## 2 Materials and Methods
### Methods  
#### 2.3.1 Mangrove Vegetation Photosynthesis Light Use Efficiency Model (MVP-LUE)  
The original MVP-LUE (Mangrove vegetation photosynthesis light use efficiency) model was developed by [PERSON] et al. in 2013 and is driven by inputting EVI, PAR, Tair, and SAL. However, in this study, we used the improved MVP-LUE model [49] derived by integrating SST on GPP and adding the limit of water condition (VPD) to GPP. [PERSON] (1972) initially suggested the idea of correlating GPP to PAR via a light use efficiency term (LUE) and multiplicative efficiency factors, which has become the theoretical basis of the LUE model. The theoretical basis of this model is the same as that of the LUE model of typical terrestrial ecosystems; and the method for estimating regional mangrove ecosystem GPP is also the same, scaling up the observations and measurements at EC sites through environmental factors. MVP-LUE not only performed well in the Gulf of Mexico [50], but also estimated the GPP of mangroves in China from 18\({}^{\circ}\)N to 28\({}^{\circ}\)N and achieved good results [49]. Therefore, MVP-LUE was selected as the tool for GPP estimation in this study, and the parameters were optimized according to the actual field surveys of mangroves on Hainan Island. The model as well as the parameters used to estimate mangrove ecosystem GPP goes as follows:  
\[\mathrm{GPP}\ =\ \mathrm{LUE}\ \times\ \mathrm{fAPAR}\ \times\ \mathrm{PAR} \tag{1}\]  
where GPP is gross primary productivity (\(\mathrm{\SIUnitSymbolMicro mol}\ \mathrm{C/m^{2}/mon}\)); fAPAR is the fraction of PAR absorbed by plant canopy; PAR is the incident photosynthetically active radiation (\(\mathrm{mmol/m^{2}/s}\)). LUE is the actual light use efficiency (\(\mathrm{mol}\ \mathrm{C/mol}\ \mathrm{PFFD}\)) which is the maximum LUE (\(\mathrm{LUE_{max}}\))) of mangroves regulated by environmental scalars, including Tair, SST, SAL, VPD and PAR, as follows:  
\[\mathrm{LUE}\ =\ \mathrm{LUE_{max}}\ \times\ \mathrm{T_{air_{scalar}}}\ \times\ \mathrm{VPD_{scalar}}\ \times\ \mathrm{PAR_{scalar}}\ \times\ \mathrm{SST_{scalar}}\ \times\ \mathrm{SAL_{scalar}} \tag{2}\]  
where \(\mathrm{T_{air_{scalar}}}\), \(\mathrm{SST_{scalar}}\), \(\mathrm{VPD_{scalar}}\), \(\mathrm{PAR_{scalar}}\), and \(\mathrm{SAL_{scalar}}\) are the regulation scalars for the limitation from air and sea water temperature, the water demand, and light and salinity conditions on LUE, respectively. The specific value of \(\mathrm{LUE_{max}}\) depends on the range of Tair: when Tair is within the optimal range for mangrove growth, the \(\mathrm{LUE_{max}}\) has the highest value (0.057); conversely, when Tair exceeds or falls below the optimal range, the \(\mathrm{LUE_{max}}\) is set to 0.047 and 0.055, respectively. The optimal \(\mathrm{T_{air}}\) varies linearly with latitude, slope \(=-0.58^{\circ}\mathrm{C}\)/lat (R\({}^{2}\) = 0.97, RMSE = 0.39). For the study of mangrove distribution areas in China, it is generally set to 21-25 \({}^{\circ}\mathrm{C}\), and in this study, it was set to 22.87-26.05 \({}^{\circ}\mathrm{C}\) based on the survey data of Hainan Island (see Supporting Materials for details, Figure S1). The photosynthetic responses of mangroves to SST are similar to Tair; we used the same equation to calculate the scalar. The air temperature dependency factors are defined by [PERSON] et al. [50] as follows:  
\[\mathrm{T_{air_{scalar}}}=(\mathrm{T-T_{min}})(\mathrm{T-T_{max}})\Bigg{/}( \mathrm{T-T_{min}})(\mathrm{T-T_{max}})-(\mathrm{T-T_{opt}})^{2}, \tag{3}\]  
where \(\mathrm{T_{opt}}\), \(\mathrm{T_{max}}\), and \(\mathrm{T_{min}}\) are the optimal, maxim um and minimum daytime air temperature for the mangrove photosynthetic activities, respectively. Mangroves cannot grow properly when Tair is below \(\mathrm{T_{min}}\) (10 \({}^{\circ}\)C), which is the same as the minimum SST of 12 \({}^{\circ}\)C, and no photosynthesis occurs below freezing temperature. High temperatures can also reduce the rate of photosynthesis in plants.