## 4 Data Analysis  
The spectral reflectance of Sentinel-2 band images (Table 1) for the average January-March period was extracted corresponding to each sampling Garmin 65 s (up to 5 m accuracy) GPS point with grass N plot value. A random forest modeling algorithm based on three modeling scenarios (bands only; vegetation indices; combination bands and vegetation indices) was used to identify and predict the grass N concentrations. The choice of random forest algorithm is influenced by its ability to overcome statistical overfitting and multicollinearity to which remote sensing data are prone; the random forest (RF) is a non-parametric statistical technique capable of predicting variables based on different configurations of datasets [27]. Firstly, the selection of the number and identity of remote sensing variables required to predict grass N was determined using recursive feature selection (RFE) implemented from the \"caret\" package programmed in the R statistical environment [9]. These selected variables were subsequently used as input into the RF regression method to model grass N; this was implemented using the \"Random Forest\" package (ref) with the R environment software verion 2022.02.0 (R Development Core Team, 2022). There are three main optimized variables: ntree, several regression trees grown based on a bootstrap sample of observation (the default value is 500 trees); mtry; and the number of predictors tested at each node (default is the square root of the total number of variables). The selected random forest feature selection band was used to compute vegetation indices (Table 2) in GEE. In total, 18 predictor variables were used for data analysis in this study: 10 remote sensing bands (B2:9, 10 and 11) and 8 vegetation indices based on red edge 4 from Sentinel-2 bands (Tables 1 and 2). \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Band Number** & **Band Name** & **Wavelength** & **Description** \\ \hline Band 1 & B1 & 443.9 nm/442.3 nm & Aerosols \\ Band 2 & B2 & 496.6 nm/492.1 nm & Blue \\ Band 3 & B3 & 560 nm/559 nm & Green \\ Band 4 & B4 & 664.5 nm/665 nm & Red \\ Band 5 & B5 & 703.9 nm/703.8 nm & Red edge 1 \\ Band 6 & B6 & 740.2 nm/739.1 nm & Red edge 2 \\ Band 7 & B7 & 782.5 nm/779.7 nm & Red edge 3 \\ Band 8 & B8 & 835.1 nm/833 nm & Near infrared \\ Band 9 & B8A & 864.8 nm/864 nm & Red edge 4 \\ Band 10 & B9 & 945 nm/943.2 nm & Water vapor \\ Band 11 & B11 & 1613.7 nm/1610.4 nm & Shortwave infrared 1 \\ Band 12 & B12 & 2202.4 nm/2185 nm & Shortwave infrared 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sentinel-2—MSI datasets. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Index** & **Used Formulae** & **Reference** \\ \hline MCARIR4 & ((NIR \(-\) Red edge 4) \(-\) 0.2*(NIR-Red edge 4))*(NIR/Red edge 4) & [28] \\ MSAVIR4 & 0.5*(2*NIR \(+\) 1 \(-\) SQRT((2*NIR \(+\) 1) \(-\) 8(NIR \(-\) Red edge 4))) & [29] \\ NDVIR4 & (NIR \(-\) Red edge 4)/(NIR \(+\) Red edge 4) & [30] \\ OSAVIR4 & (1 \(+\) 0.6)*(NIR \(-\) Red edge 4)/(NIR \(-\) Red edge 4 + 0.16) & [31] \\ RDVIR4 & (NIE \(-\) Red edge 4)/SQRT(NIR \(+\) Red edge 4) & [28] \\ SAVIR4 & (2.5*NIR \(-\) Red edge 4)/((NIR \(+\) Red edge 4) + 2) & [32] \\ SR4 & NIR/Red edge 4 & [33] \\ TCARIR4 & 3*(NIR \(-\) Red edge 4) \(-\) 0.2*(NIR \(-\) Red edge 4)*(NIR/Red edge 4) & [34] \\ TVIR4 & 0.5*(120*(NIR \(-\) Red edge 4) \(-\) 200*(NIR \(-\) Red edge 4)) & [35] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Vegetation indices used in this study. Model Performance (Validation)  
The statistical measure of model precision and robustness, the r-squared (\(R^{2}\)) and root-mean-square error (\(RMSE\)), was determined to test the performance; one-on-one relationships were tested using linear regression between response observed \(N\) and predicted \(N\).