# GPP of a Chinese Savanna Ecosystem during Different
## 2 Materials and Methods
### VPM and Model Parameters  
The VPM aims to estimate the daily GPP by using the product of the FPARchl of the vegetation canopy and the light use efficiency [54]. The parameters of the VPM can be divided into 2 parts: the vegetation index and meteorological parameters (Figure 2). The air temperature (Ta), EVI, LSWI, and PAR are the input data of the VPM. The meteorological data for Ta and PAR are both based on daily measurements from the Yuanjiang flux tower. This model can be expressed as follows:  
\[\text{GPP}=\text{LUE}\times\text{FPARchl}\times\text{PAR} \tag{5}\]  
where FPARchl is the fraction of the PAR absorbed by chlorophyll, PAR is the photosynthetically active radiation, the product FPARchl\(\times\)PAR refers to the absorbed photosynthetically active radiation (APAR), and LUE is the light use efficiency (g C mol\({}^{-1}\) photosynthetic photon flux density (PPFD)). FPARchl can be calculated as a linear function of the EVI with adjusted coefficients of 0.1 and 1.25 according to previous studies [15]:  
\[\text{FPARchl}=(\text{EVI}-0.1)\times 1.25 \tag{6}\]  
The light use efficiency (\(\epsilon_{\text{g}}\)) can be obtained from the maximum LUE (\(\epsilon_{0}\)) scaled by the effects of temperature (T\({}_{\text{scalar}}\)) and water (W\({}_{\text{scalar}}\)) (Equation (7)). \[\epsilon_{\text{g}}=\epsilon_{0}\times\text{T}_{\text{scalar}}\times\text{W}_ {\text{scalar}} \tag{7}\]  
T\({}_{\text{scalar}}\) is a measure of the sensitivity of photosynthesis to the air temperature, which can be calculated for each time interval as follows (Equation (8)):  
\[\text{T}_{\text{scalar}}=\frac{(\text{T}-\text{T}_{\text{min}})(\text{T}- \text{T}_{\text{max}})}{\left[(\text{T}-\text{T}_{\text{min}})(\text{T}- \text{T}_{\text{max}})\right]-(\text{T}-\text{T}_{\text{opt}})^{2}} \tag{8}\]  
where T, T\({}_{\text{max}}\), T\({}_{\text{min}}\), and T\({}_{\text{opt}}\) are the daytime mean, maximum, minimum, and optimum temperatures for photosynthesis, respectively. The biome-specific values for the latter three parameters can be obtained from a lookup table for a T\({}_{\text{max}}\) value of 48 \({}^{\circ}\)C and T\({}_{\text{min}}\) and T\({}_{\text{opt}}\) values of 1 \({}^{\circ}\)C and 30 \({}^{\circ}\)C, respectively [15]. The sensitivity of photosynthesis to water (W\({}_{\text{scalar}}\)) can be estimated via the LSWI, and during the growing season, the maximum LSWI was assumed to match the LSWI\({}_{\text{max}}\):  
\[\text{W}_{\text{scalar}}=\frac{1+\text{LSWI}}{1+\text{LSWI}_{\text{max}}} \tag{9}\]  
C3 and C4 plants in savannas exhibit contrasting responses to rising CO\({}_{2}\) concentrations, as well as differing responses to solar radiation and temperature changes [2]. The proportions of the net primary productivity (NPP) of C3 and C4 vegetation in the Yuanjiang savanna were surveyed [55], in which the proportion of C3 vegetation to the total NPP reached 82.57%, whereas the proportion of C4 vegetation was 17.43%; moreover, NPP field biomass surveys were linked to vegetation proportions [56]. We adopted this value as the approximated proportion of C3 and C4 vegetation. We recalculated the maximum LUE value according to the proportion of C3 and C4 vegetation in the savanna. Following the latest VPM GPP products, the LUEmax values of C3 and C4 plants were set to 0.42 and 0.63 g C/ mol APAR, respectively [15]. Furthermore, to reduce the model uncertainty [11], we fitted a curve based on two weeks of half-hourly flux data during the 2015-2018 peak savanna growth period to obtain the maximum LUE value, i.e., \(\epsilon_{0}\), via the GPP-PPFD curve relationship method [57] for model calibration (Equation (10)). \[\text{GPP}=\frac{\epsilon_{0}\times\text{GPP}_{\text{max}}\times\text{PPFD} }{\epsilon_{0}+\text{GPP}_{\text{max}}\times\text{PPFD}} \tag{10}\]where \(\text{GPP}_{\text{max}}\) is the maximum canopy \(\text{CO}_{\text{2}}\) uptake rate (\(\upmu\text{mol}\text{m}^{-2}\text{s}^{-1}\)) at light saturation.