}_{improved}=\text{SIF}_{before\;improved}\;\times\omega\times i_{0}/R_ {obs} \tag{18}\]  
where \(n\) represents the average number of interactions between the solar radiation and leaf surfaces, \(R_{obs}\) is the canopy spectral bidirectional reflectance, and \(\lambda\) is the wavelength. Other parameter information can be found in Table 3.  
Method 2: The linear deviation accuracy improvement method [55; 56]. This method uses the slope (_a_) and intercept (_b_) of the best regression-fitting equation (_y = ax + b_) between the measured GPP and SIF satellite data to comprehensively eliminate bias, thereby improving the accuracy of the SIF data. The calculation formula is as follows:  
\[\text{SIF}_{improved}=\text{SIF}_{before\;improved}-[(a-1)GP\;P+b] \tag{19}\]