## 2 Materials and Methods
### Methods  
#### 2.4.1 MLR Model  
Parameterization of MLR Model  
To construct GPP in arid regions based on improved RTSIF, [PERSON] et al. (2012) used different methods to construct an MLR model. This model is currently the latest and most comprehensive method for inverting GPP based on SIF at the spatiotemporal scale. Its basic principles are as follows. Figure 2: Linear regression fitting diagram for comprehensive applicability evaluation of MODIS GPP satellite products in arid regions. (**a**) Kelameili Station, Desert Vegetation Area; (**b**) Ulastai Station, Grassland Area; (**c**) Ulan Usu Staion, Farmland Area. The MLR model, a physical model for describing the mechanism of light-energy conversion during photosynthesis, simulates how light energy absorbed by pigments in plant leaves participates in chemical reactions during the photosynthetic process by establishing dynamic equations for the light-reaction phase. Specifically, light energy absorbed by pigments in chloroplasts (such as chlorophylll) undergoes a series of photochemical reactions and is converted into chemical energy. Focusing on the light-reaction phase, the MLR model quantitatively describes these processes to simulate the dynamic changes in photosynthetic efficiency. Moreover, photosynthesis is influenced not only by light intensity, but also regulated by environmental factors such as Tair, Tsoil, VPD, and SWC. The MLR model typically takes these factors as input parameters, offering a more comprehensive depiction of photosynthetic dynamics under varying conditions. Finally, the MLR model connects SIF with photosynthetic efficiency, using SIF data as an indicator of photosynthesis, thus enabling a more effective inversion of GPP. Therefore, compared with previous linear inversion methods, this model can better achieve GPP inversion. The specific calculation method is shown in Formula (3). \[\text{GPP}=\left\{ \begin{array}{ll}\frac{C_{C}-\Gamma}{4C_{C}+8\Gamma}\times \text{qL}\times\frac{\text{\#PTSlimax}\times(1+K_{\text{DF}})\times\text{SIF TOC, PSI, FULL}}{(1-\text{\#PTSlimax})\times\text{\#C}_{\text{C}},\text{p-c}}&\text{C3}\\ \frac{(1-\xi)}{3}\times\text{qL}\times\frac{\text{\#PTSlimax}\times(1+K_{\text{DF }})\times\text{SIF TOC, PSI, FULL}}{(1-\text{\#PTSlimax})\times\text{\#C}_{\text{C}},\text{p-c}}&\text{C4}\end{array} \right. \tag{3}\]  
In this formula, \(C_{C}\) represents the total pressure of CO\({}_{2}\) present in chlorophylll; \(\Gamma^{*}\) represents the CO\({}_{2}\) chloroplast compensation point; \(\xi\) represents the total electronic transmission score; qL represents the openness of the chlorophylll photosystem II reaction center; \(\text{\#PTSlimax}\) represents the quantum yield of chlorophyll released from channel 2 during light reflection (maximum value); \(K_{\text{DF}}\) represents the ratio (structural heat dissipation constant divided by fluorescence value); \(F_{\text{esc,p-c}}\) represents the escape coefficient; and \(SIF_{\text{TOC}}\)_PSII-FULL represents the fluorescence energy emitted by photosystem II within the chlorophylll fluorescence emission band. C4 plants have multiple carbon assimilation pathways and possess drought and high temperature resistance characteristics. These characteristics are consistent with the overall arid and high-temperature properties of Xinjiang. Therefore, in this study, we use the C4 model to invert GPP; the parameters that could not be directly obtained in the model were obtained through gradual iteration [13; 14; 15; 16; 17] (Table 3). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Iteration Process and Value** \\ \hline \hline \multirow{7}{*}{ql.} & \multirow{7}{*}{\(\lambda\)L cannot be directly calculated and can be iterated as 1 + NPQ (non-photochemical quenching).}