# A Modeling Application for GHG Fluxes Estimates in Betel Nuts Plantations in Taiwan
## 2 Materials and Methods
### VPM Model  
A VPM model was developed to estimate the gross primary production (GPP) in a seasonally moist tropical evergreen forest [10]. This model took advantages of additional spectral bands (e.g., blue and shortwave infrared--SWIR) that were available from advanced optical sensors present on the Landsat 8 satellite. The selection of images was mostly influenced by the quality related to atmospheric conditions; only images without clouds were considered. The clearest images were used for the model application. They were dated 15 and 24 January, 25 February and 13 March. The Landsat 8 bands useful for the calculations of indices were band 2 (blue: 0.452-0.512 \(\upmu\)m), band 4 (red: 0.636-0.673 \(\upmu\)m), band 5 (NIR: 0.851-0.879 \(\upmu\)m), and band 6 (SWIR: 1.566-1.651 \(\upmu\)m). From these bands, were calculated some spectral indices useful in the model calculations, such as enhanced  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Temperature** (\({}^{\circ}\)C) & **Precipitation (mm)** & \
\begin{tabular}{c} **Radiation** \\ **(MJ m\({}^{-2}\) month\({}^{-1}\))** \\ \end{tabular} &
\begin{tabular}{c} **Relative Humidity** \\ **(\%)** \\ \end{tabular} \\ \hline  & **Monthly Mean** & **Monthly Mean** & **Daily Mean** & **Monthly Mean** & **Monthly Mean** \\ \hline January & 14.57 & 144.02 & 4.64 & 298.94 & 81.6 \\ February & 13.96 & 66.14 & 2.36 & 326.62 & 81.21 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Meteorological parameters of the Chiayi County.  
Figure 1: The Chiayi County in Taiwan.  
vegetation index (EVI) used for vegetation detection (Equation (1)) and land surface water index (LWSI, Equation (2)) sensitive to vegetation water content [16].  
\[\text{EVI}=2.5\times\frac{\rho_{\text{nir}}-\rho_{\text{red}}}{\rho_{\text{nir} }+(6\times\rho_{\text{red}}-7.5\times\rho_{\text{blue}})+1} \tag{1}\]  
\[\text{LSWI}=\frac{\rho_{\text{nir}}-\rho_{\text{swir}}}{\rho_{\text{nir}}+\rho_ {\text{swir}}} \tag{2}\]  
VPM is based on the light use efficiency (LUE) approach, which estimates the conversion efficiency of absorbed photosynthetically active radiation (FAPAR) into gross primary production (GPP, Equation (3)) and assumes a linear dependence of GPP on FAPAR, reduced by environmental constraints.  
\[\text{GPP}=\ \ \varepsilon_{\text{g}}\times\text{FAPAR}_{\text{PAV}}\times \text{PAR} \tag{3}\]  
where:  
* FAPAR\({}_{\text{PAV}}\) is the fraction of photosynthetic active radiation (PAR) absorbed by plants [10] (\(\text{FAPAR}_{\text{PAR}}=\text{a}\times\text{EVI}\))
* \(\varepsilon_{\text{g}}\) is the light use efficiency (\(\upmu\text{mol}\text{CO}_{2}/\upmu\text{mol}\text{PAR}\)), which can be described as follows (Equation (4)):  
\[\varepsilon_{\text{g}}=\varepsilon_{0}\times\text{T}_{\text{scalar}}\times \text{W}_{\text{scalar}}\times\text{P}_{\text{scalar}} \tag{4}\]  
where:  
* \(\varepsilon_{0}\) is the maximum light use efficiency [16]
* T\({}_{\text{scalar}}\), \(W_{\text{scalar}}\), and \(\text{P}_{\text{scalar}}\) are the down-regulation scalars for the effect of temperature, water, and leaf phenology [16]  
For validation purposes, we decided to use evapotranspiration values and considered them strictly correlated to GPP. Because of the lack of evapotranspiration observations, we calculated them using indications in the FAO-56 report [24], beginning from the evaporation observations obtained from the class A evaporimeter of the Taiwan Central Weather Bureau. Considering the carbon that vegetation releases to the atmosphere through respiration and decomposition, the net ecosystem production can be calculated as follows (Equation (5)):  
\[NEP=GPP-Respiration \tag{5}\]  
where the respiration was calculated using the T&P&LAI model [25].