## 2 Materials and Methods
### Datasets
Using the Equation (4), the \(FVC\) is calculated from both the optical remote sensing image and field data. Step 3: Field forest \(AGB\) estimation--In this step, the field forest \(AGB\) was calculated from the collected field data. The field forest \(AGB\) was obtained at individual plot level in kilogram (kg) using the following simplified empirical model proposed by [PERSON] et al. [27] as follows:  
\[AGB=\kappa\times\mu D^{2}H, \tag{5}\]  
where \(\mu\) is specific gravity (g cm\({}^{-3}\)) of tree stem, \(D\) is the \(DBH\) (cm), \(H\) is the tree height (m), and \(\kappa\) is the constant for forest type. Step 4: Model development between \(FVC\) and \(AGB\)--In this step, linear regression modeling is performed to find the best fit curve between the calculated ground forest \(AGB\) from field data using Step 3 and the image forest \(FVC\) obtained using Step 2. The best fit linear model between the field forest \(AGB\) and the corresponding image forest \(FVC\) is represented as follows:  
\[AGB=\alpha\times FVC+\beta \tag{6}\]  
where \(\alpha\) and \(\beta\) are the gain and offset, respectively, for image forest \(FVC\) used to calculate the forest \(AGB\). Step 5: Forest \(AGB\) image generation using the forest \(FVC\) image--Suppose the forest \(FVC\) image is presented as \(FVC\)(\(i\),\(j\)) and the image of forest \(AGB\) is represented as \(AGB\)(\(ij\)), where (\(i\),\(j\)) is the pixel location. Then the pixelwise forest \(AGB\) in kg is calculated as follows:  
\[AGB(i,j)=\alpha\times\{FVC(i,j)\}+\beta \tag{7}\]  
Step 6: Accuracy assessment--The accuracy of the forest \(AGB\) calculated from the optical remote sensing image was evaluated by ground validation. The ground validation was performed by comparing the \(AGB\) value between the field calculated and the image estimate at different ground locations. The accuracy of the result in percentage is represented as:  
\[Accuracy\ (\%)=\frac{n}{N}\times 100, \tag{8}\]  
where \(N\) is the total number of validation points, and \(n\) is the number of validation points agreed with when equal or less than one standard deviation between image and field measurements. Finally, the generalized forest \(AGB\) obtained by individual plot level in kg are standardized into tons per hectare (t ha\({}^{-1}\)). Phase II. Forest \(AGB\) model evaluation using Sentinel-2 data. To test and verify the effectiveness of the proposed method, experimentation in sequential procedure was applied on Sentinel-2 as an optical remote sensing image to calculate the forest \(AGB\) from the Tundi reserved forest test site, Jharkhand, India. The sequential steps in the forest \(AGB\) calculation are given below. After preprocessing, the spatial resampling was initially performed to bring all of the spectral bands to 10 m spatial resolution (e.g., bands 2-4 with spatial resolution 10 m and bands 5-7, 8a with spatial resolution 20 m) and then resampled to 30 m spatial resolution, i.e., approximately equal to the field data spatial resolution. The direct vegetation and nonvegetation (soil) spectral information extraction for the forest \(FVC\) calculation is tricky. Thus, different vegetation indices were used to quantify the vegetation information within the pixel of an image. In our experiment, for quantifying vegetation amount in a pixel of Sentinel-2, four vegetation indices were assessed: normalized difference vegetation index (\(NDVI\)), modified vegetation index (\(MVI\)), soil-adjusted vegetation index (\(SAVI\)), and modified soil-adjusted vegetation index (\(MSAVI\)). The _NDVI, MVI, SAVI_, and _MSAVI_ images were produced from the Sentinel-2 image using the following equations:  
\[S_{vgg}=S_{v}\times F_{c}, \tag{1}\]0  
\[S_{vgg}=S_{v}\times F_{c}, \tag{1}\]1  
\[S_{vgg}=S_{v}\times F_{c}, \tag{1}\]2  
\[S_{vgg}=S_{v}\times F_{c}, \tag{1}\]3  
where \(L\) is the canopy background adjustment factor (\(L\) value as 0.5 in reflectance data) and _NIR_ and _RED_ are the reflectance values in near infrared and red bands of the multiband remote sensing image.