# Effects of Aerosols on Gross Primary Production from Ecosystems to the Globe
## 2 Materials and Methods
### Description of the AOD-LUE Model  
We developed a new LUE model, AOD-LUE, by improving the EC-LUE model [37] by incorporating the relative effects of diffuse and direct radiation on GPP. A total of 35 EC sites encompassing ten vegetation types were selected for calibration, and the remaining 35 EC sites were used for model verification (Figure 1). The EC-LUE model is expressed as:  
\[\text{GPP}=\text{PAR}\times\text{fPAR}\times\epsilon_{\text{max}}\ \times\text{min}(\text{T}_{\text{s}},\text{W}_{\text{S}}) \tag{1}\]  
where fPAR is the fraction of incident daily photosynthetically active radiation absorbed by the vegetation canopy (g C m\({}^{-2}\) MJ\({}^{-1}\) APAR) (%), PAR is the incident daily photosynthetically active radiation (M) m\({}^{-2}\)), \(\epsilon_{\text{max}}\) is the maximum light use efficiency without environmental stress (APAR) [2], min is the minimum function of two scalars varying from 0 to 1 and represents the reduction of potential LUE under limiting environmental conditions, and T\({}_{\text{s}}\) and W\({}_{\text{s}}\), are temperature and water downward regulation scalars, respectively. To explicitly consider the Df effect of aerosols, we used the D\({}_{\text{f}}\) fitting to divide PAR into PAR\({}_{\text{dir}}\) and PAR\({}_{\text{diff}}\) in the EC-LUE model. At the same time, the maximum LUE parameter (\(\epsilon\)) will also be parameterized for PAR\({}_{\text{dir}}\) and PAR\({}_{\text{diff}}\) separately. We use a nonlinear regression equation (NLS) to fit the LUE values of the two types of radiation respectively. The AOD-LUE model is as follows:  
\[\text{GPP}=\text{fPAR}\times\left(\text{PAR}\times(1-\text{D}_{\text{f}}) \times LUE_{dir}+\text{PAR}\times\text{D}_{\text{f}}\times LUE_{diff}\right) \times\text{f}(\text{T}_{\text{s}},\text{W}_{\text{s}}) \tag{2}\]  
where \(LUE_{dir}\) is the maximum LUE (g C m\({}^{-2}\) MJ\({}^{-1}\) APAR) affected by PAR\({}_{\text{dir}}\), \(LUE_{diff}\) is the maximum LUE affected by PAR\({}_{\text{diff}}\). In the overall model representation, through the NLS equation, \(LUE_{dir}\) and \(LUE_{diff}\) were estimated to be 1.68 (g C m\({}^{-2}\) MJ\({}^{-1}\)) and 3.61 (g C m\({}^{-2}\) MJ\({}^{-1}\)) respectively. In the model, fPAR is approximated as linear function of NDVI:  
\[\text{fPAR}=\text{a}\times\text{NDVI}+\text{b} \tag{3}\]  
where a and b are empirical constants. According to [PERSON] et al. [41], a and b are set to 1.24 and \(-\)0.168, and NDVI is obtained directly from 1 km MODIS data. The influence of aerosol on solar radiation is mainly manifested in two aspects, the enhancement of PAR\({}_{\text{diff}}\) and the weakening of PAR\({}_{\text{dir}}\). In order to consider the influence of aerosol on the diffusion part of global irradiance, the D\({}_{\text{f}}\) was calculated as:  
\[\text{D}_{\text{f}}=\frac{\text{PAR}_{\text{diff}}}{\text{PAR}_{\text{total}}} \tag{4}\]  
where PAR\({}_{\text{total}}\) is the total photosynthetically active radiation, and PAR\({}_{\text{total}}\) is the total PAR. Aerosol and \(\mathrm{D_{f}}\) were fitted by the Michaelis-Menten equation:  
\[\mathrm{D_{f}}=\frac{\mathrm{V_{max}\times AOD}}{\mathrm{K_{M}+ AOD}} \tag{5}\]  
where \(\mathrm{V_{max}}\) is the maximum rate achieved by the ecosystem when the substrate concentration is saturated. The Michaelis constant \(\mathrm{K_{M}}\) is the concentration of substrate at which a reaction rate is halved of \(\mathrm{V_{max}}\). The concentrations at which \(\mathrm{V_{max}}\) and \(\mathrm{K_{M}}\) were optimized in this study were 0.6 and 0.14 respectively [11; 42].