## 2 Materials and Methods
### Methods  
#### 2.3.1 Estimation of GPP and ANPP  
In this study, we utilized the eddy covariance-light use efficiency (EC-LUE) model to estimate the GPP of subtropical ecosystems in China. The EC-LUE model is based on two assumptions: firstly, the fraction of absorbed PAR (FPAR) is a linear function of NDVI; secondly, the actual light use efficiency calculated according to the constant potential LUE unrelated to the organism is controlled by temperature or soil moisture, taking the maximum of the two restrictions. The EC-LUE model was calibrated and validated using 24,349 daily GPP estimates from 28 eddy covariance flux towers in the United States and Europe, covering a range of forests, grasslands, and tropical savannas. The model explained 85% and 77% of the observed daily GPP variations at all calibration and validation sites, respectively. Compared with the GPP calculated using the Moderate Resolution Imaging Spectroradiometer (MODIS), the GPP predicted using the EC-LUE model was better matched with the tower data at these sites [39]. The EC-LUE model equation is as follows:  
\[GPP=\varepsilon_{max}\times PAR\times FPAR\times min(T_{s},W_{s}) \tag{1}\]  
where \(\varepsilon_{max}\) is the maximum light utilization efficiency, which is 2.25 gC/MJ [40]; \(PAR\) is the photosynthetically active radiation; \(FPAR\) is the photosynthetically active radiation component, which is calculated using the linear function of NDVI [41]; and \(T_{s}\) and \(W_{s}\) are the limiting effects of temperature and water on the potential light utilization rate, respectively. The EC-LUE model holds that the limiting effect of the two factors follows the minimum factor rule of ecology, that is, the ultimate environmental limit depends on the environmental factor with the strongest stress. In reference to existing research results, the calculation formulas for \(FPAR\), \(T_{s}\), and \(W_{s}\) are as follows:  
\[FPAR=a\times NDVI+b \tag{2}\]  
\[T_{s}=\frac{(T-T_{min})(T-T_{max})}{(T-T_{min})(T-T_{max})-\big{(}T-T_{opt} \big{)}^{2}} \tag{3}\]  
\[W_{s}=\frac{VPD_{0}}{(VPD_{0}+VPD)} \tag{4}\]  
where \(a\) and \(b\) are empirical coefficients, valued at 1.24 and \(-\)0.168, respectively. This formula and parameters have been verified in various ecosystems globally, showcasing extensive representativity [42]. \(T\) stands for air temperature (\({}^{\circ}\)C), and \(T_{min}\), \(T_{max}\), and \(T_{opt}\) represent the minimum, maximum, and optimum temperatures for plant photosynthesis, with values of 0 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 21 \({}^{\circ}\)C, respectively [40]. \(VPD_{0}\) is the empirical coefficient for the \(VPD\) constraint equation, with each vegetation type having a corresponding \(VPD_{0}\). The calculation formula for \(VPD\) (vapor pressure deficit) is as follows:  
\[VPD=SVP-AVP \tag{5}\]  
\[SVP=6.112\times f_{w}\times e^{\frac{17.67T}{T+23.53}} \tag{6}\]  
\[AVP=6.112\times f_{w}\times e^{\frac{17.67T_{d}}{T+23.53}} \tag{7}\]  
where \(SVP\) and \(AVP\) are saturated vapor pressure and actual vapor pressure (kPa), respectively, \(T\) is the air temperature (\({}^{\circ}\)C), and \(T_{d}\) is the dew point temperature (\({}^{\circ}\)C). \[f_{w}=1+7\times 10^{-4}+3.46\times 10^{-6}P_{mst} \tag{8}\]  
\[P_{mst}=P_{mst}\bigg{(}\frac{T+273.16}{T+273.16+0.0065\times Z}\bigg{)}^{5.625} \tag{9}\]where \(Z\) stands for elevation (m), \(p_{mst}\) is the atmospheric pressure (hPa), and \(p_{mst}\) refers to the mean sea-level pressure, valued at 1013.25 hPa. We calculated ANPP through carbon use efficiency (CUE), which is defined in terrestrial ecosystems as the ratio of net primary productivity (NPP) to gross primary productivity (GPP) [43; 44]. Usually, the value of CUE is defined as a constant 0.5, but with the increase in research and further refinement, a large number of studies have shown that the value of CUE varies with environmental factors, forestland factors, and changes in the ecosystem [45; 46].