## 2 Materials and Methods
### Research Methods
#### 2.3.2 The Process of Modeling and Assessment  
Correlation analyses were performed between canopy hyperspectral data and AGB, and the linear and non-linear (logarithmic, parabolic, power, and exponential) regression statistical models simulated the quantitative relation between VIs and AGB at different growth stages.  
Linear model:  
\[\mathrm{y}=\mathrm{ax}+\mathrm{b} \tag{1}\]  
Logarithmic model:  
\[\mathrm{y}=\mathrm{a}\times\mathrm{log(x)}+\mathrm{b} \tag{2}\]  
Parabolic model:  
\[\mathrm{y}=\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c} \tag{3}\]  
Power model:  
\[\mathrm{y}=\mathrm{ax}^{\mathrm{b}} \tag{4}\]  
Exponential model:  
\[\mathrm{y}=\mathrm{ae}^{\mathrm{x}} \tag{5}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline
\begin{tabular}{c} 24 \\ 24 \\ 24 \\ 24 \\ 27 \\ 27 \\ 27 \\ 27 \\ 27 \\ 27 \\ 27 \\ 27 \\ 27 \\ \end{tabular} \\ \hline \end{tabular}
\end{table}
Table 2: Number of calibration and validation dataset at different growth stages.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Vegetation Indices** & \multicolumn{2}{c}{**Formulas**} & **References** \\ \hline Red edge chlorophyll index (Clred edge) & (R800)/(R725) \(-\) 1 & [30] \\ Green chlorophyll index (Clgreen) & (R800)/R550 \(-\) 1 & [41] \\ Normalized Difference Vegetation Index (NDVI) & (R800 \(-\) R670)/(R800 \(+\) R670) & [42] \\ Green normalized difference vegetation index (GNDVI) & (R780 \(-\) R850)/(R780 \(+\) R550) & [43] \\ Ratio vegetation index (RVI) & R750/R550 & [44] \\ Difference Vegetation Index (DVI) & R800 \(-\) R670 & [45] \\ Soil-Adjusted Vegetation Index (SAVI) & (1 \(+\) L)(R890 \(-\) R670)/(R890 \(+\) R670 \(+\) L), L \(=\) 0.5 & [46] \\ \hline \end{tabular} Note: “\(R\)” represents the wavelength corresponding spectral reflectance values.  
\end{table}
Table 3: Vegetation indices (VIs) list.  
Note: \"y\" represents the AGB values, \"x\" represents the VIs values, \"a, b, c\" means the model fitting parameters, and \"e\" represents the natural index value  
The performances of the various regression models were evaluated by the coefficient of determination (R\({}^{2}\)), root mean square error (RMSE) for calibration (RMSEC), validation (RMSEV), and the ratio of prediction to deviation (RPD). Mathematically, the higher R\({}^{2}\) and RPD correspond to the smaller RMSE, and thus represent better model accuracy [47].  
Data modeling process: firstly, the linear and non-linear regression models were established based on VIs and AGB of the calibration dataset, we selected the best model forms (linear, logarithmic, parabolic, power, and exponential) by comparing the R\({}^{2}\) and RMSEC, and then acquired the corresponding calibration models parameters. Secondly, the predicted AGB value was calculated by the VIs of the validation dataset with the application of the selected best calibration models forms and its parameters. Thirdly, the linear regression models were established based on the predicted AGB value and the original AGB of validation dataset, and the R\({}^{2}\), RMSEV, and RPD were used to evaluate the accuracy of validation models.  
The following equations were used to calculate R\({}^{2}\), RMSE, and RPD:  
\[\text{R}^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-\text{x}_{i}\right)^{2}}{\sum_ {i=1}^{n}\left(y_{i}-\overline{y}\right)^{2}} \tag{6}\]  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(y_{i}-\text{x}_{i}\right)^{2}}{n}} \tag{7}\]  
\[\text{RPD}=\frac{\text{STD}}{\text{RMSEV}} \tag{8}\]  
Where x\({}_{i}\) and y\({}_{i}\) are the estimated and measured AGB values, respectively, \(\overline{y}\) and STD is the average and standard deviation of the measured AGB values, RMSEV represents the root mean square error of validation model, and n is the sample number, respectively.  
The linear and non-linear regression was performed using SPSS 19.0 software (SPSS, Chicago, IL, USA). Graphics were prepared using the Origin 9.1 software program (Origin 9.1, OriginLab Corporation, Northampton, USA).