# Estimating the Fractional Vegetation Cover from GLASS Leaf Area Index Product
## 3 Methodology
### Calculation of FCover
where \(lai\) is the leaf area index of the canopy, \(\Omega\) is the clumping index taking into account the non-random spatial distribution of phyto-elements within the canopy, \(a\) is the absorptivity of leaves for radiation, \(\varphi\) is the solar zenith angle, and \(k_{c}\left(\varphi\right)\) is the canopy extinction coefficient. For an ellipsoidal leaf angle distribution, \(k_{c}\left(\varphi\right)\) is calculated as follows:  
\[k_{c}\left(\varphi\right)=\frac{\sqrt{x^{2}+\tan^{2}\left(\varphi\right)}}{x+ 1.774\times\left(x+1.182\right)^{-0.733}} \tag{2}\]  
where x is the ratio of average projected areas of canopy elements on horizontal and vertical surfaces. Different values are assigned to x for different vegetation types. x is set to 0.8 for grasses and crops, 1.0 for shrubs and savannah, and 1.2 for forest [33]. FCover corresponds to the complement to unity of the transmittance of light in the nadir viewing direction:  
\[fCover=1-P_{\text{tr}}\left(0\right) \tag{3}\]  
To quantify the importance of the input parameters for Equation (3) on FCover and characterize their effects, a sensitivity analysis of FCover to target composition and architecture was performed using the extended Fourier amplitude sensitivity test (EFAST) originally developed by [PERSON] _et al._[34; 35] and extended by [PERSON] _et al._[36]. EFAST is a variance based method and has proven one of the most reliable methods among these techniques [37], although computationally expensive [38]. It provides a first-order and a total-order sensitivity index for each input parameter. The first-order sensitivity index expresses the additive effect of the corresponding input parameter, whereas the total-order sensitivity index is the overall measure of importance and incorporates the interactions of the input parameters. Various ranges of input parameters used to calculate FCover are shown in Table 2. An input sample of 49,995 combinations of input parameters was provided by EFAST and used to calculate 49,995 FCover values using Equation (3). Sensitivity analysis was performed on this set of FCover values (Figure 1). The first-order and total-order indices of sensitivity analysis demonstrate that LAI is the only sensitive parameter. Therefore, FCover values calculated from Equation (3) are primarily influenced by LAI of the vegetation canopy. For the above scheme, the GLASS LAI product and the clumping index map derived by [PERSON] _et al._[39] was used to calculate the FCover values in this study. The clumping index map has a spatial resolution of 500 m and was aggregated to 1 km resolution to maintain a spatial resolution consistent with the GLASS LAI product using a simple spatial averaging method. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Factors** & **Unit** & **Range of Variation** & **Distribution** \\ \hline Leaf area index & m\({}^{2}\)/m\({}^{2}\) & [0, 8] & uniform \\ Clumping index & – & [0.5, 1.0] & uniform \\ Solar zenith angle & Degrees & 0.0 & – \\ Absorptivity of leaves & – & 1.0 & – \\ Ratio of average projected areas of canopy & – & [0.5, 2.0] & uniform \\ elements on horizontal and vertical surfaces & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range of input parameters for Equation (3).